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