Numerical Analysis of an Organic Rankine Cycle with Adjustable Working Fluid Composition, a Volumetric Expander and a Recuperator

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Article Numerical Analysis of an Organic Rankine Cycle with Adjustable Working Fluid Composition, a Volumetric Expander and a Recuperator

Peter Collings and Zhibin Yu *

School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK; [email protected] * Correspondence: [email protected]; Tel.: +44-141-330-2530

Academic Editors: Andrew J. Haslam and Christos N. Markides Received: 31 January 2017; Accepted: 22 March 2017; Published: 27 March 2017

Abstract: Conventional Organic Rankine Cycles (ORCs) using ambient air as their coolant cannot fully utilize the greater temperature differential available to them during the colder months. However, changing the working fluid composition so its boiling temperature matches the ambient temperature as it changes has been shown to have potential to increase year-round electricity generation. Previous research has assumed that the cycle pressure ratio is able to vary without a major loss in the isentropic efficiency of the turbine. This paper investigates if small scale ORC systems that normally use positive-displacement expanders with fixed expansion ratios could also benefit from this new concept. A numerical model was firstly established, based on which a comprehensive analysis was then conducted. The results showed that it can be applied to systems with positive-displacement expanders and improve their year-round electricity generation. However, such an improvement is less than that of the systems using turbine expanders with variable expansion ratios. Furthermore, such an improvement relies on heat recovery via the recuperator. This is because expanders with a fixed expansion ratio have a relatively constant pressure ratio between their inlet and outlet. The increase of pressure ratio between the evaporator and condenser by tuning the condensing temperature to match colder ambient condition in winter cannot be utilised by such expanders. However, with the recuperator in place, the higher discharging temperature of the expander could increase the heat recovery and consequently reduce the heat input at the evaporator, increasing the thermal efficiency and the specific power. The higher the amount of heat energy transferred in the recuperator, the higher the efficiency improvement.

Keywords: dynamic; Organic Rankine Cycle; positive displacement expander; zeotropic fluid; recuperator

1. Introduction Global energy use is predicted to continue to grow over the coming decades. Diminishing fossil fuel reserves and concerns about climate change mean that this extra energy demand will have to be supplied from non-conventional sources, many of which provide heat at temperatures too low to be exploited with traditional methods. Steam power plants become uneconomical for heat sources with temperatures below 400 ◦C due to declining efﬁciency combined with increasing component sizes due to low-pressure operation [1,2]. Several alternative methods exist for exploiting heat sources at such low temperatures, including the Stirling Cycle, Organic Rankine Cycle (ORC), and Kalina Cycle. However, Bianchi and De Pascale [3] have identiﬁed the Organic Rankine Cycle as the most promising technology for their utilisation. Typical heat sources for the Organic Rankine Cycle include solar, geothermal, biomass and industrial waste heat [4]. These heat sources have temperatures ranging from 80 ◦C for solar ponds, to over 500 ◦C for high-grade industrial waste heat [4], of which most exist at temperatures between 100 ◦C and 300 ◦C[5,6].

Energies 2017, 10, 440; doi:10.3390/en10040440 www.mdpi.com/journal/energies Energies 2017, 10, 440 2 of 21

Organic Rankine Cycles replace water with an organic working fluid, which can exhibit superior thermal characteristics at low temperatures [7]. Most cycles use pure, single-component working fluids [8,9], however, there is also the potential to use a working fluid mixture. Organic Rankine Cycles are a relatively mature technology, with some market penetration, especially for geothermal applications. Their efficiency is often improved by the utilisation of a recuperative cycle [10,11], in which an internal heat exchanger is used to recover thermal energy from the expander exhaust that would otherwise be rejected in the condenser and use it to preheat the working fluid before it enters the evaporator. In this way, the heat that would otherwise be rejected from the cycle through the condenser is used to reduce the demand for input energy in the evaporator. Drescher and Brüggemann [12] performed an in-depth analysis of working fluids for biomass ORCs, between temperatures of 90 ◦C and 350 ◦C, finding a maximum efficiency of 25% for a recuperative cycle operating towards the higher end of this range. Andreasen et al. [13] performed a working fluid screening for lower heat source temperatures of 90 ◦C and 120 ◦C, with a maximum efficiency of 10.3% for the higher temperature heat source. Bruno et al. [14] analysed solar powered ORCs for reverse osmosis desalination, and found that the efficiency of the cycle strongly depended on the selection of working fluid, and also the heat source temperature, varying from 7% to over 30% at the highest heat source temperatures. Organic Rankine Cycles do suffer from several issues. Firstly, the constant temperature during phase change increases the temperature mismatch in the heat exchangers, increasing exergy destruction, and reducing the utilisation of the heat source for non-isothermal heat sources and sinks [15]. Yu et al. [16] identified a linear relationship between the integrated average temperature difference in the heat exchanger and the rate of exergy destruction. Secondly, the choice of pure working fluid is limited, meaning that not every application has an ideal working fluid. Organic Rankine Cycles are generally designed with a working fluid to match the temperatures of the heat source and heat sinks. Xu and Yu [17] showed that the efficiency of a subcritical ORC is related to the critical temperature of the working fluid. They found that the cycles tended to be less efficient when the difference between the heat source temperature and the critical temperature of the fluid becomes greater. Single-component working fluids have a particular critical temperature, and so if the critical temperature doesn’t match the operational conditions, a loss in efficiency will result. Thirdly, the small temperature differential provided by a low-enthalpy heat source means that the cycles are very sensitive to changing temperature of coolant, which can be proportionally significant compared to the cycle’s driving temperature differential. This has been identified as a problem hindering thermal cycles across the world [18]. It is of particular concern for cycles using air-cooled condensers, which are common for applications where portability or modularity is considered important, or where cooling water is too scarce or expensive. The heat sink for these cycles is the ambient air which, in continental climates, can vary in temperature by over 50 ◦C between summer and winter, and also a significant amount between day and night, as shown in previous research by the authors [19]. A cycle designed to operate in such conditions must ensure that liquid working fluid is fed to the pump at all times, as to allow vapour to be ingested into the pump compromises its efficiency and can even lead to damage due to cavitation. This requires a high condenser pressure, which means that when the ambient air is at a lower temperature, the cycle must either reduce the flow rate of coolant, or operate with significant subcooling at the pump outlet, which increases the heat energy required in the evaporator without any corresponding increase in expander work, reducing the cycle’s efficiency. This means that for much of the year, the cycle is operating at off-design conditions. The authors have recently proposed that these issues can be solved by the concept of a dynamic ORC, capable of adjusting the composition of the working fluid during operation to match the changing ambient conditions [20]. When two working fluids are combined, they can generally form what is known as a zeotropic mixture [21]. This means that, instead of undergoing phase change at a constant temperature, like pure, single-component fluids, they instead exhibit a temperature change during phase change, known as “glide”. The lower temperature end of the phase change is known as the Energies 2017, 10, 440 3 of 21 bubble point, and the higher temperature end is known as the dew point. The bubble and dew points of a zeotropic mixture lie between the boiling points of its two constituent parts. This means that with two components having different boiling points, a zeotropic mixture with a specific bubble or dew point temperature in between these two points can be formed by mixing them together. Given the right working fluid components, this can ensure that the pump in an Organic Rankine Cycle system is fed liquid for any ambient temperature between these two points. Several sources have concerned themselves with the efficiency of cycles using zeotropic mixtures as the working fluids, and found that they only cause a slight drop in cycle first law efficiency, while resulting in an increase in other metrics, such as heat source utilisation [22–24]. The proposed dynamic ORC system builds on this concept, by allowing the working fluid’s composition to be actively tuned during operation of the rig, using R245fa and R134a as the two components of the working fluid. These fluids are two commonly-selected ones for conventional Organic Rankine Cycles [25–27], are miscible with each other [28], and the difference between their boiling points is roughly equal to the annual variation in temperature in a continental climate, making them the most suitable for an initial analysis of this cycle. However, both of these fluids are HFCs (Hydrofluorocarbons), and this class of refrigerants has recently been subject to a phase-out decision over the coming decades due to their high Global Warming Potential. For a dynamic cycle, the key factor in the choice of fluids is an appropriate difference between their boiling points. Alternatives to HFCs do exist, and are presented below. Alkanes are a promising class of working fluid, and in particular pentane and isopentane have been used in real-world cycles [2]. Alkanes tend to be relatively dry working fluids, meaning that they are particularly suitable to the presence of a recuperator. They are also flammable, which means that special care must be taken with their handling, Alkanes are a large class of refrigerants and this means that working fluid pairs for a great variety of ambient conditions can be selected. HFOs (Hydrofluoro-olefins) are another fluid group under consideration in literature as a direct replacement for HFCs. R1233zd-E is the HFO replacement for R245fa [29], and R1234yf and R1234ze have been considered as replacements for R134a [27,30]. HFOs have very similar properties to HFCs, often being considered as “drop-in” replacements. R1233zd has been shown to give slightly higher thermal efficiencies than R245fa under the same operating conditions, whereas R1234yf showed slightly reduced power output due to lower density at the expander inlet. Overall they are likely to be no less suited to use in a dynamic ORC than the HFCs considered in this paper, but an investigation of alternative working fluids is an interesting avenue of further research. The cycle is initially designed to operate on the hottest day of the year with the working fluid composed entirely of R245fa, the fluid component with the higher boiling point. As the temperature drops from summer to autumn, the temperature of the coolant available to the cycle also drops. This gives excess cooling capacity. The composition of the working fluid is then adjusted by removing fluid from the receiver and replacing it with pure R134a, shifting the overall composition towards R134a. This lowers the bubble point of the fluid, and allows better utilisation of the coolant. As the temperature drops further, the composition is shifted further towards R134a. The fluid mixture removed from the system is separated by distillation to produce pure R134a and R245fa, which can then be used in further composition tuning operations. In the spring, when temperatures begin to rise again, the available coolant is no longer cold enough to ensure the working fluid is liquid at the pump inlet. Now the composition of the working fluid is shifted back towards R245fa, raising the bubble point of the fluid and ensuring the liquid condition at the pump inlet. The previous paper [19] considered a cycle using a turbine as the expander, and assumed that such a cycle can relatively simply adjust its evaporating pressure in operation by changing the shaft load on the turbine and increasing the pump power accordingly, with little change in the turbine’s isentropic efficiency. This allows the pressure ratio of the cycle to be changed in operation, increasing the evaporator pressure when the working fluid is mostly composed of R134a to minimise excess superheat. The results of this paper [19] showed a significant increase in the year-round electricity Energies 2017, 10, 440 4 of 21 generation of a dynamic cycle compared to a conventional one. An economic analysis of the dynamic cycle was also carried out, using the Chemical Engineering Plant Cost Index (CEPCI). This revealed that the additional cost of a composition tuning system capable of distilling the system’s entire charge of working fluid in 12 h was roughly 0.4% of the total cost of the system, and that the greatest increase in the capital cost of a dynamic system would come from the need to have a supply of extra working fluid for tuning purposes, which would add a further 6% to the cost of the cycle. The increased cost of the system was offset by increased electricity generation. For any increase greater than 7% the payback period of the cycle was shortened and the 20-year return on investment increased. However, turbines become uneconomical for smaller-scale applications below a few hundred kilowatts, and are outcompeted by positive displacement expansion devices, such as scroll, screw, and rotary vane expanders [30]. Quoilin et al. [31] have calculated the minimum economical operating power for a turbine in an ORC system to be roughly 40 kW for solar thermal applications, rising to over 100 kW for geothermal. This leaves a large amount of microgeneration applications for which turbines are unsuited as expanders. Positive displacement devices generally have an inbuilt volume ratio, which is constrained by their geometry. The isentropic efficiency of these devices drop off sharply if a pressure ratio different to that defined by an adiabatic expansion process between these volumes is imposed [32–34]. This pressure ratio is hereafter referred to as the “designed pressure ratio”. The working fluid in the expander is enclosed in an expansion chamber. In each case, the enclosed volume of working fluid will reach the discharge stage at a pressure defined primarily by the geometry of the expander. If this pressure is not equal to the condenser pressure, the fluid will undergo an isochoric pressure drop (i.e., under-expansion) or increase (i.e., over expansion). In the case of under-expansion, when the in-built volume ratio of the expander could provide a pressure ratio less than the actual pressure ratio between the evaporator and condenser, this will result in unused potential of the working fluid. In the case of over-expansion, when the in-built volume ratio of the expander could provide a pressure ratio greater than the actual pressure ratio between the evaporator and condenser, work will have to be expended by the expander to repressurise the fluid to the condenser pressure. Therefore, the previous approach to the dynamic cycle using a turbine as the expansion device is not applicable to small-scale ORC systems. As the considerations for designing ORC systems with positive displacement expanders are significantly different from those with turbines, this paper expands on the previous work by investigating whether the dynamic ORC concept can be applied to systems using a positive displacement expander which is constrained to a specific expansion ratio (ultimately pressure ratio). It analyses the system under a variety of ambient conditions, heat source temperatures and cycle configurations, both recuperative and non-recuperative to determine the feasibility of the development of dynamic Organic Rankine Cycle systems using positive displacement expanders having a fixed expansion ratio. It also adds an analysis of recuperative cycles applied to this dynamic concept, as well as an analysis of the specific power of the cycle and how this is affected by the changing working fluid composition in response to changing ambient temperature.

