The process described above is analyzed in two stages. The first stage analysis is the main cooling load and the second stage is the separate heat recovery precooling load. The process is most economical and makes most sense if the first stage latent cooling load is large enough to generate considerable condensate flow, the climate is humid throughout the year (high summer wetbulb temperatures), and the condensate from the first stage coil is drained by gravity to the heat recovery pre-cooling coil (second stage to save on additional pump horsepower).
The steady-flow energy equation:
(1) Qcoil = Mair1 (h1 - h2)
and mass balance equation:
(2) Mcon = Mair1 (w2-w1)
Where, Qcoil = The cooling load of the cooling coil in Btu.
Mcon = The condensate that results from the cooling of the airstream below its dewpoint (lb).
h = Enthalpy and grains of moisture per pound of air (Btu/lb).
w = Grains of moisture per pound of air.
T = Temperature in °F.
Adding time to both equations yields the rates of heat flow and condensate flow. Let this condensate discharge by gravity to another coil, which is placed in a second incoming airstream Mair2 totally independent of the first airstream cycle. The temperatures of the condensate entering and leaving the second cooling coil are designated as Tcon1 and Tcon2. Therefore the heat flow rate equation at the second coil is:
(3) Qcon = Mcon Cp (Tcon1-T2con)
Where Cp is the specific heat of water. Assuming no external heat gain or loss of the condensate, the heat balance equations between the condensate and the second airstream must balance since the heat lost by the higher enthalpy airstream is gained by the lower enthalpy condensate in the coil. Therefore:
(4) Qcon = Qair2 and
(5) Qair2 = Qcon = Mair2 x (hamb-hair2)
If we know the quantity of air in the second airstream, we may then solve for hair2:
(6) hair2 = hamb - (Qcon / Mair2)
Applying the above equations to a simple air conditioning process with chilled water as the refrigerant fluid, at standard atmospheric pressure conditions, a psychrometric chart can be used to extrapolate data. Air is cooled to saturation at 55°F. Ambient conditions are chosen for 0.4% ASHRAE values, and the derived equation for flow from equation (3) in gallons per minute (gpm) and Heat loss/Heat gain (Q) from equation (6) in Btuh are assumed to be widely familiar by HVAC engineers in the form:
(7) gpm = Q 490 x (T2-T1)
(8) Q = cfm x 4.5 x (h2-h1)
Stage 1. Main cooling and dehumidification. An air handler has the capacity to cool a volumetric flow rate of outside air "V" (in cfm) from maximum summer ambient conditions down to 55° saturation. Since mass flow rate is conserved, volumetric flow rate is converted to mass flow rate by dividing by the specific volume and converting from hours to minutes. Using the psychrometric chart, all the entering and leaving conditions including enthalpy and grains of moisture per pound of air are extrapolated. The condensate flow rate, Mcon, in pound per minute is obtained from equation (2).