This paper presents a new cycle for utilising the energy from low-temperature heat sources that combines the Organic Rankine C ycle (ORC) with the Trilateral Flash Cycle (TFC) via a cascade condenser . The model developed for analysing the cycle uses Excel as a modelling platform with special VBA functions to determine the fluid properties . To verify the functions, they were used to analyse the simple OCR by using R134a, R1234yf, R152a, propane (R290), n -butane (R600), iso - butane (R600a), and ammonia (R717) and the model’sresults are compared with published results obtained by using the EES software . When t he performance of the combined cycle was evaluated for a heat -source of 120oC at various values of the cascade -condenser temperature by using R152a as the working fluid , the results show ed that a high temperature maximise s the cycle’s power and exergetic efficiency but minimises its thermal efficiency . Therefore, a tri-objective optimisation analysis of the cycle wa s conducted that simultaneously maximises all three parameters . Compared to the temperatu re that gives the max imum power, the optimised temperature reduced the power by 11.9%, but increased the thermal efficiency by 15.3% and the exergetic efficiency by 5.7% . Compared to the temperature that gives the maxmimum thermal efficiency, the optimised temperature reduced the thermal effici ency by only 5.9 %, but increased the power by 68.8 % and the exergetic efficiency by 4.3% . Keywords : Low -temperature heat recover y, ORC, TFC , Excel , Thermax , MIDACO One of the promising technologies for the utilisation of low and moderate temperature heat sources is the organic Rankine c ycle (ORC) (Fierro et al., 2022; Wolf et al., 2023 ). Unlike the conventional Rankine cycle , the ORC does not require very high temperatures to apply and can adapt to low -temperature heat source s by using an organic fluid as the working fluid instead of steam . However, l ike the conventional cycle, the efficiency of the ORC deteriorates if the temperature of the heat source is reduced or that of the condenser is increased . Although v arious modifications to the simple ORC can be adopted for improving the cycle’s efficiency , such as reheating, regeneration, and recuperation , these modifications do not address a main drawback of the ORC which is the mismatch between the temperature of the heating source and that of the working fluid during the heat -addition process in the evaporator (Skiadopoulos et al ., 2023) . A newly proposed cycle that can solve this problem is the trilateral flash cycle (TFC) in which the saturated liquid fluid is not allowed to vaporise during the heat recovery process but directly taken to expand in a two -phase expander (Yari e t al., 2015 ; Skiadopoulos et al., 2023 ). Since the technology of TFC expanders is relatively immature compared to the conventional turbines , they are costlier and less efficient (Fierro et al., 2022 , Yari e t al., 2015). Many previous researcher s developed theoretical models for comparing the performance of the ORC and TFC from thermodynamics a nd thermoeconomic viewpoints or compared them with other cycles such as the Kalina cycle . For example, Bidgoli and Yanagihara (2023 ) analysed an ORC cycle that recover s the waste heat from the intercoolers of the compression units of a large processi ng plant. By using Aspen HYSYS ( Aspen Plus , 1992) as the modelling platform , they analysed the cycle with various working fluids including R123, n -butane, n -pentane, hexane, and n-heptane. Their results showed that a net power of up to 40 MW could be generated with R123. Wolf et al. (2023) investigated a solar powered ORC by using a zeotropic iso-pentane/CO 2 mixture. Modelling of the system was done by using EES (Klein; Alvarado, 1992) and all thermodynamic properties were determined by using REFPROP (Lemmon et al., 2004). Their exergy and exergo -economic analyses showed that the investigated unit was capable of co - producing approximately 30 kW of electricity and 160 kW district heating with a n exergetic effici ency exceeding 60%. T hey concluded that the unit was able to compete with existing renew able power generating systems in terms of specific cost of electricity. Previous researchers also reported the results of theoretical studies of cascade ORC systems or hybrid systems involving ORC with steam turbines. For example, Oko et al. (2016) presented exergoeconomic analysis of a 100 kW sola r driven ORC power plant. They considered a cascade cycle of R13 4a and R290 working fluids and developed their model in Microsoft Excel and MATLAB environments. The y determined the energy and exergy efficiencies of the proposed