System-Level Heat Exchanger (TL-TL)

Heat exchanger based on performance data between two thermal liquid networks

Since R2023b

• 

Libraries:
Simscape / Fluids / Heat Exchangers / Thermal Liquid

Description

The System-Level Heat Exchanger (TL-TL) block models a heat exchanger based on performance data between two thermal liquid networks. Each network has its own set of fluid properties.

The block uses performance data from the heat exchanger datasheet, rather than the detailed geometry of the exchanger. You can adjust the size and performance of the heat exchanger during design iterations, or model heat exchangers with uncommon geometries. You can also use this block to model heat exchangers with a certain level of performance at an early design stage, when detailed geometry data is not yet available.

You parameterize the block by the nominal operating condition. The block sizes the heat exchanger to match the specified performance at the nominal operating condition at steady state.

This block is similar to the Heat Exchanger (TL-TL) block, but uses a different parameterization model. The table compares the two blocks:

Heat Exchanger (TL-TL)	System-Level Heat Exchanger (TL-TL)
Block parameters are based on the heat exchanger geometry	Block parameters are based on performance and operating conditions
Heat exchanger geometry may be limited by the available geometry parameter options	Model is independent of the specific heat exchanger geometry
You can adjust the block for different performance requirements by tuning geometry parameters, such as fin sizes and tube lengths	You can adjust the block for different performance requirements by directly specifying the desired heat and mass flow rates
You can select between parallel, counter, shell and tube, or cross flow configurations	You can select between parallel, counter, or cross-flow arrangement at nominal operating conditions to help with sizing
Predictively accurate results over a wide range of operating conditions, subject to the applicability of the E-NTU equations and the heat transfer coefficient correlations	Very accurate results around the specified operating condition; accuracy may decrease far away from the specified operating conditions
Heat transfer calculations account for the variation of temperature along the flow path by using the E-NTU model	Heat transfer calculations approximate the variation of temperature along the flow path by dividing it into three segments

Heat Transfer

The block divides the two thermal liquid flows in the block, thermal liquid 1 and thermal liquid 2, into three segments of equal size. The block calculates heat transfer between the fluids in each segment. For simplicity, the equation in this section are for one segment.

If you clear the Wall thermal mass check box, then the heat balance in the heat exchanger is

$$Q_{seg,TL1}+Q_{seg,TL2}=0,$$

where:

• Q_seg,TL1 is the heat flow rate from the wall that is the heat transfer surface to thermal liquid 1 in the segment.

• Q_seg,TL2 is the heat flow rate from the wall to thermal liquid 2 in the segment.

If you select Wall thermal mass, then the heat balance in the heat exchanger is

$$Q_{seg,TL1}+Q_{seg,TL2}=-\frac{M_{wall}{c}_{p_{wall}}}{N}\frac{d{T}_{seg,wall}}{dt},$$

where:

• M_wall is the mass of the wall.

• c_pwall is the specific heat of the wall.

• N = 3 is the number of segments.

• T_seg,wall is the average wall temperature in the segment.

• t is time.

The heat flow rate from the wall to thermal liquid 1 in the segment is

$$Q_{seg,TL1}=U{A}_{seg,TL1}\left(T_{seg,wall}-T_{seg,TL1}\right),$$

where:

• UA_seg,TL1 is the heat transfer conductance for thermal liquid 1 in the segment.

• T_seg,TL1is the average liquid temperature in the segment.

The heat flow rate from the wall to thermal liquid 2 in the segment is

$$Q_{seg,TL2}=U{A}_{seg,TL2}\left(T_{seg,wall}-T_{seg,TL2}\right),$$

where:

• UA_seg,TL2 is the heat transfer conductance for thermal liquid 2 in the segment.

• T_seg,TL2 is the average thermal liquid 2 temperature in the segment.