2. Numerical Modelling As shown in Figure1, a dynamic Organic Rankine Cycle consists of the same major components as a standard Organic Rankine Cycle, namely the evaporator, expander, condenser, recuperator, and pump. In addition to these, the dynamic cycle has a composition tuning system attached to it. In order to simplify the analysis in this paper, the composition tuning system was considered to be a “black box”, capable of separating the working fluid into its two component parts, and reintroducing measured amounts of these pure components into circulation in the system. It was assumed to have no significant transient effects on the performance of the system as a whole apart from the change in working fluid composition. In practice such a system would most likely be a small distillation column, which is well-established technology. Previous research from the authors showed that the extra power Energies 2017, 10, 440 5 of 21 required for a distillation system to keep up with changing ambient conditions is negligible compared to the overall power output of the cycle, as the average parasitic power required for separating and compressingEnergies 2017, 10, the 440 distillate would be 23 W for a 1 MW system [19]. 5 of 22

Figure 1. SchematicSchematic Diagram Diagram of Dynamic Organic Rankine Cycle considered in this paper.

There was assumed to be no pressure losses as the fluid passed through heat exchangers. This There was assumed to be no pressure losses as the fluid passed through heat exchangers. This is a is a common assumption, but does not entirely reflect real world systems accurately. Real-world common assumption, but does not entirely reflect real world systems accurately. Real-world systems systems will experience pressure drops, especially in heat exchangers. The primary effect of this is will experience pressure drops, especially in heat exchangers. The primary effect of this is that the that the pressure ratio at the expander inlet is reduced compared to the ideal case. A preliminary pressure ratio at the expander inlet is reduced compared to the ideal case. A preliminary investigation investigation assuming a 5% pressure drop in each heat exchanger, as was carried out in [34], assuming a 5% pressure drop in each heat exchanger, as was carried out in [34], indicating that in a indicating that in a recuperative cycle this would cause an 18% decrease in pressure ratio, and a 14% recuperative cycle this would cause an 18% decrease in pressure ratio, and a 14% decrease in expander decrease in expander power, while the evaporator heat load remained relatively constant. For a non- power, while the evaporator heat load remained relatively constant. For a non-recuperative cycle, recuperative cycle, the pressure ratio decreased by 14%, causing a 10% drop in expander power. the pressure ratio decreased by 14%, causing a 10% drop in expander power. These pressure losses These pressure losses must be carefully considered in the design of real-world systems. However, for must be carefully considered in the design of real-world systems. However, for comparison of the comparison of the dynamic and non-dynamic ORCs, the pressure losses will not have a major effect dynamic and non-dynamic ORCs, the pressure losses will not have a major effect on the differences on the differences caused by the working fluid composition. caused by the working fluid composition. Further assumptions were that there was no heat transfer to and from the system outside of heat Further assumptions were that there was no heat transfer to and from the system outside of heat exchangers (i.e., a perfectly insulated system), and no effects due to changes in velocity, elevation, or exchangers (i.e., a perfectly insulated system), and no effects due to changes in velocity, elevation, or compressibility. The work required to pump heat transfer fluids through the heat exchangers was compressibility. The work required to pump heat transfer fluids through the heat exchangers was neglected in this research. Based on these assumptions, a standard steady-state numerical model was neglected in this research. Based on these assumptions, a standard steady-state numerical model was built using MATLAB R2016a (Mathworks, Natick, MA, USA) and REFPROP 9.1 (National Institute built using MATLAB R2016a (Mathworks, Natick, MA, USA) and REFPROP 9.1 (National Institute of of Standards and Technology: Gaithersburg, MD, USA) [35]. REFPROP 9.1 was used to provide Standards and Technology: Gaithersburg, MD, USA) [35]. REFPROP 9.1 was used to provide values values for the thermophysical properties of the working fluid, and can be called via MATLAB for the thermophysical properties of the working fluid, and can be called via MATLAB function. Given function. Given a state defined by two fluid properties, this function can calculate most other a state defined by two fluid properties, this function can calculate most other important thermal and important thermal and physical properties of a fluid at this state. physical properties of a fluid at this state. Figure 2 shows the numbering convention for the points of the cycle, which are the same as those Figure2 shows the numbering convention for the points of the cycle, which are the same as shown in Figure 1. An external data file containing average monthly ambient temperature data for a those shown in Figure1. An external data file containing average monthly ambient temperature data variety of locations in different climate types was linked to the numerical model. The ambient for a variety of locations in different climate types was linked to the numerical model. The ambient temperature data from this data file could be used to determine the temperature of coolant available temperature data from this data file could be used to determine the temperature of coolant available to the system over the course of the year, which was stored as an array in MATLAB. Beijing, China to the system over the course of the year, which was stored as an array in MATLAB. Beijing, China was chosen to use as a case study as it is an example of a continental climate with a high variation in was chosen to use as a case study as it is an example of a continental climate with a high variation temperature between winter and summer. The output power for the case study was selected as 10 in temperature between winter and summer. The output power for the case study was selected as kW. The pinch point temperature difference in the heat exchangers was taken to be 5 °C which is 10 kW. The pinch point temperature difference in the heat exchangers was taken to be 5 ◦C which is consistent with previous research [36,37], and an additional 2 °C of subcooling was added to the cycle consistent with previous research [36,37], and an additional 2 ◦C of subcooling was added to the cycle at State 1 to ensure an adequate Net Positive Suction Head was provided to the pump. This allowed at State 1 to ensure an adequate Net Positive Suction Head was provided to the pump. This allowed the condition of the working fluid at State 1 to be characterised using the equations = +5 the condition of the working fluid at State 1 to be characterised using the equations T1 = Tambient + 5 and = at (= +2). and P1 = Psat at (T = T1 + 2).

Energies 2017, 10, 440 6 of 21 Energies 2017, 10, 440 6 of 22

435 3 415 395 375 355 2b 335 4

Temperature (K) 315 2 295 4b 1 275 1000 1200 1400 1600 1800 2000 Specific Entropy (J/kg.K)

FigureFigure 2. T-s diagramdiagramof of a a zeotropic zeotropic ORC, ORC, with with the the recuperative recuperative portion portion of the of cycle the cycle marked marked in a thicker in a thickergreen line. green line.

