Cooling Tower (TL-MA)

Cooling tower between a thermal liquid and moist air network

Since R2023b

• 

Libraries:
Simscape / Fluids / Heat Exchangers / Thermal Liquid - Moist Air

Description

The Cooling Tower (TL-MA) block models a cooling tower between moist air and a thermal liquid network. The block models sensible and latent heat transfer from the thermal liquid side to the moist air side based on an analogous effectiveness-NTU method for heat and water vapor mass transfer. The thermal liquid side represents the water in the tower while the moist air side represents the environmental air. The block is performance based rather than geometry based, which means that the block sizes the cooling tower to match the nominal operating conditions that you specify.

Cooling Tower Geometry

Large HVAC systems use cooling towers to reject heat from water to the environment in applications where the amount of heat is too large for regular water-air heat exchangers to be practical. In a cooling tower, the hot water and air are in direct contact, which allows some of the water to evaporate into the air and cools the rest of the water by the evaporative cooling effect.

A cooling tower works by spreading and spraying hot water from the top of the tower over a large area to encourage it to evaporate into the air. Typically, there is a fill material underneath the spray nozzles with a large surface area that allows the water to form a thin film and spread out. The fill material increases the contact area between the water and the air for more evaporation. Because there is no heat source, the latent heat needed to turn liquid water into water vapor comes from the water itself. As a result, the water that did not evaporate cools. The cold water collects at the bottom of the cooling tower in a basin, and can be returned to the HVAC system.

You can use the Flow arrangement parameter to specify if the cooling tower uses a cross flow or counter flow. This block only models direct-flow cooling towers, which means the water is in direct contact with the air. The block also only models mechanical-draft cooling towers, where a fan moves the air through the cooling tower.

This figure shows a diagram of a counter-flow, direct-contact, induced mechanical-draft cooling tower.

This figure shows a diagram of a direct-contact, induced mechanical-draft cooling tower with two air entries.

Heat Transfer and Evaporation Rate

The combined heat and water vapor mass transfer is

$$Q_{combined}=ϵQ_{combined,max}=ϵC_{min}\left({\overline{h}}_{s_{T{L}_{in}}}-{\overline{h}}_{M{A}_{in}}\right),$$

where:

• Q_combined,max is the theoretically maximum combined heat and water vapor mass transfer, $$Q_{combined,max}=C_{min}\left({\overline{h}}_{s_{T{L}_{in}}}-{\overline{h}}_{M{A}_{in}}\right).$$

• $$\overline{h}$$_sTLin is the enthalpy of the saturated moist air evaluated at the temperature of the inlet at the thermal liquid side.

• $$\overline{h}$$_MAin is the mixture enthalpy of the moist air at the inlet.

• C_min is the smaller capacity ratio between the moist air and thermal liquid.

When Flow arrangement is Counter flow, the effectiveness factor, ε, is

$$ϵ=\frac{1-\text{exp}[-(1-CR)NTU]}{1-CR\text{exp}[-(1-CR)NTU]},$$

where CR is the capacity ratio and NTU is the number of transfer units.

When Flow arrangement is Cross flow, the block assumes that one fluid is mixed and the other is unmixed. If the fluid with the lower value for C is unmixed,

$$ϵ=\frac{1-\text{exp}\left(-CR[1-\text{exp}(-NTU)]\right)}{CR}.$$

Typically, the moist air will have the lower value for C. If the fluid with the lower value for C is mixed,

$$ϵ=1-\exp \left[-\frac{1-\text{exp}(-CR\ast NTU)}{CR}\right].$$

The capacity ratio is

$$CR=\frac{C_{min}}{C_{max}}=\frac{\min \left\{C_{TL},C_{MA}\right\}}{\max \left\{C_{TL},C_{MA}\right\}}.$$

C_MA and C_TL are the capacity rates for the moist air and thermal liquid, respectively,

$$\begin{array}{l}{\text{C}}_{TL}=\frac{{\dot{m}}_{TL}{c}_{p_{TL}}}{{\overline{c}}_{s_{TL}}}\\ C_{MA}={\dot{m}}_{a{g}_{MA}}\end{array}$$

where:

• ṁ_TL is the thermal liquid mass flow rate.

• c_pTL is the thermal liquid specific heat at constant pressure.

• ṁ_agMA is the mass flow rate of the dry air and trace gas.

The number of transfer units, NTU, is

$$\text{NTU=}\frac{U_{MA}A}{C_{min}{\overline{c}}_{p_{MA}}},$$

where:

• A is the heat transfer surface area.

• U_MA is the heat transfer conductance on the moist air side.

• $$\overline{c}$$_pMA is the moist air specific heat at constant pressure.

The combined heat and water vapor mass transfer, Q_combined, accounts for the sensible heat transfer, latent heat, and energy debit due to lost liquid,

$${\text{Q}}_{combined}=\text{Q+}\Delta h_{f{g}_{eff}}{\dot{m}}_e+h_{l_{eff}}{\dot{m}}_e,$$

where:

• Q is the sensible heat transfer between thermal liquid and moist air in the cooling tower. The block calculates this value with $${\text{Q=Q}}_{combined}-h_{w_{eff}}{\dot{m}}_e$$. This term represents the portion of the cooling due to the temperature difference between the thermal liquid and moist air.

• Δh_fgeff is the water vapor specific enthalpy of vaporization. When multiplied by ṁ_e, this term gives the latent heat transfer between the thermal liquid and moist air in the cooling tower. This term represents the portion of the cooling due to the energy extracted from the liquid water when converted into water vapor.

• h_leff is the liquid water specific enthalpy. When multiplied by ṁ_e, this term gives the energy debited from the energy balance of the thermal liquid flow due to the removal of a portion of the liquid.

