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Advances and challenges in ORC systems modeling for low grade thermal energy recovery
Applied Energy 121 (2014) 79–95
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Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Advances and challenges in ORC systems modeling for low grade thermal energy recovery Davide Ziviani a, Asfaw Beyene b, Mauro Venturini c,⇑ a
Ghent University - UGent, Graaf Karel de Goedelaan 5, B-8500, Kortrijk, Belgium San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-5102, USA c Università degli Studi di Ferrara, Via Giuseppe Saragat, 1, 44122 Ferrara, Italy b
h i g h l i g h t s Analysis of the most recent technologies to exploit low-grade thermal energy. Review of state-of-the-art research and development of ORC systems. Comprehensive review of modeling approaches for ORC system simulation. Guidelines to develop a powerful simulation tool for ORC systems. Development and validation of a micro-ORC system simulation model.
a r t i c l e
i n f o
Article history: Received 26 September 2013 Received in revised form 26 December 2013 Accepted 31 January 2014 Available online 22 February 2014 Keywords: Organic Rankine cycle Low-grade thermal energy Review Modeling
a b s t r a c t Low-grade thermal energy recovery has attained a renewed relevance, driven by the desire to improve system efficiency and reduce the carbon footprint of power generation. Various technologies have been suggested to exploit low-temperature thermal energy sources, otherwise difficult to access using conventional power generation systems. In this paper, the authors review the most recent advances and challenges for the exploitation of low grade thermal energy resources, with particular emphasis on ORC systems, based on information gathered from the technical literature. An outline of the issues related to ORC system modeling is also presented, and some guidelines drawn to develop an effective and powerful simulation tool. As a summary conclusion of the revised models, a simulation tool of an ORC system suitable for the exploitation of low grade thermal energy is introduced. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The world energy use has increased more than 40% in the last few decades [1], resulting in sharp increase in fuel price and causing environmental challenges that necessitated exploration of new ways to meet the rising demand with fewer footprints on the environment. The reference case of IEO2011 [2] has shown a further increase of the world energy demand by 53% from 2008 to 2035. As a consequence, waste energy recovery has attained a renewed relevance in order to provide a more sustainable environment for the future. In particular, it has been argued that low grade waste thermal energy, below 200 °C, represents a viable resource of a growing interest because of its abundance. In fact, low grade waste thermal energy accounts for more than 50% of the total heat generated in ⇑ Corresponding author. Tel.: +39 0532 974878; fax: +39 0532 974863. E-mail address: [email protected] (M. Venturini). http://dx.doi.org/10.1016/j.apenergy.2014.01.074 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.
industry [3]. Low grade thermal energy (LGTE) is readily available in thermal processes, combustion exhausts, cooling or condensing systems, as well as from equipment such as compressors. It also exists in nature, in geothermal form or as solar irradiation. Research related to recovery of LGTE from these sources has drawn increasing attention in recent years. Most of the work is restricted to the theory, mainly focusing on mathematical modeling and feasibility study. Unfortunately, the ongoing focus on the theory with little advances on the practical side leaves doubts about engineering and practical limitations of these concepts, meaning there is a lack of a suitable cost-effective technology ready for mass production. There is a wide range of technologies and design options for the recovery of LGTE for power production and Combined Heat and Power (CHP) applications [4]. Suitable thermodynamic cycles include organic Rankine cycle (ORC), supercritical Rankine cycle, Kalina cycle and trilateral flash cycle (TFC) [5], as well as, Stirling engines and new concepts such as thermo-acoustic engine (TAE)
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Nomenclature a Bo Co Fr G h ifg _ m N Np Nu p P Pr q r Re s T V
a x d
g q s U
specific Helmholtz energy (J/kg) boiling number, Bo = q/Gifg convective number, Co = qg/ql((1 x)/x)0.8 Frounde number, Fr = G2/q2gDh mass flux, (kg/(m2 s)) convective heat transfer coefficient, (W/(m2 K)); specific enthalpy (J/kg) enthalpy of vaporization (J/kg) mass flow rate (kg/s) rotational speed (rpm) number of plates Nusselt number (–) pressure (bar) power (W) Prandtl number (–) heat flux (W/m2) pressure ratio Reynolds number (–) specific entropy (J/(kg K)) temperature (°C) volume (m3) dimensionless Helmholtz energy (–) vapor quality reduced density, d = q/qcr efficiency density (kg/m3) reduced temperature, s = Tcr/T liquid level (–)
Subscripts and superscripts cd condenser cr critical d displacement E excess
and inverted Bryton cycle. Simulation models have been developed to conduct techno-economic analysis of the design options for some of these technologies to evaluate their performances [6,7]. For instance, a techno-economic analysis of a CHP system with low thermal energy recovery in process industries was conducted by Chan et al. [8], comparing various technologies including heat pumps, organic Rankine cycles, and absorption refrigeration. This paper addresses the use of ORC systems to exploit low grade waste thermal energy, and the challenges, methodologies, and the approaches available in the literature for ORC system modeling are discussed by reporting a comprehensive literature survey of currently available models of ORC system components and integration. Modeling challenges and best-practice scenarios are hinted leading to better design solutions. To illustrate the steps employed in our model comparison, the LMS Imagine Lab AMESimÒ [9] is adopted as an alternative library-orientated tool for ORC system modeling under both steady and transient conditions. The employed modeling approach is validated against numerical and experimental data taken from literature.
2. Conversion technologies for low grade thermal energy recovery 2.1. Organic Rankine cycle The ORC system represents a simple Rankine cycle in which the water is replaced by organic mediums that boil at low
eV exp fr h l p real s suc th theory v vol
evaporator expander fluid receiver hydraulic liquid pump real isentropic suction thermodynamic cycle theoretical vapor volumetric
Acronyms AL atmospheric lifetime CCHP combined cooling, heating and power CHP combined heat and power EoS equation of state GWP global warming potential HFC hydrofluorocarbon HRVG heat recovery vapor generator HVAC heating, ventilation and air-conditioning IBC inverted Bryton cycle LGTE low grade thermal energy ODP ozone depletion potential OFC organic flash cycle ORC organic Rankine cycle PHE plate heat exchanger SRC supercritical Rankine cycle TAE thermoacoustic engine TFC trilateral flash cycle TLC trilateral cycle WHR waste heat recovery
temperatures, i.e. the cycle and the working fluid are tailored to exploit hot and cold sources in the most efficient way. The layout of an ORC simple cycle layout and typical T–s diagrams of both subcritical and transcritical cycles are reported in Fig. 1. Over the years, the ORC systems have gained a moderate level of maturity and reliability, allowing heat recovery from different sources, as documented by Branchini et al. [10]. One of the main challenges of the ORC is represented by the choice of the appropriate working fluid, in order to achieve the maximum efficiency for given hot and cold sources. Many analyses of the influence of the working fluids on system efficiency have been reported in the literature, as for instance [11–13]. However, the selection of the optimal working fluid is considered not fully addressed. In fact, recent research works focus on analyzing multi-component mixtures of working fluids in order to better match the heat and cold sources. Aghahosseini and Dincer [14] analyzed different pure and zeotropic-mixture working fluids. Energy and exergy analyses were conducted. The organic working fluids selected for the study were R123, R245fa, R600a, R134a, R407c, and R404a. The technical feasibility of ORC applications for LGTE recovery has already been investigated and validated [15–17]. In fact, medium to high temperature ORCs are successfully used in several applications, such as geothermal resources [18], waste thermal energy recovery from gas turbines or internal combustion engines [19–23] and biomass-based CHP plants [24–26]. However, the research is still ongoing to expand the range of potential applications where the ORCs could be used, for example to ultra low-grade heat
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Fig. 1. ORC simple cycle layout and T–s diagrams of subcritical (a) and transcritical (b) cycles (adapted from [41]).
regimes to exploit renewable energy such as solar or ocean thermal resources [27–30], but also to reduce grid dependence for remote areas that can use distributed electric generation for fresh water production (e.g. for sea water desalination) [31–34]. Although ORCs are characterized by rather low efficiencies (8–12%) [35], they are particularly viable for small-scale unsupervised power generation systems. Absence of fuel cost, improved reliability and low maintenance may also contribute to making ORCs commercially attractive [35,36]. Quoilin et al. [37] reviewed different ORC applications and market perspectives of different modules and manufacturers. Technical challenges, i.e. working fluid selection and expansion machines, were analyzed in-depth. The selection of the expansion component represents a key aspect of power generation efficiently. The efficiency of the expanders heavily affects the overall system efficiency, especially in the small-scale range. Scroll expanders are commonly used in small-scale ORCs, while screw expanders are used for mid-scale power output. Qiu et al. [38] summarized their market research on expanders with potential for domestic applications (1–10 kWe). The study highlighted the lack of commercially available expanders for ORC-based micro-CHP systems. The analysis also showed that scroll expanders and vane-type expanders remain reasonable choices for micro-ORC systems. The optimization of the ORC systems also requires the optimization of the thermodynamic cycle. Different configurations can be considered in order to increase the heat recovery potential. These consider the introduction of a recuperator, regenerator, multi-pressure levels, flashing techniques and supercritical cycles. A detailed analysis of different ORC layouts was carried out by Branchini et al. [10]. When using working fluids with relatively low critical temperatures and pressures such as CO2, supercritical heating conditions can be reached. In such cases, the system is defined as supercritical Rankine cycle (SRC). Although the SRC allows a better thermal matching compared to ORC, mainly due to the absence of twophase region, the required higher pressure regimes lead to difficulties in operation and safety. Chen et al. [39] presented a review of ORC and SRC systems for the conversion of LGTE. The review includes a screening process for a range of working fluids operating in both cycles. Schuster et al. [40] investigated supercritical parameters of various working fluids in ORC applications, in order to achieve higher efficiency values. A second law analysis was proposed. By maximizing supercritical parameters, an efficiency increase of above 8% was claimed. In the following section, new configurations of the ORC thermodynamic cycle are considered and their potential implementation is discussed.
identical to a binary power plant, except that expansion starts from the saturated liquid water instead of the saturated, superheated or supercritical vapor phase, as shown in Fig. 2. This allows the heat transfer from a liquid thermal source to the working fluid at an optimum temperature matching which reduces irreversibilities as a consequence, i.e., offers higher efficiency [42]. The TLC system includes a pump, a heater, a two-phase expander and a condenser. Fischer [42] performed a comparison between optimized case studies of ORC and TLC under the same heat source inlet temperatures, in the range 150–350 °C, and inlet cooling agent temperatures in the range 15–62 °C. The analysis showed that TLC exergy efficiency for power production was 14–29% higher than ORC’s. On the other hand, since the TLC operates with water, the outgoing volume rate from the expander was estimated to be 2.8 times larger than the working fluid of the ORC, with a minimum fluid temperature of 85 °C. The outgoing volume rate factor can increase up to 70 with a minimum working fluid temperature of 38 °C. Large volume flows might represent a practical obstacle to implement the concept. Therefore the TLC with water as the working fluid is most suitable for higher values of the minimum working fluid temperature, as for example in CHP plants. Among low temperature power cycles, a particular case of TLC is the Trilateral Flash Cycle (TFC) [43–44]. The TFC consists of (i) pumping the saturated liquid from low pressure to high pressure, (ii) preheating the pressurized liquid, (iii) expanding the preheated liquid (partial evaporation may occur) and (iv) condensing the part of liquid which has previously evaporated [45]. The TFC improves temperature matching between the heat source and the working fluid. The drawback is that it requires an efficient and reliable two-phase expander (e.g. screw expander or scroll expander), although such expansion may be avoidable. After the heat addition, the single-phase liquid can be throttled to a two-phase mixture, subsequently extracting work from the saturated vapor. Lecompte et al. [46] proposed an optimization of the TLC by introducing a partial evaporation of the working fluid. The resulting cycle presents a higher thermal efficiency and a reduction in heat transfer area because of the larger enthalpy of vaporization of the working fluid. If organic working fluid is used, such system is called Organic Flash Cycle (OFC) (see Fig. 3). Ho et al. [47] evaluated the effectiveness of the OFC on waste thermal energy recovery at 300 °C by using isentropic and dry fluid and comparing the results to other vapor cycles, in particular ORC and transcritical CO2 cycle by adopting a second law analysis. It was demonstrated that OFC presented the highest heat addition exergetic efficiency, but on the other hand the throttling process represented a drawback. The OFC also offers the potential to exploit thermal energy sources at lower temperatures.
2.2. Modified organic Rankine cycles
2.3. Kalina cycle
Trilateral cycle (TLC) is a less-known unit, currently at a development stage [42]. The Trilateral Flash Cycle (TFC) system is
The Kalina cycle uses a binary working fluid such as ammonia and water. The binary fluid is allowed to have varying composition
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Fig. 2. Trilateral Rankine cycle (TRC) layout and T–s diagram (adapted from [8]).
Fig. 3. OFC layout and T–s diagram (adapted from [48]).
providing a richer concentration through the Heat Recovery Vapor Generator (HRVG) and leaner composition in the low-pressure condenser. Since the molecular weight of ammonia is close to that of water, a standard back-pressure turbine can be used. A rich mixture of water and ammonia is superheated in the HRVG and expanded through a turbine. At the exhaust from the turbine, the medium with high ammonia concentration is cooled and diluted with the bottoms from a vapor separator for complete condensation. Part of the working fluid is transported to the vapor separator through recuperative heat exchangers, and the other part is mixed with the stream with high ammonia concentration from the vapor separator. This restores the optimum concentration of the mixture for heat addition. The distillation and condensation processes consist of the demister, recuperative heat exchangers, condenser, and control system. The mixture of two compounds having different boiling points allows boiling of the mixture over a range of temperatures. The ratio of the two components can be varied in different stages within the cycle allowing non-isothermal boiling which in turn allows extracting more heat from the source. Such flexibility takes full advantage of the temperature differential between the LGTE heat source and the sink; therefore the Kalina cycle is able to reach higher overall efficiency than ORCs, within the same temperature range. However, in the range of LGTE (i.e. low power level and low temperature sources), the adoption of Kalina cycle is not justified because the gain over an optimized ORC is limited, and obtained as a consequence of a more complicated system layout [49]. The Kalina cycle represents a novel thermodynamic cycle and additional degree of freedom (i.e. fraction of ammonia–water mixture) compared to Rankine cycle offers wide range of further improvements. Moreover, the Kalina cycle offers better thermodynamic performance than Rankine and ORC systems under both energy and exergy point of view.
Coupling of the Kalina cycle with renewable resources such as geothermal plants have been investigated, [49,50]. Rodriguez et al. [51] compared ORC and Kalina cycle for power production from low-grade geothermal reservoir with 150 °C or lower, using first and second laws of thermodynamics. The comparison was conducted for a range of working fluids of the ORC system (fifteen working fluids have been taken into account) and an optimal ammonia-water mixture composition for the Kalina cycle. The simulations showed that the optimal system for the ORC employed R-290 as a working medium, whereas for the Kalina cycle a mixture composition of 84% of ammonia and 16% (based on water mass fractions), were registered. The comparison showed that the Kalina cycle could produce 18% more net power than the ORC, with an electricity cost of 0.18 €/kW h, compared to 0.22 €/kW h for the ORC. Bombarda et al. [52] proposed a comparison between Kalina cycle and ORC recovering heat from two diesel engines, each one having an exhaust gas flow rate of 35 kg/s at 346 °C. The thermodynamic analysis showed that, although the Kalina cycle allowed higher net electric power output (1615 kW instead of 1603 kW for the ORC), higher values of the maximum pressure are necessary to achieve high thermodynamic performances, i.e. 100 bar for the Kalina cycle instead of 10 bar for the ORC. Therefore, the adoption of the Kalina cycle for medium–high temperature thermal sources is not justified when compared to an optimized ORC. Wang et al. [53] examined a solar-driven Kalina cycle (reported in Fig. 4) which the authors believed was a better match for the varying vaporization temperature of the ammonia-water mixture. Thermal energy storage was introduced in order to ensure consistent operation for the system. A detailed mathematical model was developed and the optimization process led to a claimed system
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Fig. 4. Kalina cycle (KC) (adapted from [53]) and enthalpy vs. ammonia mass fraction diagram (adapted from [56]).
efficiency of 8.54%. Singh and Kaushik [54] proposed an energy and exergy analysis of a Kalina cycle coupled with a coal fired steam power plant, to evaluate the possibility of exploiting lowtemperature heat from exhaust gases. The simulation results showed that when the exhaust gas temperature reduced from 407.3 K to 363.15 K, the Kalina cycle efficiency reached a maximum value of 12.95%, increasing the overall plant efficiency by 0.277%. Victor et al. [55] developed an optimization method for the composition of mixed working fluids for ORCs and Kalina cycles, as well as, discussed the comparison between the thermodynamic cycles. Generally, the study demonstrated that the use of both solutions can be considered beneficial for low temperature applications. Optimization studies are still required to select the optimal working fluid. 2.4. Stirling engine The Stirling engine concept was proposed several years before the introduction of diesel engine. Also known as hot-air or hotgas engine [57], it operates as a closed thermodynamic cycle and presents attractive properties such as multi-fuel capability, which can potentially reduce the use of fossil fuel compared to traditional combustion engines. It also offers low noise levels, clean combustion and operational range even with low temperature, i.e. it is a suitable candidate to recover LGTE [57]. Although the Stirling engine has a number of advantages, it is still considered to be at a preliminary conceptual stage mainly because of system complexity compared to other technologies such as ORCs. The dynamic behavior of the engine mechanism and the thermal performance of all the heat exchangers pose a design challenge affecting reliability and efficiency of the system. Several investigations proposed in the literature were focused on addressing optimal system design challenges [58–60]. Thombare and Verma [57] provided a review on Stirling engine technological development addressing feasible solutions for a workable engine. Different engine configurations were assessed, and the influence of various working fluids and technical factors which govern the engine performance (e.g. regenerator effectiveness, regenerator materials, etc.) were addressed. The Stirling engine has the potential to be used more efficiently in micro-CHP systems driven by solar, biogas, or medium–low grade waste thermal energy. Micro-CHP Stirling systems with up to 10 kW of electric power output are available on the market. Most of these are prototypes, ranging from 1 to 9 kW capacities
with corresponding thermal power of 5 to 25 kW, which may very well suit household boilers [61]. Their electric efficiencies range from 13% to 25%, with the CHP efficiency claim boosted to 80% or even higher [61]. Li et al. [62] developed a small-scale Stirling engine driven by mid-high temperature waste gases, obtaining a maximum power output of about 3.5 kW. The experimental results were in fair agreement with the predicted power output, i.e. 3.9 kW, with predicted thermal efficiency of 26%. 2.5. Thermo-acoustic engine (TAE) and Inverted Brayton Cycle (IBC) Several novel concepts of thermal energy conversion methods have been recently proposed. One such case is the thermo-acoustic engine (TAE). This technology has been investigated to operate with small temperature gradients, opening new opportunities and challenges for LGTE recovery. Yu et al. [63] proposed a travelling-wave thermo-acoustic electricity generator to convert thermal energy into electricity. A small-scale TAE has been designed showing a potential for waste thermal energy recovery and the possibility to have an inexpensive technology, although practical challenges need to be addressed in order to build systems with large power output. The Inverted Brayton Cycle (IBC) is considered a possible solution among low to medium grade heat recovery technologies under development. The IBC system consists of a hot stream turbine which expands the gas stream to a value below the ambient pressure, followed by a heat-exchanger which cools down the outlet gas. At the end, the gas is recompressed to ambient pressure conditions by a compressor which discharges the gas to the stack. Despite previous studies, Chan et al. [8] investigated the potential use of IBC systems to low grade temperature. The results of the IBC thermodynamic analysis showed that the efficiency of the cycle is limited to 5% at the maximum temperature of 500 °C. For lower temperatures, in the range of 200–300 °C, the achievable performances are limited due to large amount of power absorbed by the compressor. A possible solution to this issue consists of an enrichment of water in the gas, to reduce the compressor inlet mass flow. By considering a percentage of water mass fraction in the range 0–30%, the maximum efficiency of IBC systems was 10% at 30% water mass fraction, with a maximum specific work of 70 kJ/kg. Although the employment of such systems is still questionable at low temperature ranges compared to other well-proved technologies, e.g. ORCs, the IBC system allows cogenerative operation especially in the temperature range above 200 °C.