KnowingKnowing the the temperature temperature of of the the fluid fluid and and the the required required saturation saturation temperature temperature allows allows the the condensercondenser pressure pressure to to be be determined determined for for the the hottest hottest day day of of the the year, year, which which is is also also when when the the working working fluidfluid is is composed composed entirely entirely of of the the working working fluid fluid comp componentonent with with the the higher higher boiling boiling point, point, in in this this case case studystudy R245fa. R245fa. REFPROP REFPROP 9.1 9.1 can can then then be be used used to to calc calculateulate the the other other fluid fluid proper properties,ties, such such as as specific specific entropy,entropy, andand specificspecific enthalpy. enthalpy. For For a givena given pressure, pressu REFPROPre, REFPROP can alsocan bealso used be toused calculate to calculate the bubble the bubbleand dew and points dew of points a fluid of as a itsfluid composition as its composition changes, allowingchanges, a allowing set of glide a set curves of glide for the curves fluid for pairing the fluidto be pairing drawn to up. be Knowing drawn up. the Knowing required the condenser required pressurecondenser and pressure the shape and ofthe the shape bubble of the line bubble of the lineglide of curve,the glide the curve, required the required fluid composition fluid composition to satisfy to the satisfy liquid the condition liquid condition at the pump at the inletpump can inlet be cancalculated be calculated for any for ambient any ambient temperature temper providedature provided to the numericalto the numerical model. model. WithWith the condenser pressure pressure and and fluid fluid composition compositio determined,n determined, the cyclethe cycle can thencan then be analysed be analysed using usingthe real the world real world climate climate data provided, data provided, according according to well-established to well-established thermodynamic thermodynamic techniques techniques [19,38]. [19,38].The pinch Thepoint pinch temperature point temperature in the evaporatorin the evaporator is taken is totaken be 5to◦ Cbe as 5 before,°C as before, and a and further a further 5 ◦C of5 °Csuperheat of superheat is added is added at the at expander the expander inlet inlet to ensure to ensure a pure a pure vapour vapour with with no dropletsno droplets is fed is fed into into the theexpander, expander, allowing allowing the evaporator the evaporator pressure pressu to bere calculated to be calculated using the equationsusing theT3 equations= Theat source −=5 and Pevap −5= P satandat (T= =T3 −5 at (). = −5). ThisThis last last was was used used to to calculate calculate the the evaporator evaporator pressure pressure on onthe the hottest hottest day day of the of theyear, year, and andas the as cyclethe cycle in this in case this casestudy study uses usesa positive a positive displace displacementment expander, expander, this evaporator this evaporator pressure pressure was held was year-round.held year-round. The isentropic The isentropic efficiency efficiency of the of pump the pump and and the theexpander expander were were set set to to90% 90% and and 70%, 70%, respectively.respectively. AsAs thethe pressure pressure ratio ratio of theof cyclethe cycle was heldwas constantheld constant over the over year, the the isentropicyear, the efficienciesisentropic efficienciesof the pump ofand the expanderpump and were expander also assumed were also to assumed remain constant. to remain constant. ForFor the the purposes purposes of of analysis, analysis, the the pumping pumping and and ex expansionpansion processes processes were were initially initially assumed assumed to to be be isentropic,isentropic, allowing hh2,isentropic2,isentropic andand h4,isentropich4,isentropic to beto bedetermined determined using using REFPROP. REFPROP. These These values values can can then then bebe used toto find find the the actual actual values values using using an isentropic an isentropic efficiency efficiency less than less 100%, than according 100%, according the equations: the equations: h2,isentropic − h1 ηpump = (ℎ, −ℎ) (1) = (h2 − h1) (1) (ℎ −ℎ)

(ℎ(h3 −ℎ− h4) ηexpander = (2)(2) (ℎh3 −ℎ− h,4,isentropic) TheThe isentropicisentropic efficienciesefficiencies of of the the pump pump and expanderand expander were takenwere to taken be 90% to and be 70%,90% respectively.and 70%, respectively.This is consistent This is with consistent previous with published previous literature.published literature. For this research, For this research, it was assumed it was assumed that the thatexpansion the expansion device used device was used designed was designed with a volume with a ratiovolume that ratio would that cause would to operatecause to at operate this efficiency at this efficiencyat the imposed at the pressure imposed ratio, pressure i.e., a ratio, different i.e., expandera different would expander be required would forbe arequired cycle operating for a cycle at a operatingdifferent pressureat a different ratio. pressure The ratio ratio. of specific The ratio heats of ofspecific the working heats of fluids the working varies by fluids less thanvaries 1% by as less the thanfluid 1% composition as the fluid is composition shifted from R245fais shifted to R134a,from R245fa so it was to R134a, assumed so it that was there assumed would that be nothere significant would

Energies 2017, 10, 440 7 of 21 over- or under-expansion losses introduced due to changing ﬂuid composition at a constant pressure and volume ratio. Knowing the evaporator and condenser pressures, and the enthalpies at states 2 and 4, the temperatures and entropies at these states can now also be obtained using REFPROP. The effect of a recuperator could also be investigated. The MATLAB program initially took the case of zero heat transfer from the hot to the cold side, giving a pinch point temperature difference of T4-T1. The program then gradually increased the amount of heat transferred while monitoring the temperature difference at 100 different points inside the heat exchanger, taking the minimum value as the new pinch point. When this pinch point reached 5 ◦C, the corresponding value of heat transfer could then be designated as Qrecuperator. Once this has been done, all six points of the cycle have been characterized: pump outlet, recuperator outlet cold, evaporator outlet, expander outlet, recuperator outlet hot and condenser outlet. Equations (3)–(6) can then be used to calculate the efﬁciency of the cycle:

Wpump = h2 − h1 (3)

Wexpander = h3 − h4 (4)

Qevaporator = h3 − h2b (5)

Wexpander − Wpump ηcycle = (6) Qevaporator This allows the efficiency of the cycle to be calculated for any value of ambient temperature. Using real-world climate data as the values for ambient temperature allows, the performance of a dynamic ORC under various climate conditions to be analysed. The program analysed several key metrics. The first was the efficiency of the conventional ORC, ηcon, which was the efficiency of the cycle ηcycle on the hottest day of the year, when the working fluid had to be composed of 100% R245fa to ensure the liquid condition at the pump inlet. This is also the year-round efficiency of a cycle utilizing a fixed working fluid composition. The second was the efficiency of the dynamic ORC, ηdyn, for a given ambient temperature at a particular point in the year. Both of these were calculated according to Equation (6). The third metric was the average annual efficiency of the dynamic ORC over the course of the year [19], ηdyn.. This is defined as: N ∑ ηdyn. η = 1 (7) dyn. N where N is the number of operational days in the year [19]. The fourth was the annual improvement in energy provision ψ. This was given by the equation previously developed by the authors in [19]:

ηdyn. − ηcon ψ = × 100% (8) ηcon

The pinch point in the heat exchangers could be analysed using an energy balance method. Using the assumption that the heat exchangers were perfectly thermally insulated from the environment, and that the temperature difference at the expander inlet was 10 ◦C, a T-Q diagram could be set up. As for the recuperator, the program took 100 points in the heat exchanger and calculated the temperature difference between the hot and cold streams. The temperature of the thermal ﬂuid (assumed to be pressurised water in this case study) after transferring a certain amount of energy to the working ﬂuid could be calculated from the equation:

0 . Q = mwatercp∆T (9) Energies 2017, 10, 440 8 of 21

0 where mwater. is the mass flow rate of the hot water and cp its specific heat capacity. The higher the flow rate, the smaller the temperature change of the water as it exchanges energy with the working fluid. The mass flow rate of water is therefore increased from zero until the pinch point reaches the required 5 ◦C in both the evaporator and condenser. Once the flow rate is known, the final and average temperatures can be calculated using the lever rule, assuming that the specific heat capacity of the thermal fluid remains constant, giving a straight line on the pinch point diagram. Knowing the mass flow rate of the hot water, the specific power output of the cycle can be calculated. The specific power is defined here as the power output from the expander per unit of mass flow of hot fluid in the evaporator, or mathematically as:

0 10, 000 W specific = 0 (10) m water where W’ is the specific power. This allowed a further performance metric to be defined, similar to the increase in annual energy generation ψ. This was the increase in average annual specific power, given the symbol φ and defined as: 0 0 W specific,dyn − W specific,con φ = (11) 0 W specific,con 0 0 where W specific,dyn. is the specific work of the dynamic cycle and where W specific,con. is the specific work of the conventional, non-dynamic cycle The exergy at a given state can be determined using the equation: X = h − h0 − T0(s − s0) (12) As the values for specific enthalpy h and specific entropies are known for all states in the system, as is the temperature of the reference state T0, the exergy at any point in the system can be calculated. This can be used to calculate the exergy destruction rate in each component:

. . . . Id = ∑ Ein − ∑ Eout − W (13)

For the pump, the exergy destruction rate can be given by:

. . . . Ipump = (E2 − E1) + (Wpump) (14)

For the recuperator by: . . . . . Iregen = (E2b − E2) − (E4 − E4b) (15) For the evaporator by:

. . . . . Ievap = (Ehw,in − Ehw,out) − (E3 − E2) (16)

For the expander by: . . . . Iexpander = (E3 − E4) − (Wexpander) (17) For the condenser by: . . . . . Icond = (E4 − E1) − (Ecw,in − Ecw,out) (18) The Overall Exergy Efﬁciency of the cycle is given by:

. Ievaporator ηexergy = . (19) Wexpander

A qualitative analysis of the effect of working ﬂuid composition on the heat transfer process was also carried out. The Nusselt number is the ratio of total to conductive heat transfer in a ﬂuid, and is Energies 2017, 10, 440 9 of 21 generally calculated for each case using empirical correlations to experimental data. Alimoradi and Veysi [38] give a rough correlation for the Nusselt number in a shell-and tube heat exchanger of:

Nu = CRe0.7Pr0.315 (20) where Re is the Reynolds Number and Pr is the Prandtl Number of the ﬂuid:

ρuD Re = (21) µ

µcp Energies 2017, 10, 440 Pr = 9 of 22 (22) k where ρ is fluid density, u is fluid velocity, D is the = characteristic length, µ is the kinematic(22) viscosity, cp is the specific heat capacity, and k is the thermal conductivity. D was set to 1 cm and u to 1.5 m/s, and allwhere of the is other fluidinformation density, u is fluid for the velocity, calculation D is the could characteristic be obtained length, from μ is the REFPROP. kinematic viscosity, cp is the specific heat capacity, and k is the thermal conductivity. D was set to 1 cm and u to 1.5 m/s, The cycle was analysed for several heat source temperatures, for recuperative and non-recuperative and all of the other information for the calculation could be obtained from REFPROP. cases, andThe for cycle five ambientwas analysed climate for conditions.several heat Forsource each temperatures, case, the dynamic for recuperative cycle was and compared non- to the conventional,recuperative cases, non-dynamic and for five cycle, ambient as climate well as conditions. comparing For the each effect case, ofthe using dynamic a recuperative cycle was or non-recuperativecompared to the dynamic conventional, cycle. non-dynamic cycle, as well as comparing the effect of using a recuperative or non-recuperative dynamic cycle. 3. Results 3. Results The MATLAB routine based on the equations given in the previous section was used to analyse a case studyThe for MATLAB the dynamic routine Organic based Rankineon the equations Cycle. Figuregiven in3 showsthe previous the annual section variation was used in to temperature, analyse and thea case change study in for working the dynamic fluid composition Organic Rankine needed Cycle. to ensure Figure the 3 shows liquid the condition annual atvariation the pump in inlet for varioustemperature, climate and conditions. the change Itin can working be seen fluid that comp in theosition colder needed winter to ensure months, the aliquid greater condition proportion at of the pump inlet for various climate conditions. It can be seen that in the colder winter months, a greater R134a in the working fluid can be tolerated due to the lower ambient temperature. During the warmer proportion of R134a in the working fluid can be tolerated due to the lower ambient temperature. summer months, more R245fa must be present to ensure the bubble point of the fluid is high enough During the warmer summer months, more R245fa must be present to ensure the bubble point of the to ensurefluid is this high condition. enough to ensure this condition. TheThe conditions conditions for for Beijing Beijing were were taken taken asas a case study study for for more more in-depth in-depth analysis, analysis, as it ashas it the has the greatestgreatest variation variation between between summer summer and and winter winter temperaturestemperatures among among the the locations locations considered. considered. It was It was also usedalso used in the in the authors’ authors’ previous previous study study [ 19[19],], whichwhich enables enables comparison. comparison.

320 1.4

310 Ambient Temperature R134a Proportion 1.2 1 300 0.8 290 0.6 280

0.4 R134a Proportion

Ambient Temperature (K) 270 0.2

260 0 Jan-13 Feb-13 Apr-13 May-13 Jul-13 Sep-13 Oct-13 Month

Figure 3. Annual temperature variation and associated changes in working fluid composition for Beijing. Figure 3. Annual temperature variation and associated changes in working fluid composition for Beijing. Figure4 shows the variation in the efficiency of the cycle depending on the ambient temperature. The heatFigure source 4 temperatureshows the variation is set asin the 100 efficiency◦C. The of winter the cycle temperature depending ison cold the ambient enough temperature. for the working fluidThe to be heat liquid source at thetemperature pump inlet, is set even as 100 when °C. The it is winter 100% temperature R134a. As the is cold ambient enough temperature for the working increases, the efficiencyfluid to be remains liquid constant,at the pump until inlet, the pointeven when at which it is the100% ambient R134a. temperature As the ambient becomes temperature too high for increases, the efficiency remains constant, until the point at which the ambient temperature becomes too high for a 100% R134a working fluid to be a liquid at the pump inlet. At this point, R245fa must be introduced. The cycle efficiency then drops off with increasing ambient temperature. The recuperative cycle in a relatively linear fashion, whereas the basic cycle shows a concave shape.

Energies 2017, 10, 440 10 of 21 a 100% R134a working ﬂuid to be a liquid at the pump inlet. At this point, R245fa must be introduced. The cycle efﬁciency then drops off with increasing ambient temperature. The recuperative cycle in a relativelyEnergiesEnergies 2017 linear 2017, 10, ,10 440 fashion,, 440 whereas the basic cycle shows a concave shape. 10 10of 22of 22

20%20%

19%19% RecuperativeRecuperative Cycle Cycle BasicBasic Cycle Cycle 18%18%

17%17%

16%16% Cycle Efficiency Cycle Efficiency 15%15%

14%14%

13%13% 253253 263 263 273 273 283 283 293 293 303 303 AmbientAmbient Temperature Temperature (K) (K)

Figure 4. Variation in Cycle Efﬁciency with ambient temperature for a heat source temperature of Figure 4. Variation in Cycle Efficiency with ambient temperature for a heat source temperature of 100Figure◦C under 4. Variation Beijing’s in ambientCycle Efficiency conditions. with ambient temperature for a heat source temperature of 100100 °C °C under under Beijing’s Beijing’s ambient ambient conditions. conditions.

FigureFigureFigure5 shows5 shows 5 shows thethe the variation variation of of ofthe the enthalpy enthalpy enthalpy ch change changeange in inthe the inexpander, expander, the expander, evaporator, evaporator, evaporator, condenser condenser condenserand and andrecuperator recuperator as astheas the ambient the ambient ambient temperatur temperatur temperaturee changes.e changes. It changes. canIt can be be seen seen It that can that the be the amount seen amount that of ofenergy the energy amount transferred transferred of energy transferredin inthe the evaporator evaporator in the evaporator and and condenser condenser and increases condenser increases relative relative increasesly lylinearly linearly relatively for for the linearlythe evaporator evaporator for theas asthe evaporator the ambient ambient as the ambienttemperaturetemperature temperature decreases, decreases, decreases, and and in ina and slightlya slightly ina convex slightly convex sh convexshapeape for for the shape the condenser. condenser. for the This condenser. This can can explain explain This the can the shape explainshape the of the response curve for the non-recuperative cycle seen in Figure 4. shapeof the of response the response curve curvefor the for non-recu the non-recuperativeperative cycle seen cycle in Figure seen 4. in Figure4.

350350

300300

250250 ExpanderExpander 200200 EvaporatorEvaporator Condenser 150150 Condenser RegeneratorRegenerator 100100 Enthalpy Change (kJ/kg) Enthalpy Change (kJ/kg) 5050

0 0 250250 260 260 270 270 280 280 290 290 300 300 310 310 AmbientAmbient Temperature Temperature (K) (K)

Figure 5. Comparison of enthalpy change in each major cycle component with varying ambient FigureFigure 5. 5.Comparison Comparison of ofenthalpy enthalpy change change in ineach each major major cycle cycle component component with with varying varying ambient ambient temperature for a heat source temperature of 100 ◦C in Beijing’s ambient conditions. temperaturetemperature for for a heat a heat source source temperature temperature of of100 100 °C °C in inBeijing’s Beijing’s ambient ambient conditions. conditions.

TheTheThe response response response curvecurve curve in inFigure Figure 5 has5 has a a steepera steeper steeper sl ope slopeslope for for the the the evaporator evaporator evaporator than than thanfor for the forthe expander theexpander expander towards the right hand side of the graph, i.e., for operation under higher temperature ambient towardstowards the the right right handhand sideside of the the graph, graph, i.e i.e.,., for for operation operation under under higher higher temperature temperature ambient ambient conditions. This means that the evaporator enthalpy change is more sensitive to changing ambient conditions.conditions. This This means means thatthat the evaporator evaporator enthalpy enthalpy change change is more is more sensitive sensitive to changing to changing ambient ambient temperature in this region. As the temperature drops, the evaporator enthalpy change will therefore temperaturetemperature in in this this region. region. As the the temperature temperature drop drops,s, the the evaporator evaporator enthalpy enthalpy change change will therefore will therefore increaseincrease more more quickly quickly than than the the expander expander enthalpy enthalpy ch change.ange. This This means means that that the the efficiency efficiency of ofthe the cycle cycle increase more quickly than the expander enthalpy change. This means that the efﬁciency of the cycle is relativelyis relatively insensitive insensitive to tochanging changing ambient ambient temp temperatureerature in inthe the higher higher ambient ambient temperature temperature regions. regions. is relativelyAnyAny increase increase insensitive in inexpander expander to changingenthalpy enthalpy change ambientchange is cancelis temperaturecancelledled out out by byin a corresponding a the corresponding higher ambient increase increase temperature in inevaporator evaporator regions. Anyenthalpy increaseenthalpy change. inchange. expander At At lower lower enthalpy temperatures, temperatures, change for for is examplecancelled example from from out 270 by270 K a Kto corresponding to280 280 K, K, the the curve curve increase in inFigure Figure in 5 evaporator for5 for

