Dynamic Simulation of Partial Load Operation of an Organic Rankine Cycle with Two Parallel Expanders

Abstract

The parallel expander ORC system is one of the solutions for providing an additional power output by improving the partial-load performance of an ORC. The parallel expander system corresponds to partial-load conditions by switching between various combinations of the expanders. During this process, the dynamic behavior occurs, which have not been characterized well in the open literature according to the best of the authors’ knowledge. In this study, we developed a dynamic modeling of an ORC system using dual expanders (DE-ORC) to study the dynamic responses during its mode changes. System components were simulated using an open-source library of ThermoCycle written in Modelica language. For each component, empirical parameters were implemented based on the experimental results. Furthermore, during the mode change that involved going from dual expander mode to singular expander mode, and to prevent the formation of the droplet in the expanders, a control strategy was proposed and simulated. The strategy involved lowering of the mass flow rate and then shifting the mode. Several timings between flow rate lowering and shifting the mode were analyzed, and the optimum shifting time was found to be in between 40 to 50 s.

1. Introduction

The thermal efficiency plays an important role in the competitiveness of the energy intensive industries. Therefore, various technologies have been proposed, developed and applied to enhance the efficiency [1]. Moreover, considering the waste heat released from the European industrial sectors, approximately, 30% are reported to present at temperature below 200 °C, and around 25% were reported to be in between 200 °C to 500 °C [2]. Another potential waste heat source is the exhaust from the cars, buses, trucks, and ships [3,4]. The temperature in this range can be harnessed by using the organic Rankine cycle (ORC) technology in a relatively efficient and economical way compared to other devices [5].

The ORC uses organic compounds as its working fluids which enables the exploitation of the low-grade heat from the above-mentioned heat sources at low to medium temperatures, attributing to their low normal boiling temperatures [6]. The ORC has been studied extensively and there are many dimensions along which the research could be conducted. In this regard, the review on the selection of the working fluids was performed by Bao et al. [7]. Similarly, for the working fluids with inclusion of heat sources and cooling media was provided by Qyyum et al. [8]. Moreover, for different architectures for the ORC was provided by Lecompte et al. [9]. Furthermore, regarding the expanders, the review was conducted by Song et al. [10], Imran et al. [11], Zhao et al. [12], and by Pethurajan et al. [13].

It has been reported that the heat source characteristics and system design have a significant impact on ORC systems performance [14]. One of the major concerns pertaining to the ORC operation is the management of fluctuations, particularly related to the vehicular and solar applications. Proper address of this concern is beneficial in order to yield maximum benefit in terms of economics and environment [15]. The issues that can arise from poor handling of the ORC system can be sought from the review performed by Imran et al. [16]. In order to achieve his aim, the dynamic modelling is the prerequisite of developing the appropriate control strategy. In this regard, Wei et al. [17] reported two methodologies for the transient modelling of heat exchangers of an ORC unit. Furthermore, Quoilin et al. [18] developed a dynamic model and presented a control strategy for a variable heat source. Casella et al. [19] presented a component library based on experimentally validated systems. Additionally, in another study, Quolin et al. [20] presented a Modellica library containing the dynamic models. An innovative method for incorporating the dynamic performance of the ORC system into the initial design phase was provided by Pierobon et al. [21]. The thermodynamic cycle computation and system component design were carried out by the numerical model. A multiobjective optimization approach was utilized to find several equally ideal system configurations using the results of these simulations. Other than this, an ORC-based solar thermal power system with an integrated multitube shell and tube thermal storage system was dynamically modelled by Lakhani et al. [22]. Apart from it, a verified transient model of an ORC unit for waste heat utilization in a diesel truck was given by Hustler et al. [23]. The transient behavior of the ORC system is further influenced by the thermal and physical characteristics of the working fluids. According to the rise and settling time, and time constant, Shu et al. [24] evaluated the dynamic response of 14 distinct working fluids. The findings imply that working fluids with low critical temperatures respond more quickly than those with high critical temperatures. The knowledge of the system is based on measurements or prior simulations, and the data-driven models use computational techniques like machine learning [25] or transfer function identification to create models with great computational efficiency [26]. Additionally, a numerical study was conducted by Bamgbopa and Uzgoren [27] investigated the dynamic reaction of the ORC and presented a dynamic model when the thermal energy available changed, either gradually or suddenly. It was shown that changing flow rates assisted preserve steady state operation in addition to increasing thermal efficiency. Similarly, Yousefzadeh and Uzgoren [28] introduced a dynamic numerical model to capture the dynamic response of the ORC for the changes in some key parameters like the working fluid pump and expander speed while still operating with the same heat source condition. In addition to it, Zhou et al. [29] also presented a modelling for a small scale ORC, capable of delivering 4 kW of electricity. The variations of the ORC against the heat source variations were identified and reported.