The evaporation rate in the cooling tower is

$${\dot{m}}_e=C_{min}\left(W_{s_{eff}}-W_{M{A}_{in}}\right)\left[1-\exp \left(-NTU\right)\right],$$

where:

• W_seff is the effective saturated humidity ratio.

• W_MAin is the humidity ratio at the moist air inlet.

The effective saturated humidity ratio is

$$W_{s_{eff}}=\frac{R_a+G\left(R_g-R_a\right)}{R_w\left(\frac{p}{{\phi }_{ws}{p}_{ws}\left(T_{eff}\right)}-1\right)},$$

where:

• R_a is the specific gas constant of dry air.

• G is the trace gas ratio.

• R_g is the specific gas constant of the trace gas.

• R_W is the specific gas constant of the water vapor.

• p is the pressure.

• φ_ws is the value of the Relative humidity at saturation parameter.

• p_ws(T_eff) is the water vapor saturation pressure evaluated at the effective liquid film surface temperature.

The effective liquid film surface temperature is

$$T_{eff}=T_{T{L}_{in}}-\frac{{\overline{h}}_{s_{T{L}_{in}}}-{\overline{h}}_{s_{eff}}}{{\overline{c}}_{s_{TL}}},$$

where:

• T_TLin is the temperature of the thermal liquid at the inlet.

• $$\overline{c}$$_sTL is the specific heat of the saturated moist air along the saturation curve when evaluated at the temperature of the thermal liquid.

• $$\overline{h}$$_seff is the saturated mixture enthalpy along the liquid film surface

  $${\overline{h}}_{s_{eff}}={\overline{h}}_{M{A}_{in}}+\frac{ϵ\left({\overline{h}}_{s_{T{L}_{in}}}-{\overline{h}}_{M{A}_{in}}\right)}{1-\exp \left(-NTU\right)}.$$

The heat transfer conductance at the moist air side, U_MAA, is

$$U_{MA}A=\max \left\{{\left(\frac{{\dot{m}}_{MA}}{{\mu }_{MA}}\right)}^b{\mathrm{Pr}}_{MA}^{c}k{\left(\frac{D_{ref}}{S_{ref}}\right)}^{b}a,N{u}_{lam}{k}_{MA}\right\}{G}_{fill},$$

where:

• U_MA is the heat transfer coefficient.

• ṁ_MA is the moist air mass flow rate.

• μ_MA is the moist air dynamic viscosity.

• a is the coefficient for the proportionality in the Nusselt number correlation.

• b is the coefficient for the Reynolds number exponent in the Nusselt number correlation.

• c is the coefficient for the Prandtl number exponent in the Nusselt number correlation.

• Pr_MA is the moist air Prandtl number.

• k_MA is the thermal conductivity of the moist air.

• D_ref is an arbitrary diameter. The block uses this value with S_ref to nondimensionalize with respect to length.

• S_ref is the flow area corresponding to D_ref.

• Nu_lam is 3.66, which is the theoretical Nusselt number for a laminar flow through a circular pipe.

• G_fill is the geometry scale factor for the cooling tower fill material. The block calculates this value at nominal operating conditions.

Cooling Tower Sizing

The block sizes the cooling tower to match the nominal performance at nominal operating conditions. On the thermal liquid side, the Nominal capacity specification parameter specifies how the block determines the nominal data:

• Water mass flow rate or Water volumetric flow rate — The block infers the nominal capacity from the nominal flow rate and the nominal inlet and outlet temperatures.

• Rate of cooling in cooling tower or Rate of cooling in evaporator — The block infers the nominal flow rate from the nominal capacity.

On the moist air side, the nominal data depends on the Specify full moist air nominal conditions parameter.

If you clear the Specify full moist air nominal conditions check box, the only nominal condition you specify is the value of the Nominal inlet wet-bulb temperature parameter. Use this option if your manufacturer datasheet provides only the nominal wet-bulb temperature. The block calculates the other nominal conditions:

• The block calculates the nominal inlet temperature based on the value of the Nominal inlet wet-bulb temperature parameter so that the relative humidity is 50%.

• The block calculates the nominal flow rate from the nominal water flow rate so that the capacity ratio at nominal operating condition is 1.

The block assumes that the nominal inlet pressure is atmospheric and that there is no nominal trace gas..

If you select Specify full moist air nominal conditions, you must specify the nominal inlet pressure, nominal inlet temperature, nominal inlet moisture level, and nominal inlet trace gas level.

The block uses nominal operating conditions to solve for the geometry scale factor for the cooling tower fill material, G_fill. This value describes the size of the cooling tower. The block inverts the expression for the heat transfer conductance of the moist air side, U_MAA, and calculates G_fill from the heat transfer conductance at nominal operating conditions. The block then uses G_fill to calculate the heat transfer conductance on the moist air side at actual operating conditions during simulation. The block does not model convective heat transfer in the thermal liquid film.

G_fill at nominal operating conditions is

$$G_{fill}=\frac{{\left(U_{MA}A\right)}_{nom}}{{\left(\frac{{\dot{m}}_{M{A}_{nom}}}{{\mu }_{M{A}_{nom}}}\right)}^b{\mathrm{Pr}}_{M{A}_{nom}}^c{k}_{M{A}_{nom}}{\left(\frac{D_{ref}}{S_{ref}}\right)}^{b}a},$$

where the subscript nom denotes the variable value at the specified nominal operating condition.

The block solves for (U_MAA)_nom with

$${\left(U_{MA}A\right)}_{nom}=C_{mi{n}_{nom}}{\overline{c}}_{p_{MA,nom}}NT{U}_{nom}.$$

The block calculates NTU_nom by inverting the applicable effectiveness equation.