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3. Challenges of ORC system modeling Even though, as discussed above, there are potentially different alternative conversion technologies for LGTE recovery, in practice, ORCs are the most prevalent, mainly because of their simplicity and off-the-shelf availability of their components. Despite these benefits, the design and modeling of ORCs can be challenging, especially for transient conditions, e.g. when the load demand or the supply thermal energy exhibits abrupt changes, but yet the working conditions of the systems have to remain within acceptable ranges to avoid unfavorable off-design conditions or temperature shocks. Such problems can be prevented at the design stage by adopting model-based techniques to simulate either the steady state or the transient behavior of the ORC system, to identify the influence of operation parameters and predict the occurrence of critical operating conditions. Furthermore, the modeling approach is very useful to optimize the operating conditions and the components of the cycle by developing proper control and diagnostic strategies. System modeling also supports the design of experimental test-rigs. The operating conditions and types of components highly affect the efficiency of the system, resulting in a lower power output. This is especially true for micro-ORCs designed for low-grade heat recovery. Among the fairly extensive modeling work conducted on ORCs, a significant portion is committed to the influence of thermodynamic properties of the working medium on ORC performance [64–68]. These modeling approaches allow detailed simulation of two-phase flow dynamics in the evaporator and condenser. In fact, while models of pumps and turbines are readily available in the literature, the two-phase flow inside heat exchangers encompassing different working fluids, geared to positive displacement machines, remains a serious research topic. Additionally, different software tools are available to develop ORC models. The choice of the software mainly depends on the type of analysis (e.g. steady or unsteady), and the coding level necessary to implement the components details. In fact, a distinction can be made between coding-based software, e.g. EESÒ [69], MatlabÒ [70], Phyton™ [71], and libraries-orientated software, e.g. SimulinkÒ [70], ModelicaÒ [72], DymolaÒ [73], Cycle-TempoÒ [74]. The difference consists of the possibility of developing a proper set of equations or using available object-oriented libraries, where the equations are already implemented, but the user has to connect them properly and set the parameters. A comprehensive summary of useful software tools for ORC modeling and their main features are reported in Table 1. In the following, a survey of common modeling approaches of ORC systems is presented. A detailed ORC model, based on developing semi-empirical models of each component instead of deterministic models, was presented and validated by Quoilin et al. [75,76]. The limited number of physically meaningful parameters identified from performance measurements allowed the development of numerically robust models, which were interconnected to simulate the overall
system. A detailed scroll expander model, accounting for pressure drops and heat transfer losses, as well as a three-zone counter-flow heat exchanger, was developed using EESÒ software and validated by using experimental data. Furthermore, an optimization process was carried out, achieving an optimum working point with a refrigerant flow rate at a given rotational speed. The cycle improvements led to nearly doubling the efficiency from 5.1% up to 9.9%. Since the expander is a key element of the ORC, Lemort et al. [77,78] presented a focused investigation of the semi-empirical simulation model on expanders. The model is also an extension of the one proposed by Winandy et al. [79] and Kane [80]. However, it is distinct in that it takes into account internal and external heat transfers and also under- and over-expansion processes identifying the parameters through a genetic optimization algorithm embedded in EESÒ. Based on the experimental results, the model accuracy was within 2%, and the computational time was low. Two dynamic models that included all ORC components were presented by Wei et al. [81]. The models, developed in ModelicaÒ language and simulated by means of DymolaÒ, are based on moving boundaries and discretization techniques, respectively. A comparison between the two modeling approaches was carried out in terms of accuracy, complexity and simulation speed. The main novelty of the research was the introduction of the moving boundaries approach to describe the two-phase flow inside both the evaporator and the condenser, which leads to simulation models with reduced order, i.e., more suitable for diagnostics and control purposes. Several additional models have been proposed to model heat exchangers in ORCs. For example, Vaja [82] defined an object-orientated library in Matlab/SimulinkÒ to simulate ORC systems. Two models for a generic heat exchanger were included to model either a steady-state heat transfer process or a dynamic approach including the phase change during the evaporation and condensation processes. García-Vallardes et al. [83] proposed numerical simulation of the thermal and fluid dynamic behavior of a double pipe heat exchanger to be used either as an evaporator or a condenser. Radial nodes were also considered. In fact, the energy conservation equations were applied to the external tube and to the insulation system, hence heat loss through insulated surfaces was not ignored. Quoilin et al. [84] presented a dynamic model of an ORC system in order to predict the transient behavior of the cycle with a varying thermal source. This work also tackles control strategies during part-load operation and start and stop procedures. The proposed dynamic model is based on the time-varying performance of heat exchangers; the time variables of the other components are assumed to have less impact on the system dynamic performance. Three control strategies were investigated, i.e. (i) constant evaporating temperature, (ii) optimum evaporating temperature and (iii) pump speed. As previously highlighted, the phase change phenomenon is one of the most complex and challenging aspects related to ORC modeling. The technical literature presents a wide range of correlations validated against experimental data. Some of these correlations are
Table 1 Survey of software tools for ORC modeling. Software
Type
REFPROPÒ
CoolPropÒ
Features
References
MatlabÒ/ SimulinkÒ
Librarybased Code-based Code-based Code-based Librarybased Librarybased Librarybased
U
U
S-Functions Steady–Unsteady analyses Several libraries included
[82,109,110]
U U U
U U U
Support non-linear algebraic systems Complete fluids and solids Libraries High level coding, comparable to Perl, Java, etc. Object-orientated language Unsteady Analyses
[75–78,142] [148] [81,84]
[115,116]
U
Ready-to-use components Steady–Unsteady analyses Complete fluids and solids Libraries FluidpropÒ integration Thermodynamic analysis Optimization of energy systems
EESÒ Phyton™ ModelicaÒ AMESimÒ Cycle-TempoÒ
[113]
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published [85–103]. These publications show that the heat transfer coefficients mainly depend on the type of fluid, on temperature and pressure conditions, as well as on heat exchanger geometry. More extensive literature reviews with focus on refrigeration, air conditioning, and heat pump applications are available [104–108]. Due to the variability of the heat source, ORC systems usually work at part-load conditions, i.e. not at the design point for which the system was optimized. The simulation of part-load operation is still a challenge. For instance, Menente et al. [109] proposed a detailed off-design model of an ORC system by using the performance curves of the main components. The model was developed in SimulinkÒ [61] by imposing mass and energy balances for each component and by introducing appropriate performance curves for the main components of the system. Lecompte et al. [110] developed a thermo-economic design methodology by taking into account the change of operating conditions and part load behavior. The thermodynamic steady-state model was implemented in MatlabÒ using REFPROPÒ [111] library to retrieve fluid properties. A three-zone approach was used to model the plate heat exchangers with phase change and the part load of the pumps were modeled by using a correlation between isentropic efficiency at nominal condition and actual value. The considered fluids were R152a, R1234yf, R245fa. Bamgbopa and Uzgoren [112] presented a simplified transient modeling approach for ORC operating under variable heat input. The model included a dynamic model for the heat exchangers, neglecting the pressure drops, and static models of pump and screw expander. The pump was modeled by means of performance curves where the pressure rise was a function of the volumetric flow rate and pump efficiency. Instead, the nominal polytropic work output of the screw expander was defined as a function of built-in volume ratio and pressure ratio. Among library-orientated software tools, Vankeirsbilck et al. [113] used Cycle-TempoÒ and FluidpropÒ [114] to compare thermodynamically simplified steam cycle and ORC for small scale power generation Bracco et al. [115] developed a numerical model of a small-scale ORC by using LMS Imagine Lab AMESimÒ, a simulation software for the modeling and the analysis of one-dimensional systems. The extensive libraries, including several refrigerants, allow the simulation of ORC system under both stationary and transient conditions and the implementation of control strategies. The Authors [116] adopted the same software tool to implement a comprehensive ORC model suitable for residential applications, able to perform both steady and transient analyses. Finally, a thorough review of available tools for thermodynamic simulations was presented by Connolly et al. [117].
4. Guidelines for orc system modeling According to the challenges outlined in the previous section, in order to accurately model an ORC system, different aspects have to be analyzed thoroughly. The main issues to be addressed include: Estimating the working fluid thermodynamic and transport properties. Determining the heat transfer rate in the evaporator and the condenser, for which reliable correlations are very difficult to come by, and experimental results usually only record specific working conditions. Modeling the expansion machine; with all the complexities of a two-phase fluid, with a specific target of raising efficiency of the expander, which, in the authors’ opinion, is a bottleneck to raise the ORC system efficiency. In addition to two-phase flow conditions mentioned above, pressure drops, part-load conditions and geometric properties of
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the components should be considered in order to maximize reliability of the simulation model. As stated in the literature, e.g. in [18,33,118], the ORC layout can be optimized in order to maximize its efficiency, but often at the cost of higher upfront cost of components. As shown in literature and also in previous works conducted by the authors, a simple cycle configuration may be cost-effective for micro-CHP applications if off the shelf components from other applications such as the HVAC industry are used [116,119,120]. Such an assembly renders the system more affordable, but less than optimum. A simple configuration of the ORC consisting of a positive displacement pump, two PHEs, i.e. evaporator and condenser, a volumetric expander, a fluid receiver, is usually considered in practical applications and thus it is also assumed to be the reference configuration in this paper (see the simulation model in AMESimÒ environment sketched Fig. 5, where section numbering is in agreement with the thermodynamic states identified in Fig. 1a). The approach selected for modeling each component will be discussed below, as well as, a comparison between the proposed model and corresponding models available in literature.
4.1. Working fluid The working fluid selection represents a challenge when considering low-temperature waste thermal energy recovery. There are several general criteria that the working fluid of low-temperature ORC systems should ideally meet such as stability, non-fouling, non-corrosiveness, non-toxicity and non-flammability [120]. To develop the simulation model of an ORC system, it is essential to retrieve the thermodynamic and transport properties of the working fluid. Moreover, it is usually desirable to compare ORC performance with different fluids, to identify the optimal solution. Different fluid libraries are available and compatible with all the main simulation tools. REFPROPÒ database represents the most extended library and also allows enhancing the properties of user-defined mixtures. CoolPropÒ [121] is an open-source, cross-platform fluid library with most of the common fluids used. Both REFPROPÒ and CoolPropÒ can be integrated into Matlab/SimulinkÒ, EESÒ, ModelicaÒ and other software. Additionally, AMESimÒ and EESÒ provide built-in thermo-physical property data of several fluids. An overview of the most common fluids available in the libraries of the above-mentioned software is reported in Appendix A. Recently, Bao and Zhao [5] proposed an extensive review of the selection of working fluids for ORCs, including an analysis of the influence of working fluids category and their thermodynamic and physical properties on the ORCs performance. Pure and mixed working fluids have been considered. Supercritical ORCs are receiving growing interest and therefore the fluid properties have to be evaluated. The investigation of the thermal performance of working fluids at supercritical conditions can be carried out by using any of the fluid libraries previously mentioned. For instance, Schuster et al. [40] compared several working fluids by retrieving the properties from REFPROPÒ. Gao et al. [122] analyzed eighteen organic working fluids for a supercritical organic Rankine cycle. In this case, the thermodynamic properties were evaluated by means of REFPROPÒ. Among the zero ODP (Ozone Depletion Potential) and low GWP (Global Warming Potential) refrigerants, the 1,1,1,3,3-Pentafluoropropane (known as HFC-245fa) is preferred as the working fluid, because of the low and ultra-low temperature range of the heat source, as discussed by Malavolta et al. [119]. The critical temperature, critical pressure and pressure at 298 K (near atmospheric conditions) are also favorable. An ORC system with HFC-245fa as the working fluid is favored to produce electricity from low temperature waste thermal energy between 450 K and 300 K. The
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Fig. 5. Complete ORC cycle simulation model developed in AMESimÒ environment.
main characteristics of the R245fa working fluid are listed in Table 2. In order to describe the behavior of the working fluid, a simple ideal gas model may introduce unacceptable inaccuracies for the study of ORCs. Numerous Equations of State (EoS) have been proposed in the literature on an empirical, semi-empirical or theoretical basis, such as the group contribution method [123–128]. Recently, the real gas effects of R245fa have been analyzed by Luián et al. [129] by comparing two cubic equations: the Redlich–Kwong–Soave (RKS) and the Peng–Robinson (PR) EoS. Instead, in the present work, AMESimÒ includes the properties of R245fa based on the Helmholtz EoS [1,130,131]. A similar formulation is also implemented in REFPROPÒ and CoolPropÒ. The Helmholtz energy represents one of the fundamental properties from which all the other thermodynamic properties can be obtained. The Helmholtz energy is expressed as the sum of the ideal gas contribution, ao, and the residual Helmholtz energy that results from intermolecular forces, ar. Generally, the dimensionless Helmholtz energy is used in practical applications, as a function of a dimensionless density and temperature [131],
Table 2 Properties of R-245fa [120]. Tv @ patm (°C) Tcr (°C) ODP GWP AL (years) Toxicity Flammability
aðq; TÞ ¼ aðd; sÞ ¼ ao ðd; sÞ þ ar ðd; sÞ RT
ð1Þ
The calculation of thermodynamic properties requires an appropriate formulation of the Helmholtz energy for a specific working fluid or mixture. In particular for R245fa, Lemmon and Span [131] provided the empirical coefficient for both ideal and residual Helmholtz energy contribution. The ideal gas and residual Helmholtz energy equations are given as follow,
ao ¼ a1 þ a2 s þ ln d þ ðco 1Þ ln s þ
4 X
v k ln½1 expðuk s=T cr Þ
k¼1
ð2Þ
ar ¼ n1 ds0:25 þ n2 ds1:25 þ n3 ds1:5 þ n4 d3 s0:25 þ n5 d7 s0:875 þ n6 ds2:375 þ n7 d2 s2 expd þ n8 d5 s2:125 expd 2
2
2
þ n9 ds3:5 expd þ n10 ds6:5 expd þ n11 d4 s4:75 expd þ n12 d2 s12:5 expd
3
ð3Þ
The coefficients of Eqs. (2) and (3) are listed in Tables B1 and B2 of the Appendix B. The detailed expressions for all thermodynamic properties can be found in [130,131]. 4.2. Working fluid pump
14.6 154 0 1020 7.6 Class B Class 1
A fixed displacement pump is commonly considered as the working fluid pump and both the mass flow rate and the enthalpy increase are usually computed as a function of swept volume, rotational speed, pressure ratio and isentropic efficiency. Quoilin et al. [75] defined the mass flow rate displaced by introducing the definition of capacity factor Xp,
D. Ziviani et al. / Applied Energy 121 (2014) 79–95
Xp ¼
_ m
ð4Þ
qV_ p;max
In order to describe the part load behavior of the volumetric pumps a correlation has to be introduced to link the isentropic efficiency with the flow rate at nominal conditions. Lecompte et al. [110] adopted the correlation proposed by Lipke [132] to calculate the isentropic efficiency and the pressure rise under part-load,
_ m
_ m
gp ¼ 2gp;nom _ gp;nom _ nom mnom m
Dp ¼ Dpnom
_ m _ nom m
2
ð5Þ
2 ð6Þ
Bamgbopa and Uzgoren [112] defined the pump efficiency as a function of the capacity factor and obtained the coefficients by interpolating the available pump data,
gp ¼ A0 þ A1 logðX p Þ þ A2 log ðX p Þ2 þ A3 log ðX p Þ3
ð7Þ
Instead, the pressure rise has been expressed as a function of the volumetric flow,
Dp ¼ C 1
_ m
qin
2
þ C2
_ m
qin
þ C3
ð8Þ
In AMESimÒ, the pump model can be characterized by providing the values of the displacement volume, the volumetric, isentropic and mechanical efficiency. Furthermore, it is possible to specify the efficiency parameters in different ways, such as (i) constant values, (ii) functional relationships (e.g. depending on pressure ratio and rotational speed) or (iii) experimental data, in order to simulate the part-load conditions. Consistent with the assumptions reported above, the volumetric and isentropic efficiency can be expressed as a function of the rotational speed and pressure ratio. However in the present study, constant values have been adopted.
_ theory ¼ qV dis N m _ m
gp;vol ¼ _ real ¼ fp;1 ðN; rÞ mtheory gp;s ¼
Dhs ¼ fp;2 ðN; rÞ Dhreal
ð9Þ ð10Þ
ð11Þ
4.3. Heat exchangers In the considered ORC system, the working fluid exchanges heat through two PHEs (an evaporator and a condenser). It is common practice to use PHEs to enhance heat exchange as well as to reduce the overall dimensions of the system. Different modeling approaches have been proposed in the literature with varying levels of complexity. Lakshamanan and Potter [133] proposed a numerical model, namely the ‘‘cinematic’’ model, to simulate the dynamic behavior of countercurrent systems such as fluidized beds. This model was applied to a plate heat exchanger, without taking into account the phase change within the heat exchanger. Zaleski and Klepacka [134] proposed an approximate solution for the heat transfer in plate heat exchangers, by using exponential approximations for the temperature in each stream. The approximate solution was also compared to the exact analytical solutions. The heat exchanger models are usually developed under the hypothesis of considering the phase change both during boiling and condensation and modeled as an equivalent counter-flow straight pipe. Vaja [82] adopted a 2D discretization model of the heat exchanger by considering the variation of state parameters both in axial and radial direction and by taking into account the
87
phase change. Quoilin et al. [75] and Wei et al. [81] described both PHEs (evaporator and condenser) as a straight pipe divided into three zones characterized by sub-cooled liquid, saturated mixture and superheated vapor. Then, for each zone, appropriate onedimensional governing equations were applied. The adopted heat transfer correlations takes into account boiling and condensing phenomena as well as the corrugation of the plate heat exchangers. Under boiling and condensation conditions, a vertical PHE with R410A has been considered as reference case and correlated to the experimental results by introducing two coefficients. Pressure drops were neglected due to the absence of differential pressure sensors. Lecompte et al. [110] adopted a similar discretization approach to a PHE and including different working fluids, i.e. R245fa, R1234yf and R152a, and internal pressure drops. The heat transfer correlations used are listed in Table 3. The AMESimÒ library allows describing a PHE from a physicsbased point of view, i.e. it is possible to graphically reproduce the channels inside the heat exchanger and depicted in Fig. 6. However, the lack of two-phase components to simulate heat transfer on both sides of a tube (highlighted in Fig. 6) make it necessary to reduce the PHE to an equivalent configuration. Therefore, a 2D discretization approach of an equivalent channel can be assumed to model the dynamic behavior of the heat exchanger, represented as a counter flow straight pipe divided into a series of longitudinal lumped volumes, as shown in Fig. 7. Such equivalent configuration consists of two counter-flow streams, i.e. one representing the hot source (hot water in this paper) and the other one simulating the cold stream on the refrigerant side. The sketch of the equivalent counter-flow heat exchanger in AMESimÒ is shown in Fig. 8. The heat exchange model takes into account both convective and conducting effects as well as internal pressure drops, attempting to simulate the real paths that the fluids follow while flowing through the heat exchanger. The model also considers the effective mass of the heat exchanger and its thermo-physical properties, as a function of temperature and pressure during the heat transfer process. The model used in the refrigerant side, highlighted in Fig. 8, allows two-phase conditions and phase-change. It is important to notice the difference in the connections available between the modules used in Figs. 6 and 7. Conduction is also allowed in longitudinal direction. This modeling approach can be applied to the condenser and the evaporator PHEs. The internal convective heat transfer in the component is evaluated by using correlations found in literature. Depending on the state of the fluid, different correlations are used during boiling or condensation and for single-phase flow (liquid or vapor). A survey of the correlations available in AMESimÒ is presented in Table 4. 4.4. Pressure drops Correlations to estimate pressure losses in components including the piping system are widely available in the literature [85–89]. The correlations are often derived as a function of the state of the fluid, accounting for the hydraulic resistances to the flow. The parameters include mass flow rate, surface roughness, geometrical dimensions, and the flow regime (laminar or turbulent). Modeling is commonly assumed to be isenthalpic and adiabatic. The correlations available in AMESimÒ are listed in Table 5. 4.5. Volumetric expander The expander represents the key component of an ORC system, since it has significant impact on the system overall efficiency. In the ORC-based micro-CHP systems for domestic applications, the lack of commercially available high efficiency expanders has hindered the development of small size ORCs. A survey of the expanders available in the market for micro-CHP applications is
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Table 3 PHEs heat transfer correlations. Quoilin et al. [75]
Lecompte et al. [110]
Type Working fluids
PHEs HCFC-123
PHE (evap.) Tube&fin (cond.) R245fa R1234yf R152a
Single-Phase heat transfer
Nu = C Rem Pr 1/3
Nu ¼ 0:299Re0:645 Pr 1=3 200 6 Re 6 15000
Boiling heat transfer Condensation heat transfer
m ¼ 0:5ðRe < 400Þ m ¼ 0:7ðRe > 400Þ hev = C hl Bo0.5
hev = 88hl Bo0.5 2:09 hcd ¼ hl 0:55 þ Pr 0:38
þ 75Bo0:75 Þ hcd ¼ 23:7 hl ð0:25Co0:45 Fr0:25 l
Table 4 Correlations used to model the heat exchange process. Single-phase correlation
Two-phase correlation
Boiling Gnielinski [85,86]
Chen [92] VDI vertical tubes [85,86] VDI horizontal tubes [85,86]
Condensation Gnielinski [85,86]
Shah [99] Cavallini and Zecchin [104] Traviss et al. [135]
Fig. 6. Graphic representation of a PHE in AMESimÒ.
