System-Level Condenser Evaporator (2P-TL)

Heat exchanger based on performance data between two-phase fluid and thermal liquid networks

Since R2022a

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Libraries:
Simscape / Fluids / Heat Exchangers / Two-Phase Fluid - Thermal Liquid

Description

The System-Level Condenser Evaporator (2P-TL) block models a heat exchanger between a two-phase fluid network and a thermal liquid network.

The block can act as a condenser or as an evaporator in a refrigeration system, depending on the direction of heat transfer. 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 heat exchanger is sized to match the specified performance at the nominal operating condition at steady state.

The Two-Phase Fluid 1 side approximates the liquid zone, mixture zone, and vapor zone based on the change in enthalpy along the flow path.

This block is similar to the Condenser Evaporator (TL-2P) block, but uses a different parameterization model. The table compares the two blocks:

Condenser Evaporator (TL-2P)	System-Level Condenser Evaporator (2P-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, 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
Accounts for different fluid properties and heat transfer coefficients for subcooled liquid, liquid-vapor mixture, and superheated vapor	Accounts for different fluid properties and heat transfer coefficients for subcooled liquid, liquid-vapor mixture, and superheated vapor
Keeps track of variable zone length fractions for subcooled liquid, liquid-vapor mixture, and superheated vapor regions based on the geometry	Approximates the effect of subcooled liquid, liquid-vapor mixture, and superheated vapor regions using weighting factors based on the difference in enthalpy between inlet and outlet
Does not model the wall thermal mass; you can approximate the effect by connecting a pipe block with a thermal mass downstream	Includes an option to model the wall thermal mass

Heat Transfer

The block divides the two-phase fluid flow and the thermal liquid flow each into three segments of equal size and calculates heat transfer between the fluids is 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

$$Q_{seg,2P}+Q_{seg,TL}=0,$$

where:

• Q_seg,2P is the heat flow rate from the wall that is the heat transfer surface to the two-phase fluid in the segment.

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

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

$$Q_{seg,2P}+Q_{seg,TL}=-\frac{M_{wall}{c}_{p_{wall}}}{N}\frac{d{T}_{seg,wall}}{dt},$$

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 the two-phase fluid in the segment is

$$Q_{seg,2P}=U{A}_{seg,2P}\left(T_{seg,wall}-T_{seg,2P}\right),$$

where:

• UA_seg,2P is the weighted-average heat transfer conductance for the two-phase fluid in the segment.

• T_seg,2P is the weighted-average fluid temperature for the two-phase fluid in the segment.

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

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

where:

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

• T_seg,TL is the average liquid temperature in the segment.

Two-Phase Fluid Heat Transfer Correlation

If the segment is subcooled liquid, then the heat transfer conductance is

$$U{A}_{seg,L,2P}=a_{L,2P}{\left({\mathrm{Re}}_{seg,L,2P}\right)}^{b_{2P}}{\left({\mathrm{Pr}}_{seg,L,2P}\right)}^{c_{2P}}{k}_{seg,L,2P}\frac{G_{2P}}{N},$$

where:

• a_L,2P, b_2P, and c_2P are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

• Re_seg,L,2P is the average liquid Reynolds number for the segment.

• Pr_seg,L,2P is the average liquid Prandtl number for the segment.

• k_seg,L,2P is the average liquid thermal conductivity for the segment.

• G_2P is the geometry scale factor for the two-phase fluid 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 liquid Reynolds number is

$${\mathrm{Re}}_{seg,L,2P}=\frac{{\dot{m}}_{seg,2P}{D}_{ref,2P}}{{\mu }_{seg,L,2P}{S}_{ref,2P}},$$

where:

• $${\dot{m}}_{seg,2P}$$ is the mass flow rate through the segment.

• μ_seg,L,2P is the average liquid dynamic viscosity for the segment.

• D_ref,2P is an arbitrary reference diameter.

• S_ref,2P is an arbitrary reference flow area.

Note

The D_ref,2P and S_ref,2P terms are included in this equation for unit calculation purposes only, to make Re_seg,L,2P nondimensional. The values of D_ref,2P and S_ref,2P are arbitrary because the G_2P calculation overrides these values.