When Flow arrangement is Counter flow,

$$NT{U}_{nom}=\frac{1}{1-C{R}_{nom}}\ln \left(\frac{1-{ϵ}_{nom}C{R}_{nom}}{1-{ϵ}_{nom}}\right),$$

where CR_nom is the capacity ratio and $${ϵ}_{nom}=\frac{Q_{combine{d}_{nom}}}{Q_{combined,ma{x}_{nom}}}$$ with Q_combined, Q_combined,max, and CR_nom evaluated at the nominal operating conditions.

When Flow arrangement is Cross flow and the fluid with the lower value for C is mixed

$$NT{U}_{nom}=-\frac{\ln \left[1+C{R}_{nom}\ln \left(1-{ϵ}_{nom}\right)\right]}{C{R}_{nom}}.$$

If the fluid with the lower value for C is unmixed,

$$NT{U}_{nom}=-\ln \left[1+\frac{\ln \left(1-{ϵ}_{nom}C{R}_{nom}\right)}{C{R}_{nom}}\right].$$

Thermal Liquid Equations

The pressure of the thermal liquid when it enters the cooling tower at port A1 is

$$p_{T{L}_{A1}}=p_{MA},$$

where p_MA is the moist air pressure inside the cooling tower. Because the block assumes that water loss due to evaporation is small, the thermal liquid mass flow rate is equal to the port A1 inflow rate, $${\dot{m}}_{TL}={\dot{m}}_{T{L}_{A1}}$$.

The steady state mass balance equation for the thermal liquid is

$${\dot{m}}_{T{L}_{A1}}-{\dot{m}}_e-\lambda {\dot{m}}_{T{L}_{A1}}={\dot{m}}_{T{L}_{fill,out}},$$

where:

• λ is the value of the Drift rate as fraction of water flow parameter. The drift accounts for liquid droplets that blow out of the cooling tower without evaporating.

• ṁ_TLfill,out is the mass flow rate of the thermal liquid at the exit point of the fill material.

The steady state mass balance equation for the thermal liquid is

$${\Phi }_{T{L}_{A1}}-Q_{combined}-\lambda {\Phi }_{T{L}_{A1}}={\Phi }_{T{L}_{fill,out}},$$

where:

• Φ_TLA1 is the energy flow rate at port A1.

• Φ_TLfill,out is the energy flow rate out of the fill material.

If you select Model cold-water basin, the block models an internal tank with the tank outlet at the bottom of the tank. Because the water in the tank must be replenished, the thermal liquid mass and energy conservation equations have two additional source terms, ṁ_TLmakeup and Φ_TLmakeup.

When you select Automatically replenish lost water,

$$\begin{array}{l}{\dot{m}}_{T{L}_{makeup}}={\dot{m}}_e+\lambda {\dot{m}}_{T{L}_{A1}}\\ {\Phi }_{T{L}_{makeup}}={\dot{m}}_{T{L}_{makeup}}{h}_{T{L}_{makeup}}\end{array}$$

where h_TLmakeup is the thermal liquid specific enthalpy specified by the Temperature of make-up water parameter.

If you clear the Automatically replenish lost water check box, you can specify the volumetric flow rate and temperature of the tank make-up water with ports Vm and Tm, respectively. Port L outputs the liquid level in the basin. The make-up water terms are

$$\begin{array}{l}{\dot{m}}_{T{L}_{makeup}}={\rho }_{TL}\left(p_{MA},T_{mu}\right)V_{mu}\\ {\Phi }_{T{L}_{makeup}}={\dot{m}}_{T{L}_{makeup}}{h}_{TL}\left(p_{MA},T_{mu}\right)\end{array}$$

where:

• p_MA is the moist air pressure in the cooling tower.

• T_mu is the temperature of the make-up water, which is the value of the signal at port Tm.

• ρ_TL(p_MA,T_mu) is the thermal liquid density evaluated at the moist air pressure and make-up water temperature.

• h_TL(p_MA,T_mu) is the thermal liquid specific enthalpy evaluated at the moist air pressure and make-up water temperature.

If you select Model cold-water basin, the block models an internal tank. ṁ_TLfill,out and Φ_TLA1 define the input flows of the internal tank. Port B1 is the outlet of the internal tank.

If you clear the Model cold-water basin check box,

$$\begin{array}{l}{\dot{m}}_{T{L}_{B1}}=-{\dot{m}}_{T{L}_{fill,out}}\\ {\Phi }_{T{L}_{B1}}=-{\Phi }_{T{L}_{fill,out}}\end{array}$$

Port B1 acts as a flow rate source for any downstream components. Connect a Tank (TL) block to port B1 to model the cold water basin. The Inlet height parameter of the Tank (TL) block must be larger than the liquid level in the tank.

Moist Air Equations

The behavior of the moist air side of the block depends on the Moist air operating conditions parameter.

Physical Signals

When you set Moist air operating conditions to Provided by input signals, the block enables physical signal ports that you can use to specify the moist air attributes:

• Port P is the input signal for the moist air inlet pressure. The moist air pressure, p_MA, is equal to the value of this signal.

• Port T is the input signal for the moist air dry-bulb temperature.

• The flow rate input port depends on the Flow rate input signal specification parameter:

  Value of Flow rate input signal specification	Enabled Port	Port Meaning
  Mass flow rate	M	Moist air mixture mass flow rate
  Volumetric flow rate	V	Moist air mixture volumetric flow rate
  Fan power	Pwr	Moist air fan power

• The moisture level input port depends on the Moisture input signal specification parameter:

  Value of Moisture input signal specification	Enabled Port	Port Meaning
  Relative humidity	W	Moist air inlet relative humidity
  Specific humidity	W	Moist air inlet specific humidity
  Mole fraction	W	Moist air inlet water vapor mole fraction
  Humidity ratio	W	Moist air inlet humidity ratio
  Wet-bulb temperature	Tw	Moist air inlet wet-bulb temperature

  When Flow rate input signal specification is Mass flow rate or Volumetric flow rate, the block uses the signal at port M or V to calculate the moist air mixture mass flow rate that enters the cooling tower, ṁ_MAin. The dry air and trace gas flow rate is

  $${\dot{m}}_{a{g}_{MA}}=\frac{{\dot{m}}_{M{A}_{in}}}{1+W_{M{A}_{in}}}.$$

  The block calculates the humidity ratio, W_MAin, from the input signals at ports P, T, and W or Tw.