Table 5 Correlations used for pressure drop estimation.
Fig. 7. PHE geometry and equivalent straight pipe model.
Fig. 8. Model of heat exchanger used as evaporator.
presented by Qiu et al. in [38]. In general, two types of expanders can be identified: the turbo-machinery type and displacement or volumetric type. The choice of the proper expander depends on the operating conditions, efficiency and cost. In general, a displacement type expander, a scroll-type in particular, is used more
Single-phase fluid
Two-phase fluid
Churchill [136]
McAdams et al. [137] Cicchitti et al. [138] Duckler et al. [139] Friedel [140] Müller-Steinhagen and Heck [141]
frequently, mainly because it is suitable for small-scale ORC systems, which are characterized by low flow rates. The scroll-expander is also suitable for high-pressure ratios, lower rotational speeds, and two-phase flows. The scroll machine has a limited number of moving parts. It is a reliable and proven technology in a compressor mode used in the refrigeration and air-conditioning industry. The performance of the scroll expanders has been investigated in several research works [142–145], where a maximum isentropic efficiency of about 70% was predicted, although this has been hard to achieve in practice. Several aspects, such as geometry, governing equations, leakages, heat dissipation and thermodynamics have to be taken into account to model the scroll expander. At the same time, the resulting model should be numerically robust and with a low computational complexity. A detailed mathematical model for the scroll compressor has been presented by Chen et al. in [146,147]. In particular, a geometric study was performed as well as a comprehensive scroll model was developed, including separated models for compression process, heat transfer between refrigerant and compressor parts and internal refrigerant leakage. Bell [148] improved the geometry-based approach to a scroll compressor by deriving the analytical solution of all the control volumes inside the machine as well as the leakage paths. The simulation model was developed in Phyton™. Quoilin [142] proposed and validated a semi-empirical model of a scroll-expander by decomposing the evolution of the working fluid through the expander into different steps, by taking into account pressure drops, the isentropic expansion followed by a fixed-volume expansion, mixing between suction flow and leakage
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flow and internal/external heat exchange process. The simulation model was optimized by using several sets of experimental data. A similar approach is adopted in the present simulation model. The main difference is represented by introducing a library-oriented environment, which is helpful to separate the different effects. Furthermore, the model developed in this paper is general and can be tailored to a specific experimental set-up by modifying the geometric characteristics and by introducing the proper performance maps. The main characteristics of the simulation model developed in this paper are: Inlet pressure drop characterized by a lumped cross sectional area and heat exchange losses with the wall of the expander. The pressure drop is evaluated by using correlations from the literature [136–141]. Internal pressure drop due to the small path between fixed and orbiting scroll. Thermal conduction with the internal wall of the scroll expander, as a function of pressure and temperature, as well as the material of the wall. Possibility of heat exchange with the environment, – the system is not considered to be fully isolated. Presence of a leakage flow to compute different internal leakages that may occur due to a gap between the upper and the lower part of the scrolls and the walls of the expander. A second gap is located between the flanks of the scrolls. After the expansion process, a mixing module is needed. Exhaust pressure drop estimation by defining the cross-sectional area of the downstream pipe system. Use of volumetric, isentropic and mechanical efficiencies to characterize the performance of the scroll expander. Adoption of the equation of mass balance to check whether each component works correctly. Both dynamic and steady-state operations are considered. The comprehensive model of the scroll expander is presented in Fig. 9, where it is possible to notice the different effects, such the heat transfer with a lumped mass and the ambient, an internal equivalent leakage, internal pressure drop, the mixing after the expansion and the discharge. The performances of the scroll expander are characterized by the volumetric efficiency and the isentropic efficiency, as reported in Eqs. (12) and (13).
gt;vol ¼ gt;s ¼
_ theor m ¼ ft;1 ðN; rÞ _ m
Dhreal ¼ ft;2 ðN; rÞ Dhs
ð12Þ
ð13Þ
As previously outlined for the volumetric pump, in AMESimÒ, the value of both efficiency parameters can be specified either as a constant or as a function of the rotational speed and the expansion ratio. Declaye et al. [149] proposed a non-dimensional performance curve based on Pacejka’s equation, by considering as parameters the rotational speed, expansion ratio and the filling factor. The general expression is defined as,
gt;s ¼ ymax ðn arctanðB ðrp rp;o Þ E ðB ðr p r p;o Þ arctanðB ðr p r p;o ÞÞÞÞÞ
ð14Þ
where all the parameters in the equation have a mathematical meaning and are derived from the linear regression of experimental data. Starting from the experimental data available from Quoilin [142], two correlations have been deduced and fitted to minimize the error between numerical and experimental data. The general form of the correlation is given by,
Fig. 9. Comprehensive model for scroll expander in AMESimÒ.
g ¼ c0 þ
n n m X X X ci N i þ cj rj þ ck N k r k i¼1
j¼1
ð15Þ
k¼1
It is important to notice that the efficiency (volumetric and isentropic) depends on the pressure ratio across the expander and the rotational speed. The geometric and performance parameters of the considered scroll expander are listed in Table 6. 4.6. Fluid receiver A fluid receiver is commonly placed after the condenser to avoid surging of the pump and to compensate the liquid level fluctuations in the evaporator, according to Quoilin et al. [84]. The pressure is considered homogeneous in the entire volume, as well as the densities of both gas and liquid phases in their respective volumes. In order to calculate the time derivatives of the pressure and the density, mass and energy balances are employed to model the receiver [81,82],
" # X dq 1 dV X _ _ ¼ q þ m m dt dt V out in
ð16Þ
Table 6 Geometric and measured data of the scroll expander [142]. Built-in volume ratio Volume swept Supply pipe diameter Internal port diameter Leakage area Supply pressure Supply temperature Exhaust pressure Mass flow rate Expander rotational speed Expander isentropic efficiency Pressure ratio
4.05 36.54 cm3 16 mm 5.91 mm 4.2 mm2 5.45–11.12 bar 101.7–165.2 °C 1.38–2.66 bar 45–86 g/s 1771 rpm; 2296 rpm; 2660 rpm 42–68% 2.7–5.4
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X X X dU _ þ _ in _ out ¼W Q_ þ ðmhÞ ðmhÞ dt
ð17Þ
The densities depend on the liquid volume percentage. By specifying the fluid receiver volume, Vfr, the initial percentage of liquid volume, xl, and initial temperature and pressure conditions, the level of fluid, /, is derived,
i d/ 1 hX _ cd;out ðmÞ _ p;in ¼ ðmÞ dt qV fr
ð18Þ
Both single and two-phase flow conditions are considered and consequently a stratification model is presented. By assuming a constant cross-sectional area of the chamber, the height of the vapor–liquid interface is obtained by multiplying the chamber height and the liquid percentage,
/ ¼ xl Hfr
ð19Þ
In order to determine the state of the fluid flowing out the chamber, the heights of the inlet and outlet ports are compared to the height of the vapor–liquid interface. If the height of a port is greater than the vapor–liquid interface height, the state of the fluid flowing out is vapor; otherwise it is liquid. 5. ORC system simulation model One of the challenges of novel modeling approaches is the validation of the results by means of numerical and/or experimental data. In fact, the modeling effort is not always adequately supported by the availability of experimental test rigs. Recently, ORC system test facilities are increasing, especially in the small scale power range [115,149–151], and consequently more data are available to validate numerical models. Below we present a model of an ORC system, which consists of two main components, i.e. the heat exchanger and the expander. Before assessing the overall performances of the system, a component-level analysis is proposed in order to investigate the accuracy of such sub-systems. This model is presented to offer a more lucid overview of the steps involved, to support the arguments and the open issues of the review discussion presented above.
Table 7 Boundary conditions for heat transfer coefficient evaluation. Tibiriçá and Ribatski [153]
Greco and Vanoli [158]
Working fluid Channel diameter (mm) Length (m) Tube
R245fa 2.32
R410a 6
0.464 Horizontal smooth tube
Boundary conditions
G = 300 kg/(m2 s) q = 15.0 kW/m2 Tsat = 31 °C
6 Horizontal smooth tube G = 363 kg/(m2 s) q = 15.0 kW/m2 pev = 4.83 bar
As previously highlighted, the heat transfer coefficient under phase-change represents a problem which has not a unique solution. In fact, the available correlations are obtained under specific conditions and for selected working fluids. Therefore, it is difficult to have equations of general validity. The ORC system considered in this work employs R245fa as the working medium. In literature, the experimental studies related to evaluate the heat transfer coefficient of such fluid are limited (for a flow boiling and condensing in micro-channels) or even absent (e.g. in the case of vertical or horizontal plate heat exchangers). For instance, Ong and Thome [152] investigated flow boiling conditions of three refrigerants, R134a, R236fa and R245fa in a 1.030 mm channel, under different boundary conditions of mass and heat fluxes. Tibiriçá and Ribatski [153] carried out flow boiling experiments in a micro-scale tube with internal diameter of 2.3 mm. R134a and R245fa were considered as the working fluids. As a test-case, the latter experimental set up has been simulated, by imposing heat flux and mass flux through a test-section represented by a horizontal stainless steel tube of 2.3 mm I.D. with a heating length of 464 mm. The boundary conditions are listed in Table 7. The simulation model is presented in Fig. 10. The aim of this numerical simulation is the evaluation of the internal convective heat transfer coefficient of R245fa under phase-change. The results are compared to the experimental and numerical data available in [153]. The Fig. 11 presents the evolution of the heat transfer coefficient with respect to vapor quality for the experimental data reported by Tibiriçá and Ribatski [153] and in other available studies. It is possible to notice that the numerical value of the heat transfer may differ by over 200% and the trends also present different behavior. However, the values predicted by the simulation model are on agreement with three out of the five documented experiences (above all, with the results in [153,155]). Therefore, the values of the heat transfer coefficient of R245fa present an acceptable agreement with the literature data, meaning the heat transfer module in AMESimÒ can be reliably coupled with other modules to simulate the entire ORC system. Different fluids may also be considered, thanks to AMESimÒ library. As discussed in Section 4.3, PHEs are usually adopted for heat transfer. Therefore, heat transfer conditions are substantially different with respect to a straight pipe. As also discussed above, there is a lack of experimental data regarding flow boiling or condensing of R245fa in PHE. In order to assess the heat transfer correlations implemented in AMESimÒ applied to a plate heat exchanger, a second case-study is considered by using another working fluid, i.e. R410a. The choice of this particular fluid is justified by the fact that Hsieh and Lin [89] investigated saturated flow boiling in a vertical PHE by using R410a and the correlations obtained were used by Quoilin et al. [75] and Lecompte et al. [110] with different fluids to model the heat transfer in PHEs. For this purpose, the experimental study carried out by Greco and Vanoli [158] has been simulated by using the same model presented in Fig. 10. The heat transfer characteristics of R410A were studied by using a smooth horizontal tube uniformly heated. The
Fig. 10. Representation in AMESimÒ environment of the test-section presented in [153].
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Fig. 11. Comparison of the heat transfer coefficient of R245fa predicted by the simulation model to the experimental and predicted data documented in [153– 157].
boundary conditions of the test set up are listed in Table 7. The values of heat transfer coefficients obtained from Greco and Vanoli [158] through several numerical correlations taken from the literature are reported in Fig. 12, together with the simulated results. It can be noticed that the values obtained through the simulation model are compatible with the available data, but the heat transfer coefficient depends on the type of correlation used. The average deviation, based on all the considered literature data, is approximately 16%. Experimental, theoretical and simulated heat transfer coefficients follow the same behavior, even though the simulation model tends to underestimate the heat transfer coefficient at very low vapor quality. The scroll expander model presented in Fig. 9 has been validated by considering the experimental data obtained by Quoilin [142]. The inputs of the model consist of the geometrical characteristics of the scroll expander and the measured data of mass flow rate, supply pressure and temperature, the exhaust pressure and the rotational speed summarized in Table 6. In Fig. 13, it is possible to notice that the agreement between measurements and predictions is very high, with a deviation always lower than 4% among efficiency values obtained in correspondence of the same pressure ratio. Furthermore, the trend is also comparable, i.e. the maximum isentropic efficiency (i.e. about 0.68) is reached for a pressure ratio of approximately 5.5, as stated by Quoilin in [142]. The validation of the expander model for the shaft power vs. pressure ratio is reported in Fig. 13 only at 2296 rpm due to the limited experimental data for the other rotational speeds. Also for this quantity, the global trend and the numerical values are in good agreement for the entire range of considered pressure ratios.
Fig. 13. Comparison between experimental data obtained in [142] and predicted values from the expander model.
Subsequently, the complete ORC system model was simulated and validated by using experimental results available in literature. The experimental data were reported by Quoilin [142] for a smallsize ORC system, with a net electric power output of approximately 1.7 kW. The system is composed of (i) two hot air sources, which are disposed in a mixed parallel/series configuration to maximize the heat recovery and supplying three PHEs (i.e. the evaporators), (ii) a scroll expander, (iii) two water-cooled PHEs (i.e. the condensers), (iv) a liquid receiver and (v) a feed pump. The working fluid, initially selected to be HCFC-123, was subsequently replaced with HFC-245fa. The variation ranges for the working conditions and the main parameters of the experimental set up are summarized in Table 8. It should be noted that the operating points with negative cycle efficiency are not considered for model validation, i.e. only pressure ratios higher than 3 are taken into account. The evaporating temperature, the evaporating and condensation pressures, the expander rotational speed and the expander isentropic efficiency were kept equal to the corresponding steady-state value measured in [142] and presented in Table 8. Expander isentropic efficiency was adopted from [142] for each operating point, and the simulations were run to evaluate the overall thermodynamic efficiency:
gth ¼
Pexp Pp PeV
ð12Þ
The direct comparison of the experimental data to the simulated values is shown in Fig. 14. The trend of the predicted ORC system thermodynamic efficiency vs. pressure ratio shows a good
Table 8 ORC system experimental data and performance [142].
Fig. 12. Comparison of the heat transfer coefficient of R410A in a PHE evaporator predicted by the simulation model to the literature data reported in [158–163].
ORC system data Working fluid Hot air source mean temperature Air mass flow rate Pressure ratio Scroll compressor swept volume Scroll built-in pressure ratio Mass flow rate Expander rotating speed Evaporating temperature Condensing temperature Liquid receiver volume
R245fa 110–134 °C 71–126 g/s 2.42–7.44 122 cm3 4 49–78 g/s 1855–3125 rpm 84.3–102.1 °C 26.5–56.5 °C 8 dm3
ORC measured performance Shaft power Net electric power Expander effectiveness Cycle efficiency
180.5–2164 W 224 to 1709 W 59.6–70.9% 1.4 to 7.3
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ORC thermodynamic efficiency
8.0%
Table A.1 (continued)
7.0%
6.0% Experimental data Simulation model
5.0% 3.0
4.0
5.0
6.0
7.0
8.0
Pressure ratio Fig. 14. Experimental [142] and predicted values of ORC system thermodynamic efficiency.
Table A.1 Most common fluids available in AMESimÒ [9], REFPROPÒ [102], CoolProp [112] and EESÒ [60]. Fluids
AMESimÒ
REFPROPÒ
CoolPropÒ
EESÒ
Air (mixture) Ar (Argon) H2 (parahydrogen) H2 (hydrogen) He (Helium) CO2 (carbon dioxide or R744) C2H4 (ethylene) C3H6 (Cyclopropane) C5H10 (Cyclopenthane) C6H12 (Cyclohexane) HFE143m HFE7500 Isobutene Isohexane Isopentane MD2M MD3M MD4M MDM MM Methane (CH4) Methanol Neopentane Nitrogen (N2) NH3 (ammonia) Oxygen R11 R113 R114 R116 R12 R123 R1233zd(E) R1234yf R1234ze(E) R1234ze(Z) R124 R125 R134a R13 R14 R141b R142b R143a R143m R152A R161 R21 R218
U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
Fluids
AMESimÒ
REFPROPÒ
CoolPropÒ
EESÒ
R22 R227ea R23 R236ea R236fa R245fa R245ca R32 R365MFC R290 (propane) R404a R407F R41 R410a R507a R600a (Isobutene) RC318 SES36 (SolkathermÒ) SO2 (Sulfurdioxide) SF6 (SulfurHexafluoride) Toluene m-Xylene n-Butane n-Decane n-Dodecane n-Heptane n-Hexane n-Nonane n-Octane n-Pentane n-Propane n-Undecane o-Xylene p-Xylene Water (H2O)
U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U
agreement with the experimental data: the average deviation between measured and predicted values is 2.9%, while the maximum deviation is 8.6% in correspondence of the highest values of the pressure ratio. 6. Conclusions The Organic Rankine Cycle (ORC) system is considered to be a growing market that will be part of the answers to energy efficiency and environmental challenges. The number of technical approaches, sizing methodologies, and modeling tools is rapidly growing as evidenced by the large number of published papers over the last decade. A review of all aspects of such fast growing technology is therefore essential to reflect and compare the available options. The literature review highlighted that, although substantial progress has been made in recent years, most in the modeling approaches, and efficient systems can be expected in high temperature ranges, while low grade thermal energy recovery should be considered to be in its infancy. Great research opportunities still exist in working medium, architecture, design of efficient expanders, modeling and evaluating heat transfer and system losses, etc. The successful recovery of waste thermal energy remains to be one of the favored topics. The review also showed that there are ample technologies suitable for waste heat recovery and ORC systems. Some of these technologies are in the conceptual range, especially in the micro-scale range. However, this trend is expected to grow, as climate change and CO2 emissions put pressure on the energy market. To optimize the performance of ORCs, which are the most prevalent and the only market-ready technologies suitable for low-grade thermal energy recovery today, flexible and reliable
93
D. Ziviani et al. / Applied Energy 121 (2014) 79–95 Table B.1 Coefficients of the ideal gas Helmholtz energy for R245fa [121]. a1
a2
c0
v1
u1/K
v2
u2/K
v3
u3/K
13.4283638514
9.8723653800
4.0
5.5728
222.0
10.385
1010.0
12.554
2450–0
Table B.2 Coefficients of the residual Helmholtz energy [121]. n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12
1.2904 3.2154 0.50693 0.093148 0.00027638 0.71458 0.87252 0.015077 0.40645 0.11701 0.13062 0.022952
simulation models are required. The paper also addressed a review of this topic including a survey of common modeling approaches available in literature, under both steady and transient conditions. Among the many available tools, AMESimÒ environment, a libraryorientated software not widely used for ORC simulation, showed good promise. It provided a wide fluid library and proved to be robust and powerful as it allowed detailed description of the ORC components. In general, given the uncertainties related to the estimation of heat transfer coefficients under boiling and condensing (i.e. two-phase) conditions and the varying operating conditions of the volumetric expander, there is room to improve modeling accuracies for a range of ORC components. The introduced model is consistent with the work of most of the authors referenced in here, and the deviation between the published data used for validation and the predictions of the simulation model can be considered acceptable. If a more accurate model is required, a more specific model tuning may be performed on the basis of the guidelines and recommendations provided in this paper. Appendix A. See Table A.1. Appendix B. See Tables B.1 and B.2. References [1] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210–21. [2] EIA, US energy information administration. International Energy Outlook 2011; 2011. [3] Maizza V, Maizza A. Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems. Appl Therm Eng 2001;21:381–90. [4] De Paepe M, D’Herdt P, Mertens D. Micro-CHP systems for residential applications. Energy Convers Manage 2006;2006(47):3435–46. [5] Bao J, Zhao L. A review of working fluid and expander selections for organic Rankine cyle. Renew Sustain Energy Rev 2013;24:325–42. [6] Bianchi M, Pascale De. A. bottoming cycles for electric energy generation: Parametric investigation of available and innovative solutions for the exploitation of low and medium temperature heat sources. Appl Energy 2011;2011(88):1500–9. [7] Quoilin S, Van Den Broek M, Declaye S, Dewallef P, Lemort V. Technoeconomic survey of Organic Rankine Cycle (ORC) systems’’. Renew Sustain Energy Rev 2013;22:168–86. [8] Chan CW, Ling-Chin J, Roskilly AP. Reprint of ‘‘A review of chemical heat pumps, thermodynamic cycles and thermal energy storage technologies for low grade heat utilisation’’. Appl Therm Eng 2013;53:160–76.
