modelYorkCalc

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 inlet and outlet temperatures of the cooling loop and the inlet air wet bulb temperature, and the rejected heat at the design condition. The design mass flow rate (of the chiller condenser loop) is then calculated based on these parameters.

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.

Parameters

Connectors

Components

Contents

Name	Description
Waterprotected	Medium package for water

Revisions

• April 22, 2026, by Michael Wetter:
  Removed parameter fraPFan_nominal and introduced instead the non-dimensional parameter PEle_Q_flow_nominal.
  This is for #4443.
• August 26, 2021, by Baptiste Ravache:
  Renamed parameter TWatIn0 to TWatIn_nominal.
• January 16, 2020, by Michael Wetter:
  Refactored model to avoid mixing textual equations and connect statements.
• December, 22, 2019, by Kathryn Hinkelman:
  Corrected fan power consumption.
  This is for issue 1691.
• November 3, 2016, by Michael Wetter:
  Corrected wrong type for FRWat0, as this variable can take on values that are bigger than 1.
  This is for issue 567.
• January 2, 2015, by Michael Wetter:
  Replaced Medium.temperature() with Water.temperature() in order for the model to work with OpenModelica. Added an assert that stops the simulation if an incompatible medium is used.
• November 13, 2014, by Michael Wetter:
  Added missing each keyword for fanRelPowDer. Added regularization in computation of TAppCor. Removed intermediate states with temperatures.
• May 30, 2014, by Michael Wetter:
  Removed undesirable annotation Evaluate=true.
• October 9, 2013, by Michael Wetter:
  Simplified the implementation for the situation if allowReverseFlow=false. Avoided the use of the conditionally enabled variables sta_a and sta_b as this was not proper use of the Modelica syntax.
• September 29, 2011, by Michael Wetter:
  Revised model to use cubic spline interpolation instead of a polynomial.
• July 12, 2011, by Michael Wetter:
  Introduced common base class for Buildings.Fluid.HeatExchangers.CoolingTowers.YorkCalc and Buildings.Fluid.HeatExchangers.CoolingTowers.FixedApproach so that they can be used as replaceable models.
• May 12, 2011, by Michael Wetter:
  Added binding equations for Q_flow and mXi_flow.
• March 8, 2011, by Michael Wetter:
  Removed base class and unused variables.
• February 25, 2011, by Michael Wetter:
  Revised implementation to facilitate scaling the model to different nominal sizes. Removed parameter mWat_flow_nominal since it is equal to m_flow_nominal, which is the water flow rate from the chiller condenser loop.
• May 16, 2008, by Michael Wetter:
  First implementation.