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Discussion in 'Home Power and Microgeneration' started by Nick Pine, Aug 24, 2003.

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  1. Nick Pine

    Nick Pine Guest

    NREL says an average June day in Phoenix is 88.2 F, with an average daily
    max of 103.5 and a humidity ratio w = 0.0056, so the vapor pressure of water
    in air is P = 14.696/(0.62198/w+1) = 0.1311 psi, and Y = 0.135T+1.92P-11.122
    = 3.1, ie it's "hot," on one ASHRAE comfort scale (0 is comfy, +1 is warm,
    and -1 is cool.) Can we evaporate water indoors to make 0.135T+1.92P-11.122
    = 0, ie T+14.22P = 82.39? Say the house thermal conductance is 200 Btu/h-F,
    and it uses 600 kWh/mo of electricity indoors, and windows are well-shaded.

    P = 29.921/(0.62198/w+1) = 0.2670 "Hg makes Tdp = 9621/(17.863-ln(P)) = 502 R
    or 42 F, less than the 55 F said to be needed for swamp cooler effectiveness.

    With indoor temp T, airflow of say, 1000 cfm brings in about (103.5-T)1000
    Btu/h of sensible heat. The house conductance adds (103.5-T)200. Electrical
    use adds 2841 Btu/h, so the peak cooling load is (103.5-T)1200+2841 Btu/h.
    It takes about 1000 Btu to evaporate a pound of water, and air weighs about
    0.075 lb/ft^3. With an indoor humidity ratio w, 1000 cfm of air can move
    about 1000x60x0.075(w-0.0056) = 4500(w-0.0056) pounds of water per hour or
    4.5x10^6w-25200 Btu/h of heat... (103.5-T)1200+2841 = 4.5x10^6w-25200 makes
    T = 126.87-3750w. P = 14.696/(0.62198/w+1), so 126.87-3750w+14.22P = 82.39
    makes 44.48-3750w+208.98w/(0.62198+w) = 0, ie 84.31w^2+46.74w-0.62198 = 0,
    which makes w = 0.0130 pounds of water per pound of dry air.

    T = 78.1 F and P = 0.3009 psi (0.613 "Hg) makes Y = -0.001, ie "comfortable."
    Adding 4500(0.0130-0.0056) = 33.3 lb/h of water (4 gph) would raise the RH
    from 100x0.267/e^(17.863-9621/(103.5+460)) = 12% outdoors to 62% indoors. We
    might use 12 40 psi 0.5 gph indoor misters, eg 2 $26.96 Mister Cool kits from
    http://www.hydropool.com/cgi-bin/hydro/pool_supplies/accessories/az-pro.htm,
    with a 67% duty cycle.

    But that's 103.5 F peak of an average June day, and houses have mass.
    At the average 88.2 temp, (88.2-T)1200+2841 = 4.5x10^6w-25200 Btu/h makes
    T = 111.57-3750w, and 128.5w^2+71.77w-0.62198 = 0 makes w = 0.008536, so
    T = 79.6 and P = 0.199 psi, as we evaporate 4500(0.008536-0.0056) = 13.2
    pounds per hour of water.

    And why 1000 cfm? It looks like an intelligent swamp cooler might use less
    air and water flow for lower outdoor temps, eg 200 cfm and 6.9 pounds of
    water per hour at 88.2 F and 300 cfm and 16.3 pounds at 103.5. Does this
    comfort equation apply all the up to 100% RH? At that point, we can't
    evaporate any water indoors...

    A 120 V solenoid valve dug out of an old washing machine might control misters
    with a $5 humidistat or a PIC microchip with a $15 Honeywell humidity sensor
    and a $5 temp sensor, and maybe a moisture sensor on the floor.

    Alternatively, we might build an air-air heat exchanger into the ceiling so
    outgoing cooler air near the ceiling cools incoming warmer air before it
    absorbs water indoors. Or trickle water over the roof at night or use a
    rock-filled pond or gabion to make water near the dew point, with an indoor
    fan-coil unit or ceiling radiator, without adding any warm air or humidity
    to the house.

    Nick

    10 WA=.0056'humidity ratio (#H20/#dryair)
    20 GH=200'house conductance (Btu/h-F)
    30 E=2841'internal energy use (Btu/h)
    40 FOR TA= 88.2 TO 103.5 STEP 15.3'outdoor temp (F)
    50 FOR CFM=100 TO 500 STEP 100'vent fan airflow (cfm)
    60 G=GH+CFM'effective house conductance (Btu/h-F)
    70 A2=(TA*G+E+4500*CFM*WA)/G
    80 A5=(82.39-A2)/(14.22*14.696)
    90 B2=4500*CFM/G/(14.22*14.696)
    100 A=-B2
    110 B=-.62198*B2+1-A5
    120 C=-.62198*A5
    130 W=(-B-SQR(B^2-4*A*C))/(2*A)
    140 PHG=29.921/(.62198/W+1)'indoor vapor pressure ("Hg)
    150 T=82.39-14.22*14.696/(.62198/W+1)
    160 PSAT=EXP(17.863-9621/(460+T))'vapor pressure at 100% RH ("Hg)
    170 RH=100*PHG/PSAT
    180 PRINT TA;CFM;TAB(15);T;TAB(26);RH;60*CFM*.075*(W-WA)
    190 NEXT CFM
    200 PRINT
    210 NEXT TA

    outdoor indoor indoor lb H20
    temp (F) cfm temp (F) RH (%) per hour

    88.2 100 75.82893 103.0296 6.552321
    88.2 200 78.02118 63.76435 6.912526 <--
    88.2 300 78.68417 52.91046 7.598912
    88.2 400 79.00403 47.83385 8.358578
    88.2 500 79.19236 44.89248 9.146326

    103.5 100 71.8588 189.0924 12.33336
    103.5 200 75.50176 109.3604 14.04029
    103.5 300 76.62033 88.23434 16.28082 <--
    103.5 400 77.16261 78.50755 18.64345
    103.5 500 77.48267 72.91886 21.05314
     
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