Similarly, if the segment is superheated vapor, then the heat transfer conductance is

$$U{A}_{seg,V,2P}=a_{V,2P}{\left({\mathrm{Re}}_{seg,V,2P}\right)}^{b_{2P}}{\left({\mathrm{Pr}}_{seg,V,2P}\right)}^{c_{2P}}{k}_{seg,V,2P}\frac{G_{2P}}{N},$$

where:

• a_V,2P, b_2P, and c_2P are the coefficients of the Nusselt number correlation. These coefficients appear as block parameters in the Correlation Coefficients section.

• Re_seg,V,2P is the average vapor Reynolds number for the segment.

• Pr_seg,V,2P is the average vapor Prandtl number for the segment.

• k_seg,V,2P is the average vapor thermal conductivity for the segment.

The average vapor Reynolds number is

$${\mathrm{Re}}_{seg,V,2P}=\frac{{\dot{m}}_{seg,2P}{D}_{ref,2P}}{{\mu }_{seg,V,2P}{S}_{ref,2P}},$$

where μ_seg,V,2P is the average vapor dynamic viscosity for the segment.

If the segment is liquid-vapor mixture, then the heat transfer conductance is

$$U{A}_{seg,M,2P}=a_{M,2P}{\left({\mathrm{Re}}_{seg,SL,2P}\right)}^{b_{2P}}CZ{\left({\mathrm{Pr}}_{seg,SL,2P}\right)}^{c_{2P}}{k}_{seg,SL,2P}\frac{G_{2P}}{N},$$

where:

• a_M,2P, b_2P, and c_2P are the coefficients of the Nusselt number correlation. These coefficients appear as block parameters in the Correlation Coefficients section.

• Re_seg,SL,2P is the saturated liquid Reynolds number for the segment.

• Pr_seg,SL,2P is the saturated liquid Prandtl number for the segment.

• k_seg,SL,2P is the saturated liquid thermal conductivity for the segment.

• CZ is the Cavallini and Zecchin term.

The saturated liquid Reynolds number is

$${\mathrm{Re}}_{seg,SL,2P}=\frac{{\dot{m}}_{seg,2P}{D}_{ref,2P}}{{\mu }_{seg,SL,2P}{S}_{ref,2P}},$$

where μ_seg,SL,2P is the saturated liquid dynamic viscosity for the segment.

The Cavallini and Zecchin term is

$$CZ=\frac{{\left(\left(\sqrt{\frac{{\nu }_{seg,SV,2P}}{{\nu }_{seg,SL,2P}}}-1\right)\left(x_{seg,out,2P}+1\right)\right)}^{1+b_{2P}}-{\left(\left(\sqrt{\frac{{\nu }_{seg,SV,2P}}{{\nu }_{seg,SL,2P}}}-1\right)\left(x_{seg,in,2P}+1\right)\right)}^{1+b_{2P}}}{\left(1+b_{2P}\right)\left(\sqrt{\frac{{\nu }_{seg,SV,2P}}{{\nu }_{seg,SL,2P}}}-1\right)\left(x_{seg,out,2P}-x_{seg,in,2P}\right)},$$

where:

• ν_seg,SL,2P is the saturated liquid specific volume for the segment.

• ν_seg,SV,2P is the saturated vapor specific volume for the segment.

• x_seg,in,2P is the vapor quality at the segment inlet.

• x_seg,out,2P is the vapor quality at the segment outlet.

The expression is based on the work of Cavallini and Zecchin [5], which derives a heat transfer coefficient correlation at a local vapor quality x. Equations for the liquid-vapor mixture are obtained by averaging Cavallini and Zecchin’s correlation over the segment from x_seg,in,2P to x_seg,out,2P.