Expanders are a crucial component of an ORC. In this regard, Zhu et al. [30] conducted experimental findings of the effect of resistive loads on a scroll expander ORC system. The expanders are generally classified into positive displacement type and the turbomachines. Kaczmarczyk [31] presented experimental findings of the expanders parameters and isentropic efficiency of the ORC system operated in series and parallel modes respectively. The maximum efficiency of the system in series and parallel modes are reported. In this regard, Witanowski et al. [32] performed the computational fluid dynamics (CFD) analysis of a single stage axial turbine. The prospects of the turbine at various operational parameters were studied. Kaczmarczyk and Żywica [33] conducted investigation on ORC based scroll expanders under constant electrical load and thermal power of heat source. They reported the maximum efficiency of the systems as 49% with a maximum power generation of 976 W. While Kaczmarczyk et al. [34] reported the performance scroll expanders operated in parallel in a regenerative ORC system. They concluded that scroll expander could be used in a small, distributed cogeneration system.

Considering the efficacy and wide utilization of the models developed and discussed above, a model of similar nature has been attempted for the parallel expander with different capacities (DE-ORC) [35]. The experiments on the ORC rig [35], established and supervised by one of the authors, revealed good practical demonstration to handle the variations in the heat source. The switching between different modes of operations enabled to ensure a better thermal performance of the system as compared to the single expander ORC system. Despite, this, the rigorous dynamic modelling required for such an ORC system remains unexplored, to the best of the authors’ knowledge. Therefore, in this study, the dynamic modeling and its validation is carried out and the discussion has been provided. The results presented thereof can be implemented and utilized for the applications that employ heat sources with variable parameters.

2. Overview of Experimental Setup and Data

The schematic of the experimental setup is shown below in Figure 1a, and the pictorial view of the expanders are shown in Figure 1b. For the experimental inquiry, a PE-ORC system having two scroll expanders of various capacities was developed. The other prominent components were a pump, an evaporator, and a condenser. The open drive expander, altered from an air compressor, manufactured by Kyungwon Machinery Co., LTD, had the upper pressure limit, expansion ratio, and the swept volumes of 10 bar, 4.05, and 25 cm³/rev, respectively. Whereas, the semi hermetic expander, manufactured by Air Squared, Inc., Lafayette, USA, possessed the upper pressure limit of 13.8 bar, expansion ratio of 3.5, and swept volume ratio of 12 cm³/rev. An electromagnetic permanent magnet motor and a torque sensor were both directly coupled to both of the scroll expanders. Furthermore, motor drivers managed the rotational speeds of expanders.

To measure the pressure, the Piezo resistive pressure transmitters with ranges 0–5 bar/0–15 bar with an accuracy of ±0.5% F.S. were used. On the other hand, the mass flow rate was determined using the Coriolis flow meter, was employed having the range from 0–0.305 kg/s, with an accuracy of ±0.1% reading. A Magneto type motor and strain gauges were used to control the rotational speed and measure the torque. The motor had a range of 0–10,000 rpm, and that of the strain gauges was 0–50 Nm. Whereas the accuracy of the rotational speed and the strain gauge was ±1 rpm and ±1 F.S. Apart from it, the k-type thermocouples were used to measure the temperature.