plant, at the optimal collector operation, as 18.92 and 21.61%, respectively. The total capital investment, levelized cost of energy (LCOE) , payback period and the earning power of the investment were estimated to be 35 2 US$/kW, 0.0072 US$/kWh, 2 years 7 months, and 14.3%, respectively. Najjar and Qatramez (2019) model led a hybrid system consisting of a single flash geothermal cycle operating on a steam turbine and ORC using R600 , R600a , R11, and R123. The highest efficiency of 18.76% and net power output of 24,887MW were obtained with R11. Mokarram and Mosaffa (2020) , who studied a cycle that integrated a steam turbine and a trans - critical ORC with R245fa, showed that the system could p roduce 7.2% more power compared to a similar cycle operating in subcritical conditions. With a maximum energy and exergy efficiencies of 14.66% and 55.15%, respectively, the LCOE was 0.2018 US $/kWh. The above literature review reveals that a cycle that combines the TFC in the high -temperature circuit (HTC) and the ORC in the low -temperature circuit (LTC) has not been considered before . This conclusion is also supported by the more comprehensive review given in (Jiménez -García et al., 2023) . While minimising the mismatch between the working fluid and the heat source for the ORC , the new cycle enables different organic fluids to be used in the HTC and LTC that suit the high and low temperature range s better than a single fluid and enables a turbine to be used in the LTC instead of the two -phase expander. T he cycle also gives cogeneration systems more flexibility than a single ORC or LTC . The present paper contributes to knowledge by presenting thermodynamic evaluation and multi -objective optimisation of this new cycle. From another perspective, t he above literature review show s that most researchers used commercial software for their analyses . However, the use of general -purpose software can enc ourage independent researchers and engineering students to contribute to the development of innovative ORC and TFC systems using environment -friendly fluids (Trædal, 2014 ; Oko and Diemuodeke, 2013 ). In this respect, the present paper uses Microsoft Excel as the modelling platform with special VBA functions to determine the thermodynamic properties of the working fluids w hile the free version of the MI DACO solver (Schlueter et al ., 2012) is used for the multi-objective optimisation analysi s. MATERIAL S AND METHOD S The combined ORC -TFC cycle The ORC system has the same components as those of the conventional steam -turbine power plant which are the evaporator (boiler), the turbine, the condenser, and the pump. However, organic fluid s are used in the ORC instead of water because they have high er boiling pressures at low temperatures . The TFC differs from the ORC by heating the working fluid without going into the vaporisation process so that t he hot pressurised fluid expands in the two-phase region . By leading to a uniform temperature glide between the heat so urce and the working fluid, this cycle reduces the losses during the heat -transfer process and improves the performance of the system. Typically, T FC system can provide 50% more work than ORC system for the same energy input, but they need sophisticated expander s that can adequately han dle the liquid -phase presence during the expansion process (Fierro et al, 2022). Apart from increasing the investment cost, two - phase expanders are less eff icient than the turbines. Figure 1 .a shows a schematic diagram of the combined ORC -TFC system in which t he heat source is first used to heat the working fluid of the TFC circuit and then to heat the working fluid of the ORC circuit . After expanding in the two -phase expander to produce power , the working fluid of the TFC circuit is condensed by the cooler working fluid of the ORC circuit in a cascade condenser (cc) and then pumped into the TFC heater . The ORC system shown on Figure 1 .a is a recuperative system in which the superheated fluid exiting the turbine is used to heat the cold fluid exiting the pump in an internal heat -exchanger (IHEX) . Accordingly, the initially superheated fluid exiting the turbine enters the condenser of the ORC as saturated vapour . In the condenser , the working fluid is cooled by the cooling water to the saturated -liquid state and then pumped into the cold side of the IHEX . After the IHEX , the fluid is heated by the heat source to the state of saturated liquid before entering the cascade condenser where it is heated by the condensing fluid of the TFC circuit until it becomes saturated vapour . Figure 1 . Schematic and T-s diagrams for the combined TFC -ORC cycle 1 2 3 4 T 1 6 7 5 8 s 2b 