# -*- coding: utf-8 -*- """ hexayurt climate control @author: Luke """ import numpy as np from matplotlib import pyplot ######### assumed parameters ########## #in imperial units, deltaT / R yields btu/hr-ft^2 R_1inch = 3.85 R_1inch_thermasheath = 6 R_1_5inch = 5.78 R_1_5inch_thermasheath = 9.6 R_tape = 0.05 #this was a typical value for paper. tape_sqft = 1.0 #total area of gaps in insulation in an assembled yurt (complete guess). # I estimated wall-> air convective transfer as 20 W/m^2/K based on this page: http://www.engineeringtoolbox.com/convective-heat-transfer-d_430.html # and I converted with this http://www.unitconverter.org/heat-transfer-coefficient-conversion-chart.html R_convection = 1.0/3.5 cfmsAndRValuesToPlot = [(0.0,R_1inch), (60.0,R_1inch), (70.0,R_1inch), (60.0,R_1_5inch_thermasheath), (70.0,R_1_5inch_thermasheath),] ASSUMED_HUMIDITY_CHANGE = 0.8 yurt_sqft = 12*4.0*8.0 shadowedTemperature = 90.0 #temperature of panels in shadow shadowed_sqft = yurt_sqft * 0.5 #rough estimate of panel area in shadow sunlitTemperature = shadowedTemperature + 20.0 #a guess at the outside temperature of panels in sunlight sunlit_sqft = yurt_sqft * 0.5 #rough estimate of panel area in direct sunlight initialInsideTemperature = 78. humanBtuHrIn = 1 * 4.0 * 60. #one person's body heat. Ends up negligible. ######### physical constants ########## POUNDS_PER_GALLON = 8.34 btuPerPoundEvaporate = 1042 #water's heat of evaporation at 90F, per https://www.engineeringtoolbox.com/water-properties-d_1573.html wtPercentWater_fullHumidity_80F = 0.0200 wtPercentWater_fullHumidity_90F = 0.0272 wtPercentWater = np.array([ #source: http://www.engineeringtoolbox.com/water-vapor-air-d_854.html (30.,0.0030), (40.,0.0047), (50.,0.0069), (60.,0.0100), (70.,0.0143), (80.,0.0200), (90.,0.0272), ]) lbAirPerFt3_90F = 0.072 C_air_JoulesPerKg = 1005 joulesPerBTU = 1055.05 kgPerPount = 0.453 C_air_btuPerLb = C_air_JoulesPerKg / joulesPerBTU * kgPerPount def printBTU(btuPerHr, title): BTUHR_PER_WATT = 3.412141633 watts = btuPerHr / BTUHR_PER_WATT print title+": %0.1f btu/hr = %0.1fW" % (btuPerHr,watts) def equilibriumEvaporation(inletTemp, humidityChange): """ Calculates outlet temperature of the swamp cooler, evaporated water per ft^3 air, and btu removed per ft^3 air. Accounts for the fact that as air cools, it absorbs less water. Assumes no heat exchange with the yurt during evaporation. If we can absorb yurt heat during evaporation we'll be able to put more water into the air.""" assumedOutletTemp = inletTemp outletTempError = 9999 while abs(outletTempError) > 0.2: wtPercentWater_fullHumidity = np.interp([assumedOutletTemp], wtPercentWater[:,0],wtPercentWater[:,1])[0] assumedWtPercentWater = wtPercentWater_fullHumidity * humidityChange btuRemovedPerPoundAir = btuPerPoundEvaporate * assumedWtPercentWater finalTemp = inletTemp - btuRemovedPerPoundAir / C_air_btuPerLb outletTempError = finalTemp - assumedOutletTemp assumedOutletTemp += np.sign(outletTempError)*0.1 print "cooler outlet temp=",assumedOutletTemp,"degF" print "for incoming air at %0.1fF, evaporation can decrease temp by up to %0.1fF" % (inletTemp,btuRemovedPerPoundAir / C_air_btuPerLb) return (assumedWtPercentWater, btuRemovedPerPoundAir) (outletWtPercentWater, btuRemovedPerPoundAirInTheseConditions) = equilibriumEvaporation(inletTemp=shadowedTemperature, humidityChange=ASSUMED_HUMIDITY_CHANGE) def runSwampCooler(outsideAirDegF, insideAirDegF, cfm, verbose = False): btuRemovedPerPoundAir = btuRemovedPerPoundAirInTheseConditions#btuPerPoundEvaporate * achievableWtPercentWater swampCoolerCFHr = cfm * 60.0 btuLetInPerPoundAir = C_air_btuPerLb * (outsideAirDegF - insideAirDegF) coolerBtuHrIn = swampCoolerCFHr * lbAirPerFt3_90F * btuLetInPerPoundAir coolerBtuHrRemoved = swampCoolerCFHr * lbAirPerFt3_90F * btuRemovedPerPoundAir coolerNetBtu = coolerBtuHrIn - coolerBtuHrRemoved gallonsPerHour = swampCoolerCFHr * lbAirPerFt3_90F * outletWtPercentWater / POUNDS_PER_GALLON if verbose and cfm > 0: print "cooler uses 1 gallon per %0.1f hr" % (1.0/gallonsPerHour) print "cooler lets in %0.1f btu/hr and absorbs %0.1f btu/hr.\nnet %0.1fbtu/hr. The hot inlet air is robbing %0.1f%% of the cooling effect." % (coolerBtuHrIn, coolerBtuHrRemoved, coolerNetBtu, 100.*(coolerBtuHrIn/coolerBtuHrRemoved)) return (coolerNetBtu, gallonsPerHour) def simulate(swampCoolerCFM, panelR): print "------ "+str(swampCoolerCFM)+"cfm ----------" insideTemperature = initialInsideTemperature times = [] temps = [] deltaT = 0.01 for hr in np.arange(0.0,4.0,deltaT): times.append(hr) temps.append(insideTemperature) btuHrIn = ((shadowedTemperature - insideTemperature) / (panelR+R_convection) * shadowed_sqft + (sunlitTemperature - insideTemperature) / (panelR+R_convection) * sunlit_sqft) tapeBtuHrIn = (sunlitTemperature - insideTemperature) / (R_tape+R_convection) * tape_sqft #multiply a wrong number x a guess. #### swamp cooler ###### (coolerNetBtu, gallonsPerHour) = runSwampCooler(outsideAirDegF=shadowedTemperature, insideAirDegF=insideTemperature, cfm=swampCoolerCFM, verbose = (hr==0.0)) if hr == 0: printBTU(btuHrIn," At t=0, heat in through insulation") printBTU(tapeBtuHrIn," through tape") printBTU(humanBtuHrIn," human generates") totalBTU = btuHrIn+tapeBtuHrIn+humanBtuHrIn printBTU(totalBTU," total heat in") btuPerGallonHeatCapacity = 1.0 * POUNDS_PER_GALLON yurtHeatCapacity = btuPerGallonHeatCapacity * 10 insideTemperature += (btuHrIn + tapeBtuHrIn + humanBtuHrIn + coolerNetBtu) * deltaT / yurtHeatCapacity print " Final temp = %0.1fF" % (insideTemperature) return (times,temps) #1.15V in heat gun output for PC fan, 1.6V for blower #2.1V in lab for PC fan, 2.5V in lab for blower #3.9V in output of cooler in both cases def v2h(v): print (v - 0.75)/3.0 """ 1 blower, 1 hole: 62CFM 1 blower, 3 holes: 86CFM with or without water, 1 filter: 3.6V humidity with 2.4V humidity in 2 filters: """ if __name__=="__main__": pyplot.figure() pyplot.title("hexayurt interior temp with outside = %.0fF"%(shadowedTemperature)) for cfm,R in cfmsAndRValuesToPlot: (times, temps) = simulate(swampCoolerCFM = cfm, panelR = R) pyplot.plot(times,temps, label = "%.0f cfm, R=%.2f" % (cfm,R) ) pyplot.xlabel("hour of direct sun") pyplot.ylabel("degF") pyplot.legend() pyplot.show()