  When Flow rate input signal specification is Fan power, the fan power, Φ_fan, is proportional to the cube of the volumetric flow rate, q, and pressure gain across the fan, Δp.

  The moist air mixture volumetric flow rate is

  $${\text{q}}_{MA}={\left(\frac{Pwr}{{\Phi }_{fa{n}_{nom}}}\right)}^{1/3}{q}_{M{A}_{nom}},$$

  where:

• Pwr is the value of the signal at port Pwr.

• Φ_fannom is the value of the Nominal fan power parameter.

• q_MAnom is the nominal volumetric flow rate. If you select Specify full moist air nominal condition, q_MAnom is the value of the Nominal moist air volumetric flow rate parameter. If you clear Specify full moist air nominal condition, the block calculates q_MAnom from the nominal water flow rate so that the capacity ratio is one.

When Moist air operating conditions is Provided by input signals, the block does not model trace gas.

Moist Air Domain Ports

When you set Moist air operating conditions to Moist air domain ports, the block enables the moist air ports A2 and B2, which you can connect to a moist air network. Because the direction of the moist air flow does not matter in this block, either port A2 or B2 can be the inlet. The dry air and trace gas flow rate is

$${\dot{m}}_{a{g}_{MA}}=\frac{{\dot{m}}_{M{A}_{in}}}{1+W_{M{A}_{in}}},$$

where:

• ṁ_MAin is the moist air mixture mass flow rate at port A2 or B2.

• W_MAin is the moist air mixture humidity ratio at port A2 or B2.

The moist air mixture mass conservation equation is

$$\frac{d{M}_{MA}}{dt}={\dot{m}}_{M{A}_{A2}}+{\dot{m}}_{M{A}_{B2}}+{\dot{m}}_e,$$

where:

• ṁ_MAA2 and ṁ_MAB2 are the mass flow rates at ports A2 and B2.

• M_MA is the total mixture mass of the moist air volume.

The water vapor mass conservation equation is

$$M_{MA}\frac{d{x}_{w_{MA}}}{dt}+x_{w_{MA}}\left({\dot{m}}_{M{A}_{A2}}+{\dot{m}}_{M{A}_{B2}}+{\dot{m}}_e\right)={\dot{m}}_{w_{M{A}_{A2}}}+{\dot{m}}_{w_{M{A}_{B2}}}+{\dot{m}}_e,$$

where x_wMA is the specific humidity of the moist air volume and ṁ_wMAA2 and ṁ_wMAB2 are the water vapor mass flow rates at ports A2 and B2.

The trace gas mass conservation equation is

$$M_{MA}\frac{d{x}_{g_{MA}}}{dt}+x_{g_{MA}}\left({\dot{m}}_{M{A}_{A2}}+{\dot{m}}_{M{A}_{B2}}+{\dot{m}}_e\right)={\dot{m}}_{g_{M{A}_{A2}}}+{\dot{m}}_{g_{M{A}_{B2}}},$$

where x_gMA is the trace gas mass fraction of the moist air volume and ṁ_gMAA2 and ṁ_gMAB2 are the trace gas mass flow rates at ports A2 and B2.

The moist air mixture energy conservation equation is

$$M_{MA}\frac{d{u}_{MA}}{dt}+u_{MA}\left({\dot{m}}_{M{A}_{A2}}+{\dot{m}}_{M{A}_{B2}}+{\dot{m}}_e\right)={\Phi }_{M{A}_{A2}}+{\Phi }_{M{A}_{B2}}+Q_{combined},$$

where u_MA is the mixture specific internal energy of the moist air volume and Φ_MAA2 and Φ_MAB2 are the moist air mixture energy flow rates at ports A2 and B2.

The pressure loss of the moist air in the cooling tower is

$$\Delta p_{MA}={\left(\frac{q_{MA}}{q_{M{A}_{nom}}}\right)}^2\Delta p_{M{A}_{nom}},$$

where:

• Δp_MAnom is the value of the Nominal moist air pressure loss parameter.

• q_MAnom is the value of the Nominal moist air volumetric flow rate parameter.

• q_MA is the volumetric flow rate of moist air through the cooling tower.

Using the Cooling Tower in a Model

When using the Cooling Tower (TL-MA), follow these guidelines:

• If you clear the Model cold-water basin check box, you must connect the cooling tower port B1 to a Tank (TL) block.

• When modeling transient situations such as startup or shutdown, connect the cooling tower port A1 to port A of a Partially Filled Pipe (TL) block to avoid a possible nonphysical situation of liquid flowing out of port A1. During startup and shutdown, port A1 may be exposed to the environment, which means there is no liquid present. The partially-filled pipe handles this scenario by allowing the liquid level to fall along the pipe while port A1 is exposed, if necessary.

• Some cooling towers may use a pressure source to force water out of the spray nozzles and spread the water over a wider area, which causes a pressure drop at the inlet. To model pressure drop through the spray nozzles, connect a block that models pressure loss, such as an Orifice (TL), Local Resistance (TL), or Flow Resistance (TL) block, to port A1 of the cooling tower.