[9] LMS Engineering Innovation – LMS Imagine. Lab AMESim
94
D. Ziviani et al. / Applied Energy 121 (2014) 79–95
[38] Qiu G, Liu H, Riffat S. Expanders for micro-CHP systems with organic Rankine cycle. Appl Therm Eng 2011;31:3301–7. [39] Chen TH, Goswami DY, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion low-grade heat. Renew Sustain Energy Rev 2010;2010(14):3059–67. [40] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical Organic Rankine Cycle. Energy 2010;35:1030–9. [41] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88:2740–54. [42] Fischer J. Comparison of trilateral cycles and organic Rankine cycles. Energy 2011;36:6208–19. [43] Öhman H, Lundqvist P. Theory and method for analysis of low temperature driven power cycles. Appl Therm Eng 2012;37:44–50. [44] Öhman H. Comparison and analysis of performance using low temperature power cycles. Appl Therm Eng 2013;52:160–9. [45] Zamfirescu C, Dincer I. Thermodynamic analysis of a novel ammonia-water trilateral Rankine cycle. Thermochim Acta 2008;477:7–15. [46] Lecompte S, van den Broek M, De Paepe M. Thermodynamic analysis of the partially evaporating trilateral cycle. In: Proceedings of the 2nd international seminar on ORC power systems. Rotterdam, Netherlands; 2013. [47] Ho T, Mao SS, Grief R. Comparison of the Organic Flash Cycle (OFC) to other advanced vapor cycles for intermediate and high temperature waste heat reclamation and solar thermal energy. Energy 2012;42:213–23. [48] Ho T, Mao SS, Greif R. Increased power production through enhancements to the Organic Flash Cycle (OFC). Energy 2012;45:686–95. [49] Zhang X, He M, Zhang Y. A review of research on the Kalina cycle. Renew Sustain Energy Rev 2012;16:5309–18. [50] Guzovic´ Zvonimir, Majcen Boris, Cvetkovic´ Svetislav. Possibilities of electricity generation in the Republic of Croatia from medium-temperature geothermal sources. Appl Energy 2012;98:404–14. [51] Rodriguez CEC, Palacio JCE, Venturini OJ, lora EES, Cobas VM, dos Santos DM, et al. Exergetic and economic comparison of ORC and Kalina cycle for low temperature enhanced geothermal system in Brazil. Appl Therm Eng 2013;52:109–19. [52] Bombarda P, Invernizzi CM, Pietra C. Heat recovery from diesel engines: a thermodynamic comparison between Kalina and ORC cycles. Appl Therm Eng 2010;30:212–9. [53] Wang J, Yan Z, Zhou E, Dai Y. Parametric analysis and optimization of Kalina cycle driven by solar energy. Appl Therm Eng 2013;50:408–15. [54] Singh OK, Kaushik SC. Energy and exergy analysis and optimization of Kalina cycle coupled with a coal fired steam power plant. Appl Therm Eng 2013;51:787–800. [55] Victor RA, Kim JK, Smith R. Composition optimization of working fluids for Organic Rankine Cycles and Kalina cycles. Energy 2013;55:114–26. [56] He J, Liu C, Xu X, li Y, Wu S, Xu J. Performance research on modified KCS (Kalina cycle system) 11 without throttle valve. Energy 2013.. [57] Thombare DG, Verma SK. Technological development in the Stirling cycle engines. Renew Sustain Energy Rev 2008;2008(12):1–38. [58] Kontragool B, Wongwises S. A review of solar-powered Stirling engines and temperature differential Stirling engines. Renew Sustain Energy Rev 2003;2003(7):131–54. [59] Puech P, Tishkova V. Thermodynamic analysis of a Stirling engine including regenerator dead volume. Renew Energy 2011;36:872–8. [60] Cheng CH, Yang HS. Optimization of geometrical parameters for Stirling engines based on theoretical analysis. Appl Energy 2012;92:395–405. [61] Barbieri ES, Spina PR, Venturini M. Analysis of innovative Micro-CHP systems to meet household energy demands. Appl Energy 2012;97:723–33. [62] Li T, Tang D, Li Z, Du J, Zhou T, Jia Y. Development and test of a Stirling engine driven by waste gases for the micro-CHP system. Appl Therm Eng 2012;33– 34:119–23. [63] Yu Z, Jaworski AJ, Backhaus S. Travelling-wave thermoacoustic electricity generator using an ultra-compliant alternator for utilization of low-grade thermal energy. Appl Energy 2012;99:135–45. [64] Hung TC. Waste heat recovery of organic Rankine cycle using dry fluids. Energy Convers Manage 2001;42:539–53. [65] Maizza V, Maizza A. Unconventional working fluids in organic Rankine cycles for waste energy recovery systems. Appl Therm Eng 2001;21:381–90. [66] Brasz LJ, Bilbow WM. Ranking of working fluids for organic Rankine cycle applications. In: Proc int refrigeration eng conf paper R068; 2004. [67] Brasz LJ. Assessment of C6F as working fluid for organic Rankine cycle applications. In: Proc int refrigeration eng conf paper 2342; 2008. [68] Angelino G, Colonna di Paliano P. Multicomponent working fluids for organic Rankine cycles (ORCs). Energy 1998;1998(23):449–63. [69] EES – Klein SA. Engineering equation solver. Middleton, WI: F-Chart Software; 2008. [70] MathWorks – Mathlab and simulink for technical computing.
[75] Quoilin S, Lemort V, Lebrun J. Experimental study and modeling of an Organic Rankine Cycle using scroll expander. Appl Energy 2010;87: 1260–8. [76] Quoilin S, Declaye S, Lemort V. Expansion machine and fluid selection for the organic Rankine cycle. In: Proc. 7th international conference on heat transfer, fluid mechanics and thermodynamics. Antalya, Turkey; 2010. [77] Lemort V, Quoilin S, Lebrun J. Numerical simulation of a scroll expander for use in a Rankine Cycle. In: Proc 19th int compressor engineering conference at Purdue University, USA. Paper # 1324; 2008. [78] Lemort V, Quoilin S, Cuevas C, Lebrun J. Testing and modeling a scroll expander integrated into an Organic Rankine Cycle. Appl Therm Eng 2009;29:3094–102. [79] Winandy E, Saavedra C, Lebrun J. Experimental analysis and simplified modelling of a hermetic scroll refrigeration compressor. Appl Therm Eng 2002;22:107–20. [80] Kane M, Larrain D, Favrat D, Allani Y. Small hybrid solar power systems. Energy 2003;28:1427–43. [81] Wei D, Lu X, Lu Z, Gu J. Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Appl Therm Eng 2008;28:1216–24. [82] Vaja I. Definition of an object oriented library for the dynamic simulation of advanced energy systems: methodologies, tools and application to combined ICE-ORC power plant, PhD Thesis in Industrial Engineering, University of Parma, Italy; January 2009. [83] García-Vallardes O, Pérez-Segarra CD, Rigola J. Numerical simulation of double-pipe condensers and evaporators. Int J Refrig 2004;27:656–70. [84] Quoilin S, Aumann R, Grill A, Shuster A, Lemort V, Spliethoff H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl Energy 2011;88:2183–90. [85] Thome JR. Engineering data book III. Wolverine Tube, Inc.; 2010. [86] VDI Heat Atlas Second Edition. VDI-Gesellschaft Verfahenstechnik und Chemieingenieurwesen. Springer; 2010. [87] Yan YY, Lin TF. Evaporation heat transfer and pressure drop of refrigerant R134a in a plate heat exchanger. J Heat Transfer 1999;121:118–27. [88] Yan YY, Lio HC, Lin TF. Condensation heat transfer and pressure drop of refrigerant R-134a in a plate heat exchanger. Int J Heat Mass Transfer 1999;42:993–1006. [89] Hsieh YY, Lin TF. Saturated flow boiling heat transfer and pressure drop of refrigerant R-410A in a vertical plate heat exchanger. Int J Heat Mass Transfer 2002;45:1033–44. [90] Kedzierski MA. A comparison of R245fa pool boiling measurement to R123 and R245fa/Isopenane on a passively enhanced, horizontal surface. Int J Trans Phenom 2006;8:331–44. [91] Shah MM. Evaluation of general correlations for heat transfer during boiling of saturated liquids in tubes and annuli. In: 2005 ASME summer heat transfer conference. San Francisco, California, USA; 2005. [92] Chen JC. A correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Process Des Dev 1966;5:322–9. [93] Shah MM. Chart correlation for saturated boiling heat transfer: equations and further study. ASHRAE Trans Part 1 1982;88:185–96. [94] Steiner D, Taborek J. Flow boiling heat transfer in vertical tubes correlated by an asymptotic model. Heat Transfer Eng 1992;13:43–68. [95] Kandlikar SG. A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. ASME J Heat Transfer 1990;112:219–28. [96] Liu Z, Winterton RHS. A general correlation for saturated and subcooled flow boiling in tubes and annuli based on a nucleate pool boiling equation. Int J Heat Mass Transf 1991;34:2759–66. [97] El Hajal J, Thome JR, Cavallini A. Condensation in horizontal tubes. Part 1: two-phase flow pattern map. Int J Heat Mass Transfer 2003;2003(46): 3349–63. [98] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 3: development of a new heat transfer model based on flow patterns. J Heat Transfer 1998;120:156–65. [99] Shah MM. A general correlation for heat transfer during film condensation inside pipes. Int J Heat Mass Transfer 1979;22:547–56. [100] Meyer JJ, Dunn WE. Investigation of the condensing and expansion behaviors of alternative refrigerants. In: ACRC Contract Report 6, University of Illinois; 1996. [101] Nozu S, Honda H. Condensation of refrigerants in horizontal, spirally grooved micro-fin tubes: numerical analysis of heat transfer in the annular flow regime. J Heat Transfer 2000;122:80–91. [102] Chamra LM, Meng-Onn T, Chea-Chun K. Evaluation of existing condensation heat transfer models in horizontal micro-fin tubes. Exp Thermal Fluid Sci 2004;28:617–28. [103] Chambra LM, Tan MO, Kung CC. Evaluation of existing condensation heat transfer models in horizontal micro-fin tubes. Exp Thermal Fluid Sci 2004;28:617–28. [104] Cavallini A, Zecchin RA. Dimensionless correlation for heat transfer in forced convection condensation. In: Proc 6th int heat transfer conference, vol. 3. 1974. p. 309–13. [105] Smith MK, Wattelet J, Newell TA. A study of evaporation heat Transfer coefficient correlations at low heat and mass fluxes for pure refrigerants and refrigerant mixtures. In: Air conditioning and refrigeration center. University of Illinois; 1993 January.
D. Ziviani et al. / Applied Energy 121 (2014) 79–95 [106] Ho-Saeng L, Jung-In Y, Jae-Dol K, Bansal PK. Characteristics of condensing and evaporating heat transfer using hydrocarbon refrigerants. Appl Therm Eng 2006;26:1054–62. [107] Dalkilic AS, Wongwises S. Intensive literature review of condensation inside smooth and enhanced tubes. Int J Heat Mass Transfer 2009;52:3409–26. [108] Rohsenow WM, Hartnett JP, Cho YI. Handbook of heat transfer. 3rd ed. New York: McGraw-Hill; 1998. [109] Menente G, Toffolo A, Lazzaretto A, Paci M. An Organic Rankine Cycle offdesign model for the search of the optimal control strategy. Energy 2013;58:97–106. [110] Lecompte S, Huisseune H, van den Broek M, De Schampheleire S, De Paepe M. Part load based thermo-economic optimization of the Organic Rankine Cycle (ORC) applied to a combined heat and power (CHP) system. Appl Energy 2013;111:871–81. [111] Lemmon EW, Huber ML, McLinden MO. National institute of standards and technology. Standard reference database 23. Reference fluid thermodynamic and transport properties – Refprop 9.1, US; 2013. [112] Bamgopa MO, Uzgoren E. Quasi-dynamic model for an organic Rankine cycle. Energy Convers Manage 2013;72:117–24. [113] Vankeirsbilck I, Vanslambrouck B, Gusev S, De Paepe M. Efficiency comparison between the steam cycle and the organic Rankine cycle for small scale power generation. In: 2nd European conference on polygeneration. Tarragona, Spain; 2011. [114] Colonna P, van der Stelt TP. FluidProp: a program for the estimation of thermo physical properties of fluids. In: Energy technology section. Delft University of Technology, The Netherlands; 2004. [115] Bracco R, Clemente S, Micheli D, Reini M. Experimental tests and modelization of a domestic-scale ORC (Organic Rankine Cycle). Energy 2013;58:107–16. [116] Ziviani D, Beyene A, Venturini M. Design, analysis and optimization of a micro-chp system based on Organic Rankine Cycle for ultralow grade thermal energy recovery. J Energy Resour Technol 2013;136. http://dx.doi.org/ 10.1115/1.4024858. [117] Connolly D, Lund H, Mathiesen BV, Leahy M. A review of computer tools for analysing the integration of renewable energy into various energy systems. Appl Energy 2010;87(2010):1059–82. [118] Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manage 2009;50:576–82. [119] Malavolta M, Beyene A, Venturini M. Experimental implementation of a micro-scale ORC based CHP Energy system for domestic applications. ASME Paper IMECE2010-37208; 2010. [120] Sami SM. Behavior of ORC low-temperature power generation with different refrigerants. Int J Ambient Energy 2011;32:37–45. [121] Bell I, Quoilin S, Wronski I, Lemort V. CoolPropÒ library.
95
[136] Churchill SW. Friction-factor equation spans all fluid flow regimes. Chem Eng 1977;84:91–2. [137] McAdams WH, Wood WK, Bryan RL. Vaporization inside horizontal tubes – II – Benzene-oil mixtures. Trans ASME 1942;64:193–200. [138] Cicchitti A, Lombardi C, Silvestri C, Soldaini G, Zavatarelli R. Two-phase cooling experiments: pressure drop, heat transfer and burnout measurements. Energia Nucleare 1960;7:407–25. [139] Duckler AE, Wicks M, Cleveland RG. Pressure drop and holdup in two phase flow Part A: a comparison of existing correlations Part B: an approach through similarity analysis. AIChE J 1964;10:38–51. [140] Friedel L. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. European Two-Phase Group Meeting, Ispra, Italy, Paper E2; 1979. [141] Müller-Steinhagen H, Heck K. A simple friction pressure drop correlation in two-phase flow in pipes. Chem Eng Process 1986;20:297–308. [142] Quoilin S. Sustainable energy conversion through the use of Organic Rankine cycles for waste heat recovery and solar applications, PhD Thesis in Applied Sciences. University of Liège (Belgium); October 2011. [143] Zanelli R, Favrat D. Experimental investigation of a hermetic scroll expander generator. Proc Int Compressor Eng Conf Purdue 1994:459–64. [144] Yanagisawa T, Fukuta M, Ogi Y, Hikichi T. Performance of an oil-free scroll type air expander. In: Proc IMechE Conf on Compressors and their systems; 2001. p. 167–74. [145] Mathias JA, Johnston JR, Cao J, Priedeman DK, Christensen RN. Experimental testing of gerotor and scroll expanders used in, and energetic and exergetic modeling of an Organic Rankine Cycle. Energy Resour Technol 2009;131(1):012201. [146] Chen Y, Halm NP, Groll EA, Braun JE. Mathematical modeling of scroll compressors—part I: compression process modeling. Int J Refrigeration 2002;25:731–50. [147] Chen Y, Halm NP, Braun JE, Groll EA. Mathematical modeling of scroll compressors — part II: overall scroll compressor modeling. Int J Refrigeration 2002;25:751–64. [148] Bell IH. Theoretical and experimental analysis of liquid flooded compression in scroll compressors, PhD Dissertation. University of Purdue; 2011. [149] Declaye S, Quoilin S, Guillaume L, Lemort V. Experimental study on an opendrive scroll expander integrated into an ORC (Organic Rankine Cycle) system with R245fa as working fluid. Energy 2013;55:173–83. [150] Zheng N, Zhao L, Wang XD, Tan YT. Experimental verification of a rollingpiston expander that applied for low-temperature Organic Rankine Cycle. Appl Energy 2013;112:1265–74. [151] Li M, Wang J, He W, Gao L, Wang B, Ma S. Construction and preliminary test of a low-temperature regenerative Organic Rankine Cycle (ORC) using R123. Renewable Energy 2013;57:216–22. [152] Ong CL, Thome JR. Flow boiling heat transfer of R134a, R236fa and R245fa in a horizontal 1.030 mm circular channel. Exp Thermal Fluid Sci 2009;2009(33):651–63. [153] Tibiriçá CB, Ribatski G. Flow boiling heat transfer of R134a and R245fa in a 2.3 mm tube. Int J Heat Mass Transfer 2010;53:2459–68. [154] Saitoh S, Daiguji H, Hihara H. Correlation for boiling heat transfer of R-134a in horizontal tubes including effect of tube diameter. Int JHeat Mass Transfer 2007;50:5215–25. [155] Thome JR, Dupont V, Jacobi AM. Heat transfer model for evaporation in microchannels. Part I: presentation of the model. Int J Heat Mass Transfer 2004;47:3375–85. [156] Liu Z, Winterton RHS. A general correlation for saturated fluids in convective flow boiling in tubes and annuli based on a nucleate pool. Int J Heat Mass Transfer 1991;34:2759–66. [157] Kandlikar SG, Balasubramanian P. An extention of the flow boiling correlation to transition, laminar, and deep laminar flows in minichannels and microchannels. Heat Transfer Eng 2004;25:86–93. [158] Greco A, Vanoli GP. Flow boiling heat transfer with HFC mixtures in a smooth horizontal tube. Part II: assessment of predictive methods. Exp Thermal Fluid Sci 2005;2005(29):199–208. [159] Yu M, Lin T, Tseng C. Heat transfer and fluid flow pattern during two-phase flow boiling of R-134a in horizontal smooth and microfin tubes. Int J Refrigeration 2002;25:789–98. [160] Yoshida S, Mari H, Hong H, Matsunaga T. Prediction of binary mixture boiling heat transfer coefficient using only phase equilibrium data. Trans JAR 1994;11:67–78. [161] Shah M. A new correlation for heat-transfer during boiling flow through pipes. ASHRAE Trans 1976;82:66–86. [162] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes: part 3 – development of a new heat transfer model based on flow patter. Trans ASHRAE 1998;1998(120). [163] Zürcher O, Favrat D, Thome JR. Evaporation of refrigerants in a horizontal tube: an improved flow pattern dependent heat transfer model compared to ammonia data. Int J Heat Mass Transfer 2002;45:303–17.