Energies 2017, 10, 440 11 of 21

Energies 2017, 10, 440 11 of 22 enthalpy change. At lower temperatures, for example from 270 K to 280 K, the curve in Figure5 for thethe expander expander is is steeper steeper than than the the curve curve for for the the evaporator. evaporator. ThisThis meansmeans thatthat thethe efficiencyefficiency of the cycle cycle is moreis more sensitive sensitive to changing to changing ambient ambient temperature temperature in this in this region, region, resulting resulting in ain steeper a steeper slope slope for for this this part ofpart the responseof the response curve incurve Figure in Figure4. 4. ForFor the the recuperative recuperative cycle, cycle, the the responseresponse curve for efficiency efficiency in in Figure Figure 44 does does not not show show the the same same convexconvex shape. shape. This This can can also also be be explained explained usingusing the data presented presented in in Figure Figure 5.5 .The The curve curve in in Figure Figure 5 5 forfor the the recuperator recuperator has has aa convexconvex shape, with with a asteep steep section section at athigh high ambient ambient temperatures, temperatures, a peak a peakat atabout 275 275 K, K, then then a a decrease decrease to to a a steady steady value value below below about about 265 265 K. K. The The energy energy recovered recovered in inthe the recuperator is subtracted directly from the energy required in the evaporator, thereby increasing recuperator is subtracted directly from the energy required in the evaporator, thereby increasing efficiency. The convex shape of the recuperator curve in Figure 5 works to cancel out the factors efficiency. The convex shape of the recuperator curve in Figure5 works to cancel out the factors causing the concave shape of the efficiency curve for the non-recuperative cycle, as seen in Figure 4. causing the concave shape of the efficiency curve for the non-recuperative cycle, as seen in Figure4. This results in the relatively straight line seen for the efficiency plot for the recuperative cycle seen in This results in the relatively straight line seen for the efficiency plot for the recuperative cycle seen in Figure 4. This can be explained by a combination of the temperature glide caused by a zeotropic fluid, Figureand 4the. This principle can be of explained operation byof athe combination recuperator. of the temperature glide caused by a zeotropic fluid, and theFigure principle 6 demonstrates of operation this of the by recuperator. comparing T-s diagrams for the cycle operating under high temperatureFigure6 demonstrates and low temperature this by comparing ambient conditions. T-s diagrams The thick for the green cycle section operating of the under T-s plot high temperaturerepresents andthe heat low transferred temperature in ambient the recuperator. conditions. It can The be thick seen greenthat in section the low-temperature of the T-s plot ambient represents theconditions heat transferred in the right in the hand recuperator. plot, there It can is signif be seenicant that superheat in the low-temperature at the expander ambient outlet. This conditions means in thethat right the hand working plot, fluid there exiting is significant the expander superheat is sign atificantly the expander warmer outlet. than the This working means fluid that exiting the working the fluidpump, exiting giving the a expander greater driving is significantly temperature warmer differentia thanl thefor the working recuperator fluid exitingto exploit. the This pump, tends giving to a greaterincrease driving the amount temperature of heat transferred differential in the for re thecuperator recuperator under to low exploit. temperature This tends conditions, to increase as seen the amountin Figure ofheat 5. transferred in the recuperator under low temperature conditions, as seen in Figure5.

FigureFigure 6. Comparison6. Comparison ofdynamic of dynamic Organic Organic Rankine Rankine Cycles Cycles operating operating underhigh under temperature high temperature (290 K, left ) and(290 low K, temperature left) and low (265 temperature K, right) (265 ambient K, right conditions.) ambient conditions.

Also to be noted is the fact that the left hand figure, representing higher temperature ambient Also to be noted is the fact that the left hand figure, representing higher temperature ambient conditions, also happens to be the T-s diagram for a zeotropic fluid, and therefore exhibits a conditions,temperature also glide happens during to bephase the T-schange. diagram This for can a zeotropicbe seen tofluid, cause and an increase therefore in exhibits the temperature a temperature of glidethe duringexpander phase outlet change. relative This to the can pump be seen outlet to causedue to anthis increase glide, which in the will temperature also tend to of increase the expander the outletamount relative of heat to the transferred pump outlet in the due recuperator. to this glide, This which could will explain also tendthe slight to increase drop in the the amount amount of of heat transferredheat transferred in the recuperator.in the recuperator This couldat higher explain proportions the slight of R134a drop inin thethe amountworking offluid, heat because transferred as inthe recuperatorworking fluid at higheronce again proportions approaches of R134a a pure in thefluid working composition, fluid, because the glide as thedecreases, working and fluid oncecounteracts again approaches the increase a purein heat fluid energy composition, transferred the in glidethe recuperator decreases, due and to counteracts increasing superheat the increase to in heatsome energy degree. transferred The response in the of recuperator the dynamic due cycle to increasingwith changing superheat ambient to temperature some degree. clearly The responseshows ofthat the dynamicthe cycle cyclehas improved with changing performance ambient over temperature a conventional clearly Organic shows thatRankine the cycle Cycle has when improved the performancetemperature over is lower. a conventional Organic Rankine Cycle when the temperature is lower. It canIt can be be seen seen from from Figure Figure7 7that that the the dynamic dynamic cyclecycle performsperforms better better than than the the conventional conventional cycle cycle forfor both both the the recuperative recuperative and and non-recuperative non-recuperative cases, cases, with with the greatestthe greatest improvement improvement occurring occurring during theduring colder the winter colder months, winter as months, predicted as bypredicted the response by the curves response shown curves in Figureshown4 .in As Figure the conventional 4. As the

EnergiesEnergies2017 2017, ,10 10,, 440 440 1212 of of 21 22

conventional ORC efficiency is based on the highest annual temperature, the lowest point of the ORC efficiency is based on the highest annual temperature, the lowest point of the monthly average monthly average for the dynamic cycle is still higher than this, as even during the hottest months, the for the dynamic cycle is still higher than this, as even during the hottest months, the temperature is temperature is generally lower than the maximum most of the time. The non-recuperative cycle generally lower than the maximum most of the time. The non-recuperative cycle increases in efficiency increases in efficiency extremely slowly in response to decreasing temperature at the higher end of extremely slowly in response to decreasing temperature at the higher end of the temperature range, the temperature range, so the non-recuperative dynamic cycle only begins to significantly outperform so the non-recuperative dynamic cycle only begins to significantly outperform the conventional cycle the conventional cycle at the beginning and end of the year when the temperature is a great deal at the beginning and end of the year when the temperature is a great deal colder than the maximum. colder than the maximum. The efficiency of the recuperative dynamic cycle increases far more The efficiency of the recuperative dynamic cycle increases far more sharply with increasing temperature, sharply with increasing temperature, and so the improvement can be seen even during the summer and so the improvement can be seen even during the summer months, when the temperature is still months, when the temperature is still close to the maximum used in the design of the conventional cycle. close to the maximum used in the design of the conventional cycle.

14% Dynamic RegenerativeCycle

Dynamic Non-Regenerative Cycle

Conventional Regenerative Cycle

12% Conventional Non-Regenerative Cycle Efficiency 10%

8% Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Month

◦ FigureFigure 7.7.Annual Annual variationvariation inincycle cycle efﬁciencyefficiencyfor fora aheat heatsource source temperature temperature of of 100 100 °CC underunder Beijing’sBeijing’s ambientambient conditions.conditions. GraphGraph showsshows monthlymonthlyaverages. averages.

TheThe valuevalue ofofψ ψchanges changes dependingdepending onon thethe annualannual variationvariation inin temperature,temperature, asas shownshown inin FigureFigure8 8.. TheThe MATLABMATLAB routine routine was was run run using using climate climate data data from from several several locations locations worldwide,worldwide, forfor heatheat sourcesource temperaturestemperatures ofof 100100 ◦°CC andand 150150 ◦°C.C. AA steadysteady increaseincrease inin ψψ cancan bebe seenseen asas thethe amplitudeamplitude ofof thethe temperaturetemperature variationsvariations increases. This This is is to to be be ex expected,pected, as asthe the greater greater the the temperature temperature variation, variation, the thegreater greater the the difference difference between between the the hot hot and and cold cold reservoirs, reservoirs, and and therefore therefore the greatergreater thethe CarnotCarnot efficiency.efficiency. TheThe plotplot deviatesdeviates slightlyslightly fromfrom thethe linearlinear increaseincrease inin CarnotCarnot efficiency,efficiency, however,however, duedue toto severalseveral factors, factors, most most notably notably the the composition composition of of the the working working fluid. fluid. When When the the temperature temperature variation variation is small,is small, only only a small a small amount amount of of R134a R134a is is needed needed to to keep keep up up with with the the changing changing heat heat sinksink temperature.temperature. WhenWhen thethe temperaturetemperature variationvariation isis muchmuch larger,larger, the the working working fluidfluid cancan bebe 100%100% R134a,R134a, andand stillstill havehave excessexcess coolingcooling capacitycapacity itit isis notnot utilising.utilising. SomeSome smallsmall deviationsdeviations fromfrom thethe theoreticaltheoretical smoothsmooth increaseincrease cancan bebe seen.seen. ForFor example,example, PhoenixPhoenix hashas aa higherhigher averageaverage temperaturetemperature thanthan anyany ofof thethe otherother locations,locations, andand thereforetherefore aa reducedreduced conventionalconventional cyclecycle efficiency.efficiency. ThisThis meansmeans thatthat thethe dynamicdynamic cyclecycle isis slightlyslightly moremore effectiveeffective here here than than the the idealised idealised case case would would predict. predict. TheThe trendtrend for for the the non-recuperative non-recuperative cycles cycles is ofis aof slightly a slightly different different shape, shape, rising rising slowly slowly at first, at thenfirst, increasingthen increasing in slope. in Thisslope. is because,This is because, as shown as in show Figuren 4in, theFigure efficiency 4, the of effici non-recuperativeency of non-recuperative cycles only increasecycles only very increase slowly very when slowly the ambient when the temperature ambient temperature decreases from decreases the annual from the maximum. annual maximum. At lower annualAt lower temperature annual temperature variations, variations, the heat sink the temperatureheat sink temperature never becomes never cold becomes enough cold to enough cause the to non-recuperativecause the non-recuperative cycle to enter cycle the to region enter the of its region response of its curve response where curve a sharp where increase a sharp in increase efficiency in canefficiency be seen. can be seen.