Two-Phase Fluid Weighted Average

The two-phase fluid flow through a segment may not be entirely represented as either subcooled liquid, superheated vapor, or liquid-vapor mixture. Instead, each segment may consist of a combination of these. The block approximates this condition by computing weighting factors (w_L, w_V, and w_M) based on the change in specific enthalpy across the segment and the saturated liquid and vapor specific enthalpies. The block assumes that the specific enthalpy across the segment varies piecewise linearly from inlet to outlet, with the breakpoints corresponding to the saturation boundaries for liquid and vapor. The zone with a larger heat transfer coefficient has a steeper slope than the zone with a lower heat transfer coefficient.

$$\begin{array}{l}{w}_L=\frac{{\Delta }_L}{{\Delta }_L+{\Delta }_M+{\Delta }_V}\\ w_V=\frac{{\Delta }_V}{{\Delta }_L+{\Delta }_M+{\Delta }_V}\\ w_M=1-w_L-w_V\end{array}$$

$$\begin{array}{l}{\Delta }_L=\left|\min \left(h_{seg,out,2P},h_{seg,SL,2P}\right)-\min \left(h_{seg,in,2P},h_{seg,SL,2P}\right)\right|\cdot U{A}_{seg,M,2P}\cdot U{A}_{seg,V,2P}\\ {\Delta }_M=\left|\min \left(\max \left(h_{seg,out,2P},h_{seg,SL,2P}\right),h_{seg,SV,2P}\right)-\min \left(\max \left(h_{seg,in,2P},h_{seg,SL,2P}\right),h_{seg,SV,2P}\right)\right|\cdot U{A}_{seg,L,2P}\cdot U{A}_{seg,V,2P}\\ {\Delta }_V=\left|\max \left(h_{seg,out,2P},h_{seg,SV,2P}\right)-\max \left(h_{seg,in,2P},h_{seg,SV,2P}\right)\right|\cdot U{A}_{seg,L,2P}\cdot U{A}_{seg,M,2P}\end{array}$$

where:

• h_seg,in,2P is the specific enthalpy at the segment inlet.

• h_seg,out,2P is the specific enthalpy at the segment outlet.

• h_seg,SL,2P is the saturated liquid specific enthalpy for the segment.

• h_seg,SV,2P is the saturated vapor specific enthalpy for the segment.

The weighted-average two-phase fluid heat transfer conductance for the segment is therefore

$$U{A}_{seg,2P}=w_L\left(U{A}_{seg,L,2P}\right)+w_V\left(U{A}_{seg,V,2P}\right)+w_M\left(U{A}_{seg,M,2P}\right).$$

The weighted-average fluid temperature for the segment is

$$T_{seg,2P}=\frac{w_L\left(U{A}_{seg,L,2P}\right)T_{seg,L,2P}+w_V\left(U{A}_{seg,V,2P}\right)T_{seg,V,2P}+w_M\left(U{A}_{seg,M,2P}\right)T_{seg,M,2P}}{U{A}_{seg,2P}},$$

where:

• T_seg,L,2P is the average liquid temperature for the segment.

• T_seg,V,2P is the average vapor temperature for the segment.

• T_seg,M,2P is the average mixture temperature for the segment, which is the saturated liquid temperature.

Thermal Liquid Heat Transfer Correlation

The heat transfer conductance 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 two-phase fluid side are

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

where:

• p_A,2P and p_B,2P are the pressures at ports A1 and B1, respectively.

• p_2P is internal two-phase fluid pressure at which the heat transfer is calculated.

• $${\dot{m}}_{A,2P}$$ and $${\dot{m}}_{B,2P}$$ are the mass flow rates into ports A1 and B1, respectively.

• ρ_avg,2P is the average two-phase fluid density over all segments.

• $${\dot{m}}_{thres,2P}$$ 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_2P, so that p_A,2P – p_B,2P matches the nominal pressure loss at the nominal mass flow rate.

The pressure losses on the thermal liquid side are

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

where:

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

• p_TL is internal thermal liquid pressure at which the heat transfer is calculated.

• $${\dot{m}}_{A,TL}$$ and $${\dot{m}}_{B,TL}$$ are the mass flow rates into ports A2 and B2, respectively.

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

• $${\dot{m}}_{thres,TL}$$ 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_TL, so that p_A,TL – p_B,TL matches the nominal pressure loss at the nominal mass flow rate.