To conduct the experimental study, R245fa was chosen as the working fluid in this investigation because of its suitability for the ORC system in terms of thermodynamic, environmental, and safety parameters. Apart from it, the air infiltration issue into the cycle can be avoided since the condensing pressure of R245fa is similar to the atmospheric pressure at ambient temperature. The working fluid was pumped using a volumetric pump, and the evaporator and condenser were both plate-type heat exchangers. The evaporator received pressured hot water produced by a 150 kW electric heater as a heat source. The condenser received cooling water from an air-cooled chiller that served as a heat sink. The straightforward on/off controls in each component can be used to regulate the temperatures of the heat source and heat sink. Frequency drivers regulate the flow rates of the working fluid, heat source, and heat sink. A Coriolis flow meter was fitted to monitor the mass flow rate of the working fluid, and pressure transmitters, and k-type thermocouples were placed at the inlets and outputs of the major components.

The control modes and the experimental conditions are provided in

Table 1. Control modes of DE-ORC system.

Operating Mode	Open-Drive Scroll Expander (Rotating Speed: 2000 rpm)	Hermetic Scroll Expander (Rotating Speed: 2200 rpm)
SINGLE MODE 1	ON	OFF
SINGLE MODE 2	OFF	ON
DUAL MODE	ON	ON

and

Table 2. Experimental conditions of DE-ORC under different operating modes.

Operating Mode	$$\begin{gathered} {\dot{\mathit{m}}}_{\mathit{h}\mathit{f}} \\ [\mathbf{kg}/\mathbf{s}] \end{gathered}$$	Thf,in [°C]	Pump [Hz]	$$\begin{gathered} {\dot{\mathit{m}}}_{\mathit{r}} \\ [\mathbf{kg}/\mathbf{s}] \end{gathered}$$	Pexp, in [bar]	Texp,in [°C]	Pexp, out [bar]	Texp, out [°C]	Qin [kW]	Wshaft [kW]
SINGLE	1.66	110	8	0.0352	5.548	88.5	1.454	70.45	9.448	0.368
MODE 1			9	0.0396	6.146	92.75	1.507	70.79	10.59	0.5428
			10	0.0438	6.735	95.42	1.574	70.35	11.63	0.705
			11	0.0485	7.503	97.36	1.759	68.90	12.82	0.9007
			12	0.0547	8.184	98.71	1.671	68.00	14.42	1.065
			13	0.0598	8.832	99.94	1.687	66.93	15.7	1.236
			14	0.0648	9.431	101.2	1.665	66.29	17	1.393
			15	0.0699	10.06	102.2	1.662	66.10	18.26	1.507
			16	0.0751	10.71	103.3	1.666	65.53	19.57	1.657
			17	0.08	11.22	104	1.569	65.03	20.76	1.767
			18	0.0849	11.88	104.9	1.621	64.53	21.92	1.895
SINGLE	1.65	120	5	0.0189	5.169	100.8	1.233	77.72	5.274	0.3198
MODE 2			6	0.0228	6.053	101.9	1.305	76.69	6.292	0.4049
			7	0.0279	7.337	103.5	1.526	75.18	7.681	0.5354
			8	0.0322	8.29	104.7	1.583	74.33	8.825	0.6366
			9	0.0367	9.279	105.9	1.634	73.28	10.01	0.7502
			10	0.0414	10.31	107.4	1.685	72.64	11.23	0.8676
			11	0.0472	11.31	108.4	1.477	71.73	12.74	0.9736
			12	0.0526	12.38	109.7	1.421	71.31	14.09	1.067
			13	0.0581	13.26	110.7	1.155	70.35	15.48	1.163
DUAL	1.65	120	12	0.0566	5.158	89.51	1.526	70.70	15.13	0.6906
MODE			14	0.0671	5.983	93.6	1.492	71.05	17.91	0.9839
			16	0.0777	6.799	98.84	1.443	73.52	20.76	1.275
			18	0.0881	8.287	100.34	2.077	70.91	23.38	1.685
			20	0.0994	9.175	101.35	2.040	69.69	26.23	1.955
			22	0.1099	10.03	102.4	2.041	68.55	28.81	2.228
			24	0.1214	10.71	103.4	1.782	67.50	31.56	2.49
			26	0.1315	11.44	104.1	1.688	66.75	33.95	2.669
			28	0.1404	12.02	104.7	1.541	65.54	35.99	2.89

.

3. Mathematical Modelling

The mathematical modelling of the expander, evaporator, and pump were modeled in the Modelica programming language (Dymola 17). To conduct the dynamic modelling, the open-source library of ThermoCycle was used. ExternalMedia library was used for calculating thermophysical properties of fluids. Figure 2 shows the dynamic modeling of DE-ORC with different capacity expanders.

