Experimental and numerical analysis of variable volume ratio as additional optimization parameter in organic Rankine cycle expanders

In this paper, the use of a variable volume ratio expander for a 10 kWe organic Rankine cycle (ORC) to be integrated in a Carnot battery has been studied. The reciprocating piston expander used in this work has a built-in mechanism which allows changing the inlet valve timing of the expander and hence the expander internal volume - and pressure ratio. The experimental results of a 10 kWe ORC prototype are presented. A total of 58 steady state points has been collected by varying the heat source and cold sink temperature, the refrigerant mass flow rate, the expander speed and the expander inlet valve timing. The experimental results for the ORC are presented in terms of electrical power output and cycle efficiency and for the expander the isentropic and volumetric efficiencies are determined for different valve timings. Although the experimental results clearly show the effect of changing the internal volume ratio on the expander performance we here present a combined experimental-numerical approach which is necessary to evaluate the performance under varying external conditions. Therefore, an empirical quasi-steady state model of the ORC has been calibrated based on the experimental results. Subsequently, in a numerical analysis, the use of various valve timings has been evaluated under time-varying boundary conditions. A maximal difference of 14.2 % in the net power production has been observed between the most optimal and least optimal valve timing. However, for the presented numerical study the use of variable valve timing only increased the net power production maximally 1 % compared to the optimal fixed timing. Altogether, this study demonstrates the benefit of variable volume ratio reciprocating piston ex-panders for ORCs under varying external conditions.