• The Cooling Tower (TL-MA) block models a direct-contact cooling tower. To model an indirect-contact cooling tower, connect the thermal liquid side of the Cooling Tower (TL-MA) block to one side of a Heat Exchanger (TL-TL) block. In this configuration, the other side of the heat exchanger block represents the thermal liquid flowing into and out of the cooling tower, and the block models the heat transfer from the coil inside the cooling tower.

• If you set Moist air operating conditions to Moist air domain ports, you can model a mechanical forced-draft or an induced-draft cooling tower. To model a forced-draft cooling tower, connect a Fan (MA) block to the moist air inlet side of the tower. To model an induced-draft cooling tower, connect a Fan (MA) block to the moist air outlet side. If you set Moist air operating conditions to Provided by input signals, the block does not distinguish between forced-draft or induced-draft cooling towers.

Assumptions and Limitations

• The block only models a mechanical-draft cooling tower, which means a fan moves the moist air through the tower.

• The block only models a direct-contact cooling tower, which means the thermal liquid is in direct contact with the moist air.

Examples

Data Center Cooling

Models the cooling system of a data center. The system consists of two separate water loops: a chilled water loop and a condenser water loop. The chilled water loop absorbs heat from the server farm and transfers it to the condenser water loop. The condenser water loop rejects this heat to the environment using a cooling tower.

Open Model

Ports

Input

M — Mass flow rate, kg/s

physical signal

Mass flow rate of the moist air entering the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals and Flow rate input signal specification to Mass flow rate.

V — Volumetric flow rate, m^3/s

physical signal

Volumetric flow rate of the moist air entering the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals and Flow rate input signal specification to Volumetric flow rate.

Pwr — Fan power, W

physical signal

Fan power that drives the moist air through the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals and set Flow rate input signal specification to Fan power.

P — Pressure, Pa

physical signal

Pressure of the moist air entering the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals.

T — Temperature, K

physical signal

Dry-bulb temperature of the moist air entering the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals.

W — Measure of humidity, unitless

physical signal

Relative humidity, specific humidity, water vapor mole fraction, or humidity ratio of the moist air entering the cooling tower. Use the Moisture input signal specification parameter to specify the type of moisture input signal.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals and Moisture input signal specification any option except Wet-bulb temperature.

Tw — Wet-bulb temperature, K

physical signal

Wet-bulb temperature of the moist air entering the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals and Moisture input signal specification to Wet-bulb temperature.

Vm — Volumetric flow rate, m^3/s

physical signal

Volumetric flow rate of the thermal liquid that replenishes the water lost to evaporation and drift.

Dependencies

To enable this port, select Model cold-water basin and clear the Automatically replenish lost water check box.

Tm — Temperature, K

physical signal

Temperature of the thermal liquid that replenishes the water lost to evaporation and drift.

Dependencies

To enable this port, select Model cold-water basin and clear the Automatically replenish lost water check box.

Output

Q — Heat transfer, W

physical signal

Total sensible and latent heat transfer between the moist air and thermal liquid.

E — Evaporation rate, kg/s

physical signal

Evaporation rate of the thermal liquid.

L — Liquid level, m

physical signal

Depth of the thermal liquid in the cooling tower basin.

Dependencies

To enable this port, select Model cold-water basin and clear the Automatically replenish lost water check box.

Pwr — Fan power, W

physical signal

Fan power required for moist air flow in the cooling tower.

Dependencies

To enable this port, set Moist air operating conditions to Provided by input signals, Flow rate input signal specification to either Mass flow rate or Volumetric flow rate and select Output fan power.

Conserving

A1 — Thermal liquid inlet

thermal liquid

Thermal liquid conserving port associated with the inlet on the thermal liquid side.

B1 — Thermal liquid outlet

thermal liquid

Thermal liquid conserving port associated with the outlet on the thermal liquid side.

A2 — Moist air inlet or outlet

moist air

Moist air conserving port associated with the inlet or outlet on the moist air side.

Dependencies

To enable this port, set Moist air operating conditions to Moist air domain port.

B2 — Moist air inlet or outlet

moist air

Moist air conserving port associated with the inlet or outlet on the moist air side.

Dependencies

To enable this port, set Moist air operating conditions to Moist air domain port.

Parameters

Thermal Liquid 1

Flow arrangement — Flow arrangement of moist air and thermal liquid

Counter flow (default) | Cross flow

Flow arrangement for flow in the cooling tower. The thermal liquid always flows down within the cooling tower. If you select Counter flow, the moist air flows upwards through the fill material. If you select Cross flow, the moist air flows horizontally across the fill material.

Nominal capacity specification — Method for specifying size of system

Water volumetric flow rate (default) | Water mass flow rate | Rate of cooling in cooling tower | Rate of cooling in evaporator

Method for specifying the size of the cooling tower. You can specify the water mass or volumetric flow rate of water entering the tower, or you can specify the rate of cooling in the evaporator in the refrigeration loop connected to the tower or in the cooling tower.

Nominal water mass flow rate — Mass flow rate at nominal conditions

42.7 kg/s (default) | positive scalar

Mass flow rate of the thermal liquid entering the tower at nominal operating conditions. The block uses this value to size the cooling tower.

Dependencies

To enable this parameter, set Nominal capacity specification to Water mass flow rate.

Nominal water volumetric flow rate — Volumetric flow rate at nominal conditions

154 m^3/hr (default) | positive scalar

Volumetric flow rate of the thermal liquid entering the tower at nominal operating conditions. The block uses this value to size the cooling tower.

Dependencies

To enable this parameter, set Nominal capacity specification to Water volumetric flow rate.

Nominal cooling tower heat transfer — Heat transfer at nominal conditions

1000 kW (default) | positive scalar

Heat transfer between the thermal liquid and moist air in the tower at nominal operating conditions. The block uses this value to size the cooling tower.