3.1. Expander

The angular momentum of the expander is negligible because it is small compared to the dynamic response due to the phase change of the heat exchanger [36]. Thus, the steady state model of the scroll expander can be used to study dynamic operating characteristics [18]. For each scroll expander, a model developed by Lemort et al. [37] was used to derive the empirical parameters as shown in Figure 3. This expander model calculates the filling factor, $\varnothing$ and expander efficiency, ${\eta }_{\exp }$ considering internal leakage, pressure losses, mechanical losses, and thermal losses. The expander power output was calculated using Equation (1):

$${\dot{W}}_{\mathrm{shaft}}={\dot{m}}_{\mathrm{wf}}·w_{\mathrm{shaft}}·{\eta }_{\exp }$$

(1)

where ${\dot{W}}_{\mathrm{shaft}}$ is the expander shaft power, ${\dot{m}}_{wf}$ is the working fluid mass flow rate, and $w_{\mathrm{shaft}}$ is the shaft work. The expander inlet density was calculated using the following Equations (2) and (3):

$${\rho }_{\exp ,\mathrm{in}}=\left(60·{\dot{m}}_{\mathrm{wf}}\right)/\varphi ·V_{\mathrm{swept}}·N_{\mathrm{rot}}$$

(2)

$$\varphi =\frac{{\dot{m}}_{\mathrm{wf}}·v_{\exp ,\mathrm{in}}}{{\dot{V}}_{\exp ,\mathrm{swept}}}$$

(3)

where ${\rho }_{\exp ,\mathrm{in}}$ is the expander inlet density, $V_{\mathrm{swept}}$ is the expander swept volume, $v_{\exp ,\mathrm{in}}$ is the expander inlet specific volume, and $N_{\mathrm{rot}}$ is the expander rotational speed. ${\dot{V}}_{\exp ,\mathrm{swept}}$ is the theoretical volume flow rate, and it can be calculated by multiplying the swept volume and the rotating speed.

The filling factor and the expander efficiency are the functions of the rotating speed and the pressure ratio.

$$\varphi =\mathrm{f}\left(N_{\mathrm{rot}},r_{exp}\right)$$

(4)

$${\eta }_{\exp }=\mathrm{f}\left(N_{\mathrm{rot}},r_{exp}\right)$$

(5)

These functions were simplified to a linear equation to reduce the computing cost as Equations (6)–(9). Figure 4 shows the filling factor and efficiency over different pressure ratios and rotating speeds.

$${\varnothing }_{op}=2.091-0.0008011·N_{\mathrm{rot}}+0.011·r_{exp}+0.0000001441·N_{\mathrm{rot}}{}^2-0.000006749·N_{\mathrm{rot}}·r_{exp}$$

(6)

$$\begin{array}{cc}{\eta }_{\exp ,\mathrm{op}}=-95.47\hfill & -0.08464·N_{\mathrm{rot}}+135.7·r_{exp}+1.449\times {10}^{-5}·N_{\mathrm{rot}}{}^2+0.04124·N_{\mathrm{rot}}·r_{exp}-43.17·r_{exp}{}^2\hfill \\ \hfill & -7.195\times {10}^{-6}·N_{\mathrm{rot}}{}^2\ast r_{exp}-0.004323·N_{\mathrm{rot}}·r_{exp}{}^2+5.433·r_{exp}{}^3+6.301\times {10}^{-7}·N_{\mathrm{rot}}{}^2\hfill \\ \hfill & ·r_{exp}{}^2+9.576\times {10}^{-5}·N_{\mathrm{rot}}·r_{exp}{}^3-0.2376·r_{exp}{}^4\hfill \end{array}$$

(7)

$${\varnothing }_{sm}=2.87-0.0007611·N_{\mathrm{rot}}+0.02955·r_{exp}+0.000000091·N_{\mathrm{rot}}{}^2-0.000004562·N_{\mathrm{rot}}·r_{exp}$$