Introduction
In December 2019, the European Commission has presented the "European Green Deal", a set of policy initiatives aiming at ensuring the EU becomes climate neutral by 2050 [1].In line with this objective, the European Commission's long-term strategy describes a number of pathways to reach this target.All pathways are supported by large-scale deployment of renewable energy sources (RES) [2].The increasing growth of renewable energy requires flexible, low-cost and efficient electrical storage systems to balance the mismatch between energy supply and demand.In a Carnot battery, electric energy is stored as thermal energy.The conversion from electricity to thermal energy is done with a power-to-heat system.This energy is later recovered during discharge when the electricity demand is higher than the production.This is done by a heat-to-power system with a suitable power cycle like an organic Rankine cycle (ORC) [3].Different types and configurations of Carnot batteries are presented in the work of Dumont et al. [3].The authors also give an overview of the different thermal energy storage technologies applied in these Carnot batteries.Latent thermal energy storage (LTES) is one of the possibilities.The advantage of LTES systems is often addressed as having a near isothermal (dis)charging behavior but reality is often different as this depends on the operating conditions.In the work of Vogel et al. the output of a large-scale industrial storage system with water/steam as heat transfer fluid has been simulated [4].The efflux of energy is far from constant as the resistance for heat transfer between the heat transfer fluid and the phase change storage material is continuously increasing during the charging or discharging process.This is also observed for an industrial size LTES system with thermal oil as heat transfer fluid when the mass flow rate is increased [5].Steinmann et al. proposed a Carnot battery in which LTES is combined with low temperature sensible heat storage for preheating or subcooling the ORC working fluid [6].In such a system, multiple scenarios thus exist where the ORC input heat source conditions and heat sink conditions will vary over time which results in changing working conditions in the ORC.
The expander in an ORC system is a critical component that affects the investment cost and overall performance of the ORC system.Expanders can be classified into two groups: volumetric expanders (displacement expanders) and turbo-expanders [7].Large scale ORC plants with nominal power higher than 500 kW use turbine technology to expand the working medium.Although turbine technology is still present in the range of 50-500 kW the use of volumetric machines in the small scale region, especially below 50 kW as in this work, are seen as more advantageous compared to turbo machines [8].In the review paper of Zhao et al. this is also recognized [9].There screw expanders are proposed to use in medium-scale ORC units and piston or scroll expanders for small ORCs.Among the volumetric expanders most attention goes to single screw and scroll expanders [10,11], but also twin screw [12], vane [13] and piston expanders [7] have been evaluated.Piston expanders are further classified into reciprocating and rolling piston on the basis of the type of motion [14].
Volumetric expanders are characterized by their internal built-in volume ratio and the internal pressure ratio of the expansion process.During this process several losses occur, these include: under-or overexpansion, pressure drops, ambient heat transfer, leakages and friction.Under-or overexpansion losses are due to a mismatch between the builtin volume ratio of the expander compared to the pressure ratio imposed to the machine.The cycle of a volumetric expansion device is schematically shown on Fig. 1 and may be considered to be composed by the following phases: constant pressure admission until the inlet valve closes (1-2), expansion until the exhaust valve opens (2-3), constant volume discharge (3)(4), constant pressure discharge until the exhaust valve closes (4-5), recompression (5)(6) and finally constant volume admission .For under-expansion, the external volume ratio over the expander is higher than its built-in volume ratio.The pressure p int in the expansion chamber at the end of the expansion process is higher than the pressure p ex at the expander exhaust.At underexpansion, some usefull work during the expansion process is not used indicated by the red colored area.In contrast, for overexpansion, the volume ratio over the expander is lower than its built-in volume ratio.In this mode, the pressure p int is thus lower than the pressure p ex .During the exhaust stroke additional work is needed to compress the working fluid back to higher pressure and work is lost, indicated by the red colored area.
It is crucial to match the external pressure ratio, which depends on the operating conditions of the ORC machine, with the internal pressure ratio to minimize these losses [15,16].Because of this, a volumetric expander with a fixed built-in volume ratio cannot provide an optimal expansion of a working fluid in a wide range of operation conditions and operation at high efficiency points cannot be guaranteed when the operation point differs from the design operating point [17,18].An installation with a variable built-in volume ratio expander is thus preferred for operation conditions with varying heat flow rate and temperature as they can appear in Carnot batteries or in industrial processes [19].This is achieved through varying the valve timing but in literature this also referred to as variable valve actuation, variable valve duration [7,20], variable admission volume control or variable cut-off [21], adjustable built-in volume ratio expander [22] or in general variable expansion/volume ratio expanders [23].Screw expanders, designed to operate under variable conditions, are equipped with a slide valve at the suction side [16,17].In the review paper of Wang et al. on screw machines a list of research can be found on controlling the built-in volume ratio of screw compressors and expanders [16].Wu et al. show that the net power output of an ORC with a single screw expander equipped with slide valves exhibits a significant improvement when compared with that of ORC without slide valves [17].The same authors also concluded that the optimal built-in volume ratio was not the bigger the better when single screw expander worked at high pressure ratio condition, because suction pressure loss also increased with the increase of built-in volume ratio [24].Dawo et al. investigated the optimal built-in volume ratio of a twin screw expander [25].A semi-empirical model is fitted to experimental data.The simulations used to determine the optimum built-in volume ratio show the importance of the selection of the optimum built-in volume ratio in dependency of the heat source.The problem of finding a compromise between optimum exploitation of the heat source and optimum expander and ORC operation is addressed.The optimum built-in volume ratio changes with varying heat source profiles showing the potential for having a variable built-in volume ratio.Bianchi et al. investigated the off-design performance optimisation of a trilateral flash cycle system using two-phase twin-screw expanders with variable built-in volume ratio [26].They concluded that expander speed and changing the builtin volume ratio are the variables that mostly impact the net power output of the ORC unit.By lowering the built-in volume ratio the volumetric efficiency of the machine increases but the resulting underexpansion of the working fluid also leads to a drop in the isentropic efficiency and to a reduction in the specific indicated power.On the other hand, by lowering the built-in volume ratio the expander can be operated with larger mass flow rates and thus, for the same pressure ratio, the total power output increases.
Antonelli et al. investigated the performance of a Wankel expander numerically [27].The effect of variable valve timing (by changing the opening degree of the inlet and exhaust valves) and rotational speed (500-3000 RPM) has been investigated for different working fluids (R152a and R600a) and operation temperatures.Evaporation temperatures in the range of 100-120 • C have been investigated, while a constant condensation temperature of 80 • C has been assumed.The rotational speed and valve timing have a significant effect on the isentropic efficiency of the expander.The optimal valve timing is determined more by the temperature drop (and thus pressure ratio over the expander) than by the working fluid used.The same authors than further presented operating maps with the isentropic efficiency of Wankel expanders for different organic fluids and various cut-offs [28].Gopal et al. investigate the effect of variable valve timing and compression ratio on the isentropic efficiency of a Wankel rotary steam expander [21].Through theoretical and experimental analysis it is shown that dynamic admission-volume control can maintain high efficiency for all mass flow rates.
Although rotary vane expander (RVE) suffer from relatively low efficiencies due to internal leakages they can provide an interesting alternative for applications requiring simple design and low manufacturing costs [29,30].The introduction of dual intake port (DIP) technology technology in RVE allows to reduce the leakages [30] and is extensively discussed by Fatigati et al. [31][32][33].It is shown that an auxiliary suction port is able to increase the output power of the machine up to 50 % through the aspiration of a greater mass flow rate while maintaining expander inlet pressure.Although this is not really addressed as a variable volume ratio expander it can be seen as such by having two built-in internal volume ratios if an active control of the use of the suction ports can be introduced.Moreover, the possibility of actively changing the angular position or the diameter of the auxiliary suction port would make this a completely variable volume ratio expander.This approach is introduced by Yan et al. which study a variable expansion ratio RVE by regulating the outlet opening angle according to variable working conditions [23].The expander performance is investigated through validating a simulation model to experimental data and evaluating it under various inlet pressure and temperature conditions to investigate the influence of a variable expansion ratio.Furthermore the optimal expansion ratio control strategy is evaluated with a case study for a 6DL engine European stationary cycle.It is shown that the optimal expansion ratio is different according to different working conditions and for a heat source with variable working conditions the feasibility of variable expansion ratio vane expander is proven.
The feasibility of introducing a further intake port placed after the main one and in correspondence of the expansion phase is also assessed for a scroll expander by Fatigati et al. [34].It is demonstrated that DIP technology can produce a 25 % increase in mechanical power with respect to the baseline machine, without modifying the in-out pressure ratio over the expander.
Reciprocating expanders have been recommended as the most optimal type of variable built-in volume ratio expanders since the expansion ratio can be easily adjusted by means of in-and outlet valve timing [22].For suction, the sliding valve, poppet valve, rotating valve or a ball valve can be used [14,35] with a favor of mechanically controlled valves as these are more reliable and cost effective than solenoid valves [36].Gao et al. analyse the influence of the duration of the intake phase of a single valve piston expander through a numerical model [35].The varying expander performance with varying valve timing is clearly illustrated but lacks an experimental set-up allowing to control the valve timing actively.In the work of Badami et al. variable valve timing is introduced to optimize the performance of a reciprocating piston expander in a steam cycle [20].Different control strategies are compared being variable valve timing, variable speed control and using a governing valve to reduce the inlet steam pressure.It is shown that the variable valve timing strategy results to be the most efficient on almost the entire controlling range.In this work also an analytical expression is given showing the influence of the inlet valve timing and the compression ratio on the isentropic efficiency.Longer intake periods result in lower efficiencies but on the other hand the net electrical power produced is increased as the area in the pV-diagram for the ideal cycle increases.This is also reported in the work of Clemente et al. [37].Besides, the supply cut-off ratio is recognized as one of the most important parameters of a reciprocating expander.Based on 3D CFD calculations of twin screw expanders, Papes et al. found that the biggest pressure drop was caused by a throttling loss at the suction port and therefore an optimized design of the suction port was necessary [38].This is also addressed by Kovacevic et al. [39] which underlines the importance of the correct design of the high pressure inlet port in terms of expander performance for a twin screw expander.Similar conclusions are found for a single-valve reciprocating expander [40].The valves used for admission and exhaust of the working fluid are thus a great source of losses and they thus have to be designed and controlled carefully to reduce the effect on the performance of the reciprocating expander [7].Wronski et al. presented a reciprocating expander proof-of-concept for ORC applications using a novel rotating variable valve timing admission system which is expected to decrease the throttling losses during the intake period [7].The concept allows for adjustment of the built-in volume ratio while the expander is running.A 2.5 kWe ORC unit using n-pentane as working fluid and a single-cylinder, single-stage expander prototype has been developed.Experimental data has been gathered for 6 operation points.The operating conditions have been characterized by the opening timing of the exhaust valve.Exhaust valve opening periods of 75 • (resulting in high internal pressure ratios) and 115 • (resulting in low internal pressure ratios), evaporation temperatures of 125 • C and 150 • C and condenser temperatures of 20 • C and 40 • C have been considered.For these conditions, the opening and closing angle of the inlet valve have been optimized.Based on these K. Couvreur et al. experiments, a dynamic model of the reciprocating expander has been developed.The results indicate that the variable valve timing can be used to operate the prototype at an almost constant isentropic efficiency of 70 % for pressure ratios ranging from 10 to 16.5.Efficient operation of the expander is furthermore closely related to the valve characteristics.Quick switching between fully closed and fully opened valves is essential to minimize throttling losses.
The potential of variable valve timing to optimize the performance of volumetric expanders and more specifically reciprocating piston in ORC systems has been illustrated by previous studies.However, a full characterization through a combined experimental-numerical approach is lacking in order to quantify the performance improvement under varying heat source or heat sink conditions.Moreover, it is also useful to evaluate this concept in a wider range of operational conditions and at larger power ratings.To this purpose, this study presents the experimental results of the performance of a 10 kWe ORC prototype with reciprocating piston expander with variable valve inlet timing and hence variable volume ratio together with a numerical case study to quantify the performance improvement under varying heat source or heat sink conditions.An extensive experimental campaign has been performed varying the heat source and cold sink temperature, the refrigerant mass flow rate, the expander speed and the expander inlet valve timing.These experimental results have been used to calibrate an empirical quasisteady state ORC model.The model is used to estimate the difference in ORC performance for different valve timings under variable boundary conditions representative for the intended integration of the ORC in a Carnot battery prototype.

