Component 610: Cooling or Dehumidifying Coil by HVACSIM+
General Description
This model represents a circular finned or continuous finned
serpentine heat exchanger with four or more rows in counterflow crossflow
configuration. The subroutine is based on a program written by Elmahdy and
Mitalas [1], with minor modifications to convert it into a Type subroutine and
to add dynamics to their steady state model.
The subroutine uses equations for log mean temperature difference
(LMTD) and log mean enthalpy difference (LMHD) which are strictly correct only
for counterflow heat exchangers. When four or more rows are arranged in
crossflow counterflow configuration, treating the coil as a counterflow heat
exchanger is a good approximation. Use of the model to represent coils with
fewer than four rows is not recommended.
The model accounts for condensation on the outside surface of the coil.
There are three possible conditions for the coil: all wet, partially wet, or
all dry. The subroutine determines which of these conditions applies, and
treats each case separately.
Component 610 requires a relatively large number of parameters
describing the physical characteristics of the coil. Fin efficiencies, heat
transfer coefficients, and time constants are calculated within the subroutine
from this information. The units given in the nomenclature section must be
used.
Nomenclature
Am - minimum area for air flow (m^2)
Ao - external surface area (m^2)
b - slope of enthalpy vs. temperature line at saturation,
DeltaH / DeltaT (kJ / kg-C^2)
Cf - correction factor (dimensionless)
Cp - specific heat (kJ / kg-C)
Cm - total thermal capacitance of coil material (kJ/C)
Di - tube inside diameter (m)
G - maximum air mass flux, wa / Am (kg / m^2-s)
h - heat transfer coefficient (kJ / kg-C)
H - enthalpy (kJ / kg)
J - Colburn heat transfer J-factor (dimensionless)
Pr - Prandtl number (dimensionless)
Q - heat transfer rate (kW)
Re - Reynolds number (dimensionless)
Tw - bulk water temperature
U - overall heat transfer coefficient, temperature basis (kW / m^2-C)
Uc - overall heat transfer coefficient, enthalpy basis (kg / m^2-s)
V - velocity
w - mass flow rate (kg/s)
n - fin efficiency (dimensionless)
Toll - time constant (s)
Omega - humidity ratio (kg water / kg dry air)
Subscripts
a - air
d - dry
i - inside, inlet
o - outside, outlet
w - water, wet
Mathematical Description
The mathematical model has been described in detail elsewhere [1,2].
A brief summary is provided below.
The average heat transfer coefficient on the water side, hw, is
evaluated using the turbulent flow relation [3]:
hw = 1.429*[1 + 0.0146*Tw]*(Vw)^0.8*(Di)^(-0.2)
with all quantities in the units indicated in the nomenclature section. Under
dry coil conditions, the average heat transfer coefficient on the air side,
had, is found from a correlation of the following form:
J = C1*Re^C2
had = J*G*Cpa*Pr^(-2/3)
The quantities C1 and C2 are constants for a particular coil, and are
calculated as functions of the coil geometry [4]. Under wet coil conditions,
the dry coil heat transfer coefficient is modified as follows:
haw = Cf*had
where the correction factor Cf is a function of the Reynolds number [5].
Separate correlations are used to determine the dry fin efficiency, nd
[6], and the wet fin efficiency, nw [7]. In addition to the inside and outside
heat transfer coefficients and the fin efficiency, the overall heat transfer
coefficient includes terms representing the thermal resistance of the tubes,
and a constant fouling factor of 5*10^(-5) C-m^2/W (3*10^(-4) F-ft^2/Btu).
Under dry coil conditions, the steady state air and water outlet
temperatures are found by simultaneous solution of the following three
equations:
Q = wa*Cpa*(Tai - Tao)
Q = ww*Cpw*(Two - Twi)
Q = U*Ao*(LMTD)
where
LMTD = [(Tai - Two) - (Tao - Twi)] / [ln(Tai - Two) - ln(Tao - Twi)]
When the coil is wet, enthalpies are used in place of temperatures:
Q = wa*(Hai - Hao)
Q = ww*(Cpw/b)*(Hwo - Hwi)
Q = Uc*Ao*(LMHD)
where
LMHD = [(Hai - Hwo) - (Hao - Hwi)] / [ln(Hai - Hwo) - ln(Hao - Hwi)]
Hwi and Hwo are saturated air enthalpies calculated at the water temperatures
Twi and Two, respectively, according to the following relation:
Hw = Ho + b*Tw
The quantities Ho and b are determined iteratively.
Initially the entire air side surface of the coil is assumed to be wet.
Based on this assumption, the outlet air and water temperatures and the air
side surface temperatures at inlet and outlet are calculated. If the surface
temperature at the inlet is lower than the inlet air dew point temperature, the
coil is in fact all wet. If the surface temperature at the air outlet is
higher than the inlet air dew point temperature, the coil surface is all dry.