Two-Phase Fluid Mass and Energy Conservation

The mass conservation equation for the overall two-phase fluid flow is

$$\left(\frac{d{p}_{2P}}{dt}{\displaystyle \sum _{segments}\left(\frac{\partial {\rho }_{seg,2P}}{\partial p}\right)}+{\displaystyle \sum _{segments}\left(\frac{d{u}_{seg,2P}}{dt}\frac{\partial {\rho }_{seg,2P}}{\partial u}\right)}\right)\frac{V_{2P}}{N}={\dot{m}}_{A,2P}+{\dot{m}}_{B,2P},$$

where:

• $$\frac{\partial {\rho }_{seg,2P}}{\partial p}$$ is the partial derivative of density with respect to pressure for the segment.

• $$\frac{\partial {\rho }_{seg,2P}}{\partial u}$$ is the partial derivative of density with respect to specific internal energy for the segment.

• u_seg,2P is the specific internal energy for the segment.

• V_2P is the total two-phase fluid volume.

The summation is over all segments.

Note

Although the block divides the two-phase fluid flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_2P. Consequentially, p_2P is outside of the summation.

The energy conservation equation for each segment is

$$\frac{d{u}_{seg,2P}}{dt}\frac{M_{2P}}{N}+u_{seg,2P}\left({\dot{m}}_{seg,in,2P}-{\dot{m}}_{seg,out,2P}\right)={\Phi }_{seg,in,2P}-{\Phi }_{seg,out,2P}+Q_{seg,2P},$$

where:

• M_2P is the total two-phase fluid mass.

• $${\dot{m}}_{seg,in,2P}$$ and $${\dot{m}}_{seg,out,2P}$$ are the mass flow rates into and out of the segment.

• Φ_seg,in,2p and Φ_seg,out,2p 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 $${\dot{m}}_{A,2P}$$ and $${\dot{m}}_{B,2P}$$.

Thermal Liquid Mass and Energy Conservation

The mass conservation for the overall thermal liquid flow is

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

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 the thermal liquid flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_TL. Consequentially, 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 specific internal energy with respect to pressure for the segment.

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

• M_TL is the total thermal liquid mass.

• $${\dot{m}}_{seg,in,TL}$$ 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 $${\dot{m}}_{B,TL}$$.

Examples

Liquid Air Energy Storage System

Models a grid-scale energy storage system based on cryogenic liquid air. When there is excess power, the system liquefies ambient air based on a variation of the Claude cycle. The cold liquid air is stored in a low-pressure insulated tank until needed. When there is high power demand, the system expands the stored liquid air to produce power based on the Rankine cycle.

• Open Model

Ports

Output

Q1 — Rate of heat transfer to two-phase fluid, W

physical signal

Rate of heat transfer to two-phase fluid, returned as a physical signal, in W. The physical signals at ports Q1 and Q2 are usually equal in value with 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, W

physical signal

Rate of heat transfer to thermal liquid, returned as a physical signal, in W. The physical signals at ports Q1 and Q2 are usually equal in value with 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 — Two-phase fluid port

two-phase fluid

Inlet or outlet port associated with the two-phase fluid.

B1 — Two-phase fluid port

two-phase fluid

Inlet or outlet port associated with the two-phase fluid.

A2 — Thermal liquid port

thermal liquid

Inlet or outlet port associated with the thermal liquid.

B2 — Thermal liquid port

thermal liquid

Inlet or outlet port associated with the thermal liquid.

Parameters

Configuration

Flow arrangement at nominal operating conditions — Flow path alignment

Counter flow - Two-Phase Fluid 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 - Two-Phase Fluid 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 two-phase fluid to nominal operating conditions or Initialize thermal liquid 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 two-phase fluid port A1.

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

0.01 m^2 (default) | positive scalar

Flow area at the two-phase fluid 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 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 port B2.

Two-Phase Fluid 1

Nominal operating condition — Select whether nominal operating condition corresponds to condenser or evaporator

Condenser - heat transfer from Two-Phase Fluid 1 to Thermal Liquid 2 (default) | Evaporator - heat transfer from Thermal Liquid 2 to Two-Phase Fluid 1

Nominal operating condition:

• Condenser - heat transfer from Two-Phase Fluid 1 to Thermal Liquid 2 — The two-phase fluid is cooled and the thermal liquid is heated.

