Cooling Tower Modeling

The cooling tower model simulates the removal of heat from the condenser water loop to ambient air by evaporative cooling, and is governed by the following key relationships.

Mass continuity

Assuming no bleed or blow-down, the water mass flow through the tower is conserved:

\[\dot{m}_{w,\mathrm{in}} = \dot{m}_{w,\mathrm{out}} = \dot{m}_w\]

Energy balance

The sensible heat removed from the water equals the tower heat duty:

\[\dot{m}_w\,c_{p,w}\,(T_{w,\mathrm{in}} - T_{w,\mathrm{out}}) = Q_{\mathrm{tower}}\]

where:

  • \(\dot{m}_w\) is the water mass flow rate

  • \(c_{p,w}\) is the specific heat capacity of water

  • \(T_{w,\mathrm{in}}\) and \(T_{w,\mathrm{out}}\) are the inlet and outlet water temperatures

Overall heat‐transfer model

Model the tower as a counter-flow heat exchanger with overall conductance \(UA\) and log-mean temperature difference \(\Delta T_{\mathrm{lm}}\):

\[Q_{\mathrm{tower}} = UA \,\Delta T_{\mathrm{lm}}\]

with

\[\Delta T_{\mathrm{lm}} = \frac{ (T_{w,\mathrm{out}} - T_{a,\mathrm{in}}) \;-\; (T_{w,\mathrm{in}} - T_{a,\mathrm{out}}) }{ \ln\!\displaystyle\frac{T_{w,\mathrm{out}} - T_{a,\mathrm{in}}} {T_{w,\mathrm{in}} - T_{a,\mathrm{out}}} }\]

where:

  • \(T_{a,\mathrm{in}}\) and \(T_{a,\mathrm{out}}\) are the inlet and outlet air wet-bulb temperatures

Evaporative mass loss

The evaporated water mass flow is tied to the latent heat of vaporization:

\[\dot{m}_{\mathrm{evap}} = \frac{Q_{\mathrm{tower}}}{h_{fg}}\]

where \(h_{fg}\) is the latent heat of vaporization of water.

Fan power consumption

Air is drawn through the tower by a fan against a pressure rise \(\Delta p_a\). The electrical power required is:

\[P_{\mathrm{fan}} = \frac{\Delta p_a \,\dot V_a}{\eta_{\mathrm{fan}}}\]

where:

  • \(\dot V_a\) is the volumetric air flow rate

  • \(\eta_{\mathrm{fan}}\) is the fan efficiency

Usage in Sustain-LC

The above equations are implemented in the cooling-tower submodel of the Sustain-LC Gymnasium environment. Users can adjust parameters such as \(UA\), \(\dot{m}_w\), and fan characteristics to study the impacts on thermal regulation and energy consumption.