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