Thermal Liquid Heat Transfer Correlation

The block calculates the heat transfer conductance in both thermal liquids by using the same expression. For simplicity, the section shows equations in this section are for one side, but apply to both sides. The heat transfer conductance equation is:

$$U{A}_{seg,TL}=a_{TL}{\left({\mathrm{Re}}_{seg,TL}\right)}^{b_{TL}}{\left({\mathrm{Pr}}_{seg,TL}\right)}^{c_{TL}}{k}_{seg,TL}\frac{G_{TL}}{N},$$

where:

• a_TL, b_TL, and c_TL are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

• Re_seg,TL is the average Reynolds number for the segment.

• Pr_seg,TL is the average Prandtl number for the segment.

• k_seg,TL is the average thermal conductivity for the segment.

• G_TL is the geometry scale factor for the thermal liquid side of the heat exchanger. The block calculates the geometry scale factor so that the total heat transfer over all segments matches the specified performance at the nominal operating conditions.

The average Reynolds number is

$${\mathrm{Re}}_{seg,\text{TL}}=\frac{{\dot{m}}_{seg,\text{TL}}{D}_{ref,\text{TL}}}{{\mu }_{seg,\text{TL}}{S}_{ref,\text{TL}}},$$

where:

• $${\dot{m}}_{seg,\text{TL}}$$ is the mass flow rate through the segment.

• μ_seg,TL is the average dynamic viscosity for the segment.

• D_ref,TL is an arbitrary reference diameter.

• S_ref,TL is an arbitrary reference flow area.

Note

The D_ref,TL and S_ref,TL terms are included in this equation for unit calculation purposes only, to make Re_seg,TL nondimensional. The values of D_ref,TL and S_ref,TL are arbitrary because the G_TL calculation overrides these values.

Pressure Loss

The pressure losses on the thermal liquid 1 side are

$$\begin{array}{l}{p}_{A,TL1}-p_{TL1}=\frac{K_{TL1}}{2}\frac{{\dot{m}}_{A,TL1}\sqrt{{\dot{m}}^2{}_{A,TL1}+{\dot{m}}^2{}_{thres,TL1}}}{2{\rho }_{avg,TL1}}\\ p_{B,TL1}-p_{TL1}=\frac{K_{TL1}}{2}\frac{{\dot{m}}_{B,TL1}\sqrt{{\dot{m}}^2{}_{B,TL1}+{\dot{m}}^2{}_{thres,TL1}}}{2{\rho }_{avg,TL1}}\end{array}$$

where:

• p_A,TL1 and p_B,TL1 are the pressures at ports A1 and B1, respectively.

• p_TL1 is internal thermal liquid 1 pressure at which the block calculates heat transfer.

• ṁ_A,TL1 and ṁ_B,TL1 are the mass flow rates into ports A1 and B1, respectively.

• ρ_avg,TL1 is the average thermal liquid 1 density over all segments.

• ṁ_thres,TL1 is the laminar threshold for pressure loss, approximated as 1e-4 of the nominal mass flow rate. The block calculates the pressure loss coefficient, K_TL1, so that p_A,TL1 – p_B,TL1 matches the nominal pressure loss at the nominal mass flow rate.

The pressure losses on the thermal liquid 2 side are

$$\begin{array}{l}{p}_{A,\text{TL2}}-p_{\text{TL2}}=\frac{K_{\text{TL2}}}{2}\frac{{\dot{m}}_{A,\text{TL2}}\sqrt{{\dot{m}}^2{}_{A,\text{TL2}}+{\dot{m}}^2{}_{thres,\text{TL2}}}}{2{\rho }_{avg,TL2}}\\ p_{B,\text{TL2}}-p_{\text{TL2}}=\frac{K_{\text{TL2}}}{2}\frac{{\dot{m}}_{B,\text{TL2}}\sqrt{{\dot{m}}^2{}_{B,\text{TL2}}+{\dot{m}}^2{}_{thres,\text{TL2}}}}{2{\rho }_{avg,\text{TL2}}}\end{array}$$

where:

• p_A,TL2 and p_B,TL2 are the pressures at ports A2 and B2, respectively.

• p_TL2 is internal thermal liquid 2 pressure at which the block calculates heat transfer.

• ṁ_A,TL2 and ṁ_B,TL2 are the mass flow rates into ports A2 and B2, respectively.