Equipment
In the framework of the European Chester Horizon2020 project a 10 kWe ORC has been designed and built for integration in a Carnot battery with a high temperature heat pump and latent heat thermal energy storage with a PCM melting temperature of 133 • C [41].As such, it is designed to work with low heat source temperatures (120-140 • C) and uses a new low GWP environmentally friendly working fluid R1336mzz (E).A schematic of the component lay-out and the measuring equipment and picture of the installation is given in Fig. 2.
The volumetric piston expander used has a maximum swept volume of 511 cm 3 and a maximum rotational speed of 1500 rpm.The rated electrical power output of the expander, as indicated by the manufacturer, is 15.5 kWe and can operate at a maximum inlet pressure and temperature of 30 bar and 215 • C.This piston has an internal variable inlet valve timing mechanism that can be manipulated to control the expansion ratio and increase the ORC flexibility to perform well under part-load conditions.The valve control and operation of the inlet valve of the expander is described in the work of Risla [42] and more details on the valve actuation can also be found in the work of Wronski et al. [7].In Fig. 3    crankshaft, but the phase shift between the two valves can be changed.This phase shift can be used to control the overlap of the flow channel opening of the two individual rotary valves, which effectively controls the onset of the fluid admission and the admission cut-off [7].
Cooling of the integrated synchronous motor is provided by a chiller (Thermoflex 10.000) with a rated capacity of 10 kWth.A diaphragm pump (G10-X from Wanner) of 30.6 l/min capacity is used to pump the refrigerant and is capable of reaching pressures up to 69 bar at the maximum speed of 1450 rpm.All heat exchangers used are SWEP brazed plate heat exchangers.The evaporator and the condenser are identical and of the B400TH type with 120 plates and a single pass.The evaporator is insulated with HT/ArmaFlex.The subcooler is a B28H type with 34 plates and is connected to a separate cooling loop connected to the Thermoflex chiller.This subcooler is used to ensure proper start-up of the ORC system without cavitation in the refrigerant pump by ensuring a minimum level of 5 • C subcooling at the pump inlet.
ORC pump and expander information is retrieved from variable frequency drives (VFD) which control the speed of the pump and expander and are connected to a Siemens S7-1200 PLC through PRO-FIBUS.Temperatures and pressures inside the ORC machine and the refrigerant mass flow rate are acquired with a National Instruments cRIO.Data capturing is done at a sampling rate of 2 Hz.Details about the measuring equipment are provided in Table 1.
Heating and cooling is provided with two main external loops.The heating loop consists of a Maxxtec heater made up of 10 × 25 kWe electrical heaters.Thermal oil (Therminol 66) is used as a heat transfer fluid with a maximum flow of 14 m 3 /h and a maximum temperature of 340 • C. The cooling loop consists of an air cooled condenser with a rated capacity of 480 kWth at 20 • C ambient and respectively water input and output temperature of 70 • C and 90 • C. The cooling medium is a mixture of water and glycol, with 27 vol% glycol.The maximum rated temperature and mass flow rate are respectively 120 • C and 20 m 3 /h.