8s 4s (b) (a) ΔTpp ΔTcc 2c 4b G Cooling water Pump Pump Condenser TFC Heater Expander 6 7 Turbine 2 3 1 4 Cascade condenser 5 8 IHEX ORC Heater 2b 2c 4b Heat source Figure 1.b shows the T-s diagram of the combined system . Unlike the TFC cycle in which the pinch point occurs where the heating fluid exits the system , that of the combined cycle occurs in the middle of the heating process which forces the heating source to exit the system at a higher temperature than that of the TFC . Although this limits the amount of heat recovered and the work produced by the ORC circuit , the combined cycle can still produce more work than the simple ORC because of the additional work produced by the TFC circuit. Compared to the simple TFC, the combined cycle can have a higher thermal efficiency by allowing two different working fluid s to be used in the TFC and ORC circuit s that lead to a better overall performance and by replacing the two -phase expander with the single -phase turbine . As shown later, the power produced by the cycle and its thermal and exergetic efficiencies depend on the temperature of the cascade condenser . While the thermal efficien cy increases by increasing this temperature, the cycle’s power decreases and the exergetic efficiency has an optimum at a certain value . Therefore, determining the cascade temperature that gives the desired trade -off between the three performance indicator s poses a tri-objective optimisation problem. The analytical model s for the TFC and ORC circuits and the combined cycle The analytical model for thermodynamic analyses of the cycle assume s steady -state operation and neglect s pressure losses and heat -transfer losses in the various components . However, t he losses due to irreversibil ity in the pumps, t he turbine, and the two-phase expander are taken into consideration via the relevant the isentropic efficiencies (Moran; Shapiro, 2006) . The analytical model for the TFC circuit Given the pinch -point temperature difference, Δ Tpp, the te mperature of the heat source exiting the TFC heater , Thso,TFC , is determined from: pp TFC,hso T T T 6 (1) Given the inlet temperature of the hea t source, Ths,in, and its mass flow rate, hsm , the rate of heat transfer from the heat source (assumed to be a stream of hot -water) to the working fluid of the TFC, TFC,hsQ , and the mass flow rate of the working fluid , TFCm , are calculated from :  TFC,hso in,hsphs TFC,hs T Tcm Q   (2) 6 7hh/ Q mTFC,hs TFC   (3) The specific work ,in kJ per kg,of the TFC pump is given by :  TFC,p TFC,cc TFC, heater TFC,p / p pv w   5 (4) Where pheater ,TFC and pcc,TFC are the pressures of the TFC fluid in the heater and cascade - condenser, respectively , and ηp,TFC is the isentropic efficiency of the TFC pump. Equation ( 5) is then used to determine the enthalpy of the fluid at state 6 after the pump: TFC,pw h h5 6 (5) The specific work of the working fluid in the TFC during the two -phase expansion process is evaluated from the enthalpy change as follows: exp s exp hh w 8 7 (6) Where ηexp is the isentropic efficiency of the expander and h8s is the enthalpy of the fluid after an isentropic expansion (refer to Figure 1.b). The thermal efficiency of the TFC circuit alone is given by:  TFC,hs TFC,p exp TFC TFC Q/ w w m    (7) The analytical model for the ORC circuit The mass flow rate of the working fluid in the ORC circuit is given by: c TFC ORC hh/hh m m2 3 5 8   (8) The specific work of the ORC pump is given by:  ORC,p ORC,con ORC,cc ORC,p / p pv w   1 (9) Where ηp,ORC is the isentropic efficiency of the ORC pump. Energy balance over the IHEX gives: b b hh h h4 4 2 2  (10) Where h4b is the enthalpy of the saturated vapour at the condenser pressure. The enthalpy h4 is determined by taking into consideration the irreversi bility of the turbine as follows: t shh h h 4 3 3 4 (11) Where h4s is the enthalp y after an isentropic expansion and ηt is the isentropic efficiency of the turbine. The turbine ’sspecific work is then calculated from: 4 3hh wt (12) The thermal efficiency of the ORC circuit alone is given by: ORC,hs ORC,p t ORC ORC Q/ w w m    (13) Where ORC,hsQ is the heat recovered in ORC circuit , which is given by: b c ORC ORC,hs h h m Q2 2   (14) The analytical model for the combined cycle The total heat recovered from the heat source, the total net power produced, and the overall thermal efficiency , respectively, are given by: ORC,hs TFC,hs tot,hs Q Q Q   (15)  TFC,p exp TFC ORC,p t ORC tot w w m w w m W      (16) tot,hs tot tot Q/W (17) The overall exergetic efficiency of the combined cycle given by (Yari et al., 2015): in,hs tot tot E/W (18) Where in,hsE is the rate of exergy flow of the heat source entering