Contents lists available at ScienceDirect
Applied Energy journal homepage: www.elsevier.com/locate/apenergy
Advances and challenges in ORC systems modeling for low grade thermal energy recovery Davide Ziviani a, Asfaw Beyene b, Mauro Venturini c,⇑ a
Ghent University - UGent, Graaf Karel de Goedelaan 5, B-8500, Kortrijk, Belgium San Diego State University, 5500 Campanile Drive, San Diego, CA 92182-5102, USA c Università degli Studi di Ferrara, Via Giuseppe Saragat, 1, 44122 Ferrara, Italy b
h i g h l i g h t s Analysis of the most recent technologies to exploit low-grade thermal energy. Review of state-of-the-art research and development of ORC systems. Comprehensive review of modeling approaches for ORC system simulation. Guidelines to develop a powerful simulation tool for ORC systems. Development and validation of a micro-ORC system simulation model.
a r t i c l e
i n f o
Article history: Received 26 September 2013 Received in revised form 26 December 2013 Accepted 31 January 2014 Available online 22 February 2014 Keywords: Organic Rankine cycle Low-grade thermal energy Review Modeling
a b s t r a c t Low-grade thermal energy recovery has attained a renewed relevance, driven by the desire to improve system efficiency and reduce the carbon footprint of power generation. Various technologies have been suggested to exploit low-temperature thermal energy sources, otherwise difficult to access using conventional power generation systems. In this paper, the authors review the most recent advances and challenges for the exploitation of low grade thermal energy resources, with particular emphasis on ORC systems, based on information gathered from the technical literature. An outline of the issues related to ORC system modeling is also presented, and some guidelines drawn to develop an effective and powerful simulation tool. As a summary conclusion of the revised models, a simulation tool of an ORC system suitable for the exploitation of low grade thermal energy is introduced. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The world energy use has increased more than 40% in the last few decades [1], resulting in sharp increase in fuel price and causing environmental challenges that necessitated exploration of new ways to meet the rising demand with fewer footprints on the environment. The reference case of IEO2011 [2] has shown a further increase of the world energy demand by 53% from 2008 to 2035. As a consequence, waste energy recovery has attained a renewed relevance in order to provide a more sustainable environment for the future. In particular, it has been argued that low grade waste thermal energy, below 200 °C, represents a viable resource of a growing interest because of its abundance. In fact, low grade waste thermal energy accounts for more than 50% of the total heat generated in ⇑ Corresponding author. Tel.: +39 0532 974878; fax: +39 0532 974863. E-mail address: [email protected] (M. Venturini). http://dx.doi.org/10.1016/j.apenergy.2014.01.074 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.
industry [3]. Low grade thermal energy (LGTE) is readily available in thermal processes, combustion exhausts, cooling or condensing systems, as well as from equipment such as compressors. It also exists in nature, in geothermal form or as solar irradiation. Research related to recovery of LGTE from these sources has drawn increasing attention in recent years. Most of the work is restricted to the theory, mainly focusing on mathematical modeling and feasibility study. Unfortunately, the ongoing focus on the theory with little advances on the practical side leaves doubts about engineering and practical limitations of these concepts, meaning there is a lack of a suitable cost-effective technology ready for mass production. There is a wide range of technologies and design options for the recovery of LGTE for power production and Combined Heat and Power (CHP) applications [4]. Suitable thermodynamic cycles include organic Rankine cycle (ORC), supercritical Rankine cycle, Kalina cycle and trilateral flash cycle (TFC) [5], as well as, Stirling engines and new concepts such as thermo-acoustic engine (TAE)
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Nomenclature a Bo Co Fr G h ifg _ m N Np Nu p P Pr q r Re s T V
a x d
g q s U
specific Helmholtz energy (J/kg) boiling number, Bo = q/Gifg convective number, Co = qg/ql((1 x)/x)0.8 Frounde number, Fr = G2/q2gDh mass flux, (kg/(m2 s)) convective heat transfer coefficient, (W/(m2 K)); specific enthalpy (J/kg) enthalpy of vaporization (J/kg) mass flow rate (kg/s) rotational speed (rpm) number of plates Nusselt number (–) pressure (bar) power (W) Prandtl number (–) heat flux (W/m2) pressure ratio Reynolds number (–) specific entropy (J/(kg K)) temperature (°C) volume (m3) dimensionless Helmholtz energy (–) vapor quality reduced density, d = q/qcr efficiency density (kg/m3) reduced temperature, s = Tcr/T liquid level (–)
Subscripts and superscripts cd condenser cr critical d displacement E excess
and inverted Bryton cycle. Simulation models have been developed to conduct techno-economic analysis of the design options for some of these technologies to evaluate their performances [6,7]. For instance, a techno-economic analysis of a CHP system with low thermal energy recovery in process industries was conducted by Chan et al. [8], comparing various technologies including heat pumps, organic Rankine cycles, and absorption refrigeration. This paper addresses the use of ORC systems to exploit low grade waste thermal energy, and the challenges, methodologies, and the approaches available in the literature for ORC system modeling are discussed by reporting a comprehensive literature survey of currently available models of ORC system components and integration. Modeling challenges and best-practice scenarios are hinted leading to better design solutions. To illustrate the steps employed in our model comparison, the LMS Imagine Lab AMESimÒ [9] is adopted as an alternative library-orientated tool for ORC system modeling under both steady and transient conditions. The employed modeling approach is validated against numerical and experimental data taken from literature.
2. Conversion technologies for low grade thermal energy recovery 2.1. Organic Rankine cycle The ORC system represents a simple Rankine cycle in which the water is replaced by organic mediums that boil at low
eV exp fr h l p real s suc th theory v vol
evaporator expander fluid receiver hydraulic liquid pump real isentropic suction thermodynamic cycle theoretical vapor volumetric
Acronyms AL atmospheric lifetime CCHP combined cooling, heating and power CHP combined heat and power EoS equation of state GWP global warming potential HFC hydrofluorocarbon HRVG heat recovery vapor generator HVAC heating, ventilation and air-conditioning IBC inverted Bryton cycle LGTE low grade thermal energy ODP ozone depletion potential OFC organic flash cycle ORC organic Rankine cycle PHE plate heat exchanger SRC supercritical Rankine cycle TAE thermoacoustic engine TFC trilateral flash cycle TLC trilateral cycle WHR waste heat recovery
temperatures, i.e. the cycle and the working fluid are tailored to exploit hot and cold sources in the most efficient way. The layout of an ORC simple cycle layout and typical T–s diagrams of both subcritical and transcritical cycles are reported in Fig. 1. Over the years, the ORC systems have gained a moderate level of maturity and reliability, allowing heat recovery from different sources, as documented by Branchini et al. [10]. One of the main challenges of the ORC is represented by the choice of the appropriate working fluid, in order to achieve the maximum efficiency for given hot and cold sources. Many analyses of the influence of the working fluids on system efficiency have been reported in the literature, as for instance [11–13]. However, the selection of the optimal working fluid is considered not fully addressed. In fact, recent research works focus on analyzing multi-component mixtures of working fluids in order to better match the heat and cold sources. Aghahosseini and Dincer [14] analyzed different pure and zeotropic-mixture working fluids. Energy and exergy analyses were conducted. The organic working fluids selected for the study were R123, R245fa, R600a, R134a, R407c, and R404a. The technical feasibility of ORC applications for LGTE recovery has already been investigated and validated [15–17]. In fact, medium to high temperature ORCs are successfully used in several applications, such as geothermal resources [18], waste thermal energy recovery from gas turbines or internal combustion engines [19–23] and biomass-based CHP plants [24–26]. However, the research is still ongoing to expand the range of potential applications where the ORCs could be used, for example to ultra low-grade heat
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Fig. 1. ORC simple cycle layout and T–s diagrams of subcritical (a) and transcritical (b) cycles (adapted from [41]).
regimes to exploit renewable energy such as solar or ocean thermal resources [27–30], but also to reduce grid dependence for remote areas that can use distributed electric generation for fresh water production (e.g. for sea water desalination) [31–34]. Although ORCs are characterized by rather low efficiencies (8–12%) [35], they are particularly viable for small-scale unsupervised power generation systems. Absence of fuel cost, improved reliability and low maintenance may also contribute to making ORCs commercially attractive [35,36]. Quoilin et al. [37] reviewed different ORC applications and market perspectives of different modules and manufacturers. Technical challenges, i.e. working fluid selection and expansion machines, were analyzed in-depth. The selection of the expansion component represents a key aspect of power generation efficiently. The efficiency of the expanders heavily affects the overall system efficiency, especially in the small-scale range. Scroll expanders are commonly used in small-scale ORCs, while screw expanders are used for mid-scale power output. Qiu et al. [38] summarized their market research on expanders with potential for domestic applications (1–10 kWe). The study highlighted the lack of commercially available expanders for ORC-based micro-CHP systems. The analysis also showed that scroll expanders and vane-type expanders remain reasonable choices for micro-ORC systems. The optimization of the ORC systems also requires the optimization of the thermodynamic cycle. Different configurations can be considered in order to increase the heat recovery potential. These consider the introduction of a recuperator, regenerator, multi-pressure levels, flashing techniques and supercritical cycles. A detailed analysis of different ORC layouts was carried out by Branchini et al. [10]. When using working fluids with relatively low critical temperatures and pressures such as CO2, supercritical heating conditions can be reached. In such cases, the system is defined as supercritical Rankine cycle (SRC). Although the SRC allows a better thermal matching compared to ORC, mainly due to the absence of twophase region, the required higher pressure regimes lead to difficulties in operation and safety. Chen et al. [39] presented a review of ORC and SRC systems for the conversion of LGTE. The review includes a screening process for a range of working fluids operating in both cycles. Schuster et al. [40] investigated supercritical parameters of various working fluids in ORC applications, in order to achieve higher efficiency values. A second law analysis was proposed. By maximizing supercritical parameters, an efficiency increase of above 8% was claimed. In the following section, new configurations of the ORC thermodynamic cycle are considered and their potential implementation is discussed.
identical to a binary power plant, except that expansion starts from the saturated liquid water instead of the saturated, superheated or supercritical vapor phase, as shown in Fig. 2. This allows the heat transfer from a liquid thermal source to the working fluid at an optimum temperature matching which reduces irreversibilities as a consequence, i.e., offers higher efficiency [42]. The TLC system includes a pump, a heater, a two-phase expander and a condenser. Fischer [42] performed a comparison between optimized case studies of ORC and TLC under the same heat source inlet temperatures, in the range 150–350 °C, and inlet cooling agent temperatures in the range 15–62 °C. The analysis showed that TLC exergy efficiency for power production was 14–29% higher than ORC’s. On the other hand, since the TLC operates with water, the outgoing volume rate from the expander was estimated to be 2.8 times larger than the working fluid of the ORC, with a minimum fluid temperature of 85 °C. The outgoing volume rate factor can increase up to 70 with a minimum working fluid temperature of 38 °C. Large volume flows might represent a practical obstacle to implement the concept. Therefore the TLC with water as the working fluid is most suitable for higher values of the minimum working fluid temperature, as for example in CHP plants. Among low temperature power cycles, a particular case of TLC is the Trilateral Flash Cycle (TFC) [43–44]. The TFC consists of (i) pumping the saturated liquid from low pressure to high pressure, (ii) preheating the pressurized liquid, (iii) expanding the preheated liquid (partial evaporation may occur) and (iv) condensing the part of liquid which has previously evaporated [45]. The TFC improves temperature matching between the heat source and the working fluid. The drawback is that it requires an efficient and reliable two-phase expander (e.g. screw expander or scroll expander), although such expansion may be avoidable. After the heat addition, the single-phase liquid can be throttled to a two-phase mixture, subsequently extracting work from the saturated vapor. Lecompte et al. [46] proposed an optimization of the TLC by introducing a partial evaporation of the working fluid. The resulting cycle presents a higher thermal efficiency and a reduction in heat transfer area because of the larger enthalpy of vaporization of the working fluid. If organic working fluid is used, such system is called Organic Flash Cycle (OFC) (see Fig. 3). Ho et al. [47] evaluated the effectiveness of the OFC on waste thermal energy recovery at 300 °C by using isentropic and dry fluid and comparing the results to other vapor cycles, in particular ORC and transcritical CO2 cycle by adopting a second law analysis. It was demonstrated that OFC presented the highest heat addition exergetic efficiency, but on the other hand the throttling process represented a drawback. The OFC also offers the potential to exploit thermal energy sources at lower temperatures.
2.2. Modified organic Rankine cycles
2.3. Kalina cycle
Trilateral cycle (TLC) is a less-known unit, currently at a development stage [42]. The Trilateral Flash Cycle (TFC) system is
The Kalina cycle uses a binary working fluid such as ammonia and water. The binary fluid is allowed to have varying composition
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Fig. 2. Trilateral Rankine cycle (TRC) layout and T–s diagram (adapted from [8]).
Fig. 3. OFC layout and T–s diagram (adapted from [48]).
providing a richer concentration through the Heat Recovery Vapor Generator (HRVG) and leaner composition in the low-pressure condenser. Since the molecular weight of ammonia is close to that of water, a standard back-pressure turbine can be used. A rich mixture of water and ammonia is superheated in the HRVG and expanded through a turbine. At the exhaust from the turbine, the medium with high ammonia concentration is cooled and diluted with the bottoms from a vapor separator for complete condensation. Part of the working fluid is transported to the vapor separator through recuperative heat exchangers, and the other part is mixed with the stream with high ammonia concentration from the vapor separator. This restores the optimum concentration of the mixture for heat addition. The distillation and condensation processes consist of the demister, recuperative heat exchangers, condenser, and control system. The mixture of two compounds having different boiling points allows boiling of the mixture over a range of temperatures. The ratio of the two components can be varied in different stages within the cycle allowing non-isothermal boiling which in turn allows extracting more heat from the source. Such flexibility takes full advantage of the temperature differential between the LGTE heat source and the sink; therefore the Kalina cycle is able to reach higher overall efficiency than ORCs, within the same temperature range. However, in the range of LGTE (i.e. low power level and low temperature sources), the adoption of Kalina cycle is not justified because the gain over an optimized ORC is limited, and obtained as a consequence of a more complicated system layout [49]. The Kalina cycle represents a novel thermodynamic cycle and additional degree of freedom (i.e. fraction of ammonia–water mixture) compared to Rankine cycle offers wide range of further improvements. Moreover, the Kalina cycle offers better thermodynamic performance than Rankine and ORC systems under both energy and exergy point of view.
Coupling of the Kalina cycle with renewable resources such as geothermal plants have been investigated, [49,50]. Rodriguez et al. [51] compared ORC and Kalina cycle for power production from low-grade geothermal reservoir with 150 °C or lower, using first and second laws of thermodynamics. The comparison was conducted for a range of working fluids of the ORC system (fifteen working fluids have been taken into account) and an optimal ammonia-water mixture composition for the Kalina cycle. The simulations showed that the optimal system for the ORC employed R-290 as a working medium, whereas for the Kalina cycle a mixture composition of 84% of ammonia and 16% (based on water mass fractions), were registered. The comparison showed that the Kalina cycle could produce 18% more net power than the ORC, with an electricity cost of 0.18 €/kW h, compared to 0.22 €/kW h for the ORC. Bombarda et al. [52] proposed a comparison between Kalina cycle and ORC recovering heat from two diesel engines, each one having an exhaust gas flow rate of 35 kg/s at 346 °C. The thermodynamic analysis showed that, although the Kalina cycle allowed higher net electric power output (1615 kW instead of 1603 kW for the ORC), higher values of the maximum pressure are necessary to achieve high thermodynamic performances, i.e. 100 bar for the Kalina cycle instead of 10 bar for the ORC. Therefore, the adoption of the Kalina cycle for medium–high temperature thermal sources is not justified when compared to an optimized ORC. Wang et al. [53] examined a solar-driven Kalina cycle (reported in Fig. 4) which the authors believed was a better match for the varying vaporization temperature of the ammonia-water mixture. Thermal energy storage was introduced in order to ensure consistent operation for the system. A detailed mathematical model was developed and the optimization process led to a claimed system
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Fig. 4. Kalina cycle (KC) (adapted from [53]) and enthalpy vs. ammonia mass fraction diagram (adapted from [56]).
efficiency of 8.54%. Singh and Kaushik [54] proposed an energy and exergy analysis of a Kalina cycle coupled with a coal fired steam power plant, to evaluate the possibility of exploiting lowtemperature heat from exhaust gases. The simulation results showed that when the exhaust gas temperature reduced from 407.3 K to 363.15 K, the Kalina cycle efficiency reached a maximum value of 12.95%, increasing the overall plant efficiency by 0.277%. Victor et al. [55] developed an optimization method for the composition of mixed working fluids for ORCs and Kalina cycles, as well as, discussed the comparison between the thermodynamic cycles. Generally, the study demonstrated that the use of both solutions can be considered beneficial for low temperature applications. Optimization studies are still required to select the optimal working fluid. 2.4. Stirling engine The Stirling engine concept was proposed several years before the introduction of diesel engine. Also known as hot-air or hotgas engine [57], it operates as a closed thermodynamic cycle and presents attractive properties such as multi-fuel capability, which can potentially reduce the use of fossil fuel compared to traditional combustion engines. It also offers low noise levels, clean combustion and operational range even with low temperature, i.e. it is a suitable candidate to recover LGTE [57]. Although the Stirling engine has a number of advantages, it is still considered to be at a preliminary conceptual stage mainly because of system complexity compared to other technologies such as ORCs. The dynamic behavior of the engine mechanism and the thermal performance of all the heat exchangers pose a design challenge affecting reliability and efficiency of the system. Several investigations proposed in the literature were focused on addressing optimal system design challenges [58–60]. Thombare and Verma [57] provided a review on Stirling engine technological development addressing feasible solutions for a workable engine. Different engine configurations were assessed, and the influence of various working fluids and technical factors which govern the engine performance (e.g. regenerator effectiveness, regenerator materials, etc.) were addressed. The Stirling engine has the potential to be used more efficiently in micro-CHP systems driven by solar, biogas, or medium–low grade waste thermal energy. Micro-CHP Stirling systems with up to 10 kW of electric power output are available on the market. Most of these are prototypes, ranging from 1 to 9 kW capacities
with corresponding thermal power of 5 to 25 kW, which may very well suit household boilers [61]. Their electric efficiencies range from 13% to 25%, with the CHP efficiency claim boosted to 80% or even higher [61]. Li et al. [62] developed a small-scale Stirling engine driven by mid-high temperature waste gases, obtaining a maximum power output of about 3.5 kW. The experimental results were in fair agreement with the predicted power output, i.e. 3.9 kW, with predicted thermal efficiency of 26%. 2.5. Thermo-acoustic engine (TAE) and Inverted Brayton Cycle (IBC) Several novel concepts of thermal energy conversion methods have been recently proposed. One such case is the thermo-acoustic engine (TAE). This technology has been investigated to operate with small temperature gradients, opening new opportunities and challenges for LGTE recovery. Yu et al. [63] proposed a travelling-wave thermo-acoustic electricity generator to convert thermal energy into electricity. A small-scale TAE has been designed showing a potential for waste thermal energy recovery and the possibility to have an inexpensive technology, although practical challenges need to be addressed in order to build systems with large power output. The Inverted Brayton Cycle (IBC) is considered a possible solution among low to medium grade heat recovery technologies under development. The IBC system consists of a hot stream turbine which expands the gas stream to a value below the ambient pressure, followed by a heat-exchanger which cools down the outlet gas. At the end, the gas is recompressed to ambient pressure conditions by a compressor which discharges the gas to the stack. Despite previous studies, Chan et al. [8] investigated the potential use of IBC systems to low grade temperature. The results of the IBC thermodynamic analysis showed that the efficiency of the cycle is limited to 5% at the maximum temperature of 500 °C. For lower temperatures, in the range of 200–300 °C, the achievable performances are limited due to large amount of power absorbed by the compressor. A possible solution to this issue consists of an enrichment of water in the gas, to reduce the compressor inlet mass flow. By considering a percentage of water mass fraction in the range 0–30%, the maximum efficiency of IBC systems was 10% at 30% water mass fraction, with a maximum specific work of 70 kJ/kg. Although the employment of such systems is still questionable at low temperature ranges compared to other well-proved technologies, e.g. ORCs, the IBC system allows cogenerative operation especially in the temperature range above 200 °C.