• ρ_avg,TL2 is the average thermal liquid density over all segments.

• ṁ_thres,TL2 is the laminar threshold for pressure loss, approximated as 1e-4 of the nominal mass flow rate. The block calculates the pressure loss coefficient, K_TL2, so that p_A,TL2 – p_B,TL2 matches the nominal pressure loss at the nominal mass flow rate.

Thermal Liquid Mass and Energy Conservation

The block uses the same expression for mass and energy conservation in both thermal liquids. For simplicity, the section shows equations in this section are for one side, but apply to both sides.

$$\left(\frac{d{p}_{TL}}{dt}{\displaystyle \sum _{segments}\left(\frac{\partial {\rho }_{seg,TL}}{\partial p}\right)}+{\displaystyle \sum _{segments}\left(\frac{d{T}_{seg,TL}}{dt}\frac{\partial {\rho }_{seg,TL}}{\partial T}\right)}\right)\frac{V_{TL}}{N}={\dot{m}}_{A,TL}+{\dot{m}}_{B,TL},$$

where:

• $$\frac{\partial {\rho }_{seg,TL}}{\partial p}$$ is the partial derivative of density with respect to pressure for the segment.

• $$\frac{\partial {\rho }_{seg,TL}}{\partial T}$$ is the partial derivative of density with respect to temperature for the segment.

• T_seg,TL is the temperature for the segment.

• V_TL is the total thermal liquid volume.

The summation is over all segments.

Note

Although the block divides both thermal liquid flows into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_TL. Consequently, p_TL is outside of the summation.

The energy conservation equation for each segment is

$$\begin{array}{l}\left(\frac{d{p}_{TL}}{dt}\frac{\partial u_{seg,TL}}{\partial p}+\frac{d{T}_{seg,TL}}{dt}\frac{\partial u_{seg,TL}}{\partial T}\right)\frac{M_{TL}}{N}+u_{seg,TL}\left({\dot{m}}_{seg,in,TL}-{\dot{m}}_{seg,out,TL}\right)=\\ {\Phi }_{seg,in,TL}-{\Phi }_{seg,out,TL}+Q_{seg,TL},\end{array}$$

where:

• $$\frac{\partial u_{seg,TL}}{\partial p}$$ is the partial derivative of the specific internal energy with respect to pressure for the segment.

• $$\frac{\partial u_{seg,TL}}{\partial T}$$ is the partial derivative of the specific internal energy with respect to temperature for the segment.

• M_TL is the total thermal liquid mass for one side.

• $${\dot{m}}_{seg,in,TL}$$ and $${\dot{m}}_{seg,out,TL}$$ are the mass flow rates into and out of the segment.

• Φ_seg,in,TL and Φ_seg,out,TL are the energy flow rates into and out of the segment.

The block assumes the mass flow rates between segments are linearly distributed between the values of $${\dot{m}}_{A,TL}$$ and $${\dot{m}}_{B,TL}$$.

Ports

Output

Q1 — Rate of heat transfer to thermal liquid 1, W

physical signal

Rate of heat transfer to thermal liquid 1, returned as a physical signal, in W. The physical signals at ports Q1 and Q2 are usually equal in value with the opposite sign. However, if you select Wall thermal mass, then these two signals may have different values because the wall may absorb and release some of the heat being transferred.

Q2 — Rate of heat transfer to thermal liquid 2, W

physical signal

Rate of heat transfer to thermal liquid 2, returned as a physical signal, in W. The physical signals at ports Q1 and Q2 are usually equal in value with the opposite sign. However, if you select Wall thermal mass, then these two signals may have different values because the wall may absorb and release some of the heat being transferred.

Conserving

A1 — Thermal liquid port on side 1

thermal liquid

Inlet or outlet port associated with the first thermal liquid network.

B1 — Thermal liquid port on side 1

thermal liquid

Inlet or outlet port associated with the first thermal liquid network.

A2 — Thermal liquid port on side 2

thermal liquid

Inlet or outlet port associated with the second thermal liquid network.

B2 — Thermal liquid port on side 2

thermal liquid

Inlet or outlet port associated with the second thermal liquid network.