• Evaporator - heat transfer from Thermal Liquid 2 to Two-Phase Fluid 1 — The thermal liquid is cooled and the two-phase fluid 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 two-phase ports during nominal operating condition

0.001 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 two-phase ports during nominal operating condition

0.01 MPa (default) | positive scalar

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

Pressure specification — Select method of pressure specification

Inlet pressure (default) | Saturation pressure at specified condensing temperature | Saturation pressure at specified evaporating temperature

Select the method of pressure specification:

• Inlet pressure — Specify the nominal inlet pressure.

• Saturation pressure at specified condensing temperature — Specify the nominal condensing temperature. This option is available if you set Nominal operating condition to Condenser - heat transfer from Two-Phase Fluid 1 to Thermal Liquid 2.

• Saturation pressure at specified evaporating temperature — Specify the nominal evaporating temperature. This option is available if you set Nominal operating condition to Evaporator - heat transfer from Thermal Liquid 2 to Two-Phase Fluid 1 .

Nominal inlet pressure — Pressure at the two-phase fluid side inlet

1 MPa (default) | positive scalar

Pressure at the two-phase fluid inlet of the heat exchanger during nominal operating condition.

Dependencies

To enable this parameter, set Pressure specification to Inlet pressure.

Nominal condensing temperature — Use nominal condensing temperature to specify pressure

313.15 K (default) | positive scalar

Liquid saturation temperature at the two-phase fluid outlet of the heat exchanger during nominal operating condition. The pressure in the heat exchanger is the corresponding saturation pressure. The nominal condensing temperature must be less than the critical temperature.

Dependencies

To enable this parameter, set Nominal operating condition to Condenser - heat transfer from Two-Phase Fluid 1 to Thermal Liquid 2 and Pressure specification to Saturation pressure at specified condensing temperature.

Nominal evaporating temperature — Use nominal evaporating temperature to specify pressure

243.15 K (default) | positive scalar

Vapor saturation temperature at the two-phase fluid outlet of the heat exchanger during nominal operating condition. The pressure in the heat exchanger is the corresponding saturation pressure. The nominal evaporating temperature must be less than the critical temperature.

Dependencies

To enable this parameter, set Nominal operating condition to Evaporator - heat transfer from Thermal Liquid 2 to Two-Phase Fluid 1 and Pressure specification to Saturation pressure at specified evaporating temperature.

Inlet condition specification — Select quantity to describe the inlet condition of the two-phase fluid

Specific enthalpy (default) | Temperature | Vapor quality

Quantity used to describe the inlet condition of the fluid at the nominal operating condition: temperature, specific enthalpy, or vapor quality.

Nominal inlet specific enthalpy — Specific enthalpy at the two-phase fluid side inlet

440 kJ/kg (default) | positive scalar

Specific enthalpy at the two-phase fluid inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet condition specification to Specific enthalpy.

Nominal inlet temperature — Temperature at the two-phase fluid side inlet

313.15 K (default) | positive scalar

Temperature at the two-phase fluid inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet condition specification to Temperature.

Nominal inlet vapor quality — Vapor quality at the two-phase fluid side inlet

1 (default) | positive scalar

Vapor quality, defined as the mass fraction of vapor in a liquid-vapor mixture, at the two-phase fluid inlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Inlet condition specification to Vapor quality.

Heat transfer capacity specification — How to specify heat transfer capacity of the two-phase fluid

Rate of heat transfer (default) | Outlet condition

Whether to specify the performance of the heat exchanger for the two-phase fluid 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

0.1 kW (default) | positive scalar

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

• If Nominal operating condition is Condenser - heat transfer from Two-Phase Fluid 1 to Thermal Liquid 2, this parameter is the rate of the of heat transfer from the two-phase fluid to the thermal liquid during the nominal operating condition.

• If Nominal operating condition is Evaporator - heat transfer from Thermal Liquid 2 to Two-Phase Fluid 1 , this parameter is the rate of the of heat transfer from the thermal liquid to the two-phase fluid during the nominal operating condition.

Dependencies

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

Outlet condition specification — Select quantity for outlet condition specification

Specific enthalpy (default) | Subcooling | Superheating | Vapor quality

Select the quantity for outlet condition specification:

• Specific enthalpy — Specify the nominal specific enthalpy.

