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Batch Processes in Heat Engines
Accepted Manuscript Batch Processes in Heat Engines
Michael Löffler PII:
S0360-5442(17)30286-4
DOI:
10.1016/j.energy.2017.02.105
Reference:
EGY 10398
To appear in:
Energy
Received Date:
30 November 2016
Revised Date:
17 February 2017
Accepted Date:
18 February 2017
Please cite this article as: Michael Löffler, Batch Processes in Heat Engines, Energy (2017), doi: 10.1016/j.energy.2017.02.105
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ACCEPTED MANUSCRIPT
Highlights Michael Löffler: Batch Processes in Heat Engines
Batch processes in heat engines lead to a drastically increased electrical output. The setup contains preheater, superheater, desuperheater. The examination is carried out using T-s- diagrams and discretisation. Thermal input, and electrical output are calculated and aggregated. Energy efficiency and exergy efficiency is calculated, compared, and discussed.
ACCEPTED MANUSCRIPT
Energy, submitted article: Batch Processes in Heat Engines Batch Processes in Heat Engines Michael Löffler1 Engineering Office Dr. Löffler, Ludowiciring 13 c, 76751 Jockgrim, Germany Heat engines transfer high-temperature heat into mechanical and electrical energy using the Clausius Rankine Cycle (CRC). Low temperature applications primarily use the Organic Rankine Cycle, in which mainly waste heat, geothermal heat and solar heat are transferred into mechanical energy. The exergy of a low temperature heat source can be transferred into electricity in so-called triangle (or trilateral) cycles. By applying batch processes in heat engines, it is possible to reach an exceptionally high approximation to triangle cycles and thus to build up high exergy-efficient heat engines. In an example case the calculated exergy efficiency is 71 % higher compared to a CRC. The proposed process is not limited to specific working media and can therefore be adapted to a wide range of temperatures. The required setup is rather simple and is derived from setups ranging from basic to more and more advanced. The thermodynamic performance of an example plant is derived from T-sdiagrams.
1. State of the Art 1.1. Clausius Rankine Cycle and Organic Rankine Cycle The Clausius Rankine Cycle (CRC) is globally applied in most large power plants. In a basic setup, it consists of an expander which is fed by superheated steam coming from a set of three heat exchangers: the preheater, the evaporator and the superheater. The expanded steam is fully condensed in a fourth heat exchanger and then pumped to the preheater. Fig. 1 shows the basic setup of the CRC. Fig. 1: Basic setup for Clausius Rankine Cycle or Organic Rankine Cycle
In the Organic Rankine Cycle (ORC), the basic setup is the same as for the CRC, but the condensable working medium is different to water. Many working media have been examined [1, 2, 3, 4, 5, 6]. In the thermodynamic analysis of cycles, the T-s-diagram plays a main role. This diagram shows the transferred heat but also the mechanical power which is proportional to the area spread up by the cycle line. Additionally, the dissipated power can be estimated by the area between the heat source curve and the curves of the heated or evaporated working medium. One objective of heat engines is to transfer as much heat into mechanical energy as possible. For this purpose, the thermodynamic cycle should cover as much area as possible. The cycle area is restricted to the space between the curve of the heat sink and the heat source. In most cases, the heat sink is an almost horizontal line and the heat source can be approximated by a sloped line. The maximum area which can be covered therefore has the shape of a triangle in the T-s-diagram. In literature, this type of cycle is called a trilateral cycle or triangle cycle. The performance of trilateral cycles has been compared with CRC and ORC by using simulation tools [7, 8, 9]. There are different ways in which triangle cycles can be reached. 1.2. Approaches for achieving triangle cycles The most common way of increasing the power output of a power plant is to construct facilities with two or more pressure levels. This requires separate expanders for each pressure level, e.g. three turbines (or turbine parts) for high, medium and low pressure and a complex structure of heat exchangers [10, 11].
1
Corresponding author. Tel: +49 7272 950184, E-mail address: [email protected]
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ACCEPTED MANUSCRIPT Transcritical cycles expand the working medium from a supercritical state to a subcritical state [12, 13, 14, 15, 16, 17, 18]. The sloped line of a high pressure working medium can adapt to the heat source curve in the T-s-diagram. In some plants, a working medium mixture is used in order to gain area in the T-s-diagram, e.g. the Kalina cycle [19, 20, 21]. Here too, a sloped line in the T-s-diagram leads to an improvement of exergy efficiency. Flash processes were also examined in order to achieve trilateral cycles [22, 23, 24, 25, 26, 27]. In this case, the liquid working medium is heated up by the heat source medium. This heat transfer can be carried out with very low dissipation in a counter flow heat exchanger.
2. Setup for applying batch processes in heat engines Batch processes have already been proposed, built up and simulated for refrigeration cycles [28, 29]. The concept closely replicates the Lorenz cycle, which is the ideal cycle for heat pumps and refrigeration plants. Enhanced setups for heat recovery using pinch analysis become possible [30, 31]. Below, the concept of batch processes is adapted to the case of heat engines. 2.1 Basic setup Fig. 2 shows the basic setup of a heat engine with batch process. The batch process requires a liquid as a heat transfer medium (e.g. water or thermal oil). Of course the liquid heat transfer medium can transfer heat originating from a hot gas, e.g. from flue gas. The heat transfer medium is pumped to the container C1 (valve V1 open, valve V3 closed). During this period, the container is charged. In a second step, the heat transfer medium is pumped from the container C1 to the evaporator at a high mass flow (V1 is closed and V3 is opened). During this period, the container is discharged. The high mass flow results in a minor temperature difference on the water side of the evaporator and, as a result, to a low level thermal dissipation in the evaporator. Since the medium in the container is losing heat, its average temperature falls, together with the evaporation pressure in the evaporator. The function and control of the depicted pumps in all figures are self-explanatory. Fig. 2: Basic setup for batch process with container C1
The drawback of this setup is that the steam entering the expander is not particularly superheated and may cool the expander down which can result in harmful condensation inside the expander. 2.2. Setup for feasible operating conditions Fig. 3 shows an enhanced setup, with a preheater and superheater. The working medium is preheated to the evaporation temperature, then evaporated, and then superheated to a high end temperature. A second superheater with a higher temperature could be installed in order to reach higher end temperatures. Superheating ensures that there is no condensation of the working medium inside the expander.