Parameters

Configuration

Flow arrangement at nominal operating conditions — Flow path alignment

Counter flow - Thermal Liquid 1 flows from A to B, Thermal Liquid 2 flows from B to A (default) | Parallel flow - Both fluids flow from A to B | Cross flow - Both fluids flow from A to B

Flow path alignment between the heat exchanger sides at nominal operating condition. The available flow arrangements are:

• Counter flow - Thermal Liquid 1 flows from A to B, Thermal Liquid 2 flows from B to A — The flows run parallel to each other, in the opposite directions.

• Parallel flow - Both fluids flow from A to B — The flows run in the same direction.

• Cross flow - Both fluids flow from A to B — The flows run perpendicular to each other.

The choice between parallel flow and counter flow affects how the block determines the size of the heat exchanger. The counter flow setting is the most effective, and needs the smallest size to meet the specified performance. Conversely, parallel flow is the least effective, and needs the biggest size to meet the specified performance.

Flow direction at the nominal condition (from A to B, or from B to A) only affects the model initialization, when you select Initialize thermal liquid 1 to nominal operating conditions or Initialize thermal liquid 2 to nominal operating conditions. If you set different initial operating conditions, the flow directions can be different.

After the block determines the size of the heat exchanger, this setting does not play a role in how the block calculates the heat transfer during simulation. Instead, the heat transfer depends on the flow directions during simulation. For example, if you set the parameter to parallel flow but set up the model to run in counter flow, then the rate of heat transfer during simulation will not match the specified performance, even if the rest of the boundary conditions are the same.

If you set the parameter to cross flow, then the block models the flow paths as perpendicular inside the heat exchanger, so the flow directions during simulation do not matter.

Wall thermal mass — Whether to enable effect of thermal mass on heat transfer surface

off (default) | on

Whether to enable the effect of thermal mass on the heat transfer surface. When you select this parameter, the block introduces additional dynamics to the simulation and takes longer to reach steady state, but this parameter does not affect the results at steady-state simulation.

Wall mass — Mass of heat transfer surface

1 kg (default) | positive scalar

Mass of the heat transfer surface.

Dependencies

To enable this parameter, select Wall thermal mass.

Wall specific heat — Specific heat of heat transfer surface

490 J/(K*kg) (default) | positive scalar

Specific heat of the heat transfer surface.

Dependencies

To enable this parameter, select Wall thermal mass.

Initialize wall temperature to nominal operating conditions — Option for initializing wall temperature

on (default) | off

Option to initialize the wall temperature to nominal operating conditions or specified values. If you select this parameter, the block calculates the initial wall temperature from the nominal operating conditions specified for both fluid sides. If you clear this parameter, you can specify the initial wall temperature directly with the Initial wall temperature parameter.

Dependencies

To enable this parameter, select Wall thermal mass.

Initial wall temperature — Initial temperature of wall

293.15 K (default) | positive scalar or two element vector

Initial temperature of the wall. If you specify a scalar, the block assumes that the initial wall temperature is uniform. If you specify a two-element vector, then the block assumes that the initial wall temperature varies linearly between ports A1 and A2 and ports B1 and B2. The first element corresponds to the temperature at ports A1 and A2 and the second element corresponds to the temperature at ports B1 and B2.

Dependencies

To enable this parameter, select Wall thermal mass and clear the Initialize wall temperature to nominal operating conditions check box.

Cross-sectional area at port A1 — Flow area at port A1

0.01 m^2 (default) | positive scalar

Flow area at the thermal liquid 1 port A1.

Cross-sectional area at port B1 — Flow area at port B1

0.01 m^2 (default) | positive scalar

Flow area at the thermal liquid 1 port B1.

Cross-sectional area at port A2 — Flow area at port A2

0.01 m^2 (default) | positive scalar

Flow area at the thermal liquid 2 port A2.

Cross-sectional area at port B2 — Area normal to flow at port B2

0.01 m^2 (default) | positive scalar

Flow area at the thermal liquid 2 port B2.