Dependencies

To enable this parameter, set Nominal capacity specification to Rate of cooling in cooling tower.

Nominal evaporator heat transfer — Evaporator heat transfer at nominal conditions

800 kW (default) | positive scalar

Heat transfer of the evaporator in the refrigeration loop connected to the cooling tower at nominal operating conditions. The block uses this value to size the cooling tower. The block assumes that the heat transfer between the thermal liquid and moist air in the cooling tower is 1.25 times the value of this parameter.

Dependencies

To enable this parameter, set Nominal capacity specification to Rate of cooling in evaporator.

Nominal hot-water inlet temperature — Thermal liquid inlet temperature

35 degC (default) | positive scalar

Temperature of the thermal liquid entering the heat exchanger at nominal operating conditions. The block uses this value to size the cooling tower.

Nominal cold-water outlet temperature — Thermal liquid outlet temperature

29.44 degC (default) | positive scalar

Temperature of the thermal liquid as it flows out of the heat exchanger after it has cooled at nominal operating conditions. The block uses this value to size the cooling tower.

Model cold-water basin — Option to model thermal liquid side 1 as a tank

on (default) | off

Select this parameter to model the cold-water basin on the thermal liquid side as a tank. If you clear this parameter, connect a Tank (TL) block to port B1 to model the cold water basin.

Basin cross-sectional area — Area of basin

8 m^2 (default) | positive scalar

Cross-sectional area of the basin that holds the cooled water in the tower.

Dependencies

To enable this parameter, select Model cold-water basin.

Cross-sectional area at port A1 — Flow area of thermal liquid inlet

0.01 m^2 (default) | positive scalar

Flow area of the thermal liquid inlet.

Cross-sectional area at port B1 — Flow area of thermal liquid outlet

0.01 m^2 (default) | positive scalar

Flow area of the thermal liquid outlet.

Drift rate as fraction of water flow — Drift rate of thermal liquid

0 (default) | positive scalar

Fraction of the thermal liquid flow that is lost to drift. The drift accounts for liquid droplets that have blow of the cooling tower without evaporating.

Automatically replenish lost water — Option to automatically replenish lost water on thermal liquid 1 side

on (default) | off

Select this parameter to have the block automatically replace water lost to evaporation or drift. If you clear this parameter, the block enables the physical signal ports Vm and Tm for you to specify the volumetric flow rate and temperature of the water that replenishes the basin.

Dependencies

To enable this parameter, select Model cold-water basin.

Temperature of make-up water — Temperature of replenishing water

15 degC (default) | positive scalar

Temperature of the water the block uses to automatically replenish water lost from the thermal liquid side due to evaporation and drift.

Dependencies

To enable this parameter, select Model cold-water basin and Automatically replenish lost water.

Initialize thermal liquid to nominal operating conditions — Option for initializing thermal liquid

on (default) | off

Option to initialize the thermal liquid to nominal operating conditions or specified values. If you select this parameter, the block initializes the thermal liquid to the nominal operating conditions. If you clear this parameter, you can specify the initial conditions directly with additional parameters.

Dependencies

To enable this parameter, select Model cold-water basin.

Initial basin liquid temperature — Basin temperature at start of simulation

29.44 degC (default) | positive scalar

Thermal liquid temperature in the cold water basin at the start of simulation.

Dependencies

To enable this parameter, select Model cold-water basin and clear the Initialize thermal liquid to nominal operating conditions check box.

Initial basin liquid level — Basin level at start of simulation

0.2 m (default) | positive scalar

Thermal liquid depth of the cold water basin at the start of simulation.

Dependencies

To enable this parameter, select Model cold-water basin.

Gravitational acceleration — Acceleration of gravity constant

9.81 m/s^2 (default) | positive scalar

Constant for the acceleration of gravity.

Dependencies

To enable this parameter, select Model cold-water basin.

Moist Air 2

Moist air operating conditions — Method to specify moist air conditions

Provided by input signals (default) | Moist air domain ports

Method the block uses to specify the moist air conditions during simulation. If you select Provided by input signals, the block enables physical signal ports that you can use to specify the moist air temperature, pressure, and flow rate. If you select Moist air domain ports, the block enables moist air ports A2 and B2 and you can connect the block to a moist air network.

Flow rate input signal specification — Method to specify actual moist air flow rate

Volumetric flow rate (default) | Mass flow rate | Fan power

Method to specify the actual moist air flow rate. When Moist air operating conditions is Provided by input signals, the block uses the flow rate specified by this parameter and the temperature and pressure to describe the moist air operating conditions.

• If you select Mass flow rate, the block enables port M.

• If you select Volumetric flow rate, the block enables port V.

• If you select Fan power, the block enables port Pwr.

Dependencies

To enable this parameter, set Moist air operating conditions to Provided by input signals.

Output fan power — Option to output fan power

off (default) | on

Select this parameter to output the calculated fan power needed for flow as a physical signal at port Pwr.

Dependencies

To enable this parameter, set Moist air operating conditions to Provided by input signals and Flow rate input signal specification to either Mass flow rate or Volumetric flow rate.

Nominal fan power — Fan power at nominal operating conditions

7.5 kW (default) | positive scalar

Fan power at nominal operating conditions. Datasheets typically provide this value.

Dependencies

To enable this parameter, set Moist air operating conditions to Provided by input signals and either:

• Set Flow rate input signal specification to Fan power.

• Set Flow rate input signal specification to Mass flow rate or Volumetric flow rate and select Output fan power.

Moisture input signal specification — Quantity used to describe actual moisture level at tower moist air inlet

Wet-bulb temperature (default) | Specific humidity | Mole fraction | Humidity ratio | Relative humidity

Physical quantity to use to specify the actual moisture level of the moist air entering the cooling tower. If you select Relative humidity, Specific humidity, Mole fraction, or Humidity ratio, the moisture level is the signal at port W. If you select Wet-bulb temperature, the moisture level is the signal at port Tw.

