# .Buildings.Fluid.HeatExchangers.CoolingTowers.Merkel

## Information

Model for a steady-state or dynamic cooling tower with a variable speed fan using Merkel's calculation method.

#### Thermal performance

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

dQ̇total = UdA/cp (hs - ha),

where hs is the enthalpy of saturated air at the wetted-surface temperature, ha is the enthalpy of air in the free stream, cp 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 cpe defined as

cpe = Δh / ΔTwb,

where Δh and ΔTwb 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

UAe = UA0 · fUA,wetbulb · fUA,airflow · fUA,waterflow,

where UAe and UA0 are the equivalent and design overall heat transfer coefficent-area products, respectively. The factors fUA,wetbulb, fUA,airflow, and fUA,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

fUA,x = cx,0  + cx,1 x + cx,2 x2 + cx,3 x3,

where x = {(T0,wetbulb - Twetbulb),   ṁair ⁄ ṁ0,air,   ṁwat ⁄ ṁ0,wat} for the respective adjustment factor, and the coefficients cx,0, cx,1, cx,2, and cx,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.

#### Comparison with the cooling tower model of EnergyPlus

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:

1. Not implemented are the basin heater power consumption and the make-up water usage.
2. The model has no built-in control to switch individual cells of the tower on or off. To switch cells on or off, use multiple instances of this model, and use your own control law to compute the input signal y.

#### Assumptions

The following assumptions are made with Merkel's theory and this implementation:

1. The moist air enthalpy is a function of wetbulb temperature only.
2. The wetted surface temperature is equal to the water temperature.
3. Cycle losses are not taken into account.

#### References

EnergyPlus 8.9.0 Engineering Reference, March 23, 2018.

## Revisions

• January 16, 2020, by Michael Wetter:
Revised model to put the thermal performance in a separate block.
• January 10, 2020, by Michael Wetter:
Revised model, changed parameters to make model easier to use with design data.
• October 22, 2019, by Yangyang Fu:
First implementation.

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