Thermal Liquid 1

Nominal operating condition — Nominal operating condition

Heat transfer from Thermal Liquid 1 to Thermal Liquid 2 (default) | Heat transfer from Thermal Liquid 2 to Thermal Liquid 1

Nominal operating condition to use for the thermal liquid 1 network: :

• Heat transfer from Thermal Liquid 1 to Thermal Liquid 2 — Side 1 is cooled and side 2 is heated.

• Heat transfer from Thermal Liquid 2 to Thermal Liquid 1 — Side 2 is cooled and side 1 is heated.

This setting relates only to the nominal operating condition parameters. It does not mean that heat transfer can only happen in the specified direction during simulation.

Nominal mass flow rate — Mass flow rate between thermal liquid 1 ports during nominal operating condition

0.1 kg/s (default) | positive scalar

Mass flow rate from port A1 to port B1 during the nominal operating condition.

Nominal pressure drop — Pressure drop between thermal liquid 1 ports during nominal operating condition

0.01 MPa (default) | positive scalar

Pressure drop from port A1 to port B1 during the nominal operating condition.

Nominal inlet pressure — Pressure at the thermal liquid 1 inlet

0.101325 MPa (default) | positive scalar

Pressure at the thermal liquid 1 inlet of the heat exchanger during nominal operating condition.

Nominal inlet temperature — Temperature at the thermal liquid 1 inlet

333.15 K (default) | positive scalar

Temperature at the thermal liquid 1 inlet of the heat exchanger during the nominal operating condition.

Heat transfer capacity specification — How to specify heat transfer capacity of thermal liquid 1

Rate of heat transfer (default) | Outlet condition

Whether to specify the performance of the heat exchanger for thermal liquid 1 at the nominal operating condition directly, by the rate of heat transfer, or indirectly, by the outlet condition.

Nominal rate of heat transfer — Rate of heat transfer

1 kW (default) | positive scalar

Rate of heat transfer. The Nominal Operating condition parameter determines the thermal liquid network that the heat transfers from and to:

• If Nominal operating condition is Heat transfer from Thermal Liquid 1 to Thermal Liquid 2, this parameter is the rate of the heat transfer from the thermal liquid side 1 to the thermal liquid side 2 during the nominal operating condition.

• If Nominal operating condition is Heat transfer from Thermal Liquid 2 to Thermal Liquid 1, this parameter is the rate of the heat transfer from the thermal liquid side 1 to the thermal liquid side 1 during the nominal operating condition.

Dependencies

To enable this parameter, set Heat transfer capacity specification to Rate of heat transfer.

Nominal outlet temperature — Outlet temperature

323.15 K (default) | positive scalar

Temperature at the thermal liquid 1 outlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Heat transfer capacity specification to Outlet condition.

Thermal liquid 1 volume — Total volume of thermal liquid 1

0.001 m^3 (default) | positive scalar

Total volume of thermal liquid 1 inside the heat exchanger.

Initialize thermal liquid 1 to nominal operating conditions — Option for initializing thermal liquid 1

on (default) | off

Option to initialize thermal liquid 1 to nominal operating conditions or specified values. If you select this parameter, the block initializes thermal liquid 1 to the nominal operating conditions. If you clear this check box, you can specify the initial conditions directly with additional parameters.

Initial thermal liquid 1 pressure — Thermal liquid 1 pressure at start of simulation

0.101325 MPa (default) | positive scalar

Thermal liquid 1 pressure at the start of simulation.

Dependencies

To enable this parameter, clear the Initialize thermal liquid 1 to nominal operating conditions check box.

Initial thermal liquid 1 temperature — Thermal liquid 1 temperature at start of simulation

293.15 K (default) | positive scalar

Thermal liquid 1 temperature at the start of simulation.

Dependencies

To enable this parameter, clear the Initialize thermal liquid 1 to nominal operating conditions check box.

Thermal Liquid 2

Nominal mass flow rate — Mass flow rate between thermal liquid 2 ports during nominal operating condition

0.1 kg/s (default) | positive scalar

Mass flow rate from port A2 to port B2 during the nominal operating condition.

Nominal pressure drop — Pressure drop between thermal liquid 2 ports during nominal operating condition

0.01 MPa (default) | positive scalar

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

Nominal inlet pressure — Pressure at thermal liquid 2 inlet

0.101325 MPa (default) | positive scalar

Pressure at the thermal liquid 2 inlet of the heat exchanger during the nominal operating condition.

Nominal inlet temperature — Temperature at the thermal liquid 2 inlet

293.15 K (default) | positive scalar

Temperature at the thermal liquid 2 inlet of the heat exchanger during the nominal operating condition.

Thermal liquid 2 volume — Total volume of thermal liquid 2 in heat exchanger

0.001 m^3 (default) | positive scalar

Total volume of thermal liquid 2 in the heat exchanger.

Initialize thermal liquid 2 to nominal operating conditions — Option for initializing thermal liquid 2

on (default) | off

Option to initialize thermal liquid 2 to nominal operating conditions or specified values. If you select this parameter, the block initializes thermal liquid 2 to the nominal operating conditions. If you clear this check box, you can specify the initial conditions directly with additional parameters.

Initial thermal liquid 2 pressure — Thermal liquid 2 pressure at start of simulation

0.101325 MPa (default) | positive scalar

Thermal liquid 2 pressure at the start of the simulation.

Dependencies

To enable this parameter, clear the Initialize thermal liquid 2 to nominal operating conditions check box.

Initial thermal liquid 2 temperature — Thermal liquid 2 temperature at start of simulation

293.15 K (default) | positive scalar | two-element vector

Thermal liquid 2 temperature at the start of simulation. If the value is a scalar, then the block assumes that the initial temperature is uniform. If the value is a two-element vector, then the block assumes that 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, clear the Initialize thermal liquid 2 to nominal operating conditions check box.

Correlation Coefficients

a in Nu = a*Re^b*Pr^c for thermal liquid 1 — Correlation coefficient for thermal liquid 1

0.023 (default) | positive scalar

Proportionality constant in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid 1. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for thermal liquid 1 — Reynolds number exponent in correlation for thermal liquid 1

0.8 (default) | positive scalar

Reynolds number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid 1.

c in Nu = a*Re^b*Pr^c for thermal liquid 1 — Prandtl number exponent in correlation for thermal liquid 1

0.33 (default) | positive scalar

Prandtl number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid 1.

a in Nu = a*Re^b*Pr^c for thermal liquid 2 — Correlation coefficient for thermal liquid 2

0.023 (default) | positive scalar

Proportionality constant in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid 2. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for thermal liquid 2 — Reynolds number exponent in correlation for thermal liquid 2

0.8 (default) | positive scalar

Reynolds number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid 2. The default value is based on the Colburn equation.

c in Nu = a*Re^b*Pr^c for thermal liquid 2 — Prandtl number exponent in correlation for thermal liquid 2

0.33 (default) | positive scalar

Prandtl number exponent in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for thermal liquid 2. The default value is based on the Colburn equation.

References

[1] Ashrae Handbook: Fundamentals. Atlanta: Ashrae, 2013.

[2] Çengel, Yunus A. Heat and Mass Transfer: A Practical Approach. 3rd ed. McGraw-Hill Series in Mechanical Engineering. Boston: McGraw-Hill, 2007.

[3] Mitchell, John W., and James E. Braun. Principles of Heating, Ventilation, and Air Conditioning in Buildings. Hoboken, NJ: Wiley, 2013.

[4] Shah, R. K., and Dušan P. Sekulić. Fundamentals of Heat Exchanger Design. Hoboken, NJ: John Wiley & Sons, 2003.

[5] Cavallini, Alberto, and Roberto Zecchin. “A DIMENSIONLESS CORRELATION FOR HEAT TRANSFER IN FORCED CONVECTION CONDENSATION.” In Proceeding of International Heat Transfer Conference 5, 309–13. Tokyo, Japan: Begellhouse, 1974. https://doi.org/10.1615/IHTC5.1220.

Extended Capabilities

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

Version History

Introduced in R2023b