Fig. 3: Setup for batch process with container, preheater, and superheater
One noticeable and main feature of the batch cycle is that all heat exchangers can be designed to work with a small mean temperature difference between the heat transfer medium and the working medium which means low levels of dissipation and a high degree of cycle efficiency. The disadvantage of the setup in Fig. 3 is that the expander works in stop and go mode due to the intermittent charging and discharging of the container C1. 2.3. Setup for continuous process and feasible operating conditions To overcome the stop and go mode of the expander, a second container C2 is introduced to the setup. In Fig. 4, C1 is charged and C2 is discharged in an initial period before C1 is 2
ACCEPTED MANUSCRIPT discharged and C2 is charged in the following period, and so on. In this way, a continuous power output of the expander is maintained and additionally a continuous thermal power transfer from the heat source to the heat engine. The check valves CV1 and CV2 are required in order to ensure that the mass flow of the heat transfer medium is both stable and defined. Fig. 4: Setup for batch process with two containers for continuous process
In many cases, the expanded gas leaving the expander contains usable sensible heat which can be recovered by a desuperheater. In the case of batch processes, a special setup for heat recovery is needed. 2.4. Setup for the use of a desuperheater in batch processes Fig. 5 shows the desuperheater and the additional containers C3 and C4 which are used to store and return recovered heat from the expanded working medium. Valves V5 to V8, and the check valves CV3 and CV4, conduct and maintain the mass flow of the heat transfer medium. The recovered heat is transferred to the preheater. In this way, the difference between the capacity flow of the working medium in the preheater (liquid, cp = 4.18 Ws/gK) and the superheater (vapour, cp = 2.05 Ws/gK) will be reduced. This method helps to reduce dissipation resulting from the difference in the specific heat of the liquid and gaseous working medium. Consequently, the efficiency of the heat transfer and the heat engine will be increased. The influence of bell-shaped or overhanging working media [24] on the need for desuperheating will be addressed in subsequent studies. Fig. 5: Setup for batch process with desuperheater Table 2 shows the valve positions for the two main states in the finite state automation. Table 1: Data used for electricity consumption of the pumps
At the end of the discharging cycle of either container, the water temperature and the evaporator temperature are at their minimum. When connected to the charged container, hot heat transfer medium is pumped and cooled down in the cold evaporator. The cold water is then pumped back into the container and mixes with the hot container water. This mixing process leads to additional dissipation and can be reduced by purging and heating the evaporator with medium directly from the heat source. 2.5. Setup for purging and heating the evaporator and purging and cooling the desuperheater Fig. 6 allows hot medium from the heat source to heat up the cold evaporator. This prevents the cold medium from mixing with hot medium in the container connected next to the evaporator. In the same way, valve V10 is used to cool the desuperheater down before it is connected to the discharged container. In this case, the hot medium is prevented from entering and mixing with the cold medium in C3 or C4. Fig. 6: Setup for batch process with additional valves V9 and V10 for heat recovery
In the thermodynamic analysis, the effect of the heat recovery in the desuperheater is balanced. The effects of purging the evaporator and the desuperheater are not balanced.
3. Thermodynamic Analysis The thermodynamic analysis shows the main effects occurring in the batch process applied to heat engines. The chosen working medium (water,) the chosen temperature levels, and the chosen expanders are not optimized for the given process conditions. For example, the size of the expander would be halved if the condensation temperature was changed from 50 °C to 65 °C. The thermodynamic analysis is conducted using the example of a heat engine with the following conditions, which apply to both the CRC and the batch cycle: 3
ACCEPTED MANUSCRIPT Heat source, Thot: 204 °C Heat sink, Tcold: 46 °C Condensation temperature: Tcond = 50 °C Mass flow in the turbine: 1 kg / s Pinch temperature of heat exchangers: ΔTpinch = 2 K Temperature difference on the water side of evaporator and condenser: ΔTevap = 2 K Constant isentropic efficiency of the expander: ηis = 66.6 % For the thermodynamic analysis, the batch process is discretised into 15 steps with evaporation temperature of 195 °C down to 55 °C in 10 K steps. The electrical power for the liquid pumps is integrated in the efficiency calculation. The pump efficiency is presumed to be 80 %. The pressure drop in heat exchangers at the water side is 0.25 bar. Table 2 shows the data of the pumps 1 to 6 used in the calculations. Table 2: Data used for electricity consumption of the pumps
The following simplifications do not influence the results to a large extent and are discounted:
the pressurisation of the cold liquid phase (not shown in the T-s diagrams). the influence of mixing and heat conduction in the liquid in the storage tanks is not taken into consideration. the influence of regenerative losses due to the tank mass and pipe mass is not taken into consideration. The following losses are presumed: electrical engine: 5 % (electrical efficiency: 95 %) mechanical friction: 20 kW (4% of the power output) Because of the high maximum expansion ratio pi of 113, the expander is preferably a set of two screw engines with variable expansion ratio or piston engines. The two screw engines would be a 7 l (expanded volume per revolution) screw engine for the high pressure expansion, and a 60 l screw engine for the low pressure expansion. Both screw engines run at a maximum 300 Hz (18,000 rpm). 3.1. Analysis in T-s-diagrams T-s-diagrams are used to calculate the ideal mechanical output power of the cycle 𝑃𝐶𝑅𝐶,𝑖𝑑 as the area within the cycle lines. They are also used, to calculate the heat input 𝑄𝑖𝑛 or recovered and transferred heat 𝑄𝑡𝑟𝑎𝑛𝑠 and the dissipated heat 𝑄𝑑𝑖𝑠𝑠 as the integral between the heat source line and T = - 273 °C. The ideal mechanical output power is used in turn to calculate the electrical output power of each CRC: 𝑃𝑒𝑙 = (𝑃𝐶𝑅𝐶,𝑖𝑑 ∙ 𝜂𝑖𝑠 - 𝑃𝑓𝑟𝑖𝑐) ∙ 𝜂𝑒𝑙 - 𝑃𝑝𝑢𝑚𝑝𝑠 The thermal efficiency is defined by the following equation: 𝜂 = 𝑃𝑒𝑙 𝑄 𝑡h
𝑖𝑛
𝑄𝑖𝑛 is the sum of heat for preheating, evaporation, and superheating minus the recovered and transferred heat: 𝑄𝑖𝑛 = 𝑄𝑝𝑟𝑒 + 𝑄𝑒𝑣𝑎𝑝 + 𝑄𝑠𝑢𝑝𝑒𝑟 - 𝑄𝑡𝑟𝑎𝑛𝑠 The exergy efficiency is defined by the relation of the electrical power output and the Exergy of the heat source in relation to the sink temperature T0. 𝜂 = 𝑃𝑒𝑙 𝐸 𝒆𝒙
𝑠𝑜𝑢𝑟𝑐𝑒
The Exergy is defined by the following equation: 𝐸𝑠𝑜𝑢𝑟𝑐𝑒 = 𝑚𝑠𝑜𝑢𝑟𝑐𝑒 ∙ [(hsource ‒ h0) ‒ T0 ∙ (ssource ‒ s0)] 3.1.1. CLAUSIUS RANKINE CYCLE The evaporation temperature of the CRC is set to 125°C which is near the set point for maximum power output for the given temperature levels. The condensation temperature is 50°C. The expansion factor pi is 18.8. Fig. 7 shows the CRC in the T-s-diagram. The wellknown sub-processes 1 to 6 are depicted as black arrows. The red arrow shows the heat 4
ACCEPTED MANUSCRIPT source curve. All calculations are based on data from the "International Association for Properties of Water and Steam Industrial Formulation 1997" (IAPWS IF-97) [32, 33]. Fig. 7: T-s-diagram for CRC
In the given example, the mass flow of the heat source is defined by: 𝑸𝒆𝒗𝒂𝒑 + 𝑸𝒔𝒖𝒑𝒆𝒓 𝑚𝑠𝑜𝑢𝑟𝑐𝑒 = 𝑐𝑝 ∙ [𝑇h𝑜𝑡 - (𝑇𝑒𝑣𝑎𝑝 + ∆𝑇𝑝𝑖𝑛𝑐h)] This mass flow defines the end temperature of the heat source: 𝑸𝒑𝒓𝒆 + 𝑸𝒆𝒗𝒂𝒑 + 𝑸𝒔𝒖𝒑𝒆𝒓 𝑇𝑒𝑛𝑑 = 𝑇h𝑜𝑡 𝑐𝑝 ∙ 𝑚𝑠𝑜𝑢𝑟𝑐𝑒 The thermal efficiency of the Clausius Rankine Cycle is 10.3 %. Since the heat source is only cooled down to 𝑇𝑒𝑛𝑑 = 117 °C, the exergy efficiency is only 31.1 %. In some cases, the expanded steam contains sensible heat which can be recovered by a desuperheater and transferred back into the process. Fig. 8 shows a CRC with an evaporation temperature of 85 °C and the heat recovered in the desuperheater (blue arrow). Fig. 8: T-s-diagram for CRC with a desuperheater
In the CRC, the recovered heat is used directly and continuously in the cycle. In the heat engine with batch process shown in Fig. 6, the recovered heat is first stored in either container C3 or C4 before then being transferred back to the cycle. Consequently, the following analysis of the cycle with batch process is much more complex compared to CRC. 3.1.2. CYCLE WITH BATCH PROCESS The batch cycle was divided into 15 consecutively occurring CRCs, each taken at condensation temperature levels of 195 °C down to 55 °C in steps of 10 K. In each period of discretisation, mean values of thermodynamic states represent the process conditions. The discretisation number of 15 is high enough to ensure that the results are sufficiently accurate, while also allowing a visual overview of all occurring phenomena. Fig. 9 only shows some of the snapshots: the first three cycles at evaporation temperatures of 195 °C, 185 °C, and 175 °C, the CRC standard cycle at 125 °C, one desuperheater cycle at 85 °C, and the lowest cycle at evaporation temperature of 55 °C. The heat source (red arrows, only for the evaporation temperature of 195 °C) and the heat sink (blue arrow, only for the evaporation temperature of 85 °C) are also depicted. The small dissipation area between the working media curve and the related heat transfer medium curves, compared to the CRC case depicted in Fig. 7, is noticeable. Fig. 9: T-s-diagram for selected snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
Fig. 10 shows all the 15 “snapshots” of the batch process as well as exemplary cooling curves of the heat transfer medium in the preheater, the evaporator, and the superheater (red lines with arrows) for an evaporation temperature of 195 °C. The blue line with arrow depicts the heat recovery at the cycle evaporation temperature of 85 °C. The dotted line shows the standard CRC without batch process.
Fig. 10: T-s-diagram for 15 snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
The main thermodynamic conditions of the 15 snapshot CRCs are calculated used as a basis on which to derive the total batch cycle performance data. 5
ACCEPTED MANUSCRIPT Fig. 11 shows the cycle pressure ratio pi and the density of the steam at the expander exit. In order to maintain the working medium mass flow of 1 kg / s, the reduced density of the steam has to be compensated by an increased rotational speed n of the expansion machine nrel. also given in Fig.11. Fig. 11: Steam density rho at expander exit, relative rotational speed nrel., and expansion ratio pi for the batch process
From 195 °C to 105 °C the steam at the exit of the expander is wet. From 95 °C and below, the dry steam density rho falls faster and consequently the rotational speed rises faster in order to maintain the working medium mass flow of 1 kg / s. Fig. 12 shows the heat transferred in the 15 snapshots in the evaporator, in the preheater, and in the superheater.
Fig. 12: Heat transfer in the evaporator, the preheater and the superheater
The evaporation heat is taken of one of the containers C1 or C2. Assuming a container volume of 5 m³ and water with a constant specific heat capacity of 4.25 Ws / gK and density of 939.2 kg / m³, Fig. 13 shows the duration 𝜏𝑖 of each step i in the discretisation process. The total discharge period of each tank amounts to 23.0 minutes. Fig. 13: Duration of each of the 15 discretisation steps
The mass flow of the heat transfer medium in the evaporator in each step i is calculated by: 𝑄𝑒𝑣𝑎𝑝,𝑖 𝑚𝑒𝑣𝑎𝑝,𝑖 = 𝑐𝑝 ∙ ∆𝑇𝑒𝑣𝑎𝑝 The mass flow in the superheater in each step i is calculated by: 𝑄𝑝𝑟𝑒 + 𝑄𝑠𝑢𝑝𝑒𝑟 - 𝑄𝑟𝑒𝑐 𝑚𝑠𝑢𝑝𝑒𝑟,𝑖 = 𝑐𝑝 ∙ [𝑇h𝑜𝑡 - (𝑇𝑐𝑜𝑛𝑑 + ∆𝑇𝑝𝑖𝑛𝑐h)] The average mass flow of the heat transfer medium results in: 15
∑ (𝑚𝑒𝑣𝑎𝑝,𝑖 + 𝑚𝑠𝑢𝑝𝑒𝑟,𝑖) ∙ τi 𝑚=
i=1 15
∑ τi i=1
With the duration and the calculated heat and mechanical power in each step of the discretisation process, the mechanical and thermal energies of the entire process are balanced and the energy and the exergy efficiency is calculated. The desuperheater only collects heat when the expansion ends outside the wet steam area. In the next batch time period, the recovered heat is transferred to the preheater depending on the temperature level of the recovered heat. The mass flow of the heat transfer medium is controlled by the temperature conditions in the preheater. The heat transfer follows the first law of thermodynamics. Fig. 14 shows the recovered heat and the heat transferred to the preheater.
Fig. 14: From expanded gas recovered and to preheater transferred heat
Fig. 15 shows the electrical output power of the CRC (red line) and the batch process (blue curve). It shows that the average output power of the batch process (green line) is similar to the power of the CRC. 6
ACCEPTED MANUSCRIPT Fig. 15: Mechanical power output of CRC and batch process
In the example chosen, the batch process does not lead to a significant reduction of the mean power output.
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ACCEPTED MANUSCRIPT 3.2. Energy and Exergy Efficiency Table 3 shows the mean output power, the energy and the exergy efficiency of CRC and batch process. Additionally the average mass flows 𝑚 of the working medium and the heat transfer medium is shown and the end temperature Tend of the heat transfer medium when leaving the heat exchangers. Table 3: Output power and efficiency of CRC and batch cycle
4. Conclusions This paper proposes the application of batch processes to heat engines and shows the potential improvement in terms of output power and efficiency improvement. For the purposes of theoretical analysis, typical approaches for evaluating the energy and exergy efficiency of heat engines are explained and the commonly accepted dissipation in the evaporator is exposed. An improved batch cycle is proposed in which storage containers are used to minimise exergy losses in the evaporator. Finally, the sensible heat in the expanded working medium is recovered and transferred back to the process, also by using two containers. Further simulations and calculations with other working media, other temperature ranges, and more precisely determined expansion engines will lead to a wider range of results and to a more precise perspective of the potential. In the given example, the batch process applied to a heat engine produces 71 % more electrical power from a given heat source compared to the CRC. To reach this improvement, a larger expansion engine, larger heat exchangers, and a set of low cost containers and valves which are available on the market have to be installed and controlled. The required investment will need to be justified on the basis of economic calculations. Since sensible (waste) heat can be stored in tanks, this concept helps to complement the increased volatile regenerative electricity production. This is a feasible and widely usable concept with clear economic benefits. The development of prototypes with suitable partners in all existing fields is envisaged so as to further analyse and validate the potential of the findings.
5. Acknowledgements The author would like to thank Professor Schaber and Professor Kauder for their feedback and advice in the field of thermodynamics, trapezoid cycles and screw engines. The author would also like to thank all scientific colleagues and friends for their support and encouragement as regards the continued pursuit of unusual research work. Thanks also to Mr Twigger for carrying out proof-reading.
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ACCEPTED MANUSCRIPT References [1]
Lecompte S, Huisseune H, Van den Broek M, De Paepe M. Methodical thermodynamic analysis and regression models of organic Rankine cycle architectures for waste heat recovery. Energy 87; 2015, p. 60-76.
[2]
Lakew A A, Bolland O. Working fluids for low-temperature heat source, Applied Thermal Engineering 30; 2010, p. 1262 – 1268.
[3]
Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Conversion and Management 50; 2009, p. 576–582.
[4]
Tchanche B F, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection for a lowtemperature solar organic Rankine cycle, Applied Thermal Engineering 29; 2009, p. 2468 – 2476.
[5]
Lai N A, Wendland M, Fischer J. Working fluids for high-temperature organic Rankine cycles. Energy 36; 2011, p. 199-211.
[6]
Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for low-temperature organic Rankine cycles, Energy 32; 2007, p. 1210–1221.
[7]
Yari M, Mehr AS, Zare V, Mahmoudi SMS, Rosen MA. Exergoeconomic comparison of TLC (trilateral Rankine cycle), ORC, (organic Rankine cycle) and Kalina cycle using a low grade heat source, Energy 83; 2015, p. 712 - 722.
[8]
Fischer J. Comparison of trilateral cycles and organic Rankine cycles. Energy 36; 2011, p. 6208-6219.
[9]
Aghahosseini S, Dincer I. Comparative performance analysis of low-temperature Organic Rankine Cycle (ORC) using pure and zeotropic working fluids, Applied Thermal Engineering 54; 2013, p. 35 - 42.
[10] Yang Y, Wang L, Dong C, Xu G, Morosuk T, Tsatsaronis G. Comprehensive exergy-based evaluation and parametric of a coal-fired ultra-supercritical power plant, Applied Energy 112; 2013, p. 1087 – 1099. [11] Website for the “Staudinger” power plant. https://de.wikipedia.org/wiki/Kraftwerk_Staudinger visited 14 November 2016. [12] Maraver D, Royo J, Lemort V, Quoilin S. Systematic optimization of subcritical and transcritical organic Rankine cycles (ORCs) constrained by technical parameters in multiple applications, Applied Energy 117; 2014, p. 11 – 29. [13] Knez Z, Markočič E, Leitgeb M, Škerget M. Industrial applications of supercritical fluids. A review. Energy 77; 2014, p. 235-243. [14] Chen H, Goswami D Y, Rahman M M, Stefanakos E K. Energetic and exergetic analysis of CO2- and R32-based transcritical Rankine cycles for low-grade heat conversion, Applied Energy 88, Issue 8; 2011, p. 2802–2808. [15] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for lowtemperature geothermal power generation, Applied Energy 88, Issue 8; 2011, p. 2740 – 2754. [16] Baik Y, Kim M, Chang K, Kim S. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Applied Energy 88, Issue 3; 2011, p. 892–898. [17] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source, Applied Energy 87, Issue 4; 2010, p. 1349– 1357. [18] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical Organic Rankine Cycles. Energy 35; 2010, p. 1033-1042.
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ACCEPTED MANUSCRIPT [19] DiPippo R. Second Law assessment of binary plants generating power from lowtemperature geothermal fluids, Geothermics 33; 2004, p. 565–586. [20] Ogriseck S. Integration of Kalina cycle in a combined heat and power plan, a case study. Applied Thermal Engineering 29, Issues 14-15; 2009, p. 2843-2848. [21] Chen H, Goswami D, Rahman M, Stefanako E A. supercritical Rankine cycle using zeotropic mixtures working fluids for the conversion of low-grade heat into power. Energy 36, Issue 1; 2011, p. 549-555. [22] Kliem B. Grundlagen des Zwei-Phasen-Schraubenmotors - Fundamentals of the TwoPhase Screw-Type Engine, doctoral thesis, University of Dortmund; 2005. [23] Löffler M. Flash Evaporation in Cyclones. Chemical Engineering & Technology 31; Issue 7/2008, Pages 1062-1065. [24] Lai N A, Fischer J. Efficiencies of power flash cycles. Energy 44, Issue 1; 2012, p. 10171027. [25] Ho T, Mao S S, Greif 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 42, Issue 1; 2012, p. 213 - 223. [26] Steffen M, Löffler M, Schaber K. Efficiency of a new Triangle Cycle with flash evaporation in a piston engine. Energy 57; 2013, p. 295-307. [27] Kanno H, Shikazono N. Experimental and modeling study on adiabatic two-phase expansion in a cylinder, International Journal of Heat and Mass Transfer 86; 2015, p. 755–763. [28] Löffler M, Griessbaum N. Storage Devices for Heat Exchangers with Phase Change. International Journal of Refrigeration 44; August 2014, p. 189-196. [29] Löffler M, Magdanz A. Transient Refrigeration Cycles - Simulation Results, Conference on Efficiency, Cost, Optimisation, Simulation and Environmental Impact of Energy Systems 29; Conference Proceedings, Publisher: University of Ljubljana, Faculty of Mechanical Engineering, Editors: Andrej Kitanovski and Alojz Poredos, ISBN 978-9616980-15-9, no page number (hypertext). [30] Löffler M. Trapezoid Cycles and Extended Pinch Analysis. International Journal of Refrigeration 49; 2014, p. 135-140. [31] Löffler M. Trapezoid vapour compression heat pump cycles and pinch point analysis. International Journal of Refrigeration 54; 2015, p. 142-150. [32] Wagner W, Prus A. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J. Phys. Chem. Ref. Data, 2002, 31, 2, 387-535. [33] website for thermophysical fluid properties with basis IAPWS: http://webbook.nist.gov/chemistry/fluid/ visited 20 January 2017.
Table 1: Valve position in the two main states of the control, 0 = closed, 1 = open
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ACCEPTED MANUSCRIPT State 1 State 2
V1 1 0
V2 0 1
V3 0 1
V4 1 0
V5 1 0
V6 0 1
V7 0 1
Table 2: Data used for electricity consumption of the pumps
Pump 1 Pump 2 CRC Pump 2 batch Pump 3 Pump 4 Pump 5 Pump 6
dm / dt in l / s Δp in bar 1.00 0.500 1.00 2.949 1.00 4.714 3.62 0.100 variable 0.250 0.50 0.250 0.50 0.250
Pel. in kW 0.063 0.369 0.589 0.045 variable 0.016 0.016
Table 3: Output power and efficiency of CRC and batch cycle
Mean electrical output power. Constant working medium mass flow of 1 kg / s. CRC batch Pel 291 kW 280 kW improvement: - 4.1 % 𝑚 1 kg / s 1 kg / s working medium 𝑚 7.3 kg / s 4.1 kg / s heat transfer medium 𝑇𝑒𝑛𝑑 116.6 °C 51.9 °C heat source end temp. Mean electrical output power. Expander size is adapted to the heat source capacity. CRC batch Pel 291 kW 501 kW improvement: + 72.1 % 𝑚 1 kg / s 1.8 kg / s working medium 𝑚 7.3 kg / s 7.3 kg / s heat transfer medium Energy efficiency CRC batch 10.3% 10.7%
improvement +2.9 %
Exergy efficiency CRC batch 31.1% 53.1%
improvement +70.6 %
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V8 1 0
V9 0 0
V10 0 0
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Fig. 1: Basic setup for Clausius Rankine Cycle or Organic Rankine Cycle
Fig. 2: Basic setup for batch process with container C1
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Fig. 3: Setup for batch process with container, preheater, and superheater
Fig. 4: Setup for batch process with two containers for continuous process
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Fig. 5: Setup for batch process with desuperheater
Fig. 6: Setup for batch process with additional valves V9 and V10 for heat recovery
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Fig. 7: T-s-diagram for CRC
Fig. 8: T-s-diagram for CRC with a desuperheater
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Fig. 9: T-s-diagram for selected snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
Fig. 10: T-s-diagram for 15 snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
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Fig. 11: Steam density rho at expander exit, relative rotational speed nrel., and expansion ratio pi for the batch process
Fig. 12: Heat transfer in the evaporator, the preheater and the superheater
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Fig. 13: Duration of each of the 15 discretisation steps
Fig. 14: From expanded gas recovered and to preheater transferred heat
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Fig. 15: Mechanical power output of CRC and batch process
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Michael Löffler PII:
S0360-5442(17)30286-4
DOI:
10.1016/j.energy.2017.02.105
Reference:
EGY 10398
To appear in:
Energy
Received Date:
30 November 2016
Revised Date:
17 February 2017
Accepted Date:
18 February 2017
Please cite this article as: Michael Löffler, Batch Processes in Heat Engines, Energy (2017), doi: 10.1016/j.energy.2017.02.105
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights Michael Löffler: Batch Processes in Heat Engines
Batch processes in heat engines lead to a drastically increased electrical output. The setup contains preheater, superheater, desuperheater. The examination is carried out using T-s- diagrams and discretisation. Thermal input, and electrical output are calculated and aggregated. Energy efficiency and exergy efficiency is calculated, compared, and discussed.
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Energy, submitted article: Batch Processes in Heat Engines Batch Processes in Heat Engines Michael Löffler1 Engineering Office Dr. Löffler, Ludowiciring 13 c, 76751 Jockgrim, Germany Heat engines transfer high-temperature heat into mechanical and electrical energy using the Clausius Rankine Cycle (CRC). Low temperature applications primarily use the Organic Rankine Cycle, in which mainly waste heat, geothermal heat and solar heat are transferred into mechanical energy. The exergy of a low temperature heat source can be transferred into electricity in so-called triangle (or trilateral) cycles. By applying batch processes in heat engines, it is possible to reach an exceptionally high approximation to triangle cycles and thus to build up high exergy-efficient heat engines. In an example case the calculated exergy efficiency is 71 % higher compared to a CRC. The proposed process is not limited to specific working media and can therefore be adapted to a wide range of temperatures. The required setup is rather simple and is derived from setups ranging from basic to more and more advanced. The thermodynamic performance of an example plant is derived from T-sdiagrams.
1. State of the Art 1.1. Clausius Rankine Cycle and Organic Rankine Cycle The Clausius Rankine Cycle (CRC) is globally applied in most large power plants. In a basic setup, it consists of an expander which is fed by superheated steam coming from a set of three heat exchangers: the preheater, the evaporator and the superheater. The expanded steam is fully condensed in a fourth heat exchanger and then pumped to the preheater. Fig. 1 shows the basic setup of the CRC. Fig. 1: Basic setup for Clausius Rankine Cycle or Organic Rankine Cycle
In the Organic Rankine Cycle (ORC), the basic setup is the same as for the CRC, but the condensable working medium is different to water. Many working media have been examined [1, 2, 3, 4, 5, 6]. In the thermodynamic analysis of cycles, the T-s-diagram plays a main role. This diagram shows the transferred heat but also the mechanical power which is proportional to the area spread up by the cycle line. Additionally, the dissipated power can be estimated by the area between the heat source curve and the curves of the heated or evaporated working medium. One objective of heat engines is to transfer as much heat into mechanical energy as possible. For this purpose, the thermodynamic cycle should cover as much area as possible. The cycle area is restricted to the space between the curve of the heat sink and the heat source. In most cases, the heat sink is an almost horizontal line and the heat source can be approximated by a sloped line. The maximum area which can be covered therefore has the shape of a triangle in the T-s-diagram. In literature, this type of cycle is called a trilateral cycle or triangle cycle. The performance of trilateral cycles has been compared with CRC and ORC by using simulation tools [7, 8, 9]. There are different ways in which triangle cycles can be reached. 1.2. Approaches for achieving triangle cycles The most common way of increasing the power output of a power plant is to construct facilities with two or more pressure levels. This requires separate expanders for each pressure level, e.g. three turbines (or turbine parts) for high, medium and low pressure and a complex structure of heat exchangers [10, 11].
1
Corresponding author. Tel: +49 7272 950184, E-mail address: [email protected]
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ACCEPTED MANUSCRIPT Transcritical cycles expand the working medium from a supercritical state to a subcritical state [12, 13, 14, 15, 16, 17, 18]. The sloped line of a high pressure working medium can adapt to the heat source curve in the T-s-diagram. In some plants, a working medium mixture is used in order to gain area in the T-s-diagram, e.g. the Kalina cycle [19, 20, 21]. Here too, a sloped line in the T-s-diagram leads to an improvement of exergy efficiency. Flash processes were also examined in order to achieve trilateral cycles [22, 23, 24, 25, 26, 27]. In this case, the liquid working medium is heated up by the heat source medium. This heat transfer can be carried out with very low dissipation in a counter flow heat exchanger.
2. Setup for applying batch processes in heat engines Batch processes have already been proposed, built up and simulated for refrigeration cycles [28, 29]. The concept closely replicates the Lorenz cycle, which is the ideal cycle for heat pumps and refrigeration plants. Enhanced setups for heat recovery using pinch analysis become possible [30, 31]. Below, the concept of batch processes is adapted to the case of heat engines. 2.1 Basic setup Fig. 2 shows the basic setup of a heat engine with batch process. The batch process requires a liquid as a heat transfer medium (e.g. water or thermal oil). Of course the liquid heat transfer medium can transfer heat originating from a hot gas, e.g. from flue gas. The heat transfer medium is pumped to the container C1 (valve V1 open, valve V3 closed). During this period, the container is charged. In a second step, the heat transfer medium is pumped from the container C1 to the evaporator at a high mass flow (V1 is closed and V3 is opened). During this period, the container is discharged. The high mass flow results in a minor temperature difference on the water side of the evaporator and, as a result, to a low level thermal dissipation in the evaporator. Since the medium in the container is losing heat, its average temperature falls, together with the evaporation pressure in the evaporator. The function and control of the depicted pumps in all figures are self-explanatory. Fig. 2: Basic setup for batch process with container C1
The drawback of this setup is that the steam entering the expander is not particularly superheated and may cool the expander down which can result in harmful condensation inside the expander. 2.2. Setup for feasible operating conditions Fig. 3 shows an enhanced setup, with a preheater and superheater. The working medium is preheated to the evaporation temperature, then evaporated, and then superheated to a high end temperature. A second superheater with a higher temperature could be installed in order to reach higher end temperatures. Superheating ensures that there is no condensation of the working medium inside the expander.
Fig. 3: Setup for batch process with container, preheater, and superheater
One noticeable and main feature of the batch cycle is that all heat exchangers can be designed to work with a small mean temperature difference between the heat transfer medium and the working medium which means low levels of dissipation and a high degree of cycle efficiency. The disadvantage of the setup in Fig. 3 is that the expander works in stop and go mode due to the intermittent charging and discharging of the container C1. 2.3. Setup for continuous process and feasible operating conditions To overcome the stop and go mode of the expander, a second container C2 is introduced to the setup. In Fig. 4, C1 is charged and C2 is discharged in an initial period before C1 is 2
ACCEPTED MANUSCRIPT discharged and C2 is charged in the following period, and so on. In this way, a continuous power output of the expander is maintained and additionally a continuous thermal power transfer from the heat source to the heat engine. The check valves CV1 and CV2 are required in order to ensure that the mass flow of the heat transfer medium is both stable and defined. Fig. 4: Setup for batch process with two containers for continuous process
In many cases, the expanded gas leaving the expander contains usable sensible heat which can be recovered by a desuperheater. In the case of batch processes, a special setup for heat recovery is needed. 2.4. Setup for the use of a desuperheater in batch processes Fig. 5 shows the desuperheater and the additional containers C3 and C4 which are used to store and return recovered heat from the expanded working medium. Valves V5 to V8, and the check valves CV3 and CV4, conduct and maintain the mass flow of the heat transfer medium. The recovered heat is transferred to the preheater. In this way, the difference between the capacity flow of the working medium in the preheater (liquid, cp = 4.18 Ws/gK) and the superheater (vapour, cp = 2.05 Ws/gK) will be reduced. This method helps to reduce dissipation resulting from the difference in the specific heat of the liquid and gaseous working medium. Consequently, the efficiency of the heat transfer and the heat engine will be increased. The influence of bell-shaped or overhanging working media [24] on the need for desuperheating will be addressed in subsequent studies. Fig. 5: Setup for batch process with desuperheater Table 2 shows the valve positions for the two main states in the finite state automation. Table 1: Data used for electricity consumption of the pumps
At the end of the discharging cycle of either container, the water temperature and the evaporator temperature are at their minimum. When connected to the charged container, hot heat transfer medium is pumped and cooled down in the cold evaporator. The cold water is then pumped back into the container and mixes with the hot container water. This mixing process leads to additional dissipation and can be reduced by purging and heating the evaporator with medium directly from the heat source. 2.5. Setup for purging and heating the evaporator and purging and cooling the desuperheater Fig. 6 allows hot medium from the heat source to heat up the cold evaporator. This prevents the cold medium from mixing with hot medium in the container connected next to the evaporator. In the same way, valve V10 is used to cool the desuperheater down before it is connected to the discharged container. In this case, the hot medium is prevented from entering and mixing with the cold medium in C3 or C4. Fig. 6: Setup for batch process with additional valves V9 and V10 for heat recovery
In the thermodynamic analysis, the effect of the heat recovery in the desuperheater is balanced. The effects of purging the evaporator and the desuperheater are not balanced.
3. Thermodynamic Analysis The thermodynamic analysis shows the main effects occurring in the batch process applied to heat engines. The chosen working medium (water,) the chosen temperature levels, and the chosen expanders are not optimized for the given process conditions. For example, the size of the expander would be halved if the condensation temperature was changed from 50 °C to 65 °C. The thermodynamic analysis is conducted using the example of a heat engine with the following conditions, which apply to both the CRC and the batch cycle: 3
ACCEPTED MANUSCRIPT Heat source, Thot: 204 °C Heat sink, Tcold: 46 °C Condensation temperature: Tcond = 50 °C Mass flow in the turbine: 1 kg / s Pinch temperature of heat exchangers: ΔTpinch = 2 K Temperature difference on the water side of evaporator and condenser: ΔTevap = 2 K Constant isentropic efficiency of the expander: ηis = 66.6 % For the thermodynamic analysis, the batch process is discretised into 15 steps with evaporation temperature of 195 °C down to 55 °C in 10 K steps. The electrical power for the liquid pumps is integrated in the efficiency calculation. The pump efficiency is presumed to be 80 %. The pressure drop in heat exchangers at the water side is 0.25 bar. Table 2 shows the data of the pumps 1 to 6 used in the calculations. Table 2: Data used for electricity consumption of the pumps
The following simplifications do not influence the results to a large extent and are discounted:
the pressurisation of the cold liquid phase (not shown in the T-s diagrams). the influence of mixing and heat conduction in the liquid in the storage tanks is not taken into consideration. the influence of regenerative losses due to the tank mass and pipe mass is not taken into consideration. The following losses are presumed: electrical engine: 5 % (electrical efficiency: 95 %) mechanical friction: 20 kW (4% of the power output) Because of the high maximum expansion ratio pi of 113, the expander is preferably a set of two screw engines with variable expansion ratio or piston engines. The two screw engines would be a 7 l (expanded volume per revolution) screw engine for the high pressure expansion, and a 60 l screw engine for the low pressure expansion. Both screw engines run at a maximum 300 Hz (18,000 rpm). 3.1. Analysis in T-s-diagrams T-s-diagrams are used to calculate the ideal mechanical output power of the cycle 𝑃𝐶𝑅𝐶,𝑖𝑑 as the area within the cycle lines. They are also used, to calculate the heat input 𝑄𝑖𝑛 or recovered and transferred heat 𝑄𝑡𝑟𝑎𝑛𝑠 and the dissipated heat 𝑄𝑑𝑖𝑠𝑠 as the integral between the heat source line and T = - 273 °C. The ideal mechanical output power is used in turn to calculate the electrical output power of each CRC: 𝑃𝑒𝑙 = (𝑃𝐶𝑅𝐶,𝑖𝑑 ∙ 𝜂𝑖𝑠 - 𝑃𝑓𝑟𝑖𝑐) ∙ 𝜂𝑒𝑙 - 𝑃𝑝𝑢𝑚𝑝𝑠 The thermal efficiency is defined by the following equation: 𝜂 = 𝑃𝑒𝑙 𝑄 𝑡h
𝑖𝑛
𝑄𝑖𝑛 is the sum of heat for preheating, evaporation, and superheating minus the recovered and transferred heat: 𝑄𝑖𝑛 = 𝑄𝑝𝑟𝑒 + 𝑄𝑒𝑣𝑎𝑝 + 𝑄𝑠𝑢𝑝𝑒𝑟 - 𝑄𝑡𝑟𝑎𝑛𝑠 The exergy efficiency is defined by the relation of the electrical power output and the Exergy of the heat source in relation to the sink temperature T0. 𝜂 = 𝑃𝑒𝑙 𝐸 𝒆𝒙
𝑠𝑜𝑢𝑟𝑐𝑒
The Exergy is defined by the following equation: 𝐸𝑠𝑜𝑢𝑟𝑐𝑒 = 𝑚𝑠𝑜𝑢𝑟𝑐𝑒 ∙ [(hsource ‒ h0) ‒ T0 ∙ (ssource ‒ s0)] 3.1.1. CLAUSIUS RANKINE CYCLE The evaporation temperature of the CRC is set to 125°C which is near the set point for maximum power output for the given temperature levels. The condensation temperature is 50°C. The expansion factor pi is 18.8. Fig. 7 shows the CRC in the T-s-diagram. The wellknown sub-processes 1 to 6 are depicted as black arrows. The red arrow shows the heat 4
ACCEPTED MANUSCRIPT source curve. All calculations are based on data from the "International Association for Properties of Water and Steam Industrial Formulation 1997" (IAPWS IF-97) [32, 33]. Fig. 7: T-s-diagram for CRC
In the given example, the mass flow of the heat source is defined by: 𝑸𝒆𝒗𝒂𝒑 + 𝑸𝒔𝒖𝒑𝒆𝒓 𝑚𝑠𝑜𝑢𝑟𝑐𝑒 = 𝑐𝑝 ∙ [𝑇h𝑜𝑡 - (𝑇𝑒𝑣𝑎𝑝 + ∆𝑇𝑝𝑖𝑛𝑐h)] This mass flow defines the end temperature of the heat source: 𝑸𝒑𝒓𝒆 + 𝑸𝒆𝒗𝒂𝒑 + 𝑸𝒔𝒖𝒑𝒆𝒓 𝑇𝑒𝑛𝑑 = 𝑇h𝑜𝑡 𝑐𝑝 ∙ 𝑚𝑠𝑜𝑢𝑟𝑐𝑒 The thermal efficiency of the Clausius Rankine Cycle is 10.3 %. Since the heat source is only cooled down to 𝑇𝑒𝑛𝑑 = 117 °C, the exergy efficiency is only 31.1 %. In some cases, the expanded steam contains sensible heat which can be recovered by a desuperheater and transferred back into the process. Fig. 8 shows a CRC with an evaporation temperature of 85 °C and the heat recovered in the desuperheater (blue arrow). Fig. 8: T-s-diagram for CRC with a desuperheater
In the CRC, the recovered heat is used directly and continuously in the cycle. In the heat engine with batch process shown in Fig. 6, the recovered heat is first stored in either container C3 or C4 before then being transferred back to the cycle. Consequently, the following analysis of the cycle with batch process is much more complex compared to CRC. 3.1.2. CYCLE WITH BATCH PROCESS The batch cycle was divided into 15 consecutively occurring CRCs, each taken at condensation temperature levels of 195 °C down to 55 °C in steps of 10 K. In each period of discretisation, mean values of thermodynamic states represent the process conditions. The discretisation number of 15 is high enough to ensure that the results are sufficiently accurate, while also allowing a visual overview of all occurring phenomena. Fig. 9 only shows some of the snapshots: the first three cycles at evaporation temperatures of 195 °C, 185 °C, and 175 °C, the CRC standard cycle at 125 °C, one desuperheater cycle at 85 °C, and the lowest cycle at evaporation temperature of 55 °C. The heat source (red arrows, only for the evaporation temperature of 195 °C) and the heat sink (blue arrow, only for the evaporation temperature of 85 °C) are also depicted. The small dissipation area between the working media curve and the related heat transfer medium curves, compared to the CRC case depicted in Fig. 7, is noticeable. Fig. 9: T-s-diagram for selected snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
Fig. 10 shows all the 15 “snapshots” of the batch process as well as exemplary cooling curves of the heat transfer medium in the preheater, the evaporator, and the superheater (red lines with arrows) for an evaporation temperature of 195 °C. The blue line with arrow depicts the heat recovery at the cycle evaporation temperature of 85 °C. The dotted line shows the standard CRC without batch process.
Fig. 10: T-s-diagram for 15 snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
The main thermodynamic conditions of the 15 snapshot CRCs are calculated used as a basis on which to derive the total batch cycle performance data. 5
ACCEPTED MANUSCRIPT Fig. 11 shows the cycle pressure ratio pi and the density of the steam at the expander exit. In order to maintain the working medium mass flow of 1 kg / s, the reduced density of the steam has to be compensated by an increased rotational speed n of the expansion machine nrel. also given in Fig.11. Fig. 11: Steam density rho at expander exit, relative rotational speed nrel., and expansion ratio pi for the batch process
From 195 °C to 105 °C the steam at the exit of the expander is wet. From 95 °C and below, the dry steam density rho falls faster and consequently the rotational speed rises faster in order to maintain the working medium mass flow of 1 kg / s. Fig. 12 shows the heat transferred in the 15 snapshots in the evaporator, in the preheater, and in the superheater.
Fig. 12: Heat transfer in the evaporator, the preheater and the superheater
The evaporation heat is taken of one of the containers C1 or C2. Assuming a container volume of 5 m³ and water with a constant specific heat capacity of 4.25 Ws / gK and density of 939.2 kg / m³, Fig. 13 shows the duration 𝜏𝑖 of each step i in the discretisation process. The total discharge period of each tank amounts to 23.0 minutes. Fig. 13: Duration of each of the 15 discretisation steps
The mass flow of the heat transfer medium in the evaporator in each step i is calculated by: 𝑄𝑒𝑣𝑎𝑝,𝑖 𝑚𝑒𝑣𝑎𝑝,𝑖 = 𝑐𝑝 ∙ ∆𝑇𝑒𝑣𝑎𝑝 The mass flow in the superheater in each step i is calculated by: 𝑄𝑝𝑟𝑒 + 𝑄𝑠𝑢𝑝𝑒𝑟 - 𝑄𝑟𝑒𝑐 𝑚𝑠𝑢𝑝𝑒𝑟,𝑖 = 𝑐𝑝 ∙ [𝑇h𝑜𝑡 - (𝑇𝑐𝑜𝑛𝑑 + ∆𝑇𝑝𝑖𝑛𝑐h)] The average mass flow of the heat transfer medium results in: 15
∑ (𝑚𝑒𝑣𝑎𝑝,𝑖 + 𝑚𝑠𝑢𝑝𝑒𝑟,𝑖) ∙ τi 𝑚=
i=1 15
∑ τi i=1
With the duration and the calculated heat and mechanical power in each step of the discretisation process, the mechanical and thermal energies of the entire process are balanced and the energy and the exergy efficiency is calculated. The desuperheater only collects heat when the expansion ends outside the wet steam area. In the next batch time period, the recovered heat is transferred to the preheater depending on the temperature level of the recovered heat. The mass flow of the heat transfer medium is controlled by the temperature conditions in the preheater. The heat transfer follows the first law of thermodynamics. Fig. 14 shows the recovered heat and the heat transferred to the preheater.
Fig. 14: From expanded gas recovered and to preheater transferred heat
Fig. 15 shows the electrical output power of the CRC (red line) and the batch process (blue curve). It shows that the average output power of the batch process (green line) is similar to the power of the CRC. 6
ACCEPTED MANUSCRIPT Fig. 15: Mechanical power output of CRC and batch process
In the example chosen, the batch process does not lead to a significant reduction of the mean power output.
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ACCEPTED MANUSCRIPT 3.2. Energy and Exergy Efficiency Table 3 shows the mean output power, the energy and the exergy efficiency of CRC and batch process. Additionally the average mass flows 𝑚 of the working medium and the heat transfer medium is shown and the end temperature Tend of the heat transfer medium when leaving the heat exchangers. Table 3: Output power and efficiency of CRC and batch cycle
4. Conclusions This paper proposes the application of batch processes to heat engines and shows the potential improvement in terms of output power and efficiency improvement. For the purposes of theoretical analysis, typical approaches for evaluating the energy and exergy efficiency of heat engines are explained and the commonly accepted dissipation in the evaporator is exposed. An improved batch cycle is proposed in which storage containers are used to minimise exergy losses in the evaporator. Finally, the sensible heat in the expanded working medium is recovered and transferred back to the process, also by using two containers. Further simulations and calculations with other working media, other temperature ranges, and more precisely determined expansion engines will lead to a wider range of results and to a more precise perspective of the potential. In the given example, the batch process applied to a heat engine produces 71 % more electrical power from a given heat source compared to the CRC. To reach this improvement, a larger expansion engine, larger heat exchangers, and a set of low cost containers and valves which are available on the market have to be installed and controlled. The required investment will need to be justified on the basis of economic calculations. Since sensible (waste) heat can be stored in tanks, this concept helps to complement the increased volatile regenerative electricity production. This is a feasible and widely usable concept with clear economic benefits. The development of prototypes with suitable partners in all existing fields is envisaged so as to further analyse and validate the potential of the findings.
5. Acknowledgements The author would like to thank Professor Schaber and Professor Kauder for their feedback and advice in the field of thermodynamics, trapezoid cycles and screw engines. The author would also like to thank all scientific colleagues and friends for their support and encouragement as regards the continued pursuit of unusual research work. Thanks also to Mr Twigger for carrying out proof-reading.
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ACCEPTED MANUSCRIPT References [1]
Lecompte S, Huisseune H, Van den Broek M, De Paepe M. Methodical thermodynamic analysis and regression models of organic Rankine cycle architectures for waste heat recovery. Energy 87; 2015, p. 60-76.
[2]
Lakew A A, Bolland O. Working fluids for low-temperature heat source, Applied Thermal Engineering 30; 2010, p. 1262 – 1268.
[3]
Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Conversion and Management 50; 2009, p. 576–582.
[4]
Tchanche B F, Papadakis G, Lambrinos G, Frangoudakis A. Fluid selection for a lowtemperature solar organic Rankine cycle, Applied Thermal Engineering 29; 2009, p. 2468 – 2476.
[5]
Lai N A, Wendland M, Fischer J. Working fluids for high-temperature organic Rankine cycles. Energy 36; 2011, p. 199-211.
[6]
Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for low-temperature organic Rankine cycles, Energy 32; 2007, p. 1210–1221.
[7]
Yari M, Mehr AS, Zare V, Mahmoudi SMS, Rosen MA. Exergoeconomic comparison of TLC (trilateral Rankine cycle), ORC, (organic Rankine cycle) and Kalina cycle using a low grade heat source, Energy 83; 2015, p. 712 - 722.
[8]
Fischer J. Comparison of trilateral cycles and organic Rankine cycles. Energy 36; 2011, p. 6208-6219.
[9]
Aghahosseini S, Dincer I. Comparative performance analysis of low-temperature Organic Rankine Cycle (ORC) using pure and zeotropic working fluids, Applied Thermal Engineering 54; 2013, p. 35 - 42.
[10] Yang Y, Wang L, Dong C, Xu G, Morosuk T, Tsatsaronis G. Comprehensive exergy-based evaluation and parametric of a coal-fired ultra-supercritical power plant, Applied Energy 112; 2013, p. 1087 – 1099. [11] Website for the “Staudinger” power plant. https://de.wikipedia.org/wiki/Kraftwerk_Staudinger visited 14 November 2016. [12] Maraver D, Royo J, Lemort V, Quoilin S. Systematic optimization of subcritical and transcritical organic Rankine cycles (ORCs) constrained by technical parameters in multiple applications, Applied Energy 117; 2014, p. 11 – 29. [13] Knez Z, Markočič E, Leitgeb M, Škerget M. Industrial applications of supercritical fluids. A review. Energy 77; 2014, p. 235-243. [14] Chen H, Goswami D Y, Rahman M M, Stefanakos E K. Energetic and exergetic analysis of CO2- and R32-based transcritical Rankine cycles for low-grade heat conversion, Applied Energy 88, Issue 8; 2011, p. 2802–2808. [15] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical Organic Rankine Cycle (ORC) and transcritical power cycle system for lowtemperature geothermal power generation, Applied Energy 88, Issue 8; 2011, p. 2740 – 2754. [16] Baik Y, Kim M, Chang K, Kim S. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Applied Energy 88, Issue 3; 2011, p. 892–898. [17] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source, Applied Energy 87, Issue 4; 2010, p. 1349– 1357. [18] Schuster A, Karellas S, Aumann R. Efficiency optimization potential in supercritical Organic Rankine Cycles. Energy 35; 2010, p. 1033-1042.
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ACCEPTED MANUSCRIPT [19] DiPippo R. Second Law assessment of binary plants generating power from lowtemperature geothermal fluids, Geothermics 33; 2004, p. 565–586. [20] Ogriseck S. Integration of Kalina cycle in a combined heat and power plan, a case study. Applied Thermal Engineering 29, Issues 14-15; 2009, p. 2843-2848. [21] Chen H, Goswami D, Rahman M, Stefanako E A. supercritical Rankine cycle using zeotropic mixtures working fluids for the conversion of low-grade heat into power. Energy 36, Issue 1; 2011, p. 549-555. [22] Kliem B. Grundlagen des Zwei-Phasen-Schraubenmotors - Fundamentals of the TwoPhase Screw-Type Engine, doctoral thesis, University of Dortmund; 2005. [23] Löffler M. Flash Evaporation in Cyclones. Chemical Engineering & Technology 31; Issue 7/2008, Pages 1062-1065. [24] Lai N A, Fischer J. Efficiencies of power flash cycles. Energy 44, Issue 1; 2012, p. 10171027. [25] Ho T, Mao S S, Greif 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 42, Issue 1; 2012, p. 213 - 223. [26] Steffen M, Löffler M, Schaber K. Efficiency of a new Triangle Cycle with flash evaporation in a piston engine. Energy 57; 2013, p. 295-307. [27] Kanno H, Shikazono N. Experimental and modeling study on adiabatic two-phase expansion in a cylinder, International Journal of Heat and Mass Transfer 86; 2015, p. 755–763. [28] Löffler M, Griessbaum N. Storage Devices for Heat Exchangers with Phase Change. International Journal of Refrigeration 44; August 2014, p. 189-196. [29] Löffler M, Magdanz A. Transient Refrigeration Cycles - Simulation Results, Conference on Efficiency, Cost, Optimisation, Simulation and Environmental Impact of Energy Systems 29; Conference Proceedings, Publisher: University of Ljubljana, Faculty of Mechanical Engineering, Editors: Andrej Kitanovski and Alojz Poredos, ISBN 978-9616980-15-9, no page number (hypertext). [30] Löffler M. Trapezoid Cycles and Extended Pinch Analysis. International Journal of Refrigeration 49; 2014, p. 135-140. [31] Löffler M. Trapezoid vapour compression heat pump cycles and pinch point analysis. International Journal of Refrigeration 54; 2015, p. 142-150. [32] Wagner W, Prus A. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use, J. Phys. Chem. Ref. Data, 2002, 31, 2, 387-535. [33] website for thermophysical fluid properties with basis IAPWS: http://webbook.nist.gov/chemistry/fluid/ visited 20 January 2017.
Table 1: Valve position in the two main states of the control, 0 = closed, 1 = open
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V1 1 0
V2 0 1
V3 0 1
V4 1 0
V5 1 0
V6 0 1
V7 0 1
Table 2: Data used for electricity consumption of the pumps
Pump 1 Pump 2 CRC Pump 2 batch Pump 3 Pump 4 Pump 5 Pump 6
dm / dt in l / s Δp in bar 1.00 0.500 1.00 2.949 1.00 4.714 3.62 0.100 variable 0.250 0.50 0.250 0.50 0.250
Pel. in kW 0.063 0.369 0.589 0.045 variable 0.016 0.016
Table 3: Output power and efficiency of CRC and batch cycle
Mean electrical output power. Constant working medium mass flow of 1 kg / s. CRC batch Pel 291 kW 280 kW improvement: - 4.1 % 𝑚 1 kg / s 1 kg / s working medium 𝑚 7.3 kg / s 4.1 kg / s heat transfer medium 𝑇𝑒𝑛𝑑 116.6 °C 51.9 °C heat source end temp. Mean electrical output power. Expander size is adapted to the heat source capacity. CRC batch Pel 291 kW 501 kW improvement: + 72.1 % 𝑚 1 kg / s 1.8 kg / s working medium 𝑚 7.3 kg / s 7.3 kg / s heat transfer medium Energy efficiency CRC batch 10.3% 10.7%
improvement +2.9 %
Exergy efficiency CRC batch 31.1% 53.1%
improvement +70.6 %
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V8 1 0
V9 0 0
V10 0 0
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Fig. 1: Basic setup for Clausius Rankine Cycle or Organic Rankine Cycle
Fig. 2: Basic setup for batch process with container C1
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Fig. 3: Setup for batch process with container, preheater, and superheater
Fig. 4: Setup for batch process with two containers for continuous process
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Fig. 5: Setup for batch process with desuperheater
Fig. 6: Setup for batch process with additional valves V9 and V10 for heat recovery
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Fig. 7: T-s-diagram for CRC
Fig. 8: T-s-diagram for CRC with a desuperheater
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Fig. 9: T-s-diagram for selected snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
Fig. 10: T-s-diagram for 15 snapshots of the batch process, and exemplary heat curves of the heat source (red arrows) and of the recycled heat (blue arrow)
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Fig. 11: Steam density rho at expander exit, relative rotational speed nrel., and expansion ratio pi for the batch process
Fig. 12: Heat transfer in the evaporator, the preheater and the superheater
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Fig. 13: Duration of each of the 15 discretisation steps
Fig. 14: From expanded gas recovered and to preheater transferred heat
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Fig. 15: Mechanical power output of CRC and batch process
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