Energies 2017, 10, 440 13 of 21 Energies 2017, 10, 440 13 of 22

Energies 2017, 10, 18%440 13 of 22 150°C, regenerator 16% 150°C, no regenerator 18% 100°C,150°C, regenerator regenerator 14% 16% 100°C,150°C, no no regenerator regenerator 100°C, regenerator 12% 14% 100°C, no regenerator 10% 12% ψ 8% 10% ψ 6% 8%

4% 6% 4% 2% 2% 0% 0%0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Annual Temperature Variation (°C) Annual Temperature Variation (°C)

Figure 8. Variation in ψ for ﬁve case studies for annual temperature variation. From left to right, FigureMumbai,Figure 8. Variation Ushuaia, 8. Variation in Glasgow, ψ in for ψ forfive Phoenix, five case case studies Beijing.studies for for annualannual temperaturetemperature variation. variation. From From left leftto right, to right, Mumbai,Mumbai, Ushuaia, Ushuaia, Glasgow, Glasgow, Phoenix, Phoenix, Beijing. Beijing. The variation in ψ with changing heat source temperature was also investigated, and the results The variationThe variation in ψ in with ψ with changing changing heat heat source source temperature temperature was was also also investigated, investigated, and and the resultsthe results for the case study of Beijing’s climate conditions plotted in Figure9. It can be seen that for both the for thefor case the studycase study of Beijing’s of Beijing’s climate climate conditions conditions plotted plotted in FigureFigure 9. 9. It It can can be be seen seen that that for bothfor both the the recuperativerecuperative and and non-recuperative non-recuperative dynamicdynamic cycles cycles,, the the improvement improvement in annual in annual energy energy provision provision ψ ψ recuperative and non-recuperative dynamic cycles◦ , the improvement in annual energy provision ψ increasesincreases gradually gradually until until a a temperature temperature of of 150 150 °C,C, wh whereatereat it peaks, it peaks, and andthen thenbegins begins to drop to away. drop away. increases gradually until a temperature of 150 °C, whereat it peaks, and then begins to drop away. ThisThis is in is contrast in contrast to the to resultsthe results previously previously obtained obtained by theby the authors authors for for a similar a similar dynamic dynamic ORC ORC concept This is in contrast to the results previously obtained by the authors for a similar dynamic ORC usingconcept a turbine using as a the turbine expander as the [19 expa], innder which [19], the in valuewhich of theψ smoothlyvalue of ψ decreased smoothly decreased with increasing with heat concept using a turbine as the expander [19], in which the value of ψ smoothly decreased with sourceincreasing temperature heat source as the temperature resulting increasedas the resultin Carnotg increased efﬁciency Carnot of efficiency the conventional of the conventional cycle made the increasing heat source temperature as the resulting increased Carnot efficiency of the conventional gainscycle caused made by the the gains dynamic caused cycleby the proportionally dynamic cycle proportionally smaller. smaller. cycle made the gains caused by the dynamic cycle proportionally smaller. 14% 14% 12% 12% 10%

10% 8% ψ 8% 6% Regenerative Cycle Non-Regenerative Cycle ψ 4% 6% Regenerative Cycle Non-Regenerative Cycle

4% 2% 0% 2% 75 95 115 135 155 175 195

0% Heat Source Temperature (°C)

75 95 115 135 155 175 195 FigureFigure 9. Variation9. Variation in inψ ψwith with changing changing heat source source temperat temperatureure under under Beijing’s Beijing’s ambient ambient conditions. conditions. Heat Source Temperature (°C)

It isIt significant is significant that that the the peak peak in in the the plot plot ofof FigureFigure 99 occursoccurs at at roughly roughly the the critical critical point point of R245fa, of R245fa, at a temperatureFigureat a temperature 9. Variation of 154 of ◦in C.154 ψ As with°C. stated As changing stated in the in heat the previous sourceprevious section,temperat section, theure the MATLABunder MATLAB Beijing’s routine routine ambient ensuredensured conditions. that the the cycle wascycle subcritical, was subcritical, by selecting by selecting the evaporator the evaporator pressure pressure either either to produce to produce zero superheatzero superheat at the at expanderthe expander inlet when the working fluid was 100% R245fa, or to 5 K below the critical temperature of inletIt whenis significant the working that the fluid peak was in 100%the plot R245fa, of Figure or to 9 5occurs K below at roughly the critical the critical temperature point of R245fa, the fluid, the fluid, whichever was the lower. atwhichever a temperature was theof 154 lower. °C. As stated in the previous section, the MATLAB routine ensured that the cycle was subcritical, by selecting the evaporator pressure either to produce zero superheat at the Figure 10 shows the variation in the evaporator and condenser pressures as the heat source expandertemperature inlet is when varied. the In working the lower fluid range, was increasing 100% R245 thefa, heat or to source 5 K below temperature the critical allows temperature the evaporator of the fluid, whichever was the lower.

Energies 2017, 10, 440 14 of 22 Energies 2017, 10, 440 14 of 21 Figure 10 shows the variation in the evaporator and condenser pressures as the heat source temperature is varied. In the lower range, increasing the heat source temperature allows the pressure to be increased, increasing the efﬁciency of the cycle. This trend continues until the critical evaporator pressure to be increased, increasing the efficiency of the cycle. This trend continues until point of R245fa is reached, at which point the pressure ratio cannot be increased any further without the critical point of R245fa is reached, at which point the pressure ratio cannot be increased any the cyclefurther becoming without the supercritical. cycle becoming After su thispercritical. point, After the cycle this point, then showsthe cycle the then same shows trend the assame the trend previous cycleas considered the previous by thecycle authors, considered with theby the increase authors, in annualwith the energy increase provision in annual dropping energy offprovision as the gains causeddropping by the off dynamic as the gains cycle caused become by lessthe dynamic proportionally cycle become signiﬁcant. less proportionally significant.

35 Condenser Pressure Evaporator Pressure 30

15 Pressure (bar) 10

0 75 95 115 135 155 175 195 Heat Source Temperature (°C)

FigureFigure 10. Variation 10. Variation in Evaporator in Evaporator and and Condenser Condenser pressure pressure with with changingchanging heat source source temperature temperature for Beijing’sfor Beijing’s ambient ambient conditions. conditions.

The previous analysis has been a first-law treatment of the dynamic ORC. However, First Law TheEfficiency previous is only analysis one metric has by been which a first-law a cycle can treatment be analysed. of the For dynamic waste heat ORC. sources, However, for example, First Law Efficiencythe specific is only power one is metric a better by metric which by a which cycle to can judge be analysed. the cycle. For waste heat sources, for example, the specificFigure power 11 isshows a better the metricvariation by in which the specific to judge power the cycle.of the cycle as the ambient temperature Figurechanges. 11 Two shows things the are variation immediately in theapparent specific from power the graph. of the Firstly, cycle the as specific the ambient power increases temperature changes.with Twodecreasing things areambient immediately temperature. apparent Second fromly, the graph.curves Firstly,for the therecuperative specific power and increasesnon- recuperative cycles are identical. with decreasing ambient temperature. Secondly, the curves for the recuperative and non-recuperative The first point can be explained by examining the pinch point diagrams for the evaporator of the cyclesEnergies are identical.2017, 10, 440 15 of 22 ORC. Figure 12 shows the evaporator pinch point diagrams for a high ambient temperature case, i.e., with the fluid composed of mostly R245fa, and a low ambient temperature case, i.e., with the fluid 90 composed mostly of R134a. The lower boiling point of the R134a has resulted in a far greater degree of superheat at the80 expander inlet, allowing a much steeper line for the evaporator. The steeper line means a lower necessary70 mass flow rate of thermal fluid. The ORC has its output fixed at 10 kW, so the reduced mass flow rate observed in Figure 12 means that the specific power increases for the 60 lower heat sink temperatures represented by the leftmost pinch point diagram. 50 40 30

Specific Power (W.s/kg) 20 10 0 250 260 270 280 290 300 310 320 Ambient Temperature (K)

Figure 11. Variation in speciﬁc power for recuperative and non-recuperative dynamic cycles over the Figure 11. Variation in specific power for recuperative and non-recuperative dynamic cycles over the course of the year for Beijing’s ambient conditions, and a heat source temperature of 100 ◦C. The speciﬁc course of the year for Beijing’s ambient conditions, and a heat source temperature of 100 °C. The powerspecific of the power cycle of does the cycle not varydoes dependingnot vary depending on whether on whether a recuperator a recuperator is present, is present, so theseso these two two curves are identical.curves are identical.

Figure 12. Evaporator Pinch Point Diagrams for a heat source temperature of 100 °C and heat sink temperatures of −11 °C (left) and 25 °C (right).

The second point, the fact that the recuperative and non-recuperative curves are identical, can be explained by the fact that the pinch point in both cases is at the bubble point of the working fluid, and that the recuperator does not cause a phase change in the evaporator. Even though the energy transferred in the evaporator will be less in the recuperative case, meaning the first law efficiency increases, this does not necessarily translate into an increase in specific power, as the expander work is still held constant, and the thermal fluid line must still satisfy the pinch point condition. This means that unless the pinch point position changes, there can be no change in the flow rate on the hot side of the evaporator, and the specific power will not change. In no cases analysed was there a phase change in the recuperator, meaning that there was no difference between the recuperative and non- recuperative plots.

