Component 612: Hot Water to Air Heating Coil (Simple) by HVACSIM+ General Description Component 612 is the simplest of three water-to-air heat exchanger models available at present in the TYPES library. A constant overall heat transfer coefficient (UA) is assumed. Steady state air and water outlet temperatures are calculated using an approximate effectiveness relationship for cross-flow heat exchangers. Dynamic outlet temperatures are calculated using first-order differential equations, in which the time constant is a function of both the coil flush time and the thermal capacitance of the coil. However, the outlet temperature is not delayed by the flush time of the coil. Nomenclature Ca - capacitance rate (specific heat times mass flow rate) of air Cmin - minimum of Ca and Cw Cw - capacitance rate (specific heat times mass flow rate) of water Ka - flow resistance parameter on air side of coil Kw - flow resistance parameter on water side of coil NTU - number of transfer units R - ratio of minimum to maximum capacitance rate UA - overall heat transfer coefficient wa - mass flow rate of air ww - mass flow rate of water e - effectiveness Toll - coil time constant Tollc - capacitive term of coil time constant Tollx - coil flush time Subscripts a - air i - inlet o - outlet ss - steady state w - water Mathematical Description The heating coil model uses an approximate equation for effectiveness as a function of NTU (number of transfer units) for a cross-flow heat exchanger with both fluids unmixed [1] to determine steady state air and water outlet temperatures: e = 1 - exp{[exp(-R*n*NTU) - 1]/(R*n)} where n = NTU^(-0.22) and NTU is defined by NTU = UA/Cmin The steady state air and water outlet temperatures are found using the definition of e: Taoss = Tai + (Twi - Tai)*e*Cmin/Ca Twoss = Twi - (Taoss - Tai)*Ca/Cw A coil time constant is also calculated by the model, using the following equation: Toll = (Tollc^(-1) + Tollx^(-1))^(-1) where Tollc is a capacitive term supplied as a parameter and Tollx is the coil flush time, which is determined from the coil volume: Tollx = p*Vol/ww The equation for the time constant was chosen to give the correct qualitative behavior of Toll as a function of water flow rate (see reference [2], figure 7). Air and water dynamic outlet temperatures are both calculated using this time constant: d(Two)/dt = (Twoss - Two)/Toll d(Tao)/dt = (Taoss - Tao)/Toll If both Tollc and the coil volume are zero, the differential equations are eliminated from the model and the steady state temperatures are used. Finally, inlet pressures are calculated from the outlet pressures and flow rates: Pai = Pao + Ka*wa^2 Pwi = Pwo + Kw*ww^2 Component 612 Configuration Inputs Description 1 Pao - outlet air pressure 2 wa - air mass flow rate 3 Tai - inlet air temperature 4 Tao - outlet air temperature (from first output) 5 Pwo - outlet water pressure 6 ww - water mass flow rate 7 Twi - inlet water temperature 8 Two - outlet water temperature (from second output) Outputs Description 1 Tao - outlet air temperature 2 Two - outlet water temperature 3 Pai - inlet air pressure 4 Pwi - inlet water pressure Parameters Description 1 UA - overall heat transfer coefficient (times area) 2 Ka - flow resistance parameter, air side 3 Kw - flow resistance parameter, water side 4 Vol - water side volume of coil 5 Tollc - capacitive term of coil time constant Reference: 1. McQuiston, F.C., and Parker, J.D. Heating, Ventilating, and Air Conditioning Analysis and Design, 2nd edition. New York: John Wiley and Sons, Inc. (1982). 2. Pearson, J.T., Leanard, R.G., and McCutchan, R.D. "Gain and time constant for finned serpentine crossflow heat exchangers." ASHRAE Transactions Vol. 80, part 2, pp. 255-267 (1974). 3. HVACSIM+ Building Systems and Equipment Simulation Program Reference Manual (NBSIR 84-2996) Daniel R. Clark United States Department of Commerce National Institute of Standards and Technology Gaithersburg, Maryland 20899-0001