Uncertainty analysis
The measurement uncertainty of the data acquisition equipment is taken into account during the discussion of the results.The maximum errors on the measured quantities follow directly from the sensor uncertainties shown in Table 1.The maximum error on the derived quantities (i.e. the quantities not measured directly) are calculated using the general rule for error propagation shown in Eq. ( 1).
The quantity, its symbol, the reference to the equation used and maximum relative error retrieved are shown in Table 2.

Experimental matrix
In total 58 different steady state points have been acquired with different heat source and cold sink temperatures, different refrigerant mass flow rates and expander speeds and different expander inlet valve positions.The valve position in degrees ( • ) mentioned here refers to the stepper motor position installed outside the casing of the expander.This stepper motor position is controlled and changes the inlet rotary valve position and with that the inlet valve timing.The expander has been operated with four different valve positions: 140 • , 150 • , 160 • , 170 • which corresponds to an expander load of 79 %, 86 %, 93 %, 100 %, respectively.At maximal expander load, the overlap between the inlet ports per revolution is maximal.This results in the maximum intake period and thus shortest expansion period.The capacity is thus largest for the 170 • valve position, while the built-in volume ratio is smallest.An overview of the experimental matrix and the tested values can be found in Table 3. Steady state points are detected according to the method described in Lecompte et al. [12].In this method, a moving window average standard deviation is compared to a reference standard deviation.Time windows with a moving standard deviation lower than the identified threshold indicate steady state.Once steady state zones are detected, the average of the measurement values is taken.Here, all variables are averaged over a 15 min period.

Empirical model
Based on the experiments, an empirical quasi-steady model has been calibrated.This model is later used to make an analysis of the ORC performance under varying boundary conditions for various valve positions.

Model components
Essentially, in the model the four main components of the system are included: the pump, the evaporator, the expander and the condenser.
The pump is modelled by assuming a constant isentropic efficiency.A constant isentropic efficiency of 0.6 has been calculated by minimizing the least-square error between the assumed constant efficiency and the measured values.This assumption is acceptable for the current modelling purpose as the isentropic efficiency of the pump has little effect on the thermodynamic cycle and ORC-performance.
The evaporator is modelled using a constant pinch-point model of a counterflow heat exchanger.From the experiments it is clear that the working fluid outlet temperature is very close to the hot fluid inlet  temperature.To get a good approximation of the experiments, a constant evaporator pinch point of 2 K has been assumed.The heat exchanger has been discretized in 10 parts.For each part, the temperature difference between the fluid flows has been verified.This is relevant as the boundary conditions to which the model is applied are an interpolation of the experimental matrix.It is thus possible that the location of the pinch point shifts depending on the operational conditions.
The expander has been modelled based on empirical correlations for the mechanical and isentropic efficiency which have been fitted to match with the experimental results.More information on the expander model and the obtained fitting coefficients is given in Appendix B.
The condenser is modelled with a constant pinch-point model of a counter-flow heat exchanger.The working fluid is leaving the expander as vapor.The condenser is used to cool down the working fluid from this superheated state.In the modelling, it is assumed that the working liquid leaves the condenser as saturated liquid.The pinch point is thus checked at two locations: at the saturated vapor point and at the saturated liquid point.The subcooler shown in Fig. 2 is not modelled as a separate heat exchanger.Instead, a constant subcooling of 5 K is assumed.This subcooling is added after the pinch-point calculation and verification of the energy balance of the condenser and thus does not influence the comparison with the measured condenser-properties.