(8)

$$\begin{array}{cc}{\eta }_{\exp ,\mathrm{sm}}=74.53\hfill & -0.08233·N_{\mathrm{rot}}+59.81·r_{exp}+2.287\times {10}^{-6}·N_{\mathrm{rot}}{}^2+0.04543·N_{\mathrm{rot}}·r_{exp}-34.01·r_{exp}{}^2\hfill \\ \hfill & -4.889\times {10}^{-7}·N_{\mathrm{rot}}{}^2\ast r_{exp}-0.008325·N_{\mathrm{rot}}·r_{exp}{}^2+6.096·r_{exp}{}^3+7.662\times {10}^{-8}·N_{\mathrm{rot}}{}^2\hfill \\ \hfill & ·r_{exp}{}^2+0.0004664·N_{\mathrm{rot}}·r_{exp}{}^3-0.3509·r_{exp}{}^4\hfill \end{array}$$

(9)

3.2. Evaporator

The most important factor to consider in dynamic modeling is the heat exchanger, which, unlike the other factors, has the greatest effect on the response time over time in the ORC system due to the phase change of the refrigerant [36]. The dynamic modeling methods of the heat exchanger can be classified into moving boundary (MB) method and finite volume (FV) method. The MB method is a method of dividing the heat exchanger into three parts by dividing the inside of the heat exchanger into the liquid phase, ideal phase and vapor phase. The FV model simplifies the heat exchanger in one dimension, divides the interior into equal volumes. Both models well predicted the dynamic operating characteristic, but MB model overestimated the dynamics when it is used for a small size heat exchanger [38]. In this study, we used FV method to avoid this overestimation as shown in Equation (10) and Figure 5.

Table 3. Evaporator parameters.

Parameter	Value	Unit
A	8.06	m2
Mw	30	kg
N	50	-
Uhotfluid	1000	W/m2 K
Ufluid,liquid	260	W/m2 K
Ufluid,twophase [39]	900	W/m2 K
Ufluid,gas	360	W/m2 K

shows the evaporator parameters used for the evaporator.

$${\dot{m}}_{\mathrm{wf},\mathrm{i}}\cdot c_{\mathrm{p}}\cdot \frac{d{T}_{\mathrm{wf},\mathrm{i}}}{dt}={\dot{Q}}_{\mathrm{hf},\mathrm{i}}-{\dot{Q}}_{\mathrm{wf},\mathrm{i}}$$

(10)

3.3. Pump

The diaphragm pump deforms the diaphragm membrane to draw liquid from the inlet to the pump chamber and to discharge the liquid to the upper discharge pipe. The flow rate of the diaphragm pump is determined by the volume of the inner chamber and the RPM of the pump. The flow rate of the pump is given by the following equation when the temperature and pressure of the fluid at the inlet side of the pump are constant. The pump performance curve, for the modes have been provided in Figure 6.

$${\dot{m}}_{\mathrm{pp}}=\frac{{\dot{V}}_{\mathrm{su},\mathrm{pp},\max }}{v_{\mathrm{su},\mathrm{pp}}}\cdot \frac{Hz}{60}$$

(11)

3.4. Model Validation

Figure 7 shows the differences for the working fluid mass flow rate, the expander inlet pressure, the evaporator heat rate, and the expander shaft power. In Figure 7a, the working fluid mass flow rate was within 10% error. In Figure 7b, the expander inlet pressure was also within 10%, however single mode 1 showed lower value in the simulation case. On the other hand, single mode 2 showed higher value in the simulation. In Figure 7c, the shaft power was overestimated. This error has resulted from the simplification of the expander model for dynamic simulation. In Figure 7d, the evaporation heat rate was well predicted within 10% error range.

4. Results and Discussion

4.1. Mode Change Operation

As shown in Table 1, the ORC system was controlled to change the operating mode. Figure 8 shows the dynamic characteristics of when the ORC system was controlled from dual expander mode to single expander mode 1. When the mode was changed, the working fluid pump frequency was controlled as 16 Hz, and the ball valves installed before and after one of the expanders was closed at the same time. In Figure 8a, the working fluid mass flow rate shows a well-matched response time of 80 s with a slightly lower undershoot. In Figure 8b, both pressures took 90 s for approaching the steady-state condition with a 0.68 bar lower pressure in the simulation result. As mentioned in model validation, the overvalued filling factor caused the undervalued expander inlet pressure. As in Equation (2), the overvalued filling factor decreases the density of the expander inlet fluid. In Figure 8d, the shaft powers took 80 s, but the error was large in dual mode, and it was small in single mode. This error also occurred due to the simplified expander model.