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3. Challenges of ORC system modeling Even though, as discussed above, there are potentially different alternative conversion technologies for LGTE recovery, in practice, ORCs are the most prevalent, mainly because of their simplicity and off-the-shelf availability of their components. Despite these benefits, the design and modeling of ORCs can be challenging, especially for transient conditions, e.g. when the load demand or the supply thermal energy exhibits abrupt changes, but yet the working conditions of the systems have to remain within acceptable ranges to avoid unfavorable off-design conditions or temperature shocks. Such problems can be prevented at the design stage by adopting model-based techniques to simulate either the steady state or the transient behavior of the ORC system, to identify the influence of operation parameters and predict the occurrence of critical operating conditions. Furthermore, the modeling approach is very useful to optimize the operating conditions and the components of the cycle by developing proper control and diagnostic strategies. System modeling also supports the design of experimental test-rigs. The operating conditions and types of components highly affect the efficiency of the system, resulting in a lower power output. This is especially true for micro-ORCs designed for low-grade heat recovery. Among the fairly extensive modeling work conducted on ORCs, a significant portion is committed to the influence of thermodynamic properties of the working medium on ORC performance [64–68]. These modeling approaches allow detailed simulation of two-phase flow dynamics in the evaporator and condenser. In fact, while models of pumps and turbines are readily available in the literature, the two-phase flow inside heat exchangers encompassing different working fluids, geared to positive displacement machines, remains a serious research topic. Additionally, different software tools are available to develop ORC models. The choice of the software mainly depends on the type of analysis (e.g. steady or unsteady), and the coding level necessary to implement the components details. In fact, a distinction can be made between coding-based software, e.g. EESÒ [69], MatlabÒ [70], Phyton™ [71], and libraries-orientated software, e.g. SimulinkÒ [70], ModelicaÒ [72], DymolaÒ [73], Cycle-TempoÒ [74]. The difference consists of the possibility of developing a proper set of equations or using available object-oriented libraries, where the equations are already implemented, but the user has to connect them properly and set the parameters. A comprehensive summary of useful software tools for ORC modeling and their main features are reported in Table 1. In the following, a survey of common modeling approaches of ORC systems is presented. A detailed ORC model, based on developing semi-empirical models of each component instead of deterministic models, was presented and validated by Quoilin et al. [75,76]. The limited number of physically meaningful parameters identified from performance measurements allowed the development of numerically robust models, which were interconnected to simulate the overall
system. A detailed scroll expander model, accounting for pressure drops and heat transfer losses, as well as a three-zone counter-flow heat exchanger, was developed using EESÒ software and validated by using experimental data. Furthermore, an optimization process was carried out, achieving an optimum working point with a refrigerant flow rate at a given rotational speed. The cycle improvements led to nearly doubling the efficiency from 5.1% up to 9.9%. Since the expander is a key element of the ORC, Lemort et al. [77,78] presented a focused investigation of the semi-empirical simulation model on expanders. The model is also an extension of the one proposed by Winandy et al. [79] and Kane [80]. However, it is distinct in that it takes into account internal and external heat transfers and also under- and over-expansion processes identifying the parameters through a genetic optimization algorithm embedded in EESÒ. Based on the experimental results, the model accuracy was within 2%, and the computational time was low. Two dynamic models that included all ORC components were presented by Wei et al. [81]. The models, developed in ModelicaÒ language and simulated by means of DymolaÒ, are based on moving boundaries and discretization techniques, respectively. A comparison between the two modeling approaches was carried out in terms of accuracy, complexity and simulation speed. The main novelty of the research was the introduction of the moving boundaries approach to describe the two-phase flow inside both the evaporator and the condenser, which leads to simulation models with reduced order, i.e., more suitable for diagnostics and control purposes. Several additional models have been proposed to model heat exchangers in ORCs. For example, Vaja [82] defined an object-orientated library in Matlab/SimulinkÒ to simulate ORC systems. Two models for a generic heat exchanger were included to model either a steady-state heat transfer process or a dynamic approach including the phase change during the evaporation and condensation processes. García-Vallardes et al. [83] proposed numerical simulation of the thermal and fluid dynamic behavior of a double pipe heat exchanger to be used either as an evaporator or a condenser. Radial nodes were also considered. In fact, the energy conservation equations were applied to the external tube and to the insulation system, hence heat loss through insulated surfaces was not ignored. Quoilin et al. [84] presented a dynamic model of an ORC system in order to predict the transient behavior of the cycle with a varying thermal source. This work also tackles control strategies during part-load operation and start and stop procedures. The proposed dynamic model is based on the time-varying performance of heat exchangers; the time variables of the other components are assumed to have less impact on the system dynamic performance. Three control strategies were investigated, i.e. (i) constant evaporating temperature, (ii) optimum evaporating temperature and (iii) pump speed. As previously highlighted, the phase change phenomenon is one of the most complex and challenging aspects related to ORC modeling. The technical literature presents a wide range of correlations validated against experimental data. Some of these correlations are
Table 1 Survey of software tools for ORC modeling. Software
Type
REFPROPÒ
CoolPropÒ
Features
References
MatlabÒ/ SimulinkÒ
Librarybased Code-based Code-based Code-based Librarybased Librarybased Librarybased
U
U
S-Functions Steady–Unsteady analyses Several libraries included
[82,109,110]
U U U
U U U
Support non-linear algebraic systems Complete fluids and solids Libraries High level coding, comparable to Perl, Java, etc. Object-orientated language Unsteady Analyses
[75–78,142] [148] [81,84]
[115,116]
U
Ready-to-use components Steady–Unsteady analyses Complete fluids and solids Libraries FluidpropÒ integration Thermodynamic analysis Optimization of energy systems
EESÒ Phyton™ ModelicaÒ AMESimÒ Cycle-TempoÒ
[113]
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published [85–103]. These publications show that the heat transfer coefficients mainly depend on the type of fluid, on temperature and pressure conditions, as well as on heat exchanger geometry. More extensive literature reviews with focus on refrigeration, air conditioning, and heat pump applications are available [104–108]. Due to the variability of the heat source, ORC systems usually work at part-load conditions, i.e. not at the design point for which the system was optimized. The simulation of part-load operation is still a challenge. For instance, Menente et al. [109] proposed a detailed off-design model of an ORC system by using the performance curves of the main components. The model was developed in SimulinkÒ [61] by imposing mass and energy balances for each component and by introducing appropriate performance curves for the main components of the system. Lecompte et al. [110] developed a thermo-economic design methodology by taking into account the change of operating conditions and part load behavior. The thermodynamic steady-state model was implemented in MatlabÒ using REFPROPÒ [111] library to retrieve fluid properties. A three-zone approach was used to model the plate heat exchangers with phase change and the part load of the pumps were modeled by using a correlation between isentropic efficiency at nominal condition and actual value. The considered fluids were R152a, R1234yf, R245fa. Bamgbopa and Uzgoren [112] presented a simplified transient modeling approach for ORC operating under variable heat input. The model included a dynamic model for the heat exchangers, neglecting the pressure drops, and static models of pump and screw expander. The pump was modeled by means of performance curves where the pressure rise was a function of the volumetric flow rate and pump efficiency. Instead, the nominal polytropic work output of the screw expander was defined as a function of built-in volume ratio and pressure ratio. Among library-orientated software tools, Vankeirsbilck et al. [113] used Cycle-TempoÒ and FluidpropÒ [114] to compare thermodynamically simplified steam cycle and ORC for small scale power generation Bracco et al. [115] developed a numerical model of a small-scale ORC by using LMS Imagine Lab AMESimÒ, a simulation software for the modeling and the analysis of one-dimensional systems. The extensive libraries, including several refrigerants, allow the simulation of ORC system under both stationary and transient conditions and the implementation of control strategies. The Authors [116] adopted the same software tool to implement a comprehensive ORC model suitable for residential applications, able to perform both steady and transient analyses. Finally, a thorough review of available tools for thermodynamic simulations was presented by Connolly et al. [117].
4. Guidelines for orc system modeling According to the challenges outlined in the previous section, in order to accurately model an ORC system, different aspects have to be analyzed thoroughly. The main issues to be addressed include: Estimating the working fluid thermodynamic and transport properties. Determining the heat transfer rate in the evaporator and the condenser, for which reliable correlations are very difficult to come by, and experimental results usually only record specific working conditions. Modeling the expansion machine; with all the complexities of a two-phase fluid, with a specific target of raising efficiency of the expander, which, in the authors’ opinion, is a bottleneck to raise the ORC system efficiency. In addition to two-phase flow conditions mentioned above, pressure drops, part-load conditions and geometric properties of
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the components should be considered in order to maximize reliability of the simulation model. As stated in the literature, e.g. in [18,33,118], the ORC layout can be optimized in order to maximize its efficiency, but often at the cost of higher upfront cost of components. As shown in literature and also in previous works conducted by the authors, a simple cycle configuration may be cost-effective for micro-CHP applications if off the shelf components from other applications such as the HVAC industry are used [116,119,120]. Such an assembly renders the system more affordable, but less than optimum. A simple configuration of the ORC consisting of a positive displacement pump, two PHEs, i.e. evaporator and condenser, a volumetric expander, a fluid receiver, is usually considered in practical applications and thus it is also assumed to be the reference configuration in this paper (see the simulation model in AMESimÒ environment sketched Fig. 5, where section numbering is in agreement with the thermodynamic states identified in Fig. 1a). The approach selected for modeling each component will be discussed below, as well as, a comparison between the proposed model and corresponding models available in literature.
4.1. Working fluid The working fluid selection represents a challenge when considering low-temperature waste thermal energy recovery. There are several general criteria that the working fluid of low-temperature ORC systems should ideally meet such as stability, non-fouling, non-corrosiveness, non-toxicity and non-flammability [120]. To develop the simulation model of an ORC system, it is essential to retrieve the thermodynamic and transport properties of the working fluid. Moreover, it is usually desirable to compare ORC performance with different fluids, to identify the optimal solution. Different fluid libraries are available and compatible with all the main simulation tools. REFPROPÒ database represents the most extended library and also allows enhancing the properties of user-defined mixtures. CoolPropÒ [121] is an open-source, cross-platform fluid library with most of the common fluids used. Both REFPROPÒ and CoolPropÒ can be integrated into Matlab/SimulinkÒ, EESÒ, ModelicaÒ and other software. Additionally, AMESimÒ and EESÒ provide built-in thermo-physical property data of several fluids. An overview of the most common fluids available in the libraries of the above-mentioned software is reported in Appendix A. Recently, Bao and Zhao [5] proposed an extensive review of the selection of working fluids for ORCs, including an analysis of the influence of working fluids category and their thermodynamic and physical properties on the ORCs performance. Pure and mixed working fluids have been considered. Supercritical ORCs are receiving growing interest and therefore the fluid properties have to be evaluated. The investigation of the thermal performance of working fluids at supercritical conditions can be carried out by using any of the fluid libraries previously mentioned. For instance, Schuster et al. [40] compared several working fluids by retrieving the properties from REFPROPÒ. Gao et al. [122] analyzed eighteen organic working fluids for a supercritical organic Rankine cycle. In this case, the thermodynamic properties were evaluated by means of REFPROPÒ. Among the zero ODP (Ozone Depletion Potential) and low GWP (Global Warming Potential) refrigerants, the 1,1,1,3,3-Pentafluoropropane (known as HFC-245fa) is preferred as the working fluid, because of the low and ultra-low temperature range of the heat source, as discussed by Malavolta et al. [119]. The critical temperature, critical pressure and pressure at 298 K (near atmospheric conditions) are also favorable. An ORC system with HFC-245fa as the working fluid is favored to produce electricity from low temperature waste thermal energy between 450 K and 300 K. The
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Fig. 5. Complete ORC cycle simulation model developed in AMESimÒ environment.
main characteristics of the R245fa working fluid are listed in Table 2. In order to describe the behavior of the working fluid, a simple ideal gas model may introduce unacceptable inaccuracies for the study of ORCs. Numerous Equations of State (EoS) have been proposed in the literature on an empirical, semi-empirical or theoretical basis, such as the group contribution method [123–128]. Recently, the real gas effects of R245fa have been analyzed by Luián et al. [129] by comparing two cubic equations: the Redlich–Kwong–Soave (RKS) and the Peng–Robinson (PR) EoS. Instead, in the present work, AMESimÒ includes the properties of R245fa based on the Helmholtz EoS [1,130,131]. A similar formulation is also implemented in REFPROPÒ and CoolPropÒ. The Helmholtz energy represents one of the fundamental properties from which all the other thermodynamic properties can be obtained. The Helmholtz energy is expressed as the sum of the ideal gas contribution, ao, and the residual Helmholtz energy that results from intermolecular forces, ar. Generally, the dimensionless Helmholtz energy is used in practical applications, as a function of a dimensionless density and temperature [131],
Table 2 Properties of R-245fa [120]. Tv @ patm (°C) Tcr (°C) ODP GWP AL (years) Toxicity Flammability
aðq; TÞ ¼ aðd; sÞ ¼ ao ðd; sÞ þ ar ðd; sÞ RT
ð1Þ
The calculation of thermodynamic properties requires an appropriate formulation of the Helmholtz energy for a specific working fluid or mixture. In particular for R245fa, Lemmon and Span [131] provided the empirical coefficient for both ideal and residual Helmholtz energy contribution. The ideal gas and residual Helmholtz energy equations are given as follow,
ao ¼ a1 þ a2 s þ ln d þ ðco 1Þ ln s þ
4 X
v k ln½1 expðuk s=T cr Þ
k¼1
ð2Þ
ar ¼ n1 ds0:25 þ n2 ds1:25 þ n3 ds1:5 þ n4 d3 s0:25 þ n5 d7 s0:875 þ n6 ds2:375 þ n7 d2 s2 expd þ n8 d5 s2:125 expd 2
2
2
þ n9 ds3:5 expd þ n10 ds6:5 expd þ n11 d4 s4:75 expd þ n12 d2 s12:5 expd
3
ð3Þ
The coefficients of Eqs. (2) and (3) are listed in Tables B1 and B2 of the Appendix B. The detailed expressions for all thermodynamic properties can be found in [130,131]. 4.2. Working fluid pump
14.6 154 0 1020 7.6 Class B Class 1
A fixed displacement pump is commonly considered as the working fluid pump and both the mass flow rate and the enthalpy increase are usually computed as a function of swept volume, rotational speed, pressure ratio and isentropic efficiency. Quoilin et al. [75] defined the mass flow rate displaced by introducing the definition of capacity factor Xp,
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Xp ¼
_ m
ð4Þ
qV_ p;max
In order to describe the part load behavior of the volumetric pumps a correlation has to be introduced to link the isentropic efficiency with the flow rate at nominal conditions. Lecompte et al. [110] adopted the correlation proposed by Lipke [132] to calculate the isentropic efficiency and the pressure rise under part-load,
_ m
_ m
gp ¼ 2gp;nom _ gp;nom _ nom mnom m
Dp ¼ Dpnom
_ m _ nom m
2
ð5Þ
2 ð6Þ
Bamgbopa and Uzgoren [112] defined the pump efficiency as a function of the capacity factor and obtained the coefficients by interpolating the available pump data,
gp ¼ A0 þ A1 logðX p Þ þ A2 log ðX p Þ2 þ A3 log ðX p Þ3
ð7Þ
Instead, the pressure rise has been expressed as a function of the volumetric flow,
Dp ¼ C 1
_ m
qin
2
þ C2
_ m
qin
þ C3
ð8Þ
In AMESimÒ, the pump model can be characterized by providing the values of the displacement volume, the volumetric, isentropic and mechanical efficiency. Furthermore, it is possible to specify the efficiency parameters in different ways, such as (i) constant values, (ii) functional relationships (e.g. depending on pressure ratio and rotational speed) or (iii) experimental data, in order to simulate the part-load conditions. Consistent with the assumptions reported above, the volumetric and isentropic efficiency can be expressed as a function of the rotational speed and pressure ratio. However in the present study, constant values have been adopted.