Model overview
Several additional assumptions have been made for the empirical model of the ORC.The thermophysical fluid properties of the working fluid, hot fluid and cold fluid are calculated using REFPROP 10.0 [43].Pressure drops in the heat exchangers are neglected after verification of the experimental results.The maximal values of the pressure drop are 0.152+/-0.106bar and 0.0243+/-0.106bar for the condenser and evaporator respectively.The corresponding mean pressure drops are 0.0778 bar and 0.00975 bar, which both lie within the measurement uncertainty of zero.This justifies the assumption of constant pressure in the heat exchangers.Evaporator pressure is assumed to be determined mainly by the refrigerant mass flow (set by the pump rotational speed)   and the expander speed.An empirical expression for the evaporator pressure as function of these parameters has been derived (Appendix A).An overview of the assumed modelling constants is given in Table 4.
The cycle model inputs and the main model output parameters of interest are given in Table 5.
The calculation procedure is illustrated in the block-diagram shown in Fig. 4. First, the refrigerant mass flow and expander speed are used to determine the evaporator pressure using the empirical expression.Once the evaporator pressure is known, the actual cycle can be solved iteratively.Based on the model inputs, appropriate starting values for the different cycle parameters are determined.After initialisation, the temperature profile of the evaporator is solved based on these starting values.The saturation temperature of the condenser is determined iteratively.The solver guesses the saturation temperature and thus condenser pressure, after which the expander-model and condensermodel are ran until the condenser temperature profile satisfies the pinch point criterium.Using the solution for the condenser pressure, the expander-outlet and condenser-outlet are calculated.Using the pump model, the refrigerant state at the pump outlet can be determined which then serves as input for the evaporator-model in the next iteration.An additional check of the technical constraints of the ORC has been added because the ORC-model has been developed to integrate in an optimizer to determine the optimal mass flow and expander speed under variable heat source and heat sink conditions.This avoids that the optimizer can select unphysical combinations of the optimization parameters.

Model validation
The proposed modelling approach has been validated by comparing the simulation results to the corresponding measurements.The maximum and mean relative deviation between the modelled and measured values has been listed in Table 5 for the six main output parameters of the model (see Table 6).
The modelling approach has been found to be sufficiently accurate for the tested measurement points.The maximum relative deviation is found for the pump power.This relative deviation corresponds with an absolute deviation of 0.18 kW which is acceptable given the measurement logging accuracy of 0.1 kW.

Experimental results and discussion
This section presents the experimental results of the ORC and the main component of interest, the expander with variable valve timing.

Cycle results
The thermal efficiency is defined as in Eq. ( 2).
The net amount of power generated by the ORC system is defined according Eq. ( 3).
Heat added to the refrigerant by the heat source, i.e. through the evaporator, is calculated according to Eq. ( 4).
The thermal efficiency as function of pressure ratio (PR) for the obtained steady state points is shown in Fig. 5.The maximum and minimum detected thermal efficiency are 6.7 ± 0.04% and 3.1 ± 0.02 %, respectively.The thermal efficiency increases with increasing pressure ratio over the expander.Higher pressure ratios in their turn result in higher expander power outputs as shown in Fig. 6.Although the prototype has been designed for a 10 kWe output this is never reached due to pressure limitations imposed by the measuring equipment and excessive cooling of the expander generator which lowers the efficiency.

