System-Level Heat Exchanger (2P-2P)

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

Since R2021b

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

Description

The System-Level Heat Exchanger (2P-2P) block models a heat exchanger between two distinct two-phase fluid 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. Either or both sides of the heat exchanger can condense or vaporize fluid as a result of the heat exchange. You can also use this block as an internal heat exchanger in a refrigeration system. An internal heat exchanger improves refrigeration system efficiency by providing additional heat exchange between the outlet of the condenser and the outlet of the evaporator.

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.

Each side of the heat exchanger approximates the liquid zone, mixture zone, and vapor zone based on the change in enthalpy along the flow path.

Heat Transfer

The block divides the two-phase fluid 1 flow and the two-phase fluid 2 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

$$Q_{seg,2P1}+Q_{seg,2P2}=0,$$

where:

• Q_seg,2P1 is the heat flow rate from the wall that is the heat transfer surface to two-phase fluid 1 in the segment.

• Q_seg,2P2 is the heat flow rate from the wall to two-phase fluid 2 in the segment.

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

$$Q_{seg,2P1}+Q_{seg,2P2}=-\frac{M_{wall}{c}_{p_{wall}}}{N}\frac{d{T}_{seg,wall}}{dt},$$

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 two-phase fluid 1 in the segment is

$$Q_{seg,2P1}=U{A}_{seg,2P1}\left(T_{seg,wall}-T_{seