Dynamic performance comparison of different cascade waste heat recovery systems for internal combustion engine in combined cooling, heating and power

Applied Energy 260 (2020) 114245

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Dynamic performance comparison of different cascade waste heat recovery systems for internal combustion engine in combined cooling, heating and power ⁎

T

⁎

Xuan Wang , Gequn Shu, Hua Tian , Rui Wang, Jinwen Cai State Key Laboratory of Engines, Tianjin University, No. 92, Weijin Road, Nankai District, Tianjin 300072, China

H I GH L IG H T S

module library is developed for building different dynamic models. • AARSvalidated has better off-design performance than ORC for low temperature heat. • Cascade systems respond much more slowly than basic single-stage cycles. • The structure of ECCS is benefit to keep perfect performance under low load. •

A R T I C LE I N FO

A B S T R A C T

Keywords: Combined cooling, heating, and power systems Waste heat recovery Dynamic performance Organic Rankine cycle Absorption refrigeration Cascade energy utilisation

The internal combustion engine is an important prime mover in combined cooling, heating and power systems. However, approximately 30–40% of the input energy is discharged by exhaust; thus, it is significant to recover the exhaust waste heat. Cascade energy-utilisation systems have high efficiencies for exhaust recovery with a large temperature drop. However, waste heat-recovery systems usually work under different conditions and therefore, it is meaningful to study the dynamic performance of cascade systems. In this work, by developing a model library of common components in thermodynamic systems, dynamic simulation models of three cascade systems are established: an electric-cooling cogeneration system (ECCS), a double-effect absorption refrigeration system, and a double-stage organic Rankine cycle. The dynamic response speed and off-design performance of each system are analysed and compared. The results indicate that all the cascade systems respond considerably more slowly than any single-stage cycle, and the ECCS achieves the best off-design performance because both its upper and lower stages (high-temperature organic Rankine cycle and absorption refrigeration) exhibit perfect working condition adaptability, especially the lower stage. Furthermore, the structure of the ECCS is more beneficial for the lower stage to maintain satisfactory off-design performance.

1. Introduction Combined cooling, heating, and power (CCHP) systems can use waste heat from power generation for heating or cooling to improve primary energy utilisation [1]. Furthermore, CCHPs can be built close to end users, which helps avoid electricity-transmission losses and provides a resilient electricity supply [2]. Because of these advantages, CCHPs are valued by many countries. For example, the US government published a policy to promote the application of CCHP, aiming at building 40GW new CCHP by 2020 [3]. The European Union (EU) set up a CCHP Committee to encourage the research, application, and development of CCHP; they predicted that CCHP will supply 20% and

⁎

25% of electricity and heat loads, respectively, in the entire EU by 2030, contributing to 23% of the EU’s carbon-reduction targets [4,5]. Other countries, such as Japan and China, have also published many policies to accelerate the application of CCHP [6,7]. The prime mover is the vital part of CCHP. Therein, the internal combustion engine (ICE) is most commonly used in CCHP systems below 1 MW [8]. According to research by the US Department of Energy, there are approximately 2400 CCHP projects using ICEs as their prime movers, accounting for 55% of the total project number in the US [8]. In Japan, there are 8900 ICEs for CCHP applications, accounting for 62% of the total installation number in 2012 [9]. However, the efficiency of the ICE is only approximately 40% [10], and a large

Corresponding authors. E-mail addresses: [email protected] (X. Wang), [email protected] (H. Tian).

https://doi.org/10.1016/j.apenergy.2019.114245 Received 23 August 2019; Received in revised form 19 November 2019; Accepted 23 November 2019 0306-2619/ © 2019 Elsevier Ltd. All rights reserved.

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Nomenclature A α Cp Cv cs D h L M m η ρ p Q t T u V W ω x Δx ηst ηsp

dis f g hs hx in l out o p r s t v w

Area (m2) Heat transfer coefficient (W/m2·K) Specific heat (kJ/kg·K) Turbine coefficient Isentropic gas speed (m/s) Diameter (m) Specific enthalpy (kJ/kg) Length (m) Mass (kg) Mass flow rate (kg/s) Efficiency Density (kg/m3) Pressure (kPa) Absorbed heat (kJ) Time (s) Temperature (K) Velocity (m/s) Volume Work (kW) Revolution speed (rpm) Concentration Unit length Isentropic efficiency of expander Isentropic efficiency of pump

Abbreviation ARS COP DORC DARS ECCS HT HP LT LP MB MV ORC WHRS

Subscript a con

Distillate Fluid Generator Heat source Heat exchange Inlet/inside Liquid Outlet Outside Pump Refrigerant Isentropy Turbine Vapor Wall

Average Condenser

Absorption refrigeration system Coefficient of Performance Dual-loop Organic Rankine Cycle Double-effect absorption refrigeration Electricity-cooling cogeneration system High temperature High pressure Low temperature Low pressure Moving boundary Moving volume Organic Rankine Cycle Waste Heat Recovery System

Liang et al. proposed an ECCS based on the Rankine–absorption refrigeration combined cycle to recover the waste heat from engine exhaust [24–26]. The structure of the ECCS is similar to that of the DORC: its upper stage is an HT ORC or RC, which is the same as that of the DORC, while the lower stage is an ARS. The electricity output, cooling capacity, total exergy output, primary energy ratio (PER), and exergy efficiency of the ECCS were studied in their research. The results indicated that the ECCS could achieve the equivalent efficiency of 27.5% at most, exhibiting much better utilisation of exhaust heat than the single-stage system. Sun et al. [27] proposed a similar ECCS consisting of a Rankine cycle and an ARS, and demonstrated 17.1% less consumed heat, compared with separate power and refrigeration systems. Mohammad et al. [28] also proposed the similar ECCS, while an expender was added in the ARS and showed a maximum primary energy efficiency of 75.79%. In addition, they did exergoeconomic analysis of an enhanced ECCS in another work [29], and the study indicated that the cost rate of the system decreased by nearly 21% at most. All the studies above only focused on the steady state of design condition, but the working condition of ICE actually changes frequently due to the fluctuating user load, leading to notable variation in exhaust waste heat. Under different engine loads, the exhaust temperature of light-duty engines varies from 500 to 900 °C and that of heavy-duty engines is in the range of 400–650 °C [30]. Simultaneously, the exhaust mass flow rate also changes greatly. Therefore, the WHRS often works under different conditions as well, and it is meaningful to study the system’s dynamic performance, including the transient behaviour and off-design performance. For example, Wen et al. [31] developed a simplified dynamic model to simulate the dynamic operation of a real ARS, aiming to enhances the model portability and computational efficiency when predicating the dynamic performance. The comparison between the simulation and experimental proved the model accuracy.

amount of energy is discharged by the waste heat of the exhaust, jacket water, and so on. Therefore, it is significant to recover the waste heat and many researchers have proven that an effective waste heat recovery system (WHRS) can increase the primary energy-utilisation rate of CCHP to greater than 80%; otherwise, it may be less than that of the traditional independent generation system [11]. The most important waste heat source of the ICE is its exhaust, which contains approximately 30–40% of the input energy and has a high temperature of approximately 450–600 °C [12]. The common methods for waste heat recovery from ICE exhaust in CCHP are the organic Rankine cycle (ORC) [13,14] and absorption refrigeration system (ARS) [15,16]. However, as the exhaust temperature is rather high and exhibits a large decrease after heat recovery, the conventional single-stage ORC or ARS cannot fully use the exhaust energy, leading to large exergy destruction [17,18]. According to the former researches [13–16], the efficiency and COP of conventional single-stage ORC and ARS for engine waste heat recovery are approximate 8–15% and 0.7, respectively. As a result, it is very meaningful to study cascade energy utilisation methods for waste heat recovery in exhaust, such as the traditional technology of the double-effect absorption refrigeration system (DARS) [16]. Recently, some other types of cascade WHRSs have been proposed. For example, the dual-loop ORC (DORC), consisting of a high-temperature (HT) and low-temperature (LT) ORC, is regarded as a promising method to recover exhaust heat by cascade utilisation, which has been studied by many researchers [19–22]. Therein, the recent study [22] indicated that the maximum efficiency of DORC could be nearly 21% and achieve 25% of the engine brake power. Because cooling is usually required in CCHPs, some researchers have proposed an electricity-cooling cogeneration system (ECCS) based on the cascade energy-utilisation principle in recent years, and the studies indicated that ECCS could output more equivalent power than DORC [23]. Previous studies on ECCS are detailed below. 2

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used more widely in CCHP systems because of its safety and reliability. Consequently, the LiBr–water working pair is adopted in this work. The upper and lower stages of the ECCS are connected by the HT cooling water, which is the cooling source of the ORC and the heat source of the ARS, as shown in Fig. 1. The schematic diagram of DARS is depicted in Fig. 2. The DARS has two generators: a high-pressure (HP) generator and a low-pressure (LP) generator. HT steam is produced in the HP generator heated by exhaust and condenses into water in the LP generator, thereby heating the LP solution. A schematic diagram of the DORC is shown in Fig. 3; its structure is quite similar to the ECCS. Their upper stages are both HT ORCs, whereas the lower stage of the DORC is ORC instead of ARS. A comparison of the three cascade WHRSs shows that they are all similar in structure and use the condensing heat of the upper stage as the heat source of the lower stage. To describe their dynamic performance conveniently in the below content, the upper stages in ECCS, DARS, and DORC are named HT ORC, HP ARS and HT ORC in DORC, respectively; the lower stages in the three systems are named LT ARS, LP ARS, and LT ORC, respectively.

Chatzopoulou et al. [32] developed an off-design optimisation tool and used it to predict the impact of varying heat source conditions on offdesign performance of ORC. Pili et al. [33] compared the methods of quasi-steady-state and dynamic simulation to predict the off-design performance of ORC under different working conditions and provided a valuable guideline for researchers to choose the most suitable method for their analyses. However, to the authors’ knowledge, except for DARS there is few research focusing on dynamic performance of cascade waste heat recovery systems, especially for ECCS. Only our previous research [34] focused on DORC dynamic performance. ECCS, DARS, and DORC have similar coupling structures, so to compare the dynamic performance of the ECCS with the other two systems and reveal the factors influencing the dynamic performance of the three systems, in this work their dynamic simulation models are developed. Based on these, the dynamic response speed and off-design performance of these cascade waste heat recovery systems are analysed in detail. This work contributes the following: (1) A module library is developed in Simulink and validated by basic thermodynamic cycles; thus, this library can be used to establish different dynamic simulation models of cascade waste heat recovery systems. (2) The dynamic performance of the ECCS is first investigated in detail by the simulation model. (3) The factors affecting the dynamic performance of each of the three systems are revealed and can be used to guide the composition of a high-efficiency cascade waste heat recovery system under all engine load.

3. Mathematical model 3.1. Module library The dynamic simulation models of the ECCS, DARS, and DORC, which are established by Simulink, are used to study their dynamic performance. The main modelling procedure involves first establishing component models and then connecting them together to develop a model of the complete system based on their interrelationships. These three systems consist of many components, so for the purpose of developing their models conveniently, a user-defined module library of common components in thermodynamic systems is established, as shown in Fig. 4. To easily change their parameters and allow the simple operation of modules, a graphical user interface (GUI) is added and the code is masked. The user only needs to set custom parameters in the GUI, when establishing component models of different design. Fig. 5 shows the GUI of the evaporator model established using the movingboundary method. The interface offers the modification of some structural and initial parameters of the heat exchanger. Using this module library, dynamic models of different thermodynamic systems can be established conveniently. For example, by selecting the components of the ECCS, DARS, and DORC from the library and combining them together according to their interrelationships, a dynamic model of the three systems can be established, as shown in Figs. 6–8. The detailed model of each component will be introduced later in the paper.

2. System description 2.1. Top cycle engine The gaseous-fuel engine studied herein is used to generate electricity for buildings, and its rated power is 1000 kW. Because the engine is used to generate electricity, the engine speed stays the same at all times to ensure constant power frequency; only the engine load changes. The heat balance experiment was performed under seven typical engine loads from 100% to 40%; the experimental parameters are shown in Table 1. Almost half of the waste heat is removed by the exhaust, and under 100% load, the exhaust waste heat accounts for 33% of the input energy according to the experimental data. This is nearly equal to the engine’s output power. Therefore, it is adopted as the waste heat source of the three cascade WHRSs in this study. 2.2. Bottom cycles of ECCS, DARS, and DORC The structure of the ECCS is shown in Fig. 1. The first stage is ORC with HT working fluid, which has a high critical temperature. HT working fluids can output large amounts of power when condensing around normal pressure, and the condensing temperature is still enough high to drive a single-effect ARS simultaneously. Single-effect ARS is quite suitable to recover LT heat [35]. LiBr–water and ammonia–water are the most common working pairs of absorption refrigeration systems. The former can only generate cooling above 0 °C and the latter can generate cooling below 0 °C; however, LiBr absorption refrigeration is

3.2. Component model The main component models of the three systems are described in this part. (1) Generator and absorber by moving volume method

Table 1 Heat-balance experiment data of the internal combustion engine. Parameter

Unit

Value

Speed Engine load Effective power Exhaust temperature Heat consumption rate Intake air volume flow rate Exhaust mass flow rate

r/min / kW °C MJ/kWh m3/s kg/s

600 40% 400 470 13.09 0.493 0.711

600 50% 500 515 11.76 0.596 0.859

600 60% 600 525 11.08 0.685 0.987

3

600 70% 700 527 10.59 0.763 1.101

600 80% 800 530 10.20 0.867 1.258

600 90% 900 532 10.26 0.975 1.414

600 100% 1000 540 9.85 1.161 1.563

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Fig. 1. Schematic diagram of the ECCS.

so the mass and energy conservation equations can be shown as Eqs. (7) and (8). Therein, subscripts of hs and hx present heat source and heat exchange, respectively. These two Eqs. (7) and (8) are also suitable for other heat exchangers of which heat or cold sources adopt lumped parameter model.

The model of generator can be extended to absorber [36], so only the former is introduced in detail here. The solution side of generator is dived into two parts as shown in Fig. 9: gas and liquid area. The volume of the two areas are tracked all the time in this model, so it is called moving volume (MV) method in the study. The subscript v, g, s and dis present vapor, generator, solution and distillate, respectively. Conservation equations of mass and energy for the two areas are shown as below: Conservation equations of mass and energy for gas area:

dMv, g dt

= ṁ v, dis, g − ṁ v, out , g

dM = mhs, in − mhs, in dt

(7)

dMhhs = mhs, in hhs, in − mhs, in hhs, out − Qhx , g dt

(8)

(1) (2) Evaporator and condenser

dMv, g h v, g

= ṁ v, dis, g h v, disg − ṁ v, out , g h v, out , g

(2)

(3)

These two heat exchanger models are nearly the same and divided into two areas like the generator model by MV method, but there is no LiBr mass conservation equation. Taking the condenser as example, its mass, energy and volume conservation equations are described as below:

(4)

dMv, con = ṁ v, in, con − ṁ l, con dt

(9)

Besides, there should be LiBr mass conservation equation and volume conservation equation in generator:

dMl, con = ṁ l, con − ṁ l, out , con dt

(10)

dMv, con h v, con = ṁ v, in, con h v, in, con − ṁ l, con hl, con − Qcon dt

(11)

dMl, con hl, con = ṁ l, con hl, con − ṁ l, out , con hl, con dt

(12)

dt

Conservation equations of mass and energy for liquid area:

dMs, g dt

= ṁ s, in, g − ṁ s, out , g − ṁ v, dis

dMs hs, g dt

Ms, g

= ṁ s, in, g hs, in, g − ṁ s, out , g hs, out , g − ṁ v, dis h v, dis + Qhx , g

dxs, g dt

+ x s, g

dMs, g dt

Vv = Vg − Ms, g / ρs, g

= ṁ s, in, g xs, weak − ṁ s, out , g xs, g

(5) (6)

The lumped parameter model is adopted on the side of heat source, 4

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Fig. 2. Schematic diagram of the DARS.

Vv, con = Vcon − Ml, con/ ρl, con

(13)

Aw Δxρw Cpw

The model above can be regarded as a condenser with a drum and the liquid at the outlet is always assumed to be saturation state. Comparing to the model with moving boundary method which will be introduced in the below content, it is much simpler and more robust. These two methods will be compared in detail thereinafter.

(4) Evaporator and condenser by moving boundary method Because there is phase change and the convective heat transfer coefficients of various phases are quite different, the dynamic model is established by the moving boundary (MB) method. The MB method has been regarded as the most popular and effective approach for dynamic modeling of heat exchangers with phase change, and proven to be precise enough by experimental data [37]. With the MB method, the phase change side of the evaporator is divided into three regions: the sub-cooling region, the two-phase region, and the super-heating region as shown in Fig. 11. The lumped parameter method is applied in every region. The general differential mass balance equation of the three regions is:

(3) Heat exchanger with no phase change The discrete method is used for the heat exchanger without phase change and large temperature drop. As shown in Fig. 10, the heat exchanger is regarded as a long straight tube. The model is dived into many segments along the heat exchange tube including the two sides of heat exchange fluid and pipe wall. Then the mass and energy conversation equations can be established in every segment. If the heat exchange fluid is liquid, the mass conversation equations can be ignored and there are only energy conversation equations as shown in Eqs. (14)–(16)

∫0

Cold fluid:

¯ f 1, ai A1 Δxρ¯f 1, ai Cp

dT¯f 1, ai dt

∫0

Hot fluid:

(

∂h¯f 2, ai f 2, ai

∂ρ¯

f 2, ai + h¯ f 2, ai ∂T¯

f 2, ai

)

dT¯f 2, ai dt

∂ (Aρ) dz + ∂t

∫0

Li

∂ṁ dz = 0 ∂z

(17)

Li

∂ (Aρh − Ap) dz + ∂t

∫0

Li

̇ ∂mh dz = ∂z

∫0

Li

αi πDi (Tw − Tr ) dz

(18)

A simplified energy balance equation of the wall is:

=

αout , i πDo Δx (Tw, i − Tf 2, ai ) + ṁ f 2 hf 2, i + 1 − ṁ f 2 hf 2, i

Li

The general differential energy balance equation of the three regions is:

= αin, i πDi Δx (Tw, i − Tf 1, ai ) + ṁ f 1 hf 1, i − ṁ f 1 hf 1, i + 1 (14)

A2 Δx ρ¯f 2, ai ∂T¯

dT¯w, ai = αout , i πDo Δx (Tf 2, ai − Tw, i ) + αin, i πDi Δx (Tf 1, ai − Tw, i ) dt (16)

cpw ρw Aw

(15)

dTw = αi πDi (Tr − Tw ) + αo πDo (Ta − Tw ) dt

(19)

Integrating the three Eqs. (16)–(18) over every region respectively, MB models for the evaporator can be obtained. More detail about the MB method can refer to [38]. Corresponding to the three regions, the

Pipe wall:

5

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Fig. 3. Schematic diagram of the DORC.

Fig. 4. Module library of common components in thermodynamic systems. 6

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found that the two methods have quite similar calculation results. Therein, the MV method responds more slowly because its initial volume of the liquid area is large, leading a great thermal inertia, but it can be adjusted by reducing the initial value. Besides, the working fluid at the outlet of condenser is always at saturation state by MV method, while there may be a little subcooling in MB method. Therefore, if the subcooling degree can be neglected, it is believed that MV method is a good selection to simply the model and calculation. (5) Pump, turbine and valve A displacement pump is applied in the study and the mass flow rate can be expressed as below [38]:

mpump = ηv ·ρpump ·Vcyl·ω

(20)

Therein, ηv, ρpump, Vcyl, and ω are the volumetric efficiency, the working fluid density at the pump inlet, the cylinder volume and pump speed. The working fluid enthalpy after ideal isentropic pumping is hspout. hpin and hpout are the actual enthalpy at the inlet and outlet of pump, respectively. ηsp is the isentropic pump efficiency and its value under off-design conditions can be approximated as a polynomial of the ratio of the fluid flow rate to the design value as shown in Eq. (23) [40]. ηg is the electromotor efficiency assumed to be a constant value of 0.9. Then the consumed work of pump is:

Wp = m (hpout − hpin )/ ηg

(21)

hpout = hpin + (hspout − hpin )·ηsp

(22)

ηsp

Fig. 5. GUI of evaporator model by moving-boundary method.

ηsp0 other side is divided into three regions as well. The condenser model is similar to evaporator model, but during the simulation the subcooling region may disappeared sometimes, while a little superheat in evaporator must be maintained by control system for the purpose of protecting turbine blades. When the subcooling region disappears, the MB model with three regions cannot calculate stably, so there should be a switching model between the models of two and three regions [39], which is quite complex and unstable. Whereas, the MV method mentioned above can avoid the switching problems and it is compared with MB method in this study as shown in Fig. 12. It can be

3 2 V̇ V̇ V̇ = c1 ⎛ ⎞ + c2 ⎛ ⎞ + c3 ⎛ ⎞ + c4 ̇ ̇ ⎝ V0 ⎠ ⎝ V0 ⎠ ⎝ V0̇ ⎠ ⎜

⎟

⎜

⎟

⎜

⎟

(23)

The turbine can be simplified as a nozzle [41]. The pressure ratio (the ratio of the pressure before and after the expansion) is much larger than the critical pressure ratio of the fluid under most conditions, so the influence of turbine outlet pressure on the mass flow rate can be ignored [41]:

ṁ t = Cv ρin p

(24)

Therein, Cv is a coefficient, ρin is working fluid density at turbine inlet, and p is evaporating pressure. The calculation of turbine power is similar to that of pump as shown in Eqs. (25) and (26).

Fig. 6. Dynamic model of the ECCS. 7

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Fig. 7. Dynamic model of the DARS.

Wt = m (htin − htout ) ηg

(25)

htout = htin − (htin − hsout ) ηst

(26)

established in this study is quite consistent with the model in the literature [36]. At the same time, it can be found that the dynamic response speed of ARS is quite low. The ORC model has been validated experimentally in our previous study [43] as shown in Fig. 14; its results exhibit good consistency. Compared with the ARS, the dynamic response speed of ORC is considerably faster.

The isentropic efficiency of turbine under off-design conditions is described as the isentropic efficiency under design condition (0.7) multiplying by two correction factors in this study [42]. As shown in Eqs. (27)–(29), the first correction factor is related to the change of u/cs. Therein, u and cs are impeller tangential speed and isentropic gas speed, respectively. The second correction factor is related to the change of mass flow rate. The specific turbine design decides the other empirical parameters like a1, b1, c1.

CF 1 = a1 (u/ cs )2 + b1 (u/ cs ) − c1

(27)

CF 2 = a2 (m / m 0)2 + b2 (m / m 0) + c2

(28)

ηst = CF 1CF 2ηs0

(29)

4. Results and analysis In this section, the optimal design of the three cascade WHRSs is first studied under the static design condition. Based on their optimal design parameters, dynamic models are established. Then the dynamic performance of ECCS, including the system response speed and offdesign performance, is analysed in detail under seven typical engine loads and compared with the DARS and DORC. Finally, the single-stage ARS is analysed in more detail to reveal its perfect adaptability to working conditions. Because the output of the ORC is electricity and that of ARS is cooling, which have different energy quality, they cannot be compared directly. The evaluation method of combined cooling and electricity is a controversial problem [44]. The exergy analysis, primary energy-utilisation rate and equivalent power are three main methods used by many researchers [44–48]. However, primary energy-utilisation rate does not distinguish the quality of cooling and electricity, so it is not a very objective evaluation indicator. Exergy analysis is somewhat unclear in practical engineering [45]. Typically, electrical refrigeration systems are used as auxiliary equipment in CCHP systems; thus, the cooling energy in an absorption refrigeration system is converted to the corresponding electrical power consumed by electric refrigeration in many studies [45–48]; this is referred to as the equivalent power. In this

3.3. Model validation In this section, the basic single-stage cycles of the ARS and ORC in the cascade waste heat recovery systems are validated, respectively. To verify the reliability of the ARS model, a model based on data in literature [36] is established in this study. The model in reference [36] has been validated carefully with experimental data, and the results indicated that the difference between the simulated and measured temperatures in the important heat exchangers, such as the generator and evaporator, is always low (within ± 0.2 °C). Therefore, the model is regarded to be reliable. The calculation results of the two models are compared in Fig. 13, which shows the variation in the absorption heat and the coefficient of performance (COP) when the temperature of the heat source rises by 10 K at 100 s. It can be seen that the model 8

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Fig. 8. Dynamic model of the DORC.

these figures, it is apparent that the ECCS and DARS have similar optimal equivalent output power, while that of the DORC is clearly much smaller. As shown in the optimisation results, when the evaporation pressure of the HT ORC becomes more than 2 MPa, the output power of ECCS and DORC does not increase with it obviously anymore. To prevent high operation pressure, the design evaporating pressure is 2 MPa for the HT ORCs in these two systems. The condensing temperature of the HT ORC in the ECCS is designed to be 383 K, enabling the ECCS to output maximum power at an evaporating pressure of 2 MPa. In contrast, it is designed to be 409 K (200 kPa) in the DORC, because the output power only changes slightly with the condensing pressure, and in order to avoid the formation of vacuum in the condenser, the condensing pressure should be high. For the DARS, when the HP generation temperature exceeds 433 K, the equivalent power no longer visibly increases. To reduce the risk of equipment corrosion and solution crystallisation due to high temperature, the generation temperature and pressure are designed as 433 K and 100 kPa, respectively. The main design parameters of the three systems are listed in Table 2.

study, the equivalent power method is adopted in the analysis. Eq. (30) describes the calculation of the equivalent power. Therein, the COP is 4.6, referring to an electrical refrigeration system which condenses and evaporates under 308 K and 278 K with a compressor isentropic efficiency of 0.7.

Weq = Qcool/ COPec

(30)

4.1. Optimal design under steady state To compare the dynamic performance of the three systems scientifically, the reasonable design parameters should be determined at first under the rated engine load. All the systems have the same conditions of the heating and cooling source, as enumerated in Table 2. Besides the condensing temperature, which is limited by the cooling water temperature, the other most important design parameters are the evaporating and condensing pressure or temperature of the HT ORC in the ECCS and DORC, and the generation temperature and pressure of the HP ARS in the DARS. Here, the HT ORC condensing pressure determines the generation temperature of the lower stage ARS and the evaporating temperature of the lower stage ORC. The optimisation of these parameters for the three systems is shown in Figs. 15–17. From 9

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In Figs. 18 and 19, it is apparent that the performance of the DORC is the worst under all engine load and decreases the fastest. For the other two systems, under 100% engine load the equivalent output power of the ECCS is only slightly greater than that of the DARS, as well as the equivalent thermal efficiency. With the decrease in engine load, the equivalent power and efficiency of the ECCS decrease more slowly than those of the DARS, and the gap between them is larger and larger under the first four kinds of engine load. However, from the fifth engine load, the gap between them stops increasing noticeably and even becomes somewhat small. The total output power of the cascade system is the sum of the power of the upper and lower stages, so the output of each single stage in these systems is analysed below. (1) Response speed analysis Fig. 20 describes the variation process of the output power of the HT ORC and the cooling of LT ARS in the ECCS. With the decrease in engine load the exhaust waste heat reduces, so the output power and cooling also decline. As can be seen from Fig. 20, the dynamic change in power is considerably faster than that in cooling. ORC exchanges heat with the exhaust directly, so the fluctuation of the heat source immediately leads to a change in the ORC state and then in the state of the HT cooling water. The HT cooling water is both the cold source of the ORC and the heat source of the ARS. The response of the ARS is slow in addition to the tardy variation in the heat source, so the change in the ARS state is slower still. In turn, the slow change in the ARS state delays the variation in the HT cooling water temperature at the generator outlet, which is also the temperature at the ORC condenser inlet. In other words, the interaction among the HT cooling water and the two cycles leads to a long stabilisation time of the ARS as well as the entire system. By contrast, the HT ORC can essentially become stable in a relatively short time, because the variation in its heat source involves stepwise changes, and when the temperature of the HT cooling water varies slightly, the ORC state is no longer sensitive to the temperature fluctuation. Similarly, the dynamically varying process of the DARS and DORC is also affected by the interaction between the upper and lower stages. Therein, because ORC responds much faster than ARS, the DARS with HP ARS instead of HT ORC responds more slowly than the ECCS, as shown in Figs. 18 and 21. In contrast, the DORC with LT ORC instead of LP ARS responds much more quickly than the ECCS, as shown in Figs. 18 and 22. (2) Off-design performance analysis To compare the variation rate in the off-design performance of the

Fig. 9. The Scheme of the generator model.

4.2. Dynamic performance analysis In this part, to analyse the dynamic performance of the three systems, the engine load decreases by 10% every time. Dimensionless power and efficiency are adopted for analysing the variation rate of the system performance conveniently; these are defined as the ratio of the value under off-design conditions to the design value. Fig. 18 describes the dynamic variation in their output power and equivalent power. Fig. 19 depicts the static system efficiency under the seven kinds of engine load. It should be noted that because the DORC responds much faster than the other cascade systems, its engine load declines every 700 s to reduce the calculation time, whereas the others decline every 4000 s to reach a stable state. As shown in the model validation above, the dynamic response of ARS is much slower than that of ORC and in addition to the gradual variation in its heat source (the HT cooling water or the refrigerant of the upper stage), the whole ECCS and DARS respond much more slowly, as shown in Fig. 18, due to the coupling of the two tardy systems. This will be explained in more detail hereinafter.

Fig. 10. The discretization model of the heat exchanger. 10

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Fig. 11. The schematic of the MB model with three regions.

less than those of the DARS under certain conditions. In other words, the variation in the turbine efficiency has a considerable impact on the off-design performance of the ECCS. In conclusion, the two factors of condensing pressure and turbine efficiency lead to the slow decrease in equivalent power of the ECCS at first and then becoming faster and faster. The power variation in the HT ORC of the DORC is also affected by these two factors with a similar trend, but it has a higher design condensing pressure and thus, the variation is not completely the same. As for the LT ORC in the DORC, its output power reduces most quickly among all of the single-stage cycles, because its thermal efficiency declines obviously with the dropping evaporating pressure, as shown in Fig. 24, which has been analysed in detail in our previous research [43]. Owing to the obviously bad offdesign performance of the LT ORC, the output power of the DORC decreases most quickly. These figures also show that as the engine load decreases, the output and COP of the LT ARS in the ECCS reduces most slowly all the time. By contrast, those of the LP ARS with the same design parameters in the DARS decrease more quickly. For systems with the same design parameters, the more slowly the load reduces, the more slowly the COP as well the output decrease. Fig. 26 shows the dimensionless absorbed heat under different static conditions. As shown in the figure, the absorbed heat of the ARS in the ECCS changes more slowly, which means its load changes more slowly as well. At the same time, it can be seen that when the absorbed heat of the two ARSs is similar under a high load, their COPs are quite similar as well. The absorbed heat of the ARS in the ECCS is the discharged heat in the HT ORC condenser, and the ratio of it to the ORC output power is (1-η)/η. η is the thermal efficiency of ORC. Because under the 100–80%

Fig. 12. Comparison of the condenser models by MV and MB methods.

single-stage cycles in the three cascade systems, Figs. 23 and 24 describe the dimensionless power and efficiency of each under seven typical engine loads. Table 3 lists the efficiency and COP values of different single-stage cycles. At the beginning, the output power of the HT ORC in the ECCS decreases most slowly, but then decreases increasingly faster, especially under 40% engine load when the decline speed nearly reaches the maximum. In our previous study [43], we showed that in the DORC, the condensing pressure of the HT ORC decreases as the engine load reduces, which contributes to improving the system efficiency; thus, its power reduces slowly at first. This is also suitable for the HT ORC in the ECCS, as shown in Fig. 24. However, with declining engine load the turbine efficiency decreases faster and faster so that the ORC efficiency declines quite quickly under low engine load, as shown in Fig. 25. Therefore, if the off-design efficiency of the turbine is too bad, the equivalent power and thermal efficiency of the ECCS may be

Fig. 13. Validation of the dynamic model of absorption refrigeration system. 11

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Fig. 14. Validation of the dynamic model of ORC [43]. Table 2 Basic design parameters of ECCS and DARS. Parameters

ECCS

DARS

DORC

HT evaporating pressure [kPa] HT condensing temperature [K] HP generation pressure [kPa] HP generation temperature [K] HT evaporating pressure [kPa] LT condensing temperature [K] ARS Condensing temperature [K] ARS evaporating temperature [K] ARS absorption temperature [K] Cooling water inlet temperature [K] Refrigerating water inlet temperature [K] Final exhaust temperature [K]

2000 383 / / / / 311 278 312 303 285/280 433

/ / 100 373 / / 311 278 312 303 285/280 433

2000 383 / / 2000 311 / / / 303 / 433

Fig. 16. Total equivalent power of DARS varying with generation temperature and pressure of high-pressure stage.

Fig. 15. Total equivalent power of the ECCS varying with the ORC evaporating pressure and condensing temperature.

engine load the ORC efficiency remains nearly constant, the dimensionless absorbed heat of the LT ARS is almost the same as the dimensionless ORC power, as shown in Fig. 26. With the decrease in the engine load, the ORC efficiency decreases more and more obviously and (1-η)/η becomes large; thus, the dimensionless absorbed heat becomes greater than the dimensionless ORC power, as shown in Fig. 26. In DARS, the absorbed heat of the LP ARS is the condensing heat of refrigerant from HP generator and almost equal to its evaporating heat, so the dimensionless absorbed heat of LP ARS is quite close to the dimensionless output cooling of HP ARS, as shown in Fig. 26. In other words, the relationship between the output of upper stage and the absorbed heat of lower stage in the ECCS is contrary, while that in the DARS is consistent. Evidently, the former cascade energy-utilisation structure with an inverse relationship between the two stages are beneficial to maintain a high system performance under low engine

Fig. 17. Total power of DORC varying with evaporating and condensing pressure of HT ORC.

loads. In a word, compared with the HP ARS of the DARS, the HT ORC of the ECCS exhibits a better off-design performance; moreover, the lower stage ARS of the ECCS also exhibits a better off-design performance than the LT ORC. Furthermore, the structure of the ECCS is the most suitable for maintaining a satisfactory off-design performance of the lower stage as well as the whole system. Consequently, the ECCS shows the best performance under all engine loads among the three systems. However, if the efficiency of the turbine in ORC is quite poor under a low engine load, these above advantages may be covered up so that the 12

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Fig. 21. Variation in cooling capacity of HP and LP stage under different engine loads.

Fig. 18. Variation in equivalent power of ECCS and DARS under different engine loads.

Fig. 22. Output power variation of HT and LT ORC in ECCS under different engine loads.

Fig. 19. Static equivalent efficiency of ECCS and DARS under different engine loads.

Fig. 23. Dimensionless power of the four single-stage systems under different engine loads.

turbine machinery, so its efficiency cannot be affected severely by the turbine efficiency, as in the case of the ORC. Therefore, the single-effect ARS exhibits the best off-design performance. The main factors affecting the COP are generation temperature, condensation pressure, evaporating pressure, and absorption temperature. Changes in COP are analysed from these parameters as described herein. Figs. 27 and 28 describe the variation in the four parameters. With the decline in engine load, the absorbed heat of ARS decreases, so the final generation temperature decreases, as does the mass of the produced refrigerant water. Because of the reduction in refrigerant, the heat load in the absorber decreases, while the mass flow and temperature of the cooling water remain unchanged. This leads to a decrease in the absorbing temperature, as shown in Fig. 28. For a similar reason, the condensing pressure drops as well. In this model, the cooling water in the evaporator is maintained at 280 K at all times by a PID controller. Because the dynamic response of the ARS is quite slow, it is very easy to control the temperature as 280 K at all times. When the

Fig. 20. Variation in power and cooling of ECCS under different engine loads.

performance of the ECCS under certain engine loads may be worse than that of the DARS. 4.3. Detailed analysis of ARS off-design performance Fig. 24 shows that the COP of the ARS changes considerably more slowly than the ORC efficiency. As shown in the figure, the dimensionless COP of the LT ARS is 0.939 under 40% engine load, while the dimensionless efficiency of the HT ORC in the ECCS is 0.823 and that of the LT ORC is only 0.606. Moreover, the ARS does not use 13

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Fig. 24. Dimensionless power of the four single-stage systems under different engine loads.

Fig. 26. Dimensionless absorbed heat and output of the single stages in ECCS and DARS.

Table 3 Efficiency and COP of different single-stage systems. Engine load

HT ORC in ECCS

HT ORC in DORC

LT ORC

LP ARS

HP ARS

LT ARS

100% 90% 80% 70% 60% 50% 40%

0.1215 0.1228 0.1225 0.1207 0.1171 0.1122 0.1012

0.1012 0.1013 0.1003 0.0981 0.0947 0.0905 0.0823

0.1022 0.0997 0.0961 0.0912 0.0854 0.0793 0.0622

0.7231 0.7223 0.7202 0.7153 0.7068 0.6941 0.6595

0.6822 0.6794 0.6752 0.6691 0.6592 0.6461 0.6114

0.7223 0.7218 0.7199 0.7171 0.7114 0.7034 0.6789

Fig. 27. Variation in evaporating pressure and condensing pressure of ARS.

Fig. 25. Variation in turbine efficiency and ORC efficiency under different engine loads.

mass flow of refrigerant reduces, the evaporating heat amount decreases, while the temperature of cooling water does not change, so the evaporating temperature will rise to shrink the heat transfer temperature difference, reducing the exchange heat amount. The rise of evaporating temperature, decrease in condensing pressure and absorption temperature all contribute to improving COP. By contrast, only the decrease in generation temperature goes against improving COP. For the above reasons, the COP of ARS decreases slightly as engine load drops, which shows perfect off-design performance.

Fig. 28. Variation in generation and absorption temperature of ARS.

models, the dynamic performance of the ECCS is analysed in detail and compared with that of the DARS and DORC. The analysis results indicate that 1. The optimal outputs of ECCS and DARS are nearly the same under static design conditions, whereas that of DORC is considerably smaller, because based on equivalent power, the ARS is more suitable for low temperature waste heat recovery than LT ORC. Moreover, the COP of ARS decreases slightly as the engine load decreases, more slowly than the LT ORC; thus, the ARS contributes

5. Conclusion In this work, a module library is established and validated to conveniently develop different dynamic simulation models of cascade waste heat recovery systems (ECCS, DORC, and DARS). Based on these 14

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to improving the off-design performance of the cascade system. 2. Owing to the coupling and interaction of the two single-stage cycles, all the three cascade systems respond much more slowly than the basic single-stage cycles. Because the ARS responds considerably more slowly than ORC, the dynamic response speed of the DARS is slower than that of the ECCS and much slower than that of the DORC. 3. The equivalent power of ECCS decreases the most slowly among the three systems, which means it has perfect adaptability to working conditions. This is because HT ORC has better off-design performance than ARS for HT heat, whereas ARS is better than LT ORC for LT heat. However, this advantage is affected greatly by the off-design turbine efficiency, and if the turbine efficiency decreases by a large value under low engine loads, these advantages may be lost. 4. The relationship between the output of the upper stage and the absorbed heat of lower stage is contrary in ECCS and DORC, whereas it is consistent in DARS. The calculation results indicate that the former cascade energy-utilisation structure with a contradictory relationship between the two stages helps maintain good offdesign performance under low engine loads.

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