Expander performance
The expander overall isentropic efficiency is defined as the ratio of the actual enthalpy drop (derived from the measured temperature and pressure at the in-and outlet of the expander) to the isentropic enthalpy drop during the expansion process as in Eq. (5).
where h su is the expander supply enthalpy, h ex the expander exhaust enthalpy and h ex,s the exhaust enthalpy following an isentropic expansion.An alternative definition of the isentropic efficiency expresses how close the power generated by the actual expansion process approximates the power of an isentropic process.This definition excludes the influence   of heat losses on the isentropic efficiency and is thus a more fair indication of the expander performance (Eq.( 6)). With: where s 6 = f(T 6 , p 6 ).Fig. 7 and Fig. 8 show the measured isentropic efficiency as function of the pressure ratio and the expander speed, respectively, for the 160 • inlet valve position.The effect of refrigerant mass flow rate on the isentropic efficiency is negligible with a maximal absolute increase of 0.68 % on the maximum isentropic efficiency across the tested mass flow ranges under similar process conditions, which is within the calculation uncertainty of 2.1 %.Similarly, the effect of the heat source temperature is low with an increasing heat source temperature from 125 to 135 • C the absolute maximum isentropic efficiency decreases with 1.2 %.The cold sink temperature shows the largest effect on the isentropic efficiency.Instead of a single continuous curve for η exp,is = f(PR) three different curves are obtained for the three different cold sink temperature tested.The cold sink temperature defines the condensing temperature and pressure inside the condenser, so the effects seen are the result of changing expander outlet pressures.Higher expander outlet pressures thus result in lower pressure ratios as the maximum working pressure at the high pressure is side is restricted to 25 bar.This restriction makes that the curves obtained for a cold sink temperature of 37 • C and 47 • C are not as complete as the curve obtained for a cold sink temperature of 26 • C. Without a maximum pressure limit the trend for all three curves is expected to be similar.However, the mechanism behind the observed effect of expander outlet pressure is rather unclear.Therefore a detailed expander model to quantify and evaluate the different contributions to the performance loss of the expander should be made.Fig. 8 further illustrates the previously discussed effects.For increasing cold fluid inlet temperatures (so increasing expander outlet pressure) at constant expander speed the isentropic efficiency increases.The only impacting factor for the increasing isentropic efficiency with increasing cold sink temperature is thus the expander outlet pressure.
For a given mass flow rate, cold sink temperature and hot source temperature, increasing the valve position results in a lower optimal PR   As most of the experiments have been conducted with a cold sink temperature of 26-28 • C this data clearly shows that the isentropic efficiency increases with increasing PR with an optimal PR > 6.Moreover, each expander load (or valve position) has a specific expansion ratio, which reflects to an optimal PR over the expander and maximizes the power output at an optimum isentropic efficiency.This optimal PR usually corresponds to expander speeds between 1000 and 1200 RPM.In the current prototype a valve position of around 150 • gives the highest isentropic efficiencies and also the highest thermal efficiencies.This can be seen in Fig. 10 where the expander power output is shown for different valve positions with similar process conditions.The expander power output increases on average with 12.4 % from a 170 • valve position to the optimal 150 • valve position.The variable valve position thus allows to optimize the expander performance to the operational conditions at hand.Note that the lowest expander speed shown for valve position 140 • is 1200 RPM.Lower expander speeds were not tested at these process conditions due to the maximum pressure restriction.
Another key criterion is the volumetric efficiency or filling factor (FF), evaluated as Eq. ( 8).rate admitted by the expander.The theoretical volume entering into the cylinder is the difference between the masses in the cylinder when the inlet valve closes and the exhaust valve closes.The theoretical mass flow rate is then given by Eq. ( 9).
where ρ ic is the density of the fluid at the end of the supply process and ρ ex is the exhaust fluid density.ρ ic is different from the density at the supply, ρ in , because of the mixing of the new fluid charge and the fluid remaining in the clearance volume, V 0 .As ρ ic is difficult to determine ρ in will be used and is calculated as f(T 6 ,p 6 ).However, since V ec is unknown in this case and as the mass encountered in the cylinder at the end of the compression phase is generally relatively low, it is often neglected.Figs.11 and 12 show the results of the filling factor as function of the pressure ratio and the expander speed, respectively.The general trend is that the volumetric efficiency increases with increasing PR (at constant cooling fluid inlet temperatures) and with decreasing expander speed.Similar to the isentropic efficiency curves, changing the cooling fluid inlet temperature results in different curves instead of one continuous curve.Furthermore, the actual refrigerant mass flow rate also affects the filling factor with lower flowrates resulting in a higher filling factors.
On the other hand, the volumetric efficiency decreases with increasing rotational speed.With higher rotational speeds, the intake period shortens.This decreased intake period causes an increase of the supply pressure drop that leads to lower working fluid densities in the working chamber after the pressure drop compared to the density at the entrance of the expander.Eventually this means a lower mass admitted in the chamber than theoretically calculated.In addition, this pressure drop also affects leakage flows, leading to a reduction in the volumetric efficiency according to Rijpkema et al. [44].The combined effect of pressure drop, leakage flows and additionally the clearance volume, valve timing, internal and external heat losses and mechanical losses could be estimated by the approach followed in Rijpkema et al. [44] and Lemort et al. [45].