Dependencies

To enable this parameter, set Moist air operating conditions to Provided by input signals.

Input signals outside valid range — Method to handle invalid signal values

Warn and limit to valid values (default) | Limit to valid values | Error

Select what the block does if the physical input signal that represents the moist air attributes is outside of the valid range:

• Limit to valid values — The block limits the signal to valid values and does not warn you.

• Warn and limit to valid values — The block limits the signal to valid values and issues a warning.

• Error — The block issues an error and the simulation ends.

Dependencies

To enable this parameter, set Moist air operating conditions to Provided by input signals.

Specify full moist air nominal condition — Option to specify moist air nominal conditions

off (default) | on

Select this parameter to provide the nominal inlet pressure, nominal inlet temperature, nominal inlet moisture level, and nominal inlet trace gas level.

If you clear this parameter, you only specify the nominal inlet wet-bulb temperature, and the block calculates or assumes the other nominal conditions. Use this option if your manufacture datasheet only provides the nominal wet-bulb temperature.

Nominal flow rate specification — Option to specify moist air flow rate

Volumetric flow rate (default) | Mass flow rate

Whether to specify the moist air flow rate at nominal conditions as a mass or volumetric flow rate.

Dependencies

To enable this parameter, select Specify full moist air nominal condition.

Nominal moist air mass flow rate — Nominal mass flow rate

36 kg/s (default) | positive scalar

Moist air mass flow rate at nominal operating conditions.

Dependencies

To enable this parameter, select Specify full moist air nominal condition and set Nominal flow rate specification to Mass flow rate.

Nominal moist air volumetric flow rate — Nominal volumetric flow rate

30 m^3/s (default) | positive scalar

Moist air volumetric flow rate at nominal operating conditions.

Dependencies

To enable this parameter, select Specify full moist air nominal condition and set Nominal flow rate specification to Volumetric flow rate.

Nominal moist air pressure loss — Pressure drop between moist air ports during nominal operating condition

250 Pa (default) | positive scalar

Pressure drop from port A2 to port B2 during the nominal operating conditions.

If the cooling tower datasheet does not include this value, you can estimate it from the nominal fan power, Φ_fannom. The nominal pressure loss is

$$\Delta p_{M{A}_{nom}}=\frac{{\Phi }_{fa{n}_{nom}}}{{\eta }_{fan}{q}_{M{A}_{nom}}},$$

where q_MAnom is the value of the Nominal moist air volumetric flow rate parameter and η_fan is the fan efficiency, which you can estimate. A reasonable value is around 0.3.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports and select Specify full moist air nominal condition.

Nominal inlet pressure — Pressure at moist air side inlet

0.101325 MPa (default) | positive scalar

Pressure at the inlet of the moist air side of the cooling tower during nominal operating condition.

Dependencies

To enable this parameter, select Specify full moist air nominal condition.

Nominal inlet temperature — Temperature at moist air side inlet

34.28 degC (default) | positive scalar

Temperature at the inlet of the moist air side of the cooling tower during the nominal operating condition.

Dependencies

To enable this parameter, select Specify full moist air nominal condition.

Nominal moisture specification — Quantity used to describe moisture level at nominal conditions

Wet-bulb temperature (default) | Specific humidity | Mole fraction | Humidity ratio | Relative humidity

Whether to describe the moist air moisture level at nominal operating conditions using the relative humidity, specific humidity, water vapor mole fraction, or humidity ratio.

Dependencies

To enable this parameter, select Specify full moist air nominal condition.

Nominal inlet relative humidity — Relative humidity at inlet

0.5 (default) | scalar in the range [0,1]

Relative humidity at the inlet of the moist air side of the cooling tower during the nominal operating conditions.

Dependencies

To enable this parameter, select Specify full moist air nominal condition and set Nominal moisture specification to Relative humidity.

Nominal inlet specific humidity — Specific humidity at inlet

0.0167 (default) | scalar in the range [0,1]

Specific humidity, defined as the mass fraction of water vapor in a moist air mixture, at the inlet of the moist air side of the cooling tower during the nominal operating conditions.

Dependencies

To enable this parameter, select Specify full moist air nominal condition and set Nominal moisture specification to Specific humidity.

Nominal inlet water vapor mole fraction — Mole fraction of water vapor at inlet

0.0266 (default) | scalar in the range [0,1]

Mole fraction of water vapor in a moist air mixture at the inlet of the moist air side of the cooling tower during the nominal operating conditions.

Dependencies

To enable this parameter, select Specify full moist air nominal condition and set Nominal moisture specification to Mole fraction.

Nominal inlet humidity ratio — Humidity ratio at inlet

0.017 (default) | scalar in the range [0,1]

Humidity ratio, defined as the mass ratio of water vapor to dry air and trace gas, at the inlet of the moist air side of the cooling tower during the nominal operating conditions.

Dependencies

To enable this parameter, select Specify full moist air nominal condition and set Nominal moisture specification to Humidity ratio.

Nominal inlet wet-bulb temperature — Wet-bulb temperature at moist air inlet

25.56 degC (default) | positive scalar

Wet-bulb temperature at the moist air inlet in nominal operating conditions.

Dependencies

To enable this parameter, either:

• Clear the Specify full moist air nominal condition check box.

• Select Specify full moist air nominal condition and set Nominal moisture specification to Wet-bulb temperature.

Nominal trace gas specification — Quantity used to describe nominal trace gas level

Mass fraction (default) | Mole fraction

Quantity the block uses to describe the trace gas level at nominal operating conditions.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports and select Specify full moist air nominal condition.