Energies 2017, 10, 440 15 of 22

90 80 70 60 50 40 30

Energies 2017, 10, 440Specific Power (W.s/kg) 20 15 of 21 10 The first point0 can be explained by examining the pinch point diagrams for the evaporator of the ORC. Figure 12 shows250 the evaporator 260 pinch 270 point 280 diagrams 290 for a high 300 ambient 310 temperature 320 case, i.e., with the fluid composed of mostly R245fa,Ambient and a low Temperature ambient temperature(K) case, i.e., with the fluid composed mostly of R134a. The lower boiling point of the R134a has resulted in a far greater degree of superheatFigure 11. at Variation the expander in specific inlet, power allowing for recuperative a much steeper and non-recuperative line for the evaporator. dynamic cycles The over steeper the line meanscourse a lower of the necessary year for mass Beijing’s flow ambient rate of thermalconditions, fluid. and The a heat ORC source has itstemperature output fixed of 100 at 10 °C. kW, The so the reducedspecific mass power flow of rate the cycle observed does not in Figurevary depending 12 means on thatwhether the specifica recuperator power is present, increases so these for the two lower heat sinkcurves temperatures are identical. represented by the leftmost pinch point diagram.

Figure 12. Evaporator Pinch Point Diagrams for a heat source temperature of 100 ◦°CC and heat sink temperatures ofof −1111 °C◦C( (leftleft)) and and 25 25 °C◦C( (rightright).).

The second point, the fact that the recuperative and non-recuperative curves are identical, can The second point, the fact that the recuperative and non-recuperative curves are identical, can be explained by the fact that the pinch point in both cases is at the bubble point of the working fluid, be explained by the fact that the pinch point in both cases is at the bubble point of the working fluid, and that the recuperator does not cause a phase change in the evaporator. Even though the energy and that the recuperator does not cause a phase change in the evaporator. Even though the energy transferred in the evaporator will be less in the recuperative case, meaning the first law efficiency transferred in the evaporator will be less in the recuperative case, meaning the first law efficiency increases, this does not necessarily translate into an increase in specific power, as the expander work increases, this does not necessarily translate into an increase in specific power, as the expander work is is still held constant, and the thermal fluid line must still satisfy the pinch point condition. This means still held constant, and the thermal fluid line must still satisfy the pinch point condition. This means that unless the pinch point position changes, there can be no change in the flow rate on the hot side that unless the pinch point position changes, there can be no change in the flow rate on the hot of the evaporator, and the specific power will not change. In no cases analysed was there a phase side of the evaporator, and the specific power will not change. In no cases analysed was there a change in the recuperator, meaning that there was no difference between the recuperative and non- phase change in the recuperator, meaning that there was no difference between the recuperative and recuperative plots. non-recuperative plots. Figure 13 shows the variation in the increase in annual heat source utilization φ as the heat source temperature changes. It can be seen that the value initially drops off slowly as the heat source temperature is increased, due primarily to the increase in the minimum value of the specific power. As the heat source temperature approaches the critical temperature, the value of φ drops off more sharply. Figure 14 shows how the specific power of the non-dynamic cycle varies with heat source temperature for Beijing’s ambient conditions. It can be seen that the specific power of the non-dynamic cycle begins to increase at amount this point as well, due to the fact that after the critical temperature of R245fa at 154 ◦C there will be a superheat at the expander inlet for the non-dynamic cycle, allowing an increased slope on the T-Q diagram for the thermal fluid and reducing its required flow rate. Energies 2017, 10, 440 16 of 22 Energies 2017, 10, 440 16 of 22 Figure 13 shows the variation in the increase in annual heat source utilization ϕ as the heat source temperatureFigure 13 changes.shows the It variation can be seenin the that increase the value in annual initially heat sourcedrops utilizationoff slowly ϕas as thethe heatheat sourcesource temperaturetemperature changes.is increased, It can due be primarily seen that to thethe incrvalueease initially in the minimumdrops off valueslowly of as the the specific heat sourcepower. temperatureAs the heat issource increased, temperature due primarily approaches to the the incr criticalease in temperature, the minimum the value value of ofthe ϕ specificdrops off power. more Assharply. the heat Figure source 14 temperatureshows how the approaches specific power the critical of the temperature, non-dynamic the cycle value varies of ϕ with drops heat off sourcemore sharply.temperature Figure for 14 Beijing’s shows how ambient the specific conditions. power It ofca then be non-dynamic seen that the cycle specific varies power with heatof the source non- temperaturedynamic cycle for begins Beijing’s to increaseambient at conditions. amount this It poincan bet as seen well, that due the to thespecific fact thatpower after of the the critical non- dynamictemperature cycle of begins R245fa to at increase 154 °C thereat amount will be this a superheat point as well,at the due expander to the inletfact that for theafter non-dynamic the critical temperaturecycle, allowing of R245fa an increased at 154 slope°C there on thewill T-Q be adiag superheatram for atthe the thermal expander fluid inlet and forreducing the non-dynamic its required cycle,flow rate.allowing an increased slope on the T-Q diagram for the thermal fluid and reducing its required Energiesflow rate.2017 , 10, 440 16 of 21 300% 300% 250% 250% 200% 200%

Ф 150%

Ф 150% 100% 100% 50% 50% 0% 0% 75 95 115 135 155 175 195 75 95Heat 115 Source 135 Temperature 155 (°C ) 175 195 Heat Source Temperature (°C )

FigureFigure 13.13. VariationVariationin inφ ϕwith with varying varying heat heat source source temperature temperature for for Beijing’s Beijing’s ambient ambient conditions. conditions. Figure 13. Variation in ϕ with varying heat source temperature for Beijing’s ambient conditions. 80 8070 70 Regenerative Cycle 60 Regenerative Cycle 6050 5040 4030 3020 Specific Power (W/kg) 2010 Specific Power (W/kg) 100 0 75 95 115 135 155 175 195 75 95 115 135 155 175 195 Heat Source Temperature (°C) Heat Source Temperature (°C) Figure 14. Variation in the Speciﬁc Power of the Non-Dynamic Cycle with varying heat source

temperature with Beijing’s ambient conditions. Figure 14. Variation in the Specific Power of the Non-Dynamic Cycle with varying heat source Figure 14. Variation in the Specific Power of the Non-Dynamic Cycle with varying heat source Atemperature brief caveat with with Beijing’s regard ambient to the analysis conditions. of specific power: Optimising the specific power output temperature with Beijing’s ambient conditions. is a complex task. Reducing the evaporator pressure will increase expander inlet superheat, and tend A brief caveat with regard to the analysis of specific power: Optimising the specific power to increase specific power, while reducing first law efficiency of the cycle. Reduced first law efficiency outputA brief is a complexcaveat with task. regard Reducing to thethe analysisevaporator of specificpressure power: will increase Optimising expander the inletspecific superheat, power tends to increase the installed cost per kW of the cycle. The optimum point will depend on the exact outputand tend is ato complex increase task.specific Reducing power, thewhile evaporator reducing pressure first law efficiencywill increase of the expander cycle. Reduced inlet superheat, first law application of the cycle and the details of the heat source. Such a specific analysis is outside the scope of andefficiency tend to tends increase to increase specific thepower, installed while cost reducing per kW first of thelaw cycle. efficiency The optimumof the cycle. point Reduced will depend first law on the general treatment applied in this paper, but the analysis presented serves to show the general trend. efficiency tends to increase the installed cost per kW of the cycle. The optimum point will depend on Figure 15 shows the variation in superheat over the course of the year. Figures 16 and 17 show the exergy destruction in each component over the course of the year. Although some irreversibility occurred in the pump, resulting in exergy destruction, its effect was negligible in comparison to other components, and therefore has been left out of the following plots in the interest of clarity. It can be seen that with a recuperator present, the evaporator is by far the greatest contributor to exergy destruction. This exergy destruction is greatest during the winter months. This seems primarily to be caused by the greater degree of superheat introduced at the expander inlet by the shifting of the working fluid composition to one rich in R134a, which reduces its dew point. Energies 2017, 10, 440 17 of 22

the exact application of the cycle and the details of the heat source. Such a specific analysis is outside the scope of the general treatment applied in this paper, but the analysis presented serves to show the general trend. Figure 15 shows the variation in superheat over the course of the year. Figures 16 and 17 show the exergy destruction in each component over the course of the year. Although some irreversibility occurred in the pump, resulting in exergy destruction, its effect was negligible in comparison to other components, and therefore has been left out of the following plots in the interest of clarity. It can be seen that with a recuperator present, the evaporator is by far the greatest contributor to exergy destruction. This exergy destruction is greatest during the winter months. This seems primarily to be caused by the greater degree of superheat introduced at the expander inlet by the shifting of the working fluid composition to one rich in R134a, which reduces its dew point. The recuperator shows the lowest exergy destruction rate, indicating the highest recuperator efficiency, during the winter months, as was noted in the previous section. Figure 17 shows the similar results for the case of a non-recuperative cycle. The specific exergy destruction in the evaporator is higher in this case, reaching 37 kJ/kg, as opposed to 33 kJ/kg in the recuperative cycle. The exergy destruction in the condenser is also noticeably higher, reaching almost 14 kJ/kg during the winter months, which are when the recuperator is at its most effective. The exergy efficiency of the cycle over the course of the year was also analysed. Figure 18 shows this variation for a heat source temperature of 75 °C. It can be seen that the exergy efficiency is higher year-round for the recuperative cycle, and that the recuperative and basic cycles diverge in the winter months as the recuperator takes up the excess heat at the expander inlet. All cycles show high second law efficiency in the summer months, which drops off slightly as the ambient temperature drops, the Energies 2017, 10, 440 17 of 21 fluid composition changes, and the temperature mismatch in the evaporator increases.

