Buildings.Fluid.HeatExchangers.CoolingTowers

Package with cooling tower models

Information

This package contains components models for cooling towers.

The model Buildings.Fluid.HeatExchangers.CoolingTowers.FixedApproach computes a fixed approach temperature.

The model Buildings.Fluid.HeatExchangers.CoolingTowers.YorkCalc computes the cooling tower performance based the York formula.

Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).

Package Content

Name	Description
FixedApproach	Cooling tower with constant approach temperature
Merkel	Cooling tower model based on Merkel's theory
YorkCalc	Cooling tower with variable speed using the York calculation for the approach temperature
Correlations	Package with correlations for cooling tower performance
Data	Cooling tower performance data
Examples	Collection of models that illustrate model use and test models
Validation	Collection of validation models
BaseClasses	Package with base classes for Buildings.Fluid.HeatExchangers.CoolingTowers

Buildings.Fluid.HeatExchangers.CoolingTowers.FixedApproach

Cooling tower with constant approach temperature

Information

Model for a steady-state or dynamic cooling tower with constant approach temperature. The approach temperature is the difference between the leaving water temperature and the entering air temperature. The entering air temperature is used from the signal TAir. If connected to the a dry-bulb temperature, then a dry cooling tower is modeled. If connected to a wet-bulb temperature, then a wet cooling tower is modeled.

By connecting a signal that contains either the dry-bulb or the wet-bulb temperature, this model can be used to estimate the water return temperature from a cooling tower. For a more detailed model, use for example the YorkCalc model.

Extends from Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTower (Base class for cooling towers).

Parameters

Connectors

Modelica definition

Buildings.Fluid.HeatExchangers.CoolingTowers.Merkel

Cooling tower model based on Merkel's theory

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

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 = UA₀ · f_UA,wetbulb · f_UA,airflow · f_UA,waterflow,

where UA_e and UA₀ 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 x² + c_x,3 x³,

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.

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.

Extends from Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTowerVariableSpeed (Base class for cooling towers with variable speed fan).

Parameters

Connectors

Modelica definition

Buildings.Fluid.HeatExchangers.CoolingTowers.YorkCalc

Cooling tower with variable speed using the York calculation for the approach temperature

Information

Model for a steady-state or dynamic cooling tower with variable speed fan using the York calculation for the approach temperature at off-design conditions.

Thermal performance

To compute the thermal performance, this model takes as parameters the approach temperature, the range temperature and the inlet air wet bulb temperature at the design condition. Since the design mass flow rate (of the chiller condenser loop) is also a parameter, these parameters define the rejected heat.

For off-design conditions, the model uses the actual range temperature and a polynomial to compute the approach temperature for free convection and for forced convection, i.e., with the fan operating. The polynomial is valid for a York cooling tower. If the fan input signal y is below the minimum fan revolution yMin, then the cooling tower operates in free convection mode, otherwise it operates in the forced convection mode. For numerical reasons, this transition occurs in the range of y ∈ [0.9*yMin, yMin].

Fan power consumption

The fan power consumption at the design condition can be specified as follows:

• The parameter fraPFan_nominal can be used to specify at the nominal conditions the fan power divided by the water flow rate. The default value is 275 Watts for a water flow rate of 0.15 kg/s.
• The parameter PFan_nominal can be set to the fan power at nominal conditions. If a user does not set this parameter, then the fan power will be PFan_nominal = fraPFan_nominal * m_flow_nominal, where m_flow_nominal is the nominal water flow rate.

In the forced convection mode, the actual fan power is computed as PFan=fanRelPow(y) * PFan_nominal, where the default value for the fan relative power consumption at part load is fanRelPow(y)=y3. In the free convection mode, the fan power consumption is zero. For numerical reasons, the transition of fan power from the part load mode to zero power consumption in the free convection mode occurs in the range y ∈ [0.9*yMin, yMin].
To change the fan relative power consumption at part load in the forced convection mode, points of fan controls signal and associated relative power consumption can be specified. In between these points, the values are interpolated using cubic splines.

Comparison the cooling tower model of EnergyPlus

This model is similar to the model Cooling Tower:Variable Speed that is implemented in the EnergyPlus building energy simulation program version 6.0. 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 and limitations

This model requires a medium that has the same computation of the enthalpy as Buildings.Media.Water, which computes

h = c_p (T-T₀),

where h is the enthalpy, c_p = 4184 J/(kg K) is the specific heat capacity, T is the temperature in Kelvin and T₀ = 273.15 Kelvin. If this is not the case, the simulation will stop with an error message. The reason for this limitation is that as of January 2015, OpenModelica failed to translate the model if Medium.temperature() is used instead of Water.temperature().

References

EnergyPlus 2.0.0 Engineering Reference, April 9, 2007.

Extends from Buildings.Fluid.HeatExchangers.CoolingTowers.BaseClasses.CoolingTowerVariableSpeed (Base class for cooling towers with variable speed fan).

Parameters

Connectors

Modelica definition