System-Level Heat Exchanger (G-G)

Heat exchanger based on performance data between two gas networks

Since R2023b

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Libraries:
Simscape / Fluids / Heat Exchangers / Gas

Description

The System-Level Heat Exchanger (G-G) block models a heat exchanger based on performance data between two distinct gas 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 (G-G) block, but uses a different parameterization model. The table compares the two blocks:

Heat Exchanger (G-G)	System-Level Heat Exchanger (G-G)
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 gas flows in the block, gas 1 and gas 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

$$Q_{seg,G1}+Q_{seg,G2}=0,$$

where:

• Q_seg,G1 is the heat flow rate from the wall that is the heat transfer surface to gas 1 in the segment.

• Q_seg,G2 is the heat flow rate from the wall to gas 2 in the segment.

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

$$Q_{seg,G1}+Q_{seg,G2}=-\frac{M_{wall}{c}_{p_{wall}}}{N}\frac{d{T}_{seg,wall}}{dt},$$

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 gas 1 in the segment is

$$Q_{seg,G1}=U{A}_{seg,G1}\left(T_{seg,wall}-T_{seg,G1}\right),$$

where:

• UA_seg,G1 is the heat transfer conductance for gas 1 in the segment.

• T_seg,G1is the average gas temperature in the segment.

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

$$Q_{seg,G2}=U{A}_{seg,G2}\left(T_{seg,wall}-T_{seg,G2}\right),$$

where:

• UA_seg,G2 is the heat transfer conductance for gas 2 in the segment.

• T_seg,G2 is the average gas 2 temperature in the segment.

Gas Heat Transfer Correlation

The block calculates the heat transfer conductance in both gasses 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:

$$U{A}_{seg,G}=a_G{\left({\mathrm{Re}}_{seg,G}\right)}^{b_G}{\left({\mathrm{Pr}}_{seg,G}\right)}^{c_G}{k}_{seg,G}\frac{G_G}{N},$$

where:

• a_G, b_G, and c_G are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

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

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

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

• G_G is the geometry scale factor for the gas 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

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

where:

• ṁ_seg,G is the mass flow rate through the segment.

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

• D_ref,G is an arbitrary reference diameter.

• S_ref,G is an arbitrary reference flow area.

Note

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

Pressure Loss

The pressure losses on the gas 1 side are

$$\begin{array}{l}{p}_{A,G1}-p_{G1}=\frac{K_{G1}}{2}\frac{{\dot{m}}_{A,G1}\sqrt{{\dot{m}}^2{}_{A,G1}+{\dot{m}}^2{}_{thres,G1}}}{2{\rho }_{avg,G1}}\\ p_{B,G1}-p_{G1}=\frac{K_{G1}}{2}\frac{{\dot{m}}_{B,G1}\sqrt{{\dot{m}}^2{}_{B,G1}+{\dot{m}}^2{}_{thres,G1}}}{2{\rho }_{avg,G1}}\end{array}$$

where:

• p_A,G1 and p_B,G1 are the pressures at ports A1 and B1, respectively.

• p_G1 is internal gas 1 pressure at which the block calculates heat transfer.

• ṁ_A,G1 and ṁ_B,G1 are the mass flow rates into ports A1 and B1, respectively.

• ρ_avg,G1 is the average gas 1 density over all segments.

• ṁ_thres,G1 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_G1, so that p_A,G1 – p_B,G1 matches the nominal pressure loss at the nominal mass flow rate.

The pressure losses on the gas 2 side are

$$\begin{array}{l}{p}_{A,G\text{2}}-p_{\text{G2}}=\frac{K_{\text{G2}}}{2}\frac{{\dot{m}}_{A,G\text{2}}\sqrt{{\dot{m}}^2{}_{A,G\text{2}}+{\dot{m}}^2{}_{thres,G\text{2}}}}{2{\rho }_{avg,G2}}\\ p_{B,G\text{2}}-p_{\text{G2}}=\frac{K_{\text{G2}}}{2}\frac{{\dot{m}}_{B,G\text{2}}\sqrt{{\dot{m}}^2{}_{B,G\text{2}}+{\dot{m}}^2{}_{thres,G\text{2}}}}{2{\rho }_{avg,G\text{2}}}\end{array}$$

where:

• p_A,G2 and p_B,G2 are the pressures at ports A2 and B2, respectively.

• p_G2 is internal gas 2 pressure at which the block calculates heat transfer.

• ṁ_A,G2 and ṁ_B,G2 are the mass flow rates into ports A2 and B2, respectively.

• ρ_avg,G2 is the average gas density over all segments.