• Subcooling — Specify the nominal subcooling. This option is available if you set Nominal operating condition to Condenser - heat transfer from Two-Phase Fluid 1 to Thermal Liquid 2.

• Superheating — Specify the nominal superheating. This option is available if you set Nominal operating condition to Evaporator - heat transfer from Thermal Liquid 2 to Two-Phase Fluid 1 .

• Vapor quality — Specify the nominal vapor quality.

Dependencies

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

Nominal outlet specific enthalpy — Specific enthalpy at the two-phase fluid side outlet

250 kJ/kg (default) | positive scalar | two-element vector

Specific enthalpy at the two-phase fluid outlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Outlet condition specification to Specific enthalpy.

Nominal subcooling — Degree of temperature below the liquid saturation temperature at the two-phase fluid side outlet

5 deltaK (default) | positive scalar

Degree of temperature below the liquid saturation temperature at the two-phase fluid outlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Outlet condition specification to Subcooling.

Nominal superheating — Degree of temperature above the vapor saturation temperature at the two-phase fluid side outlet

5 deltaK (default) | positive scalar

Degree of temperature above the vapor saturation temperature at the two-phase fluid outlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Outlet condition specification to Superheating.

Nominal outlet vapor quality — Vapor mass fraction at the two-phase fluid side outlet

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

Two-phase fluid vapor quality, defined as the mass fraction of vapor in a liquid-vapor mixture, at the two-phase fluid outlet of the heat exchanger during the nominal operating condition.

Dependencies

To enable this parameter, set Outlet condition specification to Vapor quality.

Two-phase fluid volume — Total volume of two-phase fluid

0.001 m^3 (default) | positive scalar

Total volume of two-phase fluid inside the heat exchanger.

Initialize two-phase fluid to nominal operating conditions — Option for initializing two-phase fluid

on (default) | off

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

Initial fluid energy specification — Initial state of the two-phase fluid

Specific enthalpy (default) | Temperature | Vapor quality | Vapor void fraction | Specific internal energy

Quantity used to describe the initial state of the fluid.

The value for Initial fluid energy specification parameter limits the available initial states for the two-phase fluid. When Initial fluid energy specification is:

• Temperature — Specify an initial state that is a subcooled liquid or superheated vapor. You cannot specify a liquid-vapor mixture because the temperature is constant across the liquid-vapor mixture region.

• Vapor quality — Specify an initial state that is a liquid-vapor mixture. You cannot specify a subcooled liquid or a superheated vapor because the liquid mass fraction is 0 and 1, respectively, across the whole region. Additionally, the block limits the pressure to below the critical pressure.

• Vapor void fraction — Specify an initial state that is a liquid-vapor mixture. You cannot specify a subcooled liquid or a superheated vapor because the liquid mass fraction is 0 and 1, respectively, across the whole region. Additionally, the block limits the pressure to below the critical pressure.

• Specific enthalpy — Specify the specific enthalpy of the fluid. The block does not limit the initial state.

• Specific internal energy — Specify the specific internal energy of the fluid. The block does not limit the initial state.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box.

Initial two-phase fluid pressure — Fluid pressure at start of simulation

0.101325 MPa (default) | positive scalar

Two-phase fluid pressure at the start of the simulation.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box.

Initial two-phase fluid specific enthalpy — Enthalpy per unit mass at start of simulation

1500 kJ/kg (default) | positive scalar | two-element vector

Two-phase fluid specific enthalpy at the start of simulation. If the value is a scalar, then the initial specific enthalpy is assumed uniform. If the value is a two-element vector, then the initial specific enthalpy is assumed to vary linearly between ports A1 and B1, with the first element corresponding to port A1 and the second element corresponding to port B1.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box and set Initial fluid energy specification to Specific enthalpy.

Initial two-phase fluid temperature — Temperature at start of simulation

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

Two-phase fluid temperature at the start of simulation. If the value is a scalar, then the initial temperature is assumed uniform. If the value is a two-element vector, then the initial temperature is assumed to vary linearly between ports A1 and B1, with the first element corresponding to port A1 and the second element corresponding to port B1.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box and set Initial fluid energy specification to Temperature.