_ theory ¼ qV dis N m _ m
gp;vol ¼ _ real ¼ fp;1 ðN; rÞ mtheory gp;s ¼
Dhs ¼ fp;2 ðN; rÞ Dhreal
ð9Þ ð10Þ
ð11Þ
4.3. Heat exchangers In the considered ORC system, the working fluid exchanges heat through two PHEs (an evaporator and a condenser). It is common practice to use PHEs to enhance heat exchange as well as to reduce the overall dimensions of the system. Different modeling approaches have been proposed in the literature with varying levels of complexity. Lakshamanan and Potter [133] proposed a numerical model, namely the ‘‘cinematic’’ model, to simulate the dynamic behavior of countercurrent systems such as fluidized beds. This model was applied to a plate heat exchanger, without taking into account the phase change within the heat exchanger. Zaleski and Klepacka [134] proposed an approximate solution for the heat transfer in plate heat exchangers, by using exponential approximations for the temperature in each stream. The approximate solution was also compared to the exact analytical solutions. The heat exchanger models are usually developed under the hypothesis of considering the phase change both during boiling and condensation and modeled as an equivalent counter-flow straight pipe. Vaja [82] adopted a 2D discretization model of the heat exchanger by considering the variation of state parameters both in axial and radial direction and by taking into account the
87
phase change. Quoilin et al. [75] and Wei et al. [81] described both PHEs (evaporator and condenser) as a straight pipe divided into three zones characterized by sub-cooled liquid, saturated mixture and superheated vapor. Then, for each zone, appropriate onedimensional governing equations were applied. The adopted heat transfer correlations takes into account boiling and condensing phenomena as well as the corrugation of the plate heat exchangers. Under boiling and condensation conditions, a vertical PHE with R410A has been considered as reference case and correlated to the experimental results by introducing two coefficients. Pressure drops were neglected due to the absence of differential pressure sensors. Lecompte et al. [110] adopted a similar discretization approach to a PHE and including different working fluids, i.e. R245fa, R1234yf and R152a, and internal pressure drops. The heat transfer correlations used are listed in Table 3. The AMESimÒ library allows describing a PHE from a physicsbased point of view, i.e. it is possible to graphically reproduce the channels inside the heat exchanger and depicted in Fig. 6. However, the lack of two-phase components to simulate heat transfer on both sides of a tube (highlighted in Fig. 6) make it necessary to reduce the PHE to an equivalent configuration. Therefore, a 2D discretization approach of an equivalent channel can be assumed to model the dynamic behavior of the heat exchanger, represented as a counter flow straight pipe divided into a series of longitudinal lumped volumes, as shown in Fig. 7. Such equivalent configuration consists of two counter-flow streams, i.e. one representing the hot source (hot water in this paper) and the other one simulating the cold stream on the refrigerant side. The sketch of the equivalent counter-flow heat exchanger in AMESimÒ is shown in Fig. 8. The heat exchange model takes into account both convective and conducting effects as well as internal pressure drops, attempting to simulate the real paths that the fluids follow while flowing through the heat exchanger. The model also considers the effective mass of the heat exchanger and its thermo-physical properties, as a function of temperature and pressure during the heat transfer process. The model used in the refrigerant side, highlighted in Fig. 8, allows two-phase conditions and phase-change. It is important to notice the difference in the connections available between the modules used in Figs. 6 and 7. Conduction is also allowed in longitudinal direction. This modeling approach can be applied to the condenser and the evaporator PHEs. The internal convective heat transfer in the component is evaluated by using correlations found in literature. Depending on the state of the fluid, different correlations are used during boiling or condensation and for single-phase flow (liquid or vapor). A survey of the correlations available in AMESimÒ is presented in Table 4. 4.4. Pressure drops Correlations to estimate pressure losses in components including the piping system are widely available in the literature [85–89]. The correlations are often derived as a function of the state of the fluid, accounting for the hydraulic resistances to the flow. The parameters include mass flow rate, surface roughness, geometrical dimensions, and the flow regime (laminar or turbulent). Modeling is commonly assumed to be isenthalpic and adiabatic. The correlations available in AMESimÒ are listed in Table 5. 4.5. Volumetric expander The expander represents the key component of an ORC system, since it has significant impact on the system overall efficiency. In the ORC-based micro-CHP systems for domestic applications, the lack of commercially available high efficiency expanders has hindered the development of small size ORCs. A survey of the expanders available in the market for micro-CHP applications is
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Table 3 PHEs heat transfer correlations. Quoilin et al. [75]
Lecompte et al. [110]
Type Working fluids
PHEs HCFC-123
PHE (evap.) Tube&fin (cond.) R245fa R1234yf R152a
Single-Phase heat transfer
Nu = C Rem Pr 1/3
Nu ¼ 0:299Re0:645 Pr 1=3 200 6 Re 6 15000
Boiling heat transfer Condensation heat transfer
m ¼ 0:5ðRe < 400Þ m ¼ 0:7ðRe > 400Þ hev = C hl Bo0.5
hev = 88hl Bo0.5 2:09 hcd ¼ hl 0:55 þ Pr 0:38
þ 75Bo0:75 Þ hcd ¼ 23:7 hl ð0:25Co0:45 Fr0:25 l
Table 4 Correlations used to model the heat exchange process. Single-phase correlation
Two-phase correlation
Boiling Gnielinski [85,86]
Chen [92] VDI vertical tubes [85,86] VDI horizontal tubes [85,86]
Condensation Gnielinski [85,86]
Shah [99] Cavallini and Zecchin [104] Traviss et al. [135]
Fig. 6. Graphic representation of a PHE in AMESimÒ.
Table 5 Correlations used for pressure drop estimation.
Fig. 7. PHE geometry and equivalent straight pipe model.
Fig. 8. Model of heat exchanger used as evaporator.
presented by Qiu et al. in [38]. In general, two types of expanders can be identified: the turbo-machinery type and displacement or volumetric type. The choice of the proper expander depends on the operating conditions, efficiency and cost. In general, a displacement type expander, a scroll-type in particular, is used more
Single-phase fluid
Two-phase fluid
Churchill [136]
McAdams et al. [137] Cicchitti et al. [138] Duckler et al. [139] Friedel [140] Müller-Steinhagen and Heck [141]
frequently, mainly because it is suitable for small-scale ORC systems, which are characterized by low flow rates. The scroll-expander is also suitable for high-pressure ratios, lower rotational speeds, and two-phase flows. The scroll machine has a limited number of moving parts. It is a reliable and proven technology in a compressor mode used in the refrigeration and air-conditioning industry. The performance of the scroll expanders has been investigated in several research works [142–145], where a maximum isentropic efficiency of about 70% was predicted, although this has been hard to achieve in practice. Several aspects, such as geometry, governing equations, leakages, heat dissipation and thermodynamics have to be taken into account to model the scroll expander. At the same time, the resulting model should be numerically robust and with a low computational complexity. A detailed mathematical model for the scroll compressor has been presented by Chen et al. in [146,147]. In particular, a geometric study was performed as well as a comprehensive scroll model was developed, including separated models for compression process, heat transfer between refrigerant and compressor parts and internal refrigerant leakage. Bell [148] improved the geometry-based approach to a scroll compressor by deriving the analytical solution of all the control volumes inside the machine as well as the leakage paths. The simulation model was developed in Phyton™. Quoilin [142] proposed and validated a semi-empirical model of a scroll-expander by decomposing the evolution of the working fluid through the expander into different steps, by taking into account pressure drops, the isentropic expansion followed by a fixed-volume expansion, mixing between suction flow and leakage
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flow and internal/external heat exchange process. The simulation model was optimized by using several sets of experimental data. A similar approach is adopted in the present simulation model. The main difference is represented by introducing a library-oriented environment, which is helpful to separate the different effects. Furthermore, the model developed in this paper is general and can be tailored to a specific experimental set-up by modifying the geometric characteristics and by introducing the proper performance maps. The main characteristics of the simulation model developed in this paper are: Inlet pressure drop characterized by a lumped cross sectional area and heat exchange losses with the wall of the expander. The pressure drop is evaluated by using correlations from the literature [136–141]. Internal pressure drop due to the small path between fixed and orbiting scroll. Thermal conduction with the internal wall of the scroll expander, as a function of pressure and temperature, as well as the material of the wall. Possibility of heat exchange with the environment, – the system is not considered to be fully isolated. Presence of a leakage flow to compute different internal leakages that may occur due to a gap between the upper and the lower part of the scrolls and the walls of the expander. A second gap is located between the flanks of the scrolls. After the expansion process, a mixing module is needed. Exhaust pressure drop estimation by defining the cross-sectional area of the downstream pipe system. Use of volumetric, isentropic and mechanical efficiencies to characterize the performance of the scroll expander. Adoption of the equation of mass balance to check whether each component works correctly. Both dynamic and steady-state operations are considered. The comprehensive model of the scroll expander is presented in Fig. 9, where it is possible to notice the different effects, such the heat transfer with a lumped mass and the ambient, an internal equivalent leakage, internal pressure drop, the mixing after the expansion and the discharge. The performances of the scroll expander are characterized by the volumetric efficiency and the isentropic efficiency, as reported in Eqs. (12) and (13).
gt;vol ¼ gt;s ¼
_ theor m ¼ ft;1 ðN; rÞ _ m
Dhreal ¼ ft;2 ðN; rÞ Dhs
ð12Þ
ð13Þ
As previously outlined for the volumetric pump, in AMESimÒ, the value of both efficiency parameters can be specified either as a constant or as a function of the rotational speed and the expansion ratio. Declaye et al. [149] proposed a non-dimensional performance curve based on Pacejka’s equation, by considering as parameters the rotational speed, expansion ratio and the filling factor. The general expression is defined as,
gt;s ¼ ymax ðn arctanðB ðrp rp;o Þ E ðB ðr p r p;o Þ arctanðB ðr p r p;o ÞÞÞÞÞ
ð14Þ
where all the parameters in the equation have a mathematical meaning and are derived from the linear regression of experimental data. Starting from the experimental data available from Quoilin [142], two correlations have been deduced and fitted to minimize the error between numerical and experimental data. The general form of the correlation is given by,
Fig. 9. Comprehensive model for scroll expander in AMESimÒ.
g ¼ c0 þ
n n m X X X ci N i þ cj rj þ ck N k r k i¼1
j¼1
ð15Þ
k¼1
It is important to notice that the efficiency (volumetric and isentropic) depends on the pressure ratio across the expander and the rotational speed. The geometric and performance parameters of the considered scroll expander are listed in Table 6. 4.6. Fluid receiver A fluid receiver is commonly placed after the condenser to avoid surging of the pump and to compensate the liquid level fluctuations in the evaporator, according to Quoilin et al. [84]. The pressure is considered homogeneous in the entire volume, as well as the densities of both gas and liquid phases in their respective volumes. In order to calculate the time derivatives of the pressure and the density, mass and energy balances are employed to model the receiver [81,82],
" # X dq 1 dV X _ _ ¼ q þ m m dt dt V out in
ð16Þ
Table 6 Geometric and measured data of the scroll expander [142]. Built-in volume ratio Volume swept Supply pipe diameter Internal port diameter Leakage area Supply pressure Supply temperature Exhaust pressure Mass flow rate Expander rotational speed Expander isentropic efficiency Pressure ratio
4.05 36.54 cm3 16 mm 5.91 mm 4.2 mm2 5.45–11.12 bar 101.7–165.2 °C 1.38–2.66 bar 45–86 g/s 1771 rpm; 2296 rpm; 2660 rpm 42–68% 2.7–5.4
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X X X dU _ þ _ in _ out ¼W Q_ þ ðmhÞ ðmhÞ dt
ð17Þ
The densities depend on the liquid volume percentage. By specifying the fluid receiver volume, Vfr, the initial percentage of liquid volume, xl, and initial temperature and pressure conditions, the level of fluid, /, is derived,
i d/ 1 hX _ cd;out ðmÞ _ p;in ¼ ðmÞ dt qV fr
ð18Þ
Both single and two-phase flow conditions are considered and consequently a stratification model is presented. By assuming a constant cross-sectional area of the chamber, the height of the vapor–liquid interface is obtained by multiplying the chamber height and the liquid percentage,
/ ¼ xl Hfr
ð19Þ
In order to determine the state of the fluid flowing out the chamber, the heights of the inlet and outlet ports are compared to the height of the vapor–liquid interface. If the height of a port is greater than the vapor–liquid interface height, the state of the fluid flowing out is vapor; otherwise it is liquid. 5. ORC system simulation model One of the challenges of novel modeling approaches is the validation of the results by means of numerical and/or experimental data. In fact, the modeling effort is not always adequately supported by the availability of experimental test rigs. Recently, ORC system test facilities are increasing, especially in the small scale power range [115,149–151], and consequently more data are available to validate numerical models. Below we present a model of an ORC system, which consists of two main components, i.e. the heat exchanger and the expander. Before assessing the overall performances of the system, a component-level analysis is proposed in order to investigate the accuracy of such sub-systems. This model is presented to offer a more lucid overview of the steps involved, to support the arguments and the open issues of the review discussion presented above.
Table 7 Boundary conditions for heat transfer coefficient evaluation. Tibiriçá and Ribatski [153]
Greco and Vanoli [158]
Working fluid Channel diameter (mm) Length (m) Tube
R245fa 2.32
R410a 6
0.464 Horizontal smooth tube
Boundary conditions
G = 300 kg/(m2 s) q = 15.0 kW/m2 Tsat = 31 °C
6 Horizontal smooth tube G = 363 kg/(m2 s) q = 15.0 kW/m2 pev = 4.83 bar
As previously highlighted, the heat transfer coefficient under phase-change represents a problem which has not a unique solution. In fact, the available correlations are obtained under specific conditions and for selected working fluids. Therefore, it is difficult to have equations of general validity. The ORC system considered in this work employs R245fa as the working medium. In literature, the experimental studies related to evaluate the heat transfer coefficient of such fluid are limited (for a flow boiling and condensing in micro-channels) or even absent (e.g. in the case of vertical or horizontal plate heat exchangers). For instance, Ong and Thome [152] investigated flow boiling conditions of three refrigerants, R134a, R236fa and R245fa in a 1.030 mm channel, under different boundary conditions of mass and heat fluxes. Tibiriçá and Ribatski [153] carried out flow boiling experiments in a micro-scale tube with internal diameter of 2.3 mm. R134a and R245fa were considered as the working fluids. As a test-case, the latter experimental set up has been simulated, by imposing heat flux and mass flux through a test-section represented by a horizontal stainless steel tube of 2.3 mm I.D. with a heating length of 464 mm. The boundary conditions are listed in Table 7. The simulation model is presented in Fig. 10. The aim of this numerical simulation is the evaluation of the internal convective heat transfer coefficient of R245fa under phase-change. The results are compared to the experimental and numerical data available in [153]. The Fig. 11 presents the evolution of the heat transfer coefficient with respect to vapor quality for the experimental data reported by Tibiriçá and Ribatski [153] and in other available studies. It is possible to notice that the numerical value of the heat transfer may differ by over 200% and the trends also present different behavior. However, the values predicted by the simulation model are on agreement with three out of the five documented experiences (above all, with the results in [153,155]). Therefore, the values of the heat transfer coefficient of R245fa present an acceptable agreement with the literature data, meaning the heat transfer module in AMESimÒ can be reliably coupled with other modules to simulate the entire ORC system. Different fluids may also be considered, thanks to AMESimÒ library. As discussed in Section 4.3, PHEs are usually adopted for heat transfer. Therefore, heat transfer conditions are substantially different with respect to a straight pipe. As also discussed above, there is a lack of experimental data regarding flow boiling or condensing of R245fa in PHE. In order to assess the heat transfer correlations implemented in AMESimÒ applied to a plate heat exchanger, a second case-study is considered by using another working fluid, i.e. R410a. The choice of this particular fluid is justified by the fact that Hsieh and Lin [89] investigated saturated flow boiling in a vertical PHE by using R410a and the correlations obtained were used by Quoilin et al. [75] and Lecompte et al. [110] with different fluids to model the heat transfer in PHEs. For this purpose, the experimental study carried out by Greco and Vanoli [158] has been simulated by using the same model presented in Fig. 10. The heat transfer characteristics of R410A were studied by using a smooth horizontal tube uniformly heated. The
Fig. 10. Representation in AMESimÒ environment of the test-section presented in [153].
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Fig. 11. Comparison of the heat transfer coefficient of R245fa predicted by the simulation model to the experimental and predicted data documented in [153– 157].
boundary conditions of the test set up are listed in Table 7. The values of heat transfer coefficients obtained from Greco and Vanoli [158] through several numerical correlations taken from the literature are reported in Fig. 12, together with the simulated results. It can be noticed that the values obtained through the simulation model are compatible with the available data, but the heat transfer coefficient depends on the type of correlation used. The average deviation, based on all the considered literature data, is approximately 16%. Experimental, theoretical and simulated heat transfer coefficients follow the same behavior, even though the simulation model tends to underestimate the heat transfer coefficient at very low vapor quality. The scroll expander model presented in Fig. 9 has been validated by considering the experimental data obtained by Quoilin [142]. The inputs of the model consist of the geometrical characteristics of the scroll expander and the measured data of mass flow rate, supply pressure and temperature, the exhaust pressure and the rotational speed summarized in Table 6. In Fig. 13, it is possible to notice that the agreement between measurements and predictions is very high, with a deviation always lower than 4% among efficiency values obtained in correspondence of the same pressure ratio. Furthermore, the trend is also comparable, i.e. the maximum isentropic efficiency (i.e. about 0.68) is reached for a pressure ratio of approximately 5.5, as stated by Quoilin in [142]. The validation of the expander model for the shaft power vs. pressure ratio is reported in Fig. 13 only at 2296 rpm due to the limited experimental data for the other rotational speeds. Also for this quantity, the global trend and the numerical values are in good agreement for the entire range of considered pressure ratios.
Fig. 13. Comparison between experimental data obtained in [142] and predicted values from the expander model.
Subsequently, the complete ORC system model was simulated and validated by using experimental results available in literature. The experimental data were reported by Quoilin [142] for a smallsize ORC system, with a net electric power output of approximately 1.7 kW. The system is composed of (i) two hot air sources, which are disposed in a mixed parallel/series configuration to maximize the heat recovery and supplying three PHEs (i.e. the evaporators), (ii) a scroll expander, (iii) two water-cooled PHEs (i.e. the condensers), (iv) a liquid receiver and (v) a feed pump. The working fluid, initially selected to be HCFC-123, was subsequently replaced with HFC-245fa. The variation ranges for the working conditions and the main parameters of the experimental set up are summarized in Table 8. It should be noted that the operating points with negative cycle efficiency are not considered for model validation, i.e. only pressure ratios higher than 3 are taken into account. The evaporating temperature, the evaporating and condensation pressures, the expander rotational speed and the expander isentropic efficiency were kept equal to the corresponding steady-state value measured in [142] and presented in Table 8. Expander isentropic efficiency was adopted from [142] for each operating point, and the simulations were run to evaluate the overall thermodynamic efficiency:
gth ¼
Pexp Pp PeV
ð12Þ
The direct comparison of the experimental data to the simulated values is shown in Fig. 14. The trend of the predicted ORC system thermodynamic efficiency vs. pressure ratio shows a good
Table 8 ORC system experimental data and performance [142].
Fig. 12. Comparison of the heat transfer coefficient of R410A in a PHE evaporator predicted by the simulation model to the literature data reported in [158–163].
ORC system data Working fluid Hot air source mean temperature Air mass flow rate Pressure ratio Scroll compressor swept volume Scroll built-in pressure ratio Mass flow rate Expander rotating speed Evaporating temperature Condensing temperature Liquid receiver volume
R245fa 110–134 °C 71–126 g/s 2.42–7.44 122 cm3 4 49–78 g/s 1855–3125 rpm 84.3–102.1 °C 26.5–56.5 °C 8 dm3
ORC measured performance Shaft power Net electric power Expander effectiveness Cycle efficiency
180.5–2164 W 224 to 1709 W 59.6–70.9% 1.4 to 7.3
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ORC thermodynamic efficiency
8.0%
Table A.1 (continued)
7.0%
6.0% Experimental data Simulation model
5.0% 3.0
4.0
5.0
6.0
7.0
8.0
Pressure ratio Fig. 14. Experimental [142] and predicted values of ORC system thermodynamic efficiency.