• ṁ_thres,G2 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_G2, so that p_A,G2 – p_B,G2 matches the nominal pressure loss at the nominal mass flow rate.

Gas Mass and Energy Conservation

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

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

where:

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

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

• T_seg,G is the temperature for the segment.

• V_G is the total gas volume.

The summation is over all segments.

Note

Although the block divides the gas flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_G. Consequently, p_G is outside of the summation.

The energy conservation equation for each segment is

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

where:

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

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

• M_G is the total gas mass.

• ṁ_seg,in,G and ṁ_seg,out,G are the mass flow rates into and out of the segment.

• Φ_seg,in,G and Φ_seg,out,G 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 ṁ_A,G and ṁ_B,G.

Ports

Output

Q1 — Rate of heat transfer to gas 1, W

physical signal

Rate of heat transfer to gas 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 gas 2, W

physical signal

Rate of heat transfer to gas 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 — Gas port on side 1

gas

Inlet or outlet port associated with the first gas network.

B1 — Gas port on side 1

gas

Inlet or outlet port associated with the first gas network.

A2 — Gas port on side 2

gas

Inlet or outlet port associated with the second gas network.

B2 — Gas port on side 2

gas

Inlet or outlet port associated with the second gas network.

Parameters

Configuration

Flow arrangement at nominal operating conditions — Flow path alignment

Counter flow - Gas 1 flows from A to B, Gas 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 - Gas 1 flows from A to B, Gas 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 gas 1 to nominal operating conditions or Initialize gas 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 gas 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 gas 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 gas 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 gas 2 port B2.

Gas 1

Nominal operating condition — Nominal operating condition

Heat transfer from Gas 1 to Gas 2 (default) | Heat transfer from Gas 2 to Gas 1

Nominal operating condition to use for the gas 1 network: :

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

• Heat transfer from Gas 2 to Gas 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 gas 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 gas 1 ports during nominal operating condition

0.001 MPa (default) | positive scalar

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

Nominal inlet pressure — Pressure at the gas 1 inlet

0.101325 MPa (default) | positive scalar

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

Nominal inlet temperature — Temperature at the gas 1 inlet

333.15 K (default) | positive scalar

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

Heat transfer capacity specification — How to specify heat transfer capacity of gas 1

Rate of heat transfer (default) | Outlet condition

Whether to specify the performance of the heat exchanger for gas 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 gas network that the heat transfers from and to:

• If Nominal operating condition is Heat transfer from Gas 1 to Gas 2, this parameter is the rate of the heat transfer from the gas side 1 to the gas side 2 during the nominal operating condition.

• If Nominal operating condition is Heat transfer from Gas 2 to Gas 1, this parameter is the rate of the heat transfer from the gas side 2 to the gas 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 gas 1 outlet of the heat exchanger during the nominal operating condition.

Dependencies

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

Gas 1 volume — Total volume of gas 1

0.1 m^3 (default) | positive scalar

Total volume of gas 1 inside the heat exchanger.

Initialize gas 1 to nominal operating conditions — Option for initializing gas 1

on (default) | off

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

Initial gas 1 pressure — Gas 1 pressure at start of simulation

0.101325 MPa (default) | positive scalar

Gas 1 pressure at the start of simulation.

Dependencies

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

Initial gas 1 temperature — Gas 1 temperature at the start of simulation

293.15 K (default) | positive scalar

Gas 1 temperature at the start of simulation.

Dependencies

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

Gas 2

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

0.001 MPa (default) | positive scalar

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

Nominal inlet pressure — Pressure at gas 2 inlet

0.101325 MPa (default) | positive scalar

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

Nominal inlet temperature — Temperature at the gas 2 inlet

293.15 K (default) | positive scalar

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

Gas 2 volume — Total volume of gas 2 in heat exchanger

0.1 m^3 (default) | positive scalar

Total volume of gas 2 in the heat exchanger.

Initialize gas 2 to nominal operating conditions — Option for initializing gas 2

on (default) | off

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

Initial gas 2 pressure — Gas 2 pressure at start of simulation

0.101325 MPa (default) | positive scalar

Gas 2 pressure at the start of the simulation.

Dependencies

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

Initial gas 2 temperature — Gas 2 temperature at start of simulation

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

Gas 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 gas 2 to nominal operating conditions check box.

Correlation Coefficients

a in Nu = a*Re^b*Pr^c for gas 1 — Correlation coefficient for gas 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 gas 1. The default value is based on the Colburn equation.

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

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

a in Nu = a*Re^b*Pr^c for gas 2 — Correlation coefficient for gas 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 gas 2. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for gas 2 — Reynolds number exponent in correlation for gas 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 gas 2. The default value is based on the Colburn equation.

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