Initial two-phase fluid vapor quality — Vapor mass fraction at start of simulation

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

Two-phase fluid vapor quality, defined as the mass fraction of vapor in a liquid-vapor mixture, at the start of simulation. If the value is a scalar, then the initial vapor quality is assumed uniform. If the value is a two-element vector, then the initial vapor quality is assumed to vary linearly between ports A1 and B1, with the first element corresponding to port A1 and the second element corresponding to port B1.

If using this option, the initial pressure cannot be higher than the critical pressure.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box and set Initial fluid energy specification to Vapor quality.

Initial two-phase fluid vapor void fraction — Vapor volume fraction at start of simulation

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

Two-phase fluid vapor void fraction, defined as the volume fraction of vapor in a liquid-vapor mixture,at the start of simulation. If the value is a scalar, then the initial vapor void fraction is assumed uniform. If the value is a two-element vector, then the initial vapor void fraction is assumed to vary linearly between ports A1 and B1, with the first element corresponding to port A1 and the second element corresponding to port B1.

If using this option, the initial pressure cannot be higher than the critical pressure.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box and set Initial fluid energy specification to Vapor void fraction.

Initial two-phase fluid specific internal energy — Internal energy per unit mass at start of simulation

1500 kJ/kg (default) | positive scalar | two-element vector

Two-phase fluid specific internal energy at the start of simulation. If the value is a scalar, then the initial specific internal energy is assumed uniform. If the value is a two-element vector, then the initial specific internal energy is assumed to vary linearly between ports A1 and B1, with the first element corresponding to port A1 and the second element corresponding to port B1.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid to nominal operating conditions check box and set Initial fluid energy specification to Specific internal energy.

Thermal Liquid 2

Nominal mass flow rate — Mass flow rate between thermal liquid 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 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 the thermal liquid side inlet

0.101325 MPa (default) | positive scalar

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

Nominal inlet temperature — Temperature at the thermal liquid side inlet

293.15 K (default) | positive scalar

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

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

0.001 m^3 (default) | positive scalar

Total volume of thermal liquid in the heat exchanger.

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 check box, you can specify the initial conditions directly with additional parameters.

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

0.101325 MPa (default) | positive scalar

Thermal liquid pressure at the start of the simulation.

Dependencies

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

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

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

Thermal liquid temperature at the start of simulation. If the value is a scalar, then the initial temperature is assumed uniform. If the value is a two-element vector, then the initial temperature is assumed to vary 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 to nominal operating conditions check box.

Correlation Coefficients

a in Nu = a*Re^b*Pr^c for two-phase fluid liquid — Correlation coefficient for subcooled liquid in two-phase fluid

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 subcooled liquid in two-phase fluid. The default value is based on the Colburn equation.

a in Nu = a*Re^b*Pr^c for two-phase fluid mixture — Correlation coefficient for liquid-vapor mixture in two-phase fluid

0.005 (default) | positive scalar

Proportionality constant in the correlation of the Nusselt number as a function of the Reynolds number and Prandtl number for liquid-vapor mixture in two-phase fluid. The default value is based on the Cavallini and Zecchin correlation.

a in Nu = a*Re^b*Pr^c for two-phase fluid vapor — Correlation coefficient for superheated vapor in two-phase fluid

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 superheated vapor in two-phase fluid. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for two-phase fluid — Reynolds number exponent in correlation for two-phase fluid

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 two-phase fluid. The same value applies to subcooled liquid, liquid-vapor mixture, and superheated vapor.

c in Nu = a*Re^b*Pr^c for two-phase fluid — Prandtl number exponent in correlation for two-phase fluid

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 two-phase fluid. The same value applies to subcooled liquid, liquid-vapor mixture, and superheated vapor.

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

0.005 (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. The default value is based on the Colburn equation.

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

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. The default value is based on the Colburn equation.

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

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. 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 R2022a

R2023b: Specify initial wall temperature

If you select Wall thermal mass and clear the Initialize wall temperature to nominal operating conditions check box, you can use the new Initial wall temperature parameter to specify the initial conditions directly.