Mechanical Engineering - Energy Systems LM

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Group Activity 3: Heat Pumps Mechanical Engineering - Energy Systems Authors: •Group xx: xxxxx xxxxx (xxxxxxxx), xxxxx xxxxx (xxxxxxxx) •Group xx: xxxxx xxxxx (xxxxxxxx), Fabio Santoro (xxxxxxxx) Lecturer:Prof. Stefano Consonni Teaching Assistants:Riccardo Cremona, Hamidreza Heydari and Nima Razmjoo Academic year:2025-2026Contents Introduction2 1 Part A: Winter heating21.1 Thermodynamic properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3 1.2p−handT−sdiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 1.3 Compressor isoentropic efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.4 Compressor electric consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.5 Compressor volumetric displacement. . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.6 Evaporation heat power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.7 Cycle COP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.8 Mass flow rate of brine and water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 1.9T−˙ Qdiagram of both heat exchanger. . . . . . . . . . . . . . . . . . . . . . . . . . .5 2 Part B: Summer cooling62.1 Plant Scheme. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 2.2 Thermodynamic properties and refrigerant mass flow rate. . . . . . . . . . . . . . . .7 2.3p−handT−sdiagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 2.4 Compressor electric consumption. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 2.5 Condensation heat power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 2.6 Compressor rotational speed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2.7 Cycle COP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2.8 Mass flow rate of brine and water. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10 2.9T−˙ Qdiagram of both heat exchanger. . . . . . . . . . . . . . . . . . . . . . . . . . .10 GA Assessment and References11 1 Energy Systems- Report GA3 - Groups xx and xx Introduction The scope of this group activity is the analysis of a closed loop (hypothesis horizontal) geothermal heat pump system for residential application. This system is design to heat the house during winter1 but, it is also possible to extract heat from the house during summer2. With the excel routine [1], we are able to estimate the thermodynamic properties of the fluids we consider in the system. 1.Part A: Winter heatingFigure 1:HP configuration scheme The figure1is a schematic representation of the geothermal heat pump system that ex- tract heat from the ground (at 15◦ C the whole year) to increase the temperature of brine (a mixture of water and salt that we will ap- proximate as pure water) and enters the heat exchanger HEX2. In the heat exchanger we evaporate the working fluid (R134a) then, we compress it and we cool it down till saturated liquid conditions in the heat exchanger HEX2 (condenser). The heat released in the con- denser is used to heat up the water that goes through house piping and provides heat power to the house. At the condenser outlet, the working fluid is throttled into a dissipative valve to reach the evaporation pressure. We assume both water and brine at atmospheric pressure with no losses in the piping system. On the contrary, we assume pressure drop in both heat exchangers on the working fluid side but, only in the section in which there is a phase change. For the refrigerant, we con- sider no superheating at compressor inlet and no subcooling at condenser outlet. In table1, we listed extra data for this problem. Table 1:GHP winter configuration dataSymbolValueUnitDescription T amb5◦ C ambient temperature ousideT ground15◦ C ground temperatureT brine,in12◦ C brine inlet temperatureT brine,out8◦ C brine outlet temperature˙ Qheating32 kW heating power of the heat pump˙m ref0.2 kg/s refrigerant mass flow rateη vol70 % volumetric efficiency of the compressorη el70 % electric efficiency of the compressor drivern2970 rpm rotating speed of the compressor shaft T hot,water50◦ C temperature of hot water produced in HEX-1T cold,water45◦ C temperature of cold water returning from house spacesT cond58◦ C refrigerant temperature at condensation inlet (condensation)∆T min,eva8◦ C minimum temperature difference in the evaporation process∆p hexs3 % pressure drop in heat exchanger2condenser HEX1 evaporator HEX2 valve throttling compressor 2 3 4 1 ~ Q EVA Q COND W compr,el house ground brine in brine out water out water in Energy Systems- Report GA3 - Groups xx and xx 1.1.Thermodynamic properties Figure 2:p−hgeneric diagram We are required to compute the thermodynamic properties of the refrigeration cycle. We can refer to the generic diagram2. Let’s consider each point separately:•Point 4 We have the constraint of minimum temperature difference in the evaporator and considering a counter flow heat exchanger, we can compute the temperatureT4=T brine,out−∆T min,eva. We can evaluate the pressurep4=p sat@(T 4). The remaining properties can be evaluated later with more information. •Point 1 In point 1 we are in saturated vaporx1= 1conditions. In the evaporator the pressure drops to p1=p 4·(1−∆p hexs)and we can evaluate the other thermodynamic propertiesh 1,s 1andv 1with the excel macro.•Point 3sv We know the temperature at the inlet of the condensation section of the condenserT3=T cond. Again, we are in saturated vaporx3sv= 1conditions, so we can compute the other thermodynamic properties p3sv,h 3sv,s 3svandv 3svwith the excel macro. •Point 3 In the condenser, 2 phases section, the pressure dropsp3=p 3sv·(1−∆p hexs)and we reach saturated liquid conditionsx3= 0without sub-cooling. Given the pressure, we can compute the other properties T3,h 3,s 3andv 3. •Point 4continue A the condenser outlet, the fluid is throttled in a delamination valveh4=h 3till reaching the a pressure of the evaporator inlet. The other propertiess4,x 4andv 4can be evaluated with the excel macro. •Point 2 A the compressor outlet we are in super heated vapour conditions at the same pressurep2=p 3sv. We can estimate the enthalpy with the condenser heat power: ˙ Qcond=˙ Qheating= ˙m ref·(h 2−h 3)⇒h 2=h 3+˙ Qheating˙m ref The other propertiess2,T 2andv 2can be evaluated with the excel macro. We can evaluate also the properties of the brine and water since we have the temperatures and we can assume the pressure atpbrine=p water= 1atm. For the brine it is clear the inlet and outlet temperature but, for the water we have:Tw,in=T cold,waterandT w,out=T hot,water. The other properties can be evaluated with the Excel macro. All numerical values of the properties are collected in Table2in the next page. 3p h 4 4 sv 3 3 sv 1 p cond,in Q COND Q EVA log scale 2 iso 2 s iso s real p cond,out p eva,out p eva,in W compr Energy Systems- Report GA3 - Groups xx and xx Table 2:Winter heating: TDN properties value ipThsvxstatus [bar][ ◦ C][kJ/kg][kJ/(kgK)][m 3 /kg]1 2.84019 -0.838 398.114 1.72756 0.07137 1 SV 2 16.03608 70.751 442.230 1.75141 0.01346 - sup heated 3sv 16.03608 58 426.071 1.70351 0.01209 1 SV 3 15.55500 56.732 282.230 1.26927 0.00093 0 SL 4 2.92803 0 282.230 1.30104 0.02915 0.414 L-V brine in 1.01325 12 50.506 0.18059 0.00100 - sub cooled brine out 1.01325 8 33.725 0.12133 0.00100 - sub cooled water in 1.01325 45 188.515 0.63857 0.00101 - sub cooled water out 1.01325 50 209.418 0.70377 0.00101 - sub cooled 1.2.p−handT−sdiagrams In Figure3we represented thep−handT−sdiagrams created with python coolprop package [1].Figure 3:p−h(top) andT−s(bottom) diagram: winter heating 4 250 275 300 325 350 375 400 425 450 475 Entalpy h [kJ/kg] 2 3 6 10 16 20 Pressure p [bar] (logarithm) 1 4 3 3sv 2 2is 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Entropy s [kJ/(kgK)]10 0 10 20 30 40 50 60 70 80 Temperature T [°C] 1 4 3 3sv 2 2is Energy Systems- Report GA3 - Groups xx and xx 1.3.Compressor isoentropic efficiency The isoentropic efficiency of the compressor is: h2is=h@(p 2, s 1)η is,c=h 2is−h 1h 2−h 1≈81.58% 1.4.Compressor electric consumption The compressor electric consumption˙ Wel,c=˙m ref·(h 2−h 1)η is,c≈12.605kWe 1.5.Compressor volumetric displacement The compressor volumetric displacementVcilis computed with the inlet volumetric rate˙ V1: ˙ V1=v 1·˙m ref≈51.39m3 /hVcil=˙ V1n·η vol≈411.97cm 3 1.6.Evaporation heat power The evaporation heat power extracted from the ground is˙ Qeva= ˙m ref·(h 1−h 4)≈23.177kWth 1.7.Cycle COP The coefficient of performance of the cycle isC OPcycle=˙ Qcond˙ Wc= ˙ Qcond˙m ref(h 2−h 1)≈3.627 1.8.Mass flow rate of brine and water The mass flow rates of brine and water are: ˙mbrine=˙ Qevah brine,in−h brine,out≈1.381kg/s˙m water=˙ Qcondh water,in−h water,out≈1.531kg/s 1.9.T−˙ Qdiagram of both heat exchanger In the following diagram we plotted theT−˙ Qdiagram with evaporator and condenser:Figure 4:T− ˙ Qdiagram of evaporator and condenser: winter heating 5 Energy Systems- Report GA3 - Groups xx and xx 2.Part B: Summer cooling During the summer, the same plant can be modified to extract heat from the house and send it into the ground. Through a 4-way valve and another throttling valve we can invert the sequence of operations so, the heat exchangers HEX1 and HEX2 switch function condenser/evaporator. From the winter, we keep some feature equal: •Approximation brine as water •Same volumetric displacement of the compressorVcil •Same compressor isoentropic and electric efficiency •No superheating at compressor inlet and no sub-cooling at condenser outlet For the sake of clarity, every variable that refers to the part A1will be specified explicitly (i.e.Vcil,A). In Table3we have a collection of data for the new configuration. Table 3:GHP summer configuration dataSymbolValueUnitDescription T amb30◦ C ambient temperature ousideT ground15◦ C ground temperatureT room23◦ C Desired room temperatureT hot,brine22◦ C brine outlet temperatureT cold,brine18◦ C brine inlet temperature˙ Qcooling28 kW heating power of the heat pumpT hot,water12◦ C temperature of hot water produced in HEX-1T cold,water7◦ C temperature of cold water returning from house spacesT cond32◦ C wf temperature at the beginning of condensation∆T min,eva8◦ C minimum temperature difference in the evaporation process∆p hexs3 % pressure drop in heat exchangerη vol75 % volumetric efficiency of the compressor6 Energy Systems- Report GA3 - Groups xx and xx 2.1.Plant Scheme The summer cooling configuration is represented in the scheme5.Figure 5:Summer cooling configuration scheme 2.2.Thermodynamic properties and refrigerant mass flow rate We are required to compute the thermodynamic properties of the refrigeration cycle. We can refer to the same generic diagram2at page3. The procedure is almost the same of winter configuration1.1. Let’s consider each point separately:•Point 4 We have the constraint of minimum temperature difference in the evaporator and considering a counter flow heat exchanger, we can compute the temperatureT4=T cold,water−∆T min,eva. We can evaluate the pressurep4=p sat@(T 4). The remaining properties can be evaluated later with more information. •Point 1 In point 1 we are in saturated vaporx1= 1conditions. In the evaporator the pressure drops to p1=p 4·(1−∆p hexs)and we can evaluate the other thermodynamic propertiesh 1,s 1andv 1with the excel macro.•Point 3sv We know the temperature at the inlet of the condensation section of the condenserT3=T cond. Again, we are in saturated vaporx3sv= 1conditions, so we can compute the other thermodynamic properties p3sv,h 3sv,s 3svandv 3svwith the excel macro. •Point 3 In the condenser, 2 phases section, the pressure dropsp3=p 3sv·(1−∆p hexs)and we reach saturated liquid conditionsx3= 0without sub-cooling. Given the pressure, we can compute the other properties T3,h 3,s 3andv 3. •Point 4continue A the condenser outlet, the fluid is throttled in a delamination valveh4=h 3till reaching the a pressure of the evaporator inlet. The other propertiess4,x 4andv 4can be evaluated with the excel macro. 7condenser HEX2 evaporator HEX1 valve throttling compressor 2 3 4 1 ~ Q EVA Q COND W compr,el ground house water in water out brine out brine in Energy Systems- Report GA3 - Groups xx and xx •Point 2is We keep the same isoentropic efficiencyηA is,cof the compressor from winter configuration:s 2is=s 1 andp2is=p 3sv. The other properties can be evaluated with macro excel:h 2is,T 2isandv 2is. •Point 2 A the compressor outlet we are in super heated vapour conditions at the same pressurep2=p 3sv. We can estimate the enthalpy with the condenser heat power: h2=h 1+h 2is−h 1η A is,c The other propertiess2,T 2andv 2can be evaluated with the excel macro. We can evaluate also the properties