the system as given by: in,hsE   0 0 0 s sT h h min,hs in,hs hs  (19) Finally, the temperature of the heat source exiting the system is given by: phs tot,hs in,hs out,hs cm/ Q T T  (20) Validation of the VBA functions for fluid properties The Excel -based models developed for the present analyses determine the fluid thermodynamic properties by using the Thermax add-in (El-Awad, 2019) . Thermax , which has been deve loped for educational purposes, provides property functions for ideal gases, saturated water and superheated steam, synthetic and natural refrigerants, psychrometric analyses, two aqua solutions for vapour -absorption refrigeration, combustion and chemically -reacting substances, and air at standard atmospheric pressure. Regarding the functions used in the present analyses, which are those from the refrigerants ’ group, t he functions for saturated liquid s and saturated vapour s simply interp olate the data given by ASHRAE ( 2017) . For superheated refrigerants, the specific volume is determined by the Redlich -Kwang equation and the enthalpy and entropy are determined by ideal-gas equation s in which the specific heat is determined at an adjusted pressure by mu ltiplying the actual pressure by a “compressibility factor” for which an average value of 0.5 is adopted (El-Awad et al. 2019) . The use of the adjusted pressure instead of the actual pressure extends the range of these functions to super critical conditions, but the accuracy of the functions needs to be verified. In what follows, the functions are validated by comparing the results of the model developed for the simple ORC with the data given by Yari et al . (2015) . Figure 2 shows the Excel model developed for the simple ORC by using the data shown on Table 1. The sheet consists of four blocks of cells. The first block on the left side of the sheet stores the specified data, while the second and third blocks in the middle p erform the ca lculations for the ORC model . The fourth block on the right side of the sheet determines the overall parameters that include the total amount of recovered heat (Qhs_tot), the net power produced by the system (Work_net), the exit temperature of the heating source (Ths_out), and the overall energetic and exergetic efficiencies. The sheet uses R152a as the working fluid, but the name of the fluid is stored as a variable so that the model can be used for other fluids. Figure 2. The Excel -aided model for the ORC with the data given by Yari et al. (2015) Table 1. Values of the parameters used for validating the ORC model (Yari et al., 2015) Parameter Value P0 [kPa] 101.325 T0 [oC] 25 Ths [oC] 120 hsm [kg/s] 100 ΔTpp [K] 10 ηp (%) 85 ηt [%] 85 Yari et al. (2015) developed their model by using the EES software and analysed the cycle’s performance with seven working fluids which are : R134a, R1234yf, R152a, propane (R290), n - butane (R600), iso -butane (R600a), and ammonia (R717). The system’s power output, thermal efficiency, and exergetic efficiency were calculated at various values of the turbine’s inlet temperature, T3. The results obtained by the pr esent model for the power and thermal and exergetic efficiencies of the same fluids are compared to those obtained by Yari et al . (2015) on Figure 3 and Figure 4 . The two figure s show that the results obtained by the present model agree well with the results obtained by Yari et al. (2015) . Figure 3. Comparison of (a) the estimations for the present model for the system’s power at various values of T3 with (b) those obtained by Yari et al. (2015) Figure 4 . Comparison of (a) the estimations for the present model for the thermal and exergetic efficiencies at various values of T3 with (b) those obtained by Yari et al. (2015) RESULTS AND DISCUSSION Performance of the combined cycle at various cascade temperatures Figure 5 shows the model developed for the combined cycle in which t he first block of cells on the left side of the sheet stores the specified data, while the second and third blocks in the middle perform the calculations for the TFC and ORC circuits, respectively . The names of the working fluids in the TFC and ORC circuits are stored as variables so that the model can be used for different fluid pairs , but R152a is used in both circuits . The model uses the data shown on Table 1 according to which the heat source temperature is 120oC. The temperature of the TFC fluid entering the expander, T6, is taken as 110oC and the cascade -condenser temperature difference is 025050075010001250150017502000 60 70 80 90 100 110Net power (kW) Turbine inlet temperature (oC) R152a R134a R290 R1234yf R600 R717 -55152535 579111315 60 70 80 90 100 110 Exergetic efficiency (%) Thermal efficiency (%) Turbine inlet temperature (oC) R152a R134a R290 R1234yf R600 R600a R717 R152a R134a taken as 3oC. The temperature of the TFC fluid in the cascade condenser is specified as 50oC. By using t he model, the cycle’s power, thermal efficiency, and exergeti c efficiency were calculated at various values of its cascade -condenser temperature and the results are plotted on Figure 6. The figure shows that the power drops as the cascade temperature incre ases, but the thermal efficiency increases steadily while the exergetic efficiency has an optimum at 75oC. Selecting the appropriate cascade temperature requires a trade -off between the three performance indicators as discussed in the following section. Figure 5. Excel -aided model for the combined cycle using R152a Figure 6. Variation of the combined -cycle’s power and thermal and exergetic efficiencies with the temperature of the TFC fluid in the cascade condenser 05101520253035404550 05001000150020002500 45 55 65 75 85 95 105 Thermal and exergetic efficiencies (%) Net power (kW) Temperature of the TFC fluid in the cascade condenser (oC) Power η ε Tevap,TFC = 110oC Tri-objective optimisation of the combined cycle Determining the cascade temperature that gives the best trade -off between the three cycle’s parameters is a tri-objective optimisation problem that requires the cycle’s power, thermal efficiency , and exergetic efficiency to be simulta neously maximised . In general, multi-objective optimisation (MOO) analysis can involve other factors such as the economic and environmental facto rs. While single -objective optimisation analyses can easily be done by using Excel’s Solver , MOO analyses require a multi -objective solver. Fortunately, the present analysis involves a single changing variable, which is the temperature in the cascade condenser and, t herefore , can be conducted by using the free version of the MIDACO solver (Schlueter et al ., 2012) that allows up to four changing variables to be considered . The set -up for MIDACO is shown on Figure 7. Figure 7. MIDACO’s set -up for the dual -objective optimisation of the combined cycle Three objective functions are involved in the analysis, which are the power, thermal efficiency, and exergetic efficiency of the combined cycle stored in cells N21, N22, and N23 of the model, respectively. All three objectives require the relevant paramete r to be maximised by MIDACO by changing a single variable which is the cascade temperature of the fluid used in the TFC circuit stored in cell B10. The lower and upper limits imposed on the changing variable are 50oC and 95oC, respectively. MIDACO and othe r MOO solvers do not generate a single solution but a Pareto front that contains a set of un -dominated solutions from which one solution is selected. Figure 8 shows the solution selected by MIDACO according to which the temperature of the cascade condenser is 72.83oC. Figure 8. Performance of the optimised combined cycle with the dual -objective solution obtained by MIDACO Table 2 compares various key parameters of the optimised solution determined by MIDACO with those of the cycle at the lower and upper limits of the cascade temperature Tcc,TFC that yield the maximum power and the maximum thermal efficiency, respectively. The table figures show that the heating source of the optimised solutio n exits at a temperature of 7 1.61oC, which is higher than that for the maxmum power but lower than that for the maximum efficiency. Compared to the cycle that gives the maxmimum po wer, the optimised cycle reduced the rate of recovereed heat by 23.6 % and the power by 11.9 %, while increasing the exergetic efficiency by 15.3% and the thermal efficiency by 5.7 %. Compared to the cycle that gives the maxmimum thermal efficie ncy, the optimised cycle reduced the thermal efficiency by only 5.9 %, but increased the power by 68.8 % and the exergetic efficiency by 4.3%. Determining the most suitable fluid pair for the cycle and the appropriate cascade temperat ure requires a multi -objective optimisation analysis that also takes into consideration the economic and environmental factors. Table 2 . Comparison of the thermodynamic performance of the optimised combined cycle Maximise power Maximise efficiency Tri-objective Cascade temperature for TFC fluid, Tcc,TFC (oC) 50 95 72.830 Cascade temperature for ORC fluid, Tcc,ORC (oC) 47 92 69.831 Heat -source exit temperature, Ths,out (oC) 56.69 93.04 71.61 Heat rejected, outQ (kW) 24847.38 10387.04 18753.52 Heat recovered, tot,hsQ (kW) 26869.88 11442.67 20535.42 Total power, tot,netW (kW) 2022.498 1055.63 1781.895 Thermal efficiency, ηtot (%) 7.527 9.225 8.677 Exergetic efficiency, εtot (%) 41.69 8 42.288 44.09