Numerical results and discussion
The numerical model has been used to optimize the ORC net electricity production under variable heat source and sink boundary conditions to assess the difference in performance between the different valve positions.The heat source considered has a constant hot fluid mass flow rate of 3.0 kg/s.This value corresponds with the value tested during the experiments.It is assumed however that the hot fluid inlet temperature drops linearly from 135 to 125 • C over the course of one hour.This temperature profile mimics the decreasing outlet temperature of the hot fluid with diminishing state-of-charge of the thermal storage system of a Carnot battery during the discharge phase of the storage system.The cold sink mass flow rate is considered constant at 2.25 kg/s.The cold sink temperature is assumed constant for the modelled hour.However, this constant temperature has been varied from 15 to 60 • C. In practise, the cold sink temperature of the Carnot battery is closely related to the cooling technology used and the installation location.Therefore, the ORC-performance is looked at in a wide range of sink temperatures.
The profiles of the heat source and cold sink are discretised in 60 timesteps.The quasi-steady state model discussed above is used to optimize the net power output by the system in each timestep.The instantaneous temperatures and mass flows of the heat source and heat sink are used as model input.The working fluid mass flow and the expander speed are used as optimization parameters.The optimizer can vary the expander speed from 800 to 1500 RPM.The working fluid mass flow rate is not restricted by set limits.As explained before, additional constraints are implemented in the ORC-model to assure the solver selects feasible combinations of the optimization parameters.A maximum allowable pressure of the working fluid of 25 bar and a minimum superheat of 5 K at the expander inlet are imposed.The optimized parameters should still fulfil the pinch-point conditions of the heat exchangers.The refrigerant mass flow rate is thus limited indirectly by     the evaporator pressure, the temperature drop of the hot fluid in the evaporator and the temperature rise of the cold fluid in the condenser.The total net electricity production has been optimized for the different valve positions.A valve position of 150 • has not been included in this analysis as this position has only been tested in a very small range of pressure ratios.Although the empirical modelling approach results in satisfactory accuracy for this small range, the derived correlations cannot be safely extrapolated outside this range.The other valve positions have been tested at multiple heat source and heat sink temperatures, resulting in a satisfactory accuracy for the tested temperature ranges.The performance of an expander with variable valve timing has been evaluated by selecting the optimal valve position in every timestep.
The results of these simulations are summarized in Fig. 13 for different valve positions and cold sink temperatures.The figure shows the total net electricity production as function of the constant cold sink temperature for different fixed valve positions.The trend is similar for all valve positions.The total electricity production increases first with decreasing cold sink temperature, an optimum is reached after which the total production diminishes with a further increase of the temperature difference.Three major factors influence the total production: the refrigerant mass flow, the pressure ratio over the expander and the expander efficiency.
During the case study, the refrigerant mass flow decreases with decreasing hot source inlet temperature for all valve positions.This can be explained by the minimum superheat imposed.Lower inlet temperatures require lower evaporation pressures to maintain a sufficiently high superheat.The influence of the cold sink temperature at a certain valve position on the refrigerant mass flow is limited.The pressure ratio over the expander increases for each valve position with decreasing cold sink temperature.The influence of the heat source inlet temperature is limited, although lower inlet temperatures result in slightly lower evaporation pressures.The cold sink inlet temperature influences the pressure ratio more however.Lower cold sink inlet temperatures result in lower condenser pressures and thus higher PR.Higher pressure ratios increase the potential for power production.The overall expander efficiency drops with decreasing cold sink temperature and thus higher pressure ratios for all valve positions.The rate at which this efficiency drops increases at lower cold sink temperatures.
The trend of the production curve can thus be explained by the combination of these factors.At high condenser temperatures, the pressure ratio is the lowest, resulting in a low electricity production.Initially, the increasing PR with lowering the cold sink temperature results in higher electricity production, despite the lower overall expander efficiency.An optimum is reached because at the lowest cold source inlet temperatures and thus highest PR the overall efficiency of the expander drops faster which offsets the higher theoretical enthalpy drop corresponding with these higher PRs.
Although the trend is similar for all valve positions, it can be seen that the valve position has a significant influence on the total electricity production.In Fig. 14, the relative net electricity production is shown for different valve positions and cold sink temperatures to illustrate this difference more clearly.The relative net electricity production has been defined as the ratio of the net electricity production at a fixed valve position relative to the most optimal case with variable valve timing.Looking at the different fixed valve positions, a valve position of 170 • (100 % expander load) performs best at the lowest cold sink temperatures, while a valve position of 160 • (86 % expander load) performs best for the smaller temperature differences between the hot source and the cold sink.It may seem counterintuitive that the highest valve position, which corresponds with the lowest built-in volume ratio performs best at the highest temperature differences.This difference can be explained by comparing the three influencing factors discussed before across the different valve positions.
The refrigerant mass flow decreases with decreasing valve position.The 170 • valve position (100 % expander load) thus has the highest mass flows, which is beneficial for a high power production.
The PR across the expander increases with decreasing valve position.At low valve positions the valve opening overlap is lower, which results in higher evaporator pressures.The condenser pressure is mainly determined by the cold sink inlet temperature and is thus similar for all valve positions.
The overall expander efficiency is the lowest for the highest valve positions at all condenser temperatures.This difference is most pronounced at high cold sink inlet temperatures.At a condenser temperature of 15 • C the mean overall expander efficiency of the case study at the 140 • position is 1.9 % higher than the mean overall expander efficiency at the 170 • , while at a condenser temperature of 60 • C this difference has increased to 13.9 %.A closer examination of the isentropic and mechanical efficiency illustrates that this difference can be attributed mainly to the decrease in mechanical efficiency with increasing condenser temperature.Although the mechanical efficiency drops for all valve positions with increasing condenser temperature, this decrease is stronger the higher the valve position.The mean mechanical efficiency at the 140 • position drops with 9.5 %, while it drops with 28,1 % at the 170 • position when the condenser temperature increases from 15 At low condenser temperatures, the positive influence of the higher mass flow for the 170 • thus offsets the lower PR and overall expander efficiency compared to valve positions of 160 • and 140 • .With increasing condenser temperature the difference in overall expander efficiency between the 170 • valve position and 160 • valve position increases, which can mainly be attributed to the decrease in mechanical efficiency in the former position.The reduced efficiency becomes dominant and the performance of the 170 • valve position drops compared to the 160 • valve position.
The differences in performance between the most and least optimal fixed volume ratio expander are most pronounced at the minimal and maximal cold sink temperatures tested.The net electricity production of the 170 • valve position is 12.6 % higher than the production of the 140 • position at a cold sink temperature of 15 • C. The maximum difference in net electricity production between the most and least optimal fixed volume ratio expander is 14.2 % and has been observed at a cold sink temperature of 60 • C.Although the importance of proper selection of the valve position depending on the operational conditions is clearly visible, the additional benefit of variable valve timing during operation is more modest.For most cold sink temperatures, one of the fixed valve positions performs best for the whole duration of the test.Only at cold sink temperatures higher than 50 • C the optimal valve position changes over the course of the test.An expander with variable valve timing achieves a 1 % higher electricity production than the most optimal fixed volume ratio expander at a cold sink temperature of 55 • C.