10 Superheat at Expander Inlet (K)

0 Jan-13 Jan-13 Mar-13 Apr-13 May-13 May-13 Jun-13 Jul-13 Aug-13 Sep-13 Oct-13 Nov-13 Month

Figure 15. Superheat at expander inlet over the course of the year for a heat source temperature of ◦ Figure 15. Superheat at expander inlet over the course of the year for a heat source temperature of 75EnergiesEnergiesC under 2017 2017, 10,Beijing’s 10, 440, 440 ambient conditions. 1818 of of 22 22 75 °C under Beijing’s ambient conditions.

100000100000

1000010000

10001000

EvaporatorEvaporator ExpanderExpander

Specific Exergy Destruction (J/kg) Specific Exergy Destruction (J/kg) CondenserCondenser RegeneratorRegenerator 100100 Dec-12Dec-12 Jan-13 Jan-13 Mar-13 Mar-13 May-13 May-13 Jun-13 Jun-13 Aug-13 Aug-13 Oct-13 Oct-13 Nov-13 Nov-13 Jan-14 Jan-14 MonthMonth

FigureFigureFigure 16. Variation 16. 16. Variation Variation in exergy in in exergy exergy destruction destruction destruction in in in each each eachcycle cycl cycle e component component over over the the the course course course of of the ofthe theyear year year for for a fora a heat sourceheatheat source source temperature temperature temperature of 75 of of ◦75 C75 °C with°C with with a recuperator.a a recuperator. recuperator.

4000040000

3500035000

3000030000

2500025000 EvaporatorEvaporator 2000020000 ExpanderExpander 1500015000 CondenserCondenser 1000010000

5000

Specific Exergy Destruction (J/kg) 5000 Specific Exergy Destruction (J/kg)

00 Dec-12Dec-12 Jan-13 Jan-13 Mar-13 Mar-13 May-13 May-13 Jun-13 Jun-13 Aug-13 Aug-13 Oct-13 Oct-13 Nov-13 Nov-13 Jan-14 Jan-14 MonthMonth

Figure 17. Variation in exergy destruction in each cycle component over the course of the year for a FigureFigure 17. 17. Variation Variation in in exergy exergy destruction destruction in in each each cycl cycle ecomponent component over over the the course course of of the the year year for for a a ◦ heat sourceheatheat source source temperature temperature temperature of 75 of of 75 C75 °C without°C without without a a recuperator. a recuperator. recuperator.

Energies 2017, 10, 440 18 of 21

The recuperator shows the lowest exergy destruction rate, indicating the highest recuperator efficiency, during the winter months, as was noted in the previous section. Figure 17 shows the similar results for the case of a non-recuperative cycle. The specific exergy destruction in the evaporator is higher in this case, reaching 37 kJ/kg, as opposed to 33 kJ/kg in the recuperative cycle. The exergy destruction in the condenser is also noticeably higher, reaching almost 14 kJ/kg during the winter months, which are when the recuperator is at its most effective. The exergy efficiency of the cycle over the course of the year was also analysed. Figure 18 shows this variation for a heat source temperature of 75 ◦C. It can be seen that the exergy efficiency is higher year-round for the recuperative cycle, and that the recuperative and basic cycles diverge in the winter months as the recuperator takes up the excess heat at the expander inlet. All cycles show high second law efficiency in the summer months, which drops off slightly as the ambient temperature drops, Energies 2017, 10, 440 19 of 22 the fluidEnergies composition 2017, 10, 440 changes, and the temperature mismatch in the evaporator increases.19 of 22

55% 55%

50% 50%

45% 45%

40% 40% Exergy Efficiency

Exergy Efficiency Regenerative Cycle Regenerative Cycle 35% 35% Basic Cycle Basic Cycle Conventional ORC 30% Conventional ORC 30% Dec-12 Jan-13 Mar-13 May-13 Jun-13 Aug-13 Oct-13 Nov-13 Jan-14 12月-12 1月-13 3月-13 5月-13 6月-13 8月-13 10月-13 11月-13 1月-14 Month Month ◦ FigureFigure 18. 18.Variation Variation in in ExergyExergy Efficiency Efficiency over over the theyear year for a forheata source heat temperature source temperature of 75 °C under of 75 C Figure 18. Variation in Exergy Efficiency over the year for a heat source temperature of 75 °C under underBeijing’s Beijing’s ambient ambient conditions conditions for forthe the Recuperative, Recuperative, Non-Recuperative, Non-Recuperative, and andConventional Conventional Beijing’s ambient conditions for the Recuperative, Non-Recuperative, and Conventional (Non-Dynamic)(Non-Dynamic) cycles. cycles. (Non-Dynamic) cycles. An analysis of how the heat transfer coefficients in the heat exchangers varied depending on An analysisAn analysis of howof how the the heat heat transfer transfer coefficientscoefficients in in the the heat heat exchangers exchangers varied varied depending depending on on working fluid composition was also carried out. Figure 19 shows how the Nusselt numbers for liquid workingworking fluid fluid composition composition was was also also carried carried out.out. FigureFigure 19 19 shows shows how how the the Nusselt Nusselt numbers numbers for liquid for liquid and vapour varied depending on the working fluid composition. and vapourand vapour varied varied depending depending on on the the working working fluidfluid composition. 300 300 Liquid Nusselt Number Vapour Nusselt Number Liquid Nusselt Number Vapour Nusselt Number 250 250 200 200 150 150 100

Nusselt Number 100 Nusselt Number 50 50 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Mass Proportion of R134a in working fluid Mass Proportion of R134a in working fluid

FigureFigure 19. Variation19. Variation in Nusseltin Nusselt Number Number in in thethe evaporatorevaporator for for a aheat heat source source temperature temperature of 100 of °C. 100 ◦C. Figure 19. Variation in Nusselt Number in the evaporator for a heat source temperature of 100 °C. It can be seen in Figure 19 that the Nusselt number is around 270 for the pure R245fa, drops to It can be seen in Figure 19 that the Nusselt number is around 270 for the pure R245fa, drops to 110 for the vapour Nusselt number and 165 for the liquid Nusselt number. Even for a situation with 110 for the vapour Nusselt number and 165 for the liquid Nusselt number. Even for a situation with minimal superheating of the working fluid, this implies that an oversized heat exchanger will be minimal superheating of the working fluid, this implies that an oversized heat exchanger will be needed for the dynamic cycle compared to a non-dynamic cycle using R245fa as the working fluid. needed for the dynamic cycle compared to a non-dynamic cycle using R245fa as the working fluid. This will add to the capital cost of the dynamic cycle compared to a non-dynamic equivalent. This will add to the capital cost of the dynamic cycle compared to a non-dynamic equivalent. 4. Conclusions 4. Conclusions This paper investigates if the recently developed dynamic ORC cycle can be applied to small- This paper investigates if the recently developed dynamic ORC cycle can be applied to small- scale systems based on positive-displacement expanders with fixed expansion ratios. The results scale systems based on positive-displacement expanders with fixed expansion ratios. The results show that the dynamic ORC is capable of increasing the system’s annual average efficiency for a show that the dynamic ORC is capable of increasing the system’s annual average efficiency for a given heat source. However, such an improvement is much less than that of the large scale system given heat source. However, such an improvement is much less than that of the large scale system

Energies 2017, 10, 440 19 of 21

It can be seen in Figure 19 that the Nusselt number is around 270 for the pure R245fa, drops to 110 for the vapour Nusselt number and 165 for the liquid Nusselt number. Even for a situation with minimal superheating of the working ﬂuid, this implies that an oversized heat exchanger will be needed for the dynamic cycle compared to a non-dynamic cycle using R245fa as the working ﬂuid. This will add to the capital cost of the dynamic cycle compared to a non-dynamic equivalent.

4. Conclusions This paper investigates if the recently developed dynamic ORC cycle can be applied to small-scale systems based on positive-displacement expanders with fixed expansion ratios. The results show that the dynamic ORC is capable of increasing the system’s annual average efficiency for a given heat source. However, such an improvement is much less than that of the large scale system using turbine expanders with variable expansion ratios. Furthermore, such benefit strongly depends on heat recovery via the recuperator. The higher the heat recuperation, the higher the efficiency improvement. This is because an expander with a fixed expansion ratio approximately has a constant pressure ratio between its inlet and outlet. The increase of pressure ratio between the evaporator and condenser by tuning the condensing temperature to match colder ambient condition in winter cannot be utilized by such expanders. However, with the recuperator in place, the higher discharging temperature of the expander could increase the heat recovery and consequently reduce the heat input at the evaporator, ultimately increasing the thermal efficiency. The dynamic cycle also showed an improvement in specific power, implying better heat source utilization. This was caused by increasing expander inlet superheat as the working fluid composition changed, allowing for the same amount of electricity to be generated from a smaller flow rate of thermal fluid. An exergy analysis has also been conducted, and it was found that the exergy destruction in the cycle was dominated by the evaporator. The exergy efficiency was improved by the dynamic cycle, particularly in the winter months, as the recuperator and increased superheat caused by the change in working fluid composition made better use of the increased available driving temperature differential, compared to the conventional, non-dynamic cycle.

Acknowledgments: This research is funded by Royal Society (RG130051) and EPSRC (EP/N005228/1 and EP/N020472/1) in the United Kingdom, and a joint Programme “Royal Society–National Natural Science Foundation of China (Ref: IE150866)”. Author Contributions: Zhibin Yu developed the initial concept. Peter Collings and Zhibin Yu performed the literature review and collaborated on the introduction. Peter Collings produced the mathematical model and MATLAB program. Peter Collings and Zhibin Yu analysed the results and interpreted the data. Peter Collings and Zhibin Yu wrote the paper. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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