Model for a steady-state or dynamic cooling tower with a variable speed fan using Merkel's calculation method.
To compute the thermal performance, this model takes as parameters the nominal water mass flow rate, the water-to-air mass flow ratio at nominal condition, the nominal inlet air wetbulb temperature, and the nominal water inlet and outlet temperatures. Cooling tower performance is modeled using the effectiveness-NTU relationships for various heat exchanger flow regimes.
The total heat transfer between the air and water entering the tower is computed based on Merkel's theory. The fundamental basis for Merkel's theory is that the steady-state total heat transfer is proportional to the difference between the enthalpy of air and the enthalpy of air saturated at the wetted-surface temperature. This is represented by
dQ̇_{total} = UdA/c_{p} (h_{s} - h_{a}),
where h_{s} is the enthalpy of saturated air at the wetted-surface temperature, h_{a} is the enthalpy of air in the free stream, c_{p} is the specific heat of moist air, U is the cooling tower overall heat transfer coefficient, and A is the heat transfer surface area.
The model also treats the moist air as an equivalent gas with a mean specific heat c_{pe} defined as
c_{pe} = Δh / ΔT_{wb},
where Δh and ΔT_{wb} are the enthalpy difference and wetbulb temperature difference, respectively, between the entering and leaving air.
For off-design conditions, Merkel's theory is modified to include Sheier's adjustment factors that change the current UA value. The three adjustment factors, based on the current wetbulb temperature, air flow rates, and water flow rates, are used to calculate the UA value as
UA_{e} = UA_{0} · f_{UA,wetbulb} · f_{UA,airflow} · f_{UA,waterflow},
where UA_{e} and UA_{0} are the equivalent and design overall heat transfer coefficent-area products, respectively. The factors f_{UA,wetbulb}, f_{UA,airflow}, and f_{UA,waterflow} adjust the current UA value for the current wetbulb temperature, air flow rate, and water flow rate, respectively. These adjustment factors are third-order polynomial functions defined as
f_{UA,x} = c_{x,0} + c_{x,1} x + c_{x,2} x^{2} + c_{x,3} x^{3},
where x = {(T_{0,wetbulb} - T_{wetbulb}),
ṁ_{air} ⁄ ṁ_{0,air},
ṁ_{wat} ⁄ ṁ_{0,wat}}
for the respective adjustment factor, and the
coefficients c_{x,0}, c_{x,1}, c_{x,2}, and c_{x,3}
are the user-defined
values for the respective adjustment factor functions obtained from
Buildings.Fluid.HeatExchangers.CoolingTowers.Data.UAMerkel.
By changing the parameter UACor
, the
user can update the values in this record based on the performance characteristics of
their specific cooling tower.
This model is similar to the model CoolingTower:VariableSpeed:Merkel
that is implemented in the EnergyPlus building energy simulation program version 8.9.0.
The main differences are:
The following assumptions are made with Merkel's theory and this implementation:
EnergyPlus 8.9.0 Engineering Reference, March 23, 2018.