Conclusion
In this study, the use of a variable volume ratio reciprocating expander in an ORC has been analyzed.Experiments have been performed on a 10 kWe ORC prototype with a reciprocating piston expander charged with R1336mzz(E) to illustrate the effects of variable valve timing on the system performance.Based on these measurements, the use of a variable volume ratio expander has been compared to the use of fixed volume ratio expanders under varying boundary conditions.58 steady-state measurement points have been collected.The thermal efficiencies range from 3.1 to 6.7 %, while the power output varies from 4.0 to 8.1 kW.The isentropic efficiency of the expander ranges from 40 to 58 %.Filling factors range from 52.6 to 82.8 %.The effect of an increasing heat source temperature on the maximum isentropic efficiency of the expander is low.A maximum difference of 1.2 % has been observed for heat source temperatures ranging from 125 to 135 • C. The effect of refrigerant mass flow rate on the isentropic efficiency is negligible with a maximal absolute increase of 0.68 % on the maximum isentropic efficiency across the tested mass flow ranges under similar process conditions.Both these differences are within the calculation uncertainty.The cold source inlet temperature, and thus condensing pressure, has a significant effect on the expander performance.Higher condensing pressures directly result in lower pressure ratios when the expander inlet pressure is kept constant.Instead of having one continuous efficiency curve multiple efficiency curves exist, each corresponding to a given condenser pressure.Higher condenser pressures result in higher isentropic efficiencies.For a valve position of 160 • , the maximum isentropic efficiency increases with 7.4 % when the condenser temperature increases from 26 to 47 • C.Although the expander efficiencies are highest with higher condenser pressures, the overall thermal efficiency increases with low condenser pressures as more work can be produced with higher pressure ratios over the expander.The maximum thermal efficiency of 6.7 ± 0.04% has been measured for a cold sink temperature of approximately 26 • C. The operational conditions can be matched in order to work at maximum efficiency by using an expander with variable inlet valve timing.Under similar process conditions the isentropic efficiency of the expander increases maximally 3.8 % from the worst to best valve position.Choosing the optimal working conditions of the expander for given process conditions will be a trade off in terms of working at highest possible expander inlet pressures by changing the inlet valve timing and working at optimal expander efficiency.
An empirical numerical model has been calibrated using these experimental results.The numerical model has been used to calculate the maximal electricity production for different valve positions under a time-varying heat source boundary condition at different condenser temperatures.The results indicate that a proper selection of the built-in volume ratio for the boundary conditions has indeed a significant influence on the net electricity production.A maximum difference of 14.2 % has been observed between the most and least optimal fixed volume expander at a condenser temperature of 60 • C. The use of a variable volume ratio expander resulted in a higher total electricity production compared the most optimal fixed built-in volume ratio in 3 of the 10 use cases simulated.For the test case, a maximal improvement of 1 % has been observed.
The importance of a proper selection of the built-in volume ratio of a reciprocating expander for the intended operational conditions has thus been illustrated experimentally and numerically.The additional benefit of variable valve timing during operation is limited for the current case study.
Variable valve timing has thus proven an effective way to change the built-in volume ratio of reciprocating expanders and a promising technology for further optimization of reciprocating expanders for a wide range of operational conditions.
• T nom = 403.15K • P nom = 25*10 5 Pa • PR nom = 7 • N nom = 1200 rpm The correlation coefficients are determined using the curve_fit-function of the scipy.optimize-package in Python.The fitting parameters for the different valve positions are summarized in Tables 8, 9, 10 and 11.

Fig. 1 .
Fig. 1.Schematic illustration of under-and overexpansion for an ideal cycle.
the working mechanism is further visualized.Two rotary valves are used in series and rotate in opposite directions.The working fluid admission can only occur if the flow channels in both valves are aligned.The rotational speed of both valves is directly linked to the

Fig. 2 .
Fig. 2. Left: Schematic of the component lay-out and measuring equipment with temperature and pressure sensors indicated as 'T' and 'P', respectively.Right: Picture of the 10 kWe prototype installation.

Fig. 3 .
Fig. 3. Illustration of the working mechanism of the variable inlet valve timing.

Fig. 6 .
Fig. 6.Expander power output as function of PR for the different tested expander speeds.

Fig. 7 .
Fig. 7. Expander isentropic efficiency as function of PR with the inlet valve in 160 • position.Different refrigerant mass flow rates, heat source and cold sink temperatures are used.

Fig. 8 .
Fig. 8. Expander isentropic efficiency as function of expander speed with the inlet valve in 160 • position.Different refrigerant mass flow rates, heat source and cold sink temperatures are used.

Fig. 9 .
Fig. 9. Optimal pressure ratio and expander isentropic efficiency as function of the inlet valve position, process conditions for all datapoints are similar with a 0.4 kg/s refrigerant mass flow rate, 130 • C heat source temperature and 26 • C cold sink temperature.

FF = ṁ ṁth ( 8 )Fig. 10 .Fig. 11 .
Fig. 10.Expander power output as function of the expander inlet valve position for different expander speeds, process conditions are similar for all data points with a 0.5 kg/s refrigerant mass flow rate, 130 • C heat source temperature and 26 • C cold sink temperature.

Fig. 12 .
Fig. 12. FF as function for different expander inlet valve positions, process conditions for all datapoints are similar with a 0.5 kg/s refrigerant mass flow rate, 130 • C heat source temperature and 26 • C cold sink temperature.

Fig. 13 .
Fig. 13.Total net electricity production for different valve positions as function of the cold sink temperature.

Fig. 14 .
Fig. 14.Total relative electricity production for different valve positions as function of the cold sink temperature.

Table 1
Measuring equipment and sensor uncertainties.

Table 2
Maximum relative errors and equation number for the derived quantities.

Table 4
Overview model constants.

Table 5
Overview of the cycle model inputs and model output parameters.

Table 6
Overview accuracy modelling approach.

Table 7
Fitting coefficients for evaporator pressure correlation.