In addition to turning on and off one of the expanders, the DE-ORC with different capacity expanders can change its operation from one expander to another. In Figure 9 shows the comparison for this case. The working fluid pump was controlled as 10 Hz. In Figure 9a, the mass flow rate showed a large difference. The experiment results took 6 s for approaching the steady-state condition, however, the stabilization taken 52 s. This error occurred because the internal volume was not taken into account. When the semihermetic expander has been turning on, the working fluid first filled the internal volume of the expander, and the expander inlet pressure is also suddenly dropped (Figure 9b). In Figure 9c, the evaporator heat rate also showed the opposite response characteristics because of the flow rate change. In Figure 9d, the shaft power was overestimated due to the simplification of the expander.

4.2. Pump Control Simulation

When the heat source condition is changing, the ORC pump needs to be controlled to avoid liquid entrainment to the expander. Excessive mass flow rate provides the turbine with fluid that has not fully evaporated yet. The DE-ORC system changes the operating mode according to the variation of the heat source to generate the power continuously. Stopping one of the two expanders sharply reduces the volumetric flow rate of the expanders. At this time, maintaining the working fluid pump rpm increases the density of the expander inlet according to Equation (11). If the expander inlet temperature is constant, the expander inlet pressure rises and thus the superheat decreases. Thus, enough superheating is needed to be secured before the mode change by controlling the pump speed. To ensure the sufficient degree of superheating at the expander inlet, working fluid mass flow rate is required to be lowered prior to shifting from DUAL MODE to SINGLE MODE 1. This is because as the mass flow rate is decreased, the evaporator pressure consequently decreases, and the degree of superheating increases. This can be seen from the shifting from line 1 to line 2 in Figure 10. Afterwards, the degree of heating is sustainable, the process 2 to process 3 in Figure 10. Meanwhile, when the vice versa operation is needed, that is the shifting from lower to higher capacity, the inlet pressure of the expander decreases by default. This eliminates the concerns related to degree of superheating as it increases with decrement in pressure. This scheme was modeled and simulated as shown in Figure 11.

Using the developed dynamic model, the control strategy was simulated as shown in Figure 10. Initial conditions were heat source temperature of 110 °C, and heat source mass flow rate of 0.8 kg/s. The working fluid pump rotating speed was controlled from 27 Hz to 10 Hz. The dual mode ORC has a superheat of 10°C when the pump speed is 27 Hz. Single mode ORC has the same superheat at 10 Hz. If the mode was changed before 30 s, the superheat rapidly decreases and then goes to the 10°C. The pressure increased up to 13.1 bar and superheat decreased to 4.1 °C in the simultaneous control (zero delay) case. If the mode was changed after 40 s, the pressure and superheat show opposite changes. As a result, the system pressure ratio decreased, and the system power was decreased. From this simulation study, it is recommended that mode change delay ranges from 40 to 50 s to produce the maximum power output and provides a stable operation.

5. Conclusions

The DE-ORC holds great potential to enhance the ability of using the ORC for the cases, where the variations of the heat source parameters are imminent. The main concern for the DE-ORC is that there exists a threat for the formation of the droplets in the expander, as the operating mode is switched from high to low capacity due to the significant decrement of superheating.

To prevent the formation of droplets, the devised control strategy involved the reduction of the working fluid mass flow rate. Forwarded to lowering of the working fluid flow rate, the expander inlet pressure should be suitably lowered to ensure sufficient degree of superheating prior to mode change.

In this study, the empirical models for the rotational components, the expander and pump, and the evaporator were developed. The developed models were compared with the experimental results to understand and perform the analytical evaluation of the devised control strategy. From the carried out simulations, it was concluded that the best time when lower and shifting the mode is in between 40 to 50 s. The presented study can provide beneficial outcomes for the potential utilization of the multiple expanders for the applications that involves fluctuating heat source conditions.

The proposed mathematical models for the transient operation can be useful for the potential researchers to conduct further research regarding the control system design for the DE-ORCs.