Nominal inlet trace gas mass fraction — Mass fraction of trace gas at inlet

6e-4 (default) | scalar in the range [0,1]

Mass fraction of the trace gas in a moist air mixture at the inlet of the moist air side of the cooling tower during nominal operating conditions.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, select Specify full moist air nominal condition, and set Nominal trace gas specification to Mass fraction.

Nominal inlet trace gas mole fraction — Mole fraction of trace gas at inlet

4e-4 (default) | scalar in the range [0,1]

Mole fraction of the trace gas in a moist air mixture at the inlet of the moist air side of the cooling tower during nominal operating conditions.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, select Specify full moist air nominal condition, and set Nominal trace gas specification to Mole fraction.

Moist air volume — Total volume of moist air in cooling tower

24 m^3 (default) | positive scalar

Total volume of the moist air in the cooling tower.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports.

Cross-sectional area at port A2 — Area of moist air inlet or outlet

4 m^2 (default) | positive scalar

Flow area of the moist air inlet or outlet.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports.

Cross-sectional area at port B2 — Area of moist air inlet or outlet

4 m^2 (default) | positive scalar

Flow area of the moist air inlet or outlet.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports.

Initialize moist air to nominal operating conditions — Option for initializing moist air

on (default) | off

Select this parameter to initialize the moist air to the nominal operating conditions. If you clear this parameter, you can specify the initial conditions directly.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports.

Initial moist air pressure — Moist air pressure at start of simulation

0.101325 MPa (default) | positive scalar

Moist air pressure at the start of the simulation.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports and clear the Initialize moist air to nominal operating conditions check box.

Initial moist air temperature — Moist air temperature at start of simulation

34.28 degC (default) | scalar | two-element vector

Moist air temperature at the start of simulation. If the value is a scalar, then the initial temperature is uniform. If the value is a two-element vector, then the initial temperature varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports and clear the Initialize moist air to nominal operating conditions check box.

Initial moisture specification — Quantity used to describe initial moisture level

Relative humidity (default) | Specific humidity | Mole fraction | Humidity ratio | Wet-bulb temperature

Whether to describe the initial moist air moisture level using the relative humidity, specific humidity, water vapor mole fraction, or humidity ratio.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports and clear the Initialize moist air to nominal operating conditions check box.

Initial moist air relative humidity — Relative humidity at start of simulation

0.5 (default) | scalar in the range [0,1] | two-element vector

Moist air relative humidity at the start of simulation. If the value is a scalar, then the initial relative humidity is uniform. If the value is a two-element vector, then the initial relative humidity varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial moisture specification to Relative humidity.

Initial moist air specific humidity — Specific humidity at start of simulation

0.0167 (default) | scalar in the range [0,1] | two-element vector

Moist air specific humidity, defined as the mass fraction of water vapor in a moist air mixture, at the start of simulation. If the value is a scalar, then the initial specific humidity is uniform. If the value is a two-element vector, then the initial specific humidity varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial moisture specification to Specific humidity.

Initial moist air water vapor mole fraction — Mole fraction of water vapor at start of simulation

0.0266 (default) | scalar in the range [0,1] | two-element vector

Mole fraction of the water vapor in a moist air mixture at the start of simulation. If the value is a scalar, then the initial mole fraction is uniform. If the value is a two-element vector, then the initial mole fraction varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial moisture specification to Mole fraction.

Initial moist air humidity ratio — Humidity ratio at start of simulation

0.017 (default) | scalar in the range [0,1] | two-element vector

Moist air humidity ratio, defined as the mass ratio of water vapor to dry air and trace gas, at the start of simulation. If the value is a scalar, then the initial humidity ratio is uniform. If the value is a two-element vector, then the initial humidity ratio varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial moisture specification to Humidity ratio.

Initial moist air wet-bulb temperature — Wet-bulb temperature at start of simulation

25.56 degC (default) | positive scalar

Wet-bulb temperature of the moist air mixture at the start of simulation. If the value is a scalar, then the initial mole fraction is uniform. If the value is a two-element vector, then the initial mole fraction varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial moisture specification to Wet-bulb temperature.

Initial trace gas specification — Quantity used to describe initial trace gas level

Mass fraction (default) | Mole fraction

Whether to use the mass fraction or mole fraction to describe the trace gas level at the start of simulation.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports and clear the Initialize moist air to nominal operating conditions check box.

Initial moist air trace gas mass fraction — Mass fraction of trace gas at start of simulation

6e-4 (default) | scalar in the range [0,1]

Mass fraction of the trace gas in a moist air mixture at the start of simulation. If the value is a scalar, then the initial mass fraction is uniform. If the value is a two-element vector, then the initial mass fraction varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial trace gas specification to Mass fraction.

Initial moist air trace gas mole fraction — Mole fraction of trace gas at start of simulation

4e-4 (default) | scalar in the range [0,1]

Mole fraction of the trace gas in a moist air mixture at the start of simulation. If the value is a scalar, then the initial mole fraction is uniform. If the value is a two-element vector, then the initial mole fraction varies linearly between ports A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

Dependencies

To enable this parameter, set Moist air operating conditions to Moist air domain ports, clear the Initialize moist air to nominal operating conditions check box, and set Initial trace gas specification to Mole fraction.

Relative humidity at saturation — Relative humidity above which condensation occurs

1 (default) | positive scalar

Relative humidity above which condensation occurs in the tower.

References

[1] Mitchell JW, Braun JE. Principles of heating, ventilation, and air conditioning in buildings. Hoboken: Wiley, 2013.

[2] ASHRAE Standard Committee. 2012 ASHRAE Handbook—HVAC Systems and Equipment (SI). 2012.

[3] ASHRAE Standard Committee. 2013 ASHRAE Handbook—Fundamentals (SI). 2013.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2023b