If neither of these conditions is met, the surface is partly wet and partly
dry. In this case, an iterative procedure is used to find the position in the
air flow direction at which the surface temperature is equal to the dew point
temperature. This position is the boundary between the dry and wet sections of
the coil.
Dynamics have been added to the steady state model in a very simple
and somewhat artificial manner:
d(T'ao)/dt = (Tao - T'ao) / Toll
d(T'wo)/dt = (Two - T'wo) / Toll
d(Omega'ao)/dt = (Omegaao - Omega'ao) / Toll
where
Toll = Cm / (U*Ao)
Note that the dynamic variables T'ao, T'wo, and Omega'ao are used only in the
three differential equations given above. Steady state variables are used in
determining whether the coil is wet or dry.
Model Verification
The steady state cooling coil model has been tested extensively by its
authors. comparisons between the steady state model and experimental data for
a variety of coils and operating conditions can be found elsewhere [8,9].
The dynamics of the coil model have been investigated experimentally
for changes in the water flow rate and for changes in the water inlet
temperature. In both experiments, measured air and water inlet temperatures
and a measured water flow rate were used as inputs to the model. The air flow
rate was calculated from the measurements under steady state conditions. In
both cases, the outside surface of the coil remained dry. Agreement between
the model and the experiments is excellent.
Component 610 Configuration
Inputs Description
1 ww - water mass flow rate
2 Twi - inlet water temperature
3 wa - dry air mass flow rate
4 Tai - inlet air dry bulb temperature
5 Omegaai - inlet air humidity ratio
6 T'wo - dynamic outlet water temperature
7 T'ao - dynamic outlet air temperature
8 Omega'ao - dynamic outlet air humidity ratio
Outputs Description
1 T'wo - dynamic outlet water temperature (C)
2 T'ao - dynamic outlet air temperature (C)
3 Omega'ao - dynamic outlet air humidity ratio ( - )
4 Qt - total cooling load at steady state (kW)
5 Qs - sensible cooling load at steady state (kW)
6 fw - wet fraction of total surface area ( - )
Parameters Description
1 Ic - coil type: 0 = flat continuous fins,
1 = circular fins
2 Ap - primary (tube exterior) surface area (m^2)
3 As - secondary (fin) surface area (m^2)
4 Ai - internal surface area (m^2)
5 Am/Af - ratio of minimum flow area to face area ( - )
6 kf - thermal conductivity of fin material (kW / m-C)
7 Af - coil face area (m^2)
8 Nf - number of fins per centimeter
9 Np - number of tubes per row
10 Nr - number of rows
11 Do - tube outside diameter (m)
12 Di - tube inside diameter (m)
13 Delta - fin thickness (m)
14 Cm - mass times specific heat of coil material (kJ/C)
15 S1 - tube longitudinal spacing (in air flow direction) (m)
16 Df - fin diameter (if Ic = 1) or fin length
(if Ic = 0) (m)
17 Dc - coil depth in air flow direction (m)
18 kt - thermal conductivity of tube material (kW / m-C)
Reference:
1. Elmahdy, A.H., and Mitalas, G.P. "FORTRAN IV program to simulate
cooling and dehumidifying finned-tube multi-row heat exchangers."
Computer Program No. 43, Division of Building Research, National
Research Council of Canada, Ottawa (1977).
2. Elmahdy, A.H., and Mitalas, G.P. "A simple model for cooling and
dehumidifying coils for use in calculating energy requirements for
buildings." ASHRAE Transactions Vol. 83, part 2, pp. 103-117 (1977).
3. McAdams, W.H. "Review and summary of developments in heat transfer by
conduction and convection." Trans. A.I.Ch.E., Vol. 36, p. 1 (1940).
4. Elmahdy, A.H., and Biggs, R.C. "Finned tube heat exchanger:
correlation of dry surface heat transfer data." ASHRAE Transactions
Vol. 85, part 2, pp. 262-273 (1979).
5. Elmahdy, A.H. "Analytical and experimental multi-row finned tube heat
exchanger performance during cooling and dehumidifying processes."
Ph.D. Thesis, Carleton University, Ottawa, Canada (1975).
6. Gardner, K.A. "Efficiency of extended surfaces." Trans. ASME, Vol. 67,
pp. 621-631 (1945).
7. Elmahdy, A.H., and Biggs, R.C. "Efficiency of extended surfaces with
simultaneous heat and mass transfer." ASHRAE Transactions, Vol. 89,
part 1 (1983).
8. Elmahdy, A.H., and Mitalas, G.P. "Facility for testing cooling and
dehumidifying coils: description, procedures and test results." DBR
Paper No. 756, Division of building Research, National Research Council
of Canada, Ottawa (1978).
9. Elmahdy, A.H., and Biggs, R.C. "Performance simulation of multi-row dry
(and/or wet) heat exchangers." DBR Paper No. 797, Division of Building
Research, National Research Council of Canada, Ottawa (1978).
10. 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