Table A.1 Most common fluids available in AMESimÒ [9], REFPROPÒ [102], CoolProp [112] and EESÒ [60]. Fluids
AMESimÒ
REFPROPÒ
CoolPropÒ
EESÒ
Air (mixture) Ar (Argon) H2 (parahydrogen) H2 (hydrogen) He (Helium) CO2 (carbon dioxide or R744) C2H4 (ethylene) C3H6 (Cyclopropane) C5H10 (Cyclopenthane) C6H12 (Cyclohexane) HFE143m HFE7500 Isobutene Isohexane Isopentane MD2M MD3M MD4M MDM MM Methane (CH4) Methanol Neopentane Nitrogen (N2) NH3 (ammonia) Oxygen R11 R113 R114 R116 R12 R123 R1233zd(E) R1234yf R1234ze(E) R1234ze(Z) R124 R125 R134a R13 R14 R141b R142b R143a R143m R152A R161 R21 R218
U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
Fluids
AMESimÒ
REFPROPÒ
CoolPropÒ
EESÒ
R22 R227ea R23 R236ea R236fa R245fa R245ca R32 R365MFC R290 (propane) R404a R407F R41 R410a R507a R600a (Isobutene) RC318 SES36 (SolkathermÒ) SO2 (Sulfurdioxide) SF6 (SulfurHexafluoride) Toluene m-Xylene n-Butane n-Decane n-Dodecane n-Heptane n-Hexane n-Nonane n-Octane n-Pentane n-Propane n-Undecane o-Xylene p-Xylene Water (H2O)
U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U U
U U U U U U U U U U U U U U U U U U U U U U U U U U U
agreement with the experimental data: the average deviation between measured and predicted values is 2.9%, while the maximum deviation is 8.6% in correspondence of the highest values of the pressure ratio. 6. Conclusions The Organic Rankine Cycle (ORC) system is considered to be a growing market that will be part of the answers to energy efficiency and environmental challenges. The number of technical approaches, sizing methodologies, and modeling tools is rapidly growing as evidenced by the large number of published papers over the last decade. A review of all aspects of such fast growing technology is therefore essential to reflect and compare the available options. The literature review highlighted that, although substantial progress has been made in recent years, most in the modeling approaches, and efficient systems can be expected in high temperature ranges, while low grade thermal energy recovery should be considered to be in its infancy. Great research opportunities still exist in working medium, architecture, design of efficient expanders, modeling and evaluating heat transfer and system losses, etc. The successful recovery of waste thermal energy remains to be one of the favored topics. The review also showed that there are ample technologies suitable for waste heat recovery and ORC systems. Some of these technologies are in the conceptual range, especially in the micro-scale range. However, this trend is expected to grow, as climate change and CO2 emissions put pressure on the energy market. To optimize the performance of ORCs, which are the most prevalent and the only market-ready technologies suitable for low-grade thermal energy recovery today, flexible and reliable
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D. Ziviani et al. / Applied Energy 121 (2014) 79–95 Table B.1 Coefficients of the ideal gas Helmholtz energy for R245fa [121]. a1
a2
c0
v1
u1/K
v2
u2/K
v3
u3/K
13.4283638514
9.8723653800
4.0
5.5728
222.0
10.385
1010.0
12.554
2450–0
Table B.2 Coefficients of the residual Helmholtz energy [121]. n1 n2 n3 n4 n5 n6 n7 n8 n9 n10 n11 n12
1.2904 3.2154 0.50693 0.093148 0.00027638 0.71458 0.87252 0.015077 0.40645 0.11701 0.13062 0.022952
simulation models are required. The paper also addressed a review of this topic including a survey of common modeling approaches available in literature, under both steady and transient conditions. Among the many available tools, AMESimÒ environment, a libraryorientated software not widely used for ORC simulation, showed good promise. It provided a wide fluid library and proved to be robust and powerful as it allowed detailed description of the ORC components. In general, given the uncertainties related to the estimation of heat transfer coefficients under boiling and condensing (i.e. two-phase) conditions and the varying operating conditions of the volumetric expander, there is room to improve modeling accuracies for a range of ORC components. The introduced model is consistent with the work of most of the authors referenced in here, and the deviation between the published data used for validation and the predictions of the simulation model can be considered acceptable. If a more accurate model is required, a more specific model tuning may be performed on the basis of the guidelines and recommendations provided in this paper. Appendix A. See Table A.1. Appendix B. See Tables B.1 and B.2. References [1] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210–21. [2] EIA, US energy information administration. International Energy Outlook 2011; 2011. [3] Maizza V, Maizza A. Unconventional working fluids in organic Rankine-cycles for waste energy recovery systems. Appl Therm Eng 2001;21:381–90. [4] De Paepe M, D’Herdt P, Mertens D. Micro-CHP systems for residential applications. Energy Convers Manage 2006;2006(47):3435–46. [5] Bao J, Zhao L. A review of working fluid and expander selections for organic Rankine cyle. Renew Sustain Energy Rev 2013;24:325–42. [6] Bianchi M, Pascale De. A. bottoming cycles for electric energy generation: Parametric investigation of available and innovative solutions for the exploitation of low and medium temperature heat sources. Appl Energy 2011;2011(88):1500–9. [7] Quoilin S, Van Den Broek M, Declaye S, Dewallef P, Lemort V. Technoeconomic survey of Organic Rankine Cycle (ORC) systems’’. Renew Sustain Energy Rev 2013;22:168–86. [8] Chan CW, Ling-Chin J, Roskilly AP. Reprint of ‘‘A review of chemical heat pumps, thermodynamic cycles and thermal energy storage technologies for low grade heat utilisation’’. Appl Therm Eng 2013;53:160–76.
[9] LMS Engineering Innovation – LMS Imagine. Lab AMESim
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D. Ziviani et al. / Applied Energy 121 (2014) 79–95
[38] Qiu G, Liu H, Riffat S. Expanders for micro-CHP systems with organic Rankine cycle. Appl Therm Eng 2011;31:3301–7. [39] Chen TH, Goswami DY, Stefanakos EK. A review of thermodynamic cycles and working fluids for the conversion low-grade heat. Renew Sustain Energy Rev 2010;2010(14):3059–67. [40] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical Organic Rankine Cycle. Energy 2010;35:1030–9. [41] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88:2740–54. [42] Fischer J. Comparison of trilateral cycles and organic Rankine cycles. Energy 2011;36:6208–19. [43] Öhman H, Lundqvist P. Theory and method for analysis of low temperature driven power cycles. Appl Therm Eng 2012;37:44–50. [44] Öhman H. Comparison and analysis of performance using low temperature power cycles. Appl Therm Eng 2013;52:160–9. [45] Zamfirescu C, Dincer I. Thermodynamic analysis of a novel ammonia-water trilateral Rankine cycle. Thermochim Acta 2008;477:7–15. [46] Lecompte S, van den Broek M, De Paepe M. Thermodynamic analysis of the partially evaporating trilateral cycle. In: Proceedings of the 2nd international seminar on ORC power systems. Rotterdam, Netherlands; 2013. [47] Ho T, Mao SS, Grief R. Comparison of the Organic Flash Cycle (OFC) to other advanced vapor cycles for intermediate and high temperature waste heat reclamation and solar thermal energy. Energy 2012;42:213–23. [48] Ho T, Mao SS, Greif R. Increased power production through enhancements to the Organic Flash Cycle (OFC). Energy 2012;45:686–95. [49] Zhang X, He M, Zhang Y. A review of research on the Kalina cycle. Renew Sustain Energy Rev 2012;16:5309–18. [50] Guzovic´ Zvonimir, Majcen Boris, Cvetkovic´ Svetislav. Possibilities of electricity generation in the Republic of Croatia from medium-temperature geothermal sources. Appl Energy 2012;98:404–14. [51] Rodriguez CEC, Palacio JCE, Venturini OJ, lora EES, Cobas VM, dos Santos DM, et al. Exergetic and economic comparison of ORC and Kalina cycle for low temperature enhanced geothermal system in Brazil. Appl Therm Eng 2013;52:109–19. [52] Bombarda P, Invernizzi CM, Pietra C. Heat recovery from diesel engines: a thermodynamic comparison between Kalina and ORC cycles. Appl Therm Eng 2010;30:212–9. [53] Wang J, Yan Z, Zhou E, Dai Y. Parametric analysis and optimization of Kalina cycle driven by solar energy. Appl Therm Eng 2013;50:408–15. [54] Singh OK, Kaushik SC. Energy and exergy analysis and optimization of Kalina cycle coupled with a coal fired steam power plant. Appl Therm Eng 2013;51:787–800. [55] Victor RA, Kim JK, Smith R. Composition optimization of working fluids for Organic Rankine Cycles and Kalina cycles. Energy 2013;55:114–26. [56] He J, Liu C, Xu X, li Y, Wu S, Xu J. Performance research on modified KCS (Kalina cycle system) 11 without throttle valve. Energy 2013.
[75] Quoilin S, Lemort V, Lebrun J. Experimental study and modeling of an Organic Rankine Cycle using scroll expander. Appl Energy 2010;87: 1260–8. [76] Quoilin S, Declaye S, Lemort V. Expansion machine and fluid selection for the organic Rankine cycle. In: Proc. 7th international conference on heat transfer, fluid mechanics and thermodynamics. Antalya, Turkey; 2010. [77] Lemort V, Quoilin S, Lebrun J. Numerical simulation of a scroll expander for use in a Rankine Cycle. In: Proc 19th int compressor engineering conference at Purdue University, USA. Paper # 1324; 2008. [78] Lemort V, Quoilin S, Cuevas C, Lebrun J. Testing and modeling a scroll expander integrated into an Organic Rankine Cycle. Appl Therm Eng 2009;29:3094–102. [79] Winandy E, Saavedra C, Lebrun J. Experimental analysis and simplified modelling of a hermetic scroll refrigeration compressor. Appl Therm Eng 2002;22:107–20. [80] Kane M, Larrain D, Favrat D, Allani Y. Small hybrid solar power systems. Energy 2003;28:1427–43. [81] Wei D, Lu X, Lu Z, Gu J. Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery. Appl Therm Eng 2008;28:1216–24. [82] Vaja I. Definition of an object oriented library for the dynamic simulation of advanced energy systems: methodologies, tools and application to combined ICE-ORC power plant, PhD Thesis in Industrial Engineering, University of Parma, Italy; January 2009. [83] García-Vallardes O, Pérez-Segarra CD, Rigola J. Numerical simulation of double-pipe condensers and evaporators. Int J Refrig 2004;27:656–70. [84] Quoilin S, Aumann R, Grill A, Shuster A, Lemort V, Spliethoff H. Dynamic modeling and optimal control strategy of waste heat recovery Organic Rankine Cycles. Appl Energy 2011;88:2183–90. [85] Thome JR. Engineering data book III. Wolverine Tube, Inc.; 2010. [86] VDI Heat Atlas Second Edition. VDI-Gesellschaft Verfahenstechnik und Chemieingenieurwesen. Springer; 2010. [87] Yan YY, Lin TF. Evaporation heat transfer and pressure drop of refrigerant R134a in a plate heat exchanger. J Heat Transfer 1999;121:118–27. [88] Yan YY, Lio HC, Lin TF. Condensation heat transfer and pressure drop of refrigerant R-134a in a plate heat exchanger. Int J Heat Mass Transfer 1999;42:993–1006. [89] Hsieh YY, Lin TF. Saturated flow boiling heat transfer and pressure drop of refrigerant R-410A in a vertical plate heat exchanger. Int J Heat Mass Transfer 2002;45:1033–44. [90] Kedzierski MA. A comparison of R245fa pool boiling measurement to R123 and R245fa/Isopenane on a passively enhanced, horizontal surface. Int J Trans Phenom 2006;8:331–44. [91] Shah MM. Evaluation of general correlations for heat transfer during boiling of saturated liquids in tubes and annuli. In: 2005 ASME summer heat transfer conference. San Francisco, California, USA; 2005. [92] Chen JC. A correlation for boiling heat transfer to saturated fluids in convective flow. Ind Eng Chem Process Des Dev 1966;5:322–9. [93] Shah MM. Chart correlation for saturated boiling heat transfer: equations and further study. ASHRAE Trans Part 1 1982;88:185–96. [94] Steiner D, Taborek J. Flow boiling heat transfer in vertical tubes correlated by an asymptotic model. Heat Transfer Eng 1992;13:43–68. [95] Kandlikar SG. A general correlation for saturated two-phase flow boiling heat transfer inside horizontal and vertical tubes. ASME J Heat Transfer 1990;112:219–28. [96] Liu Z, Winterton RHS. A general correlation for saturated and subcooled flow boiling in tubes and annuli based on a nucleate pool boiling equation. Int J Heat Mass Transf 1991;34:2759–66. [97] El Hajal J, Thome JR, Cavallini A. Condensation in horizontal tubes. Part 1: two-phase flow pattern map. Int J Heat Mass Transfer 2003;2003(46): 3349–63. [98] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes. Part 3: development of a new heat transfer model based on flow patterns. J Heat Transfer 1998;120:156–65. [99] Shah MM. A general correlation for heat transfer during film condensation inside pipes. Int J Heat Mass Transfer 1979;22:547–56. [100] Meyer JJ, Dunn WE. Investigation of the condensing and expansion behaviors of alternative refrigerants. In: ACRC Contract Report 6, University of Illinois; 1996. [101] Nozu S, Honda H. Condensation of refrigerants in horizontal, spirally grooved micro-fin tubes: numerical analysis of heat transfer in the annular flow regime. J Heat Transfer 2000;122:80–91. [102] Chamra LM, Meng-Onn T, Chea-Chun K. Evaluation of existing condensation heat transfer models in horizontal micro-fin tubes. Exp Thermal Fluid Sci 2004;28:617–28. [103] Chambra LM, Tan MO, Kung CC. Evaluation of existing condensation heat transfer models in horizontal micro-fin tubes. Exp Thermal Fluid Sci 2004;28:617–28. [104] Cavallini A, Zecchin RA. Dimensionless correlation for heat transfer in forced convection condensation. In: Proc 6th int heat transfer conference, vol. 3. 1974. p. 309–13. [105] Smith MK, Wattelet J, Newell TA. A study of evaporation heat Transfer coefficient correlations at low heat and mass fluxes for pure refrigerants and refrigerant mixtures. In: Air conditioning and refrigeration center. University of Illinois; 1993 January.
D. Ziviani et al. / Applied Energy 121 (2014) 79–95 [106] Ho-Saeng L, Jung-In Y, Jae-Dol K, Bansal PK. Characteristics of condensing and evaporating heat transfer using hydrocarbon refrigerants. Appl Therm Eng 2006;26:1054–62. [107] Dalkilic AS, Wongwises S. Intensive literature review of condensation inside smooth and enhanced tubes. Int J Heat Mass Transfer 2009;52:3409–26. [108] Rohsenow WM, Hartnett JP, Cho YI. Handbook of heat transfer. 3rd ed. New York: McGraw-Hill; 1998. [109] Menente G, Toffolo A, Lazzaretto A, Paci M. An Organic Rankine Cycle offdesign model for the search of the optimal control strategy. Energy 2013;58:97–106. [110] Lecompte S, Huisseune H, van den Broek M, De Schampheleire S, De Paepe M. Part load based thermo-economic optimization of the Organic Rankine Cycle (ORC) applied to a combined heat and power (CHP) system. Appl Energy 2013;111:871–81. [111] Lemmon EW, Huber ML, McLinden MO. National institute of standards and technology. Standard reference database 23. Reference fluid thermodynamic and transport properties – Refprop 9.1, US; 2013. [112] Bamgopa MO, Uzgoren E. Quasi-dynamic model for an organic Rankine cycle. Energy Convers Manage 2013;72:117–24. [113] Vankeirsbilck I, Vanslambrouck B, Gusev S, De Paepe M. Efficiency comparison between the steam cycle and the organic Rankine cycle for small scale power generation. In: 2nd European conference on polygeneration. Tarragona, Spain; 2011. [114] Colonna P, van der Stelt TP. FluidProp: a program for the estimation of thermo physical properties of fluids. In: Energy technology section. Delft University of Technology, The Netherlands; 2004
95
[136] Churchill SW. Friction-factor equation spans all fluid flow regimes. Chem Eng 1977;84:91–2. [137] McAdams WH, Wood WK, Bryan RL. Vaporization inside horizontal tubes – II – Benzene-oil mixtures. Trans ASME 1942;64:193–200. [138] Cicchitti A, Lombardi C, Silvestri C, Soldaini G, Zavatarelli R. Two-phase cooling experiments: pressure drop, heat transfer and burnout measurements. Energia Nucleare 1960;7:407–25. [139] Duckler AE, Wicks M, Cleveland RG. Pressure drop and holdup in two phase flow Part A: a comparison of existing correlations Part B: an approach through similarity analysis. AIChE J 1964;10:38–51. [140] Friedel L. Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow. European Two-Phase Group Meeting, Ispra, Italy, Paper E2; 1979. [141] Müller-Steinhagen H, Heck K. A simple friction pressure drop correlation in two-phase flow in pipes. Chem Eng Process 1986;20:297–308. [142] Quoilin S. Sustainable energy conversion through the use of Organic Rankine cycles for waste heat recovery and solar applications, PhD Thesis in Applied Sciences. University of Liège (Belgium); October 2011. [143] Zanelli R, Favrat D. Experimental investigation of a hermetic scroll expander generator. Proc Int Compressor Eng Conf Purdue 1994:459–64. [144] Yanagisawa T, Fukuta M, Ogi Y, Hikichi T. Performance of an oil-free scroll type air expander. In: Proc IMechE Conf on Compressors and their systems; 2001. p. 167–74. [145] Mathias JA, Johnston JR, Cao J, Priedeman DK, Christensen RN. Experimental testing of gerotor and scroll expanders used in, and energetic and exergetic modeling of an Organic Rankine Cycle. Energy Resour Technol 2009;131(1):012201. [146] Chen Y, Halm NP, Groll EA, Braun JE. Mathematical modeling of scroll compressors—part I: compression process modeling. Int J Refrigeration 2002;25:731–50. [147] Chen Y, Halm NP, Braun JE, Groll EA. Mathematical modeling of scroll compressors — part II: overall scroll compressor modeling. Int J Refrigeration 2002;25:751–64. [148] Bell IH. Theoretical and experimental analysis of liquid flooded compression in scroll compressors, PhD Dissertation. University of Purdue; 2011. [149] Declaye S, Quoilin S, Guillaume L, Lemort V. Experimental study on an opendrive scroll expander integrated into an ORC (Organic Rankine Cycle) system with R245fa as working fluid. Energy 2013;55:173–83. [150] Zheng N, Zhao L, Wang XD, Tan YT. Experimental verification of a rollingpiston expander that applied for low-temperature Organic Rankine Cycle. Appl Energy 2013;112:1265–74. [151] Li M, Wang J, He W, Gao L, Wang B, Ma S. Construction and preliminary test of a low-temperature regenerative Organic Rankine Cycle (ORC) using R123. Renewable Energy 2013;57:216–22. [152] Ong CL, Thome JR. Flow boiling heat transfer of R134a, R236fa and R245fa in a horizontal 1.030 mm circular channel. Exp Thermal Fluid Sci 2009;2009(33):651–63. [153] Tibiriçá CB, Ribatski G. Flow boiling heat transfer of R134a and R245fa in a 2.3 mm tube. Int J Heat Mass Transfer 2010;53:2459–68. [154] Saitoh S, Daiguji H, Hihara H. Correlation for boiling heat transfer of R-134a in horizontal tubes including effect of tube diameter. Int JHeat Mass Transfer 2007;50:5215–25. [155] Thome JR, Dupont V, Jacobi AM. Heat transfer model for evaporation in microchannels. Part I: presentation of the model. Int J Heat Mass Transfer 2004;47:3375–85. [156] Liu Z, Winterton RHS. A general correlation for saturated fluids in convective flow boiling in tubes and annuli based on a nucleate pool. Int J Heat Mass Transfer 1991;34:2759–66. [157] Kandlikar SG, Balasubramanian P. An extention of the flow boiling correlation to transition, laminar, and deep laminar flows in minichannels and microchannels. Heat Transfer Eng 2004;25:86–93. [158] Greco A, Vanoli GP. Flow boiling heat transfer with HFC mixtures in a smooth horizontal tube. Part II: assessment of predictive methods. Exp Thermal Fluid Sci 2005;2005(29):199–208. [159] Yu M, Lin T, Tseng C. Heat transfer and fluid flow pattern during two-phase flow boiling of R-134a in horizontal smooth and microfin tubes. Int J Refrigeration 2002;25:789–98. [160] Yoshida S, Mari H, Hong H, Matsunaga T. Prediction of binary mixture boiling heat transfer coefficient using only phase equilibrium data. Trans JAR 1994;11:67–78. [161] Shah M. A new correlation for heat-transfer during boiling flow through pipes. ASHRAE Trans 1976;82:66–86. [162] Kattan N, Thome JR, Favrat D. Flow boiling in horizontal tubes: part 3 – development of a new heat transfer model based on flow patter. Trans ASHRAE 1998;1998(120). [163] Zürcher O, Favrat D, Thome JR. Evaporation of refrigerants in a horizontal tube: an improved flow pattern dependent heat transfer model compared to ammonia data. Int J Heat Mass Transfer 2002;45:303–17.