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EnergyEfficientBuildingDesignCollegeofArchitectureIllinoisInstituteofTechnology(IIT),ChicagoPLATE&FRAMEHEATEXCHANGERSIZINGWATERSIDEECONOMIZER(WSE)OperatesfromNov-MarwhenWB=40FFORMULASHeaterinClgTwrBasinorByPassCooling2285gpmCFM(ft3/min)x7.48052=GPM(gals/min)topreventfreezing??CWRTowerCWSGPM/7.48052(ft3/lb)xD(lbs/ft3)x60(min/hr)=M(lbs/hr)CW-to-HXorGPMx8.021xD=MBy-PassCW-to-HXQ(mbh)=MxSHx(Ti-To)/1000=Ti1=Fluid-1-InTo2=Ti2=(GPMx8.021xD)xSHx(Ti-To)/1000=To1=Fluid-1-Out4842GPMx0.008021xDxSHx(Ti-To)Ti2=Fluid-2-InCW-OutP+FHeatCW-InLMTD(LogMeanTempDiff)=To2=Fluid-2-OutExchanger[(To2-Ti1)-(Ti2-To1)]/[LN{(To2-Ti1)/(Ti2-To1)}]CHW-In(chiller)CHW-Outwhere(To2-Ti1)(Ti2-To1)To1=Ti1=LMTD=(DT1-DT2)/(LN(DT1/DT2))DT1=ABS(Ti1-To2)5444whereDT1Dt2DT2=ABS(Ti2-To1)CHW-toCHW-FrmQ=AxUxLMTDSurfaceArea(A)=Q/(UxLMTD)HXHXTo1=CHW-In54CHWRCoolingCHWSTi1=CHW-Out44Coils1985gpmLogMeanTemperatureDifference(LMTD)Ti2=CW-In42WHXPlatesTo2=CW-Out48P&FHX-COUNTERFLOWCWSCW-in:Ti2CW-from-HX2.PrimaryFluidCWRTi2=422285gpmCW-to-HXHCHW-out:To1To2=48DT2=2DT1=6CW-out:To2To1=44CHW-in:Ti1CHW-from-HXCHWS1985gpmL1.SecondaryFluidTi1=54CHW-to-HXCHWRAirHandlingUnit(AHU)CoolingCoilCOILING-COIL-CROSS-FLOWCoolingCoilCHW-from-HXTo1=54CHWSTi1=4444degFDT2=36Ti2=90DT1=6Air-IN90degFAir-OUT50degFTo2=5054degFCHW-to-HXCHWRVarkieC.Thomas,Ph.D.,P.E.Skidmore,OwingsMerrill,LLPWater-Side-EconomizerEnergyEfficientBuildingDesignCollegeofArchitectureIllinoisInstituteofTechnology(IIT),ChicagoHeatExchangerCalculationsTwobasicformulasareusedinallheatexchangercalculations.Theseare:HeattransferBtu/hr=lbs/hrxsphtxtemp.change°FInthecaseofwater,thespecificheatcanusuallybeconsideredas1.0andtheformulaexpressedas:Btu/hr=flowrateinGPMx500xtemp.change°F(1)where:500=8.33lbs/galx60min/hrconversiontolbs/hrHeattransferinBtu/hr=(U)(A)(LMTD)(2)where:U=overallheattransfercoefficientA=heattransferareainsq.ft.U=overallheattransfercoefficientA=heattransferareainsq.ft.LMTD=logmeantemperaturedifference=(largetemp.diff.)-(smalltemp.diff.)alldividedby:thenaturallogof(largetemp.diff-smalltemp.diff)TherangeoftheheattransfercoefficientUvarieswidely,dependinguponthephysicalconditionssuchasthesolutionviscosities,surfacefouling,fluidvelocitiesandturbulence,involved,constantorchangeofstate,andmetalresistance.Forexample,water-to-waterheatexchangerstypicallyhaveUvaluerangeslike:Plate-frame:500to1,200Btu/(hrxsqftx°F)Shellandtube:150to350Btu/(hrxsqftx°F)Plate-coil:50to250Btu/(hrxsqftx°F)ThesecanbecontrastedtoUvaluesof4to8forair-to-airorsteam-to-airheattransfer,whichiswhytheseareusuallyplate-fincoilswithverylargesurfaceareasQ=UxAxLMTDxCfwhere:Q=HeatloadinBtu/hrU=OverallheattransfercoefficientinBtu/hr·ft2oFA=Area(ft2)LMTD=Logmeantemperaturedifference(oF)Cf=LMTDcorrectionfactor(0.85-1.0formostgeothermalapplications).Exampleselection:Application-radiantfloorheatingin350,000ft2factoryResourcetemperature-170oFAvailablegeothermalflow-375gpmLoad-7,500,000Btu/hrBuildingloopsupplywatertemperature-135oFmax.Geothermaltemperaturedrop:=7,500,000Btu/hr÷(500·375gpm)=40oF.Geothermalexittemperature:=170oF-40oF=130oF.Geothermalside170oFto130oFBuildingside135oFto120oFDt1=170oF-135oF=35oFDt2=130oF-120oF=10oFQ=UxAxLMTDxCfUsingaLMTDconvectionfactorof0.90,requiredheatexchangerareais:Area=7,500,000Btu/hr÷(19.9oF·0.90·950Btu/hr·ft2oF)=441ft2VarkieC.Thomas,Ph.D.,P.E.Skidmore,OwingsMerrill,LLPHXformulasEnergyEfficientBuildingDesignCollegeofArchitectureIllinoisInstituteofTechnology(IIT),ChicagoU=overallheattransfercoefficientA=heattransferareainsq.ft.LMTD=logmeantemperaturedifference=(largetemp.diff.)-(smalltemp.diff.)alldividedby:thenaturallogof(largetemp.diff-smalltemp.diff)TherangeoftheheattransfercoefficientUvarieswidely,dependinguponthephysicalconditionssuchasthesolutionviscosities,surfacefouling,fluidvelocitiesandturbulence,involved,constantorchangeofstate,andmetalresistance.Forexample,water-to-waterheatexchangerstypicallyhaveUvaluerangeslike:ThesecanbecontrastedtoUvaluesof4to8forair-to-airorsteam-to-airheattransfer,whichiswhytheseareusuallyplate-fincoilswithverylargesurfaceareasGeothermaltemperaturedrop:=7,500,000Btu/hr÷(500·375gpm)=40oF.VarkieC.Thomas,Ph.D.,P.E.Skidmore,OwingsMerrill,LLPHXformulasEnergyEfficientBuildingDesignCollegeofArchitectureIllinoisInstituteofTechnology(IIT),ChicagoTRANTER://=73VarkieC.Thomas,Ph.D.,P.E.Skidmore,OwingsMerrill,LLPHXPicturesEnergyEfficientBuildingDesignCollegeofArchitectureIllinoisInstituteofTechnology(IIT),ChicagoPROPERTIESOFLIQUIDSKinematicViscosity(sq.ft./sec)inLiquidTablesare:(valueshown)/1,000,000LiquidPropertiesTemperature(F)PROPERTIESOFHIGHTEMPERATUREHOTWATER-3003060100150210WaterDensity(lb/cuft)62.4262.3762.0061.2059.81TempSatrPrDensitySpecificKinViscSp.HeatSpecificGravity=Dens/62.41.001.000.990.980.96degFpsiglb/cuftGravitysqft/secBtu/lb-FKinematicViscosity(sqft/sec)19.3112.177.394.763.20TPDD/62.4VHSpecificHeat(Btu/lboF)1.001.001.001.001.012120.059.810.963.201.0055GlycolDensity(lb/cuft)67.9867.5567.1166.5565.7464.6