of the brine and water since we have the temperatures and we can assume the pressure atpbrine=p water= 1atm. For the brine and water we have:T w,in=T hot,water, Tw,out=T cold,water,T brine,in=T cold,brineandT brine,out=T hot,brine. The other properties can be evaluated with the Excel macro. All numerical values of the properties are collected in Table4. Table 4:Summer cooling: TDN properties valuepThsvxstatus [bar][ ◦ C][kJ/kg][kJ/(kgK)][m 3 /kg]1 2.73871 -1.831 397.531 1.7281 0.0739 1 SV 2is 8.15427 36.117 420.179 1.7281 0.0258 - sup heated 2 8.15427 40.997 425.290 1.7445 0.0266 - sup heated 3sv 8.15427 32 415.781 1.7138 0.0251 1 SV 3 7.90964 30.929 243.067 1.1479 0.0008 0 SL 4 2.82341 -1 243.067 1.1583 0.0166 0.223 L-V brine in 1.01325 18 75.638 0.2678 0.0010 - sub cooled brine out 1.01325 22 92.374 0.3249 0.0010 - sub cooled water in 1.01325 12 50.506 0.1806 0.0010 - sub cooled water out 1.01325 7 29.526 0.1064 0.0010 - sub cooled The refrigerant (R134a) mass flow rate for this configuration is lower than winter mode: ˙mref=˙ Qevah 1−h 4≈0.181kg/s(∼90.6%·˙m A ref) 8 Energy Systems- Report GA3 - Groups xx and xx 2.3.p−handT−sdiagrams In Figure6we represented thep−handT−sdiagrams created with python coolprop package [1].Figure 6:p−h(top) andT−s(bottom) diagram: summer cooling For the configuration of summer cooling, the cycle operates on lower pressure and temperature ratios. 2.4.Compressor electric consumption The compressor electric consumption˙ Wel,c=˙m ref·(h 2−h 1)η A is,c≈7.188kWe It is lower than configu- ration A because we deal with lower mass flow rate and low high pressure/temperature, so lower fluid enthalpy value at the compressor outlet. 2.5.Condensation heat power The heat power discharged to the brine and subsequently to the ground is: ˙ Qcond= ˙m ref·(h 2−h 3)≈33.032kWth The power discharged to the ground is slightly higher than configuration A. 9 225 250 275 300 325 350 375 400 425 450 Entalpy h [kJ/kg] 2 3 4 5 6 7 8 9 10 Pressure p [bar] (logarithm) 1 4 3 3sv 2 2is 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Entropy s [kJ/(kgK)]10 0 10 20 30 40 50 Temperature T [°C] 1 4 3 3sv 2 2is Energy Systems- Report GA3 - Groups xx and xx 2.6.Compressor rotational speed The compressor volumetric displacementVA cildoes not change respect to the winter configuration, for summer we can change the rotational speed. First, it is computed the inlet volumetric rate˙ V1: ˙ V1=v 1·˙m ref≈48.24m3 /hn=˙ V1V A cil·η vol≈2602rpm(∼87.6%·n A ) The thermodynamic properties of 1 are almost the same for both winter and summer, it is just slightly lower for summer. The lower mass flow rate produces lower volumetric flow rate at compressor inlet. The compressor rotates at lower rate 2.7.Cycle COP The coefficient of performance of the cycle isC OPcycle=˙ Qeva˙ Wc= ˙ Qeva˙m ref(h 2−h 1)≈5.564which is higher than configuration A because we extract more cooling heat power and we require less effort on the compressor. 2.8.Mass flow rate of brine and water The mass flow rates of brine and water are: ˙mbrine=˙ Qcondh brine,in−h brine,out≈1.974kg/s˙m water=˙ Qevah water,in−h water,out≈1.335kg/s We require respective more and less mass flow rate of brine and water for the summer cooling system. 2.9.T−˙ Qdiagram of both heat exchanger In the following diagram we plotted theT−˙ Qdiagram with evaporator and condenser:Figure 7:T− ˙ Qdiagram of evaporator and condenser: summer cooling For this case, the condenser and evaporator curves are closer respect to before and the distance be- tween the two vertical dashed lines that define the total evaporation and condensation heat power (respectively˙ QLand˙ QH) are closer and this is coherent to the fact that we require less power to run the compressor. 10 Energy Systems- Report GA3 - Groups xx and xx GA Assessment and References GroupMember NameContribution Riccardo Marchesi 3 out of 3 13 Federico Normanno 3 out of 3Vijay Mani 3 out of 3 46 Fabio Santoro 3 out of 3References [1]Ian H. Bell, Jorrit Wronski, Sylvain Quoilin, and Vincent Lemort. Pure and pseudo-pure fluidthermophysical property evaluation and the open-source thermophysical property library coolprop. Industrial & Engineering Chemistry Research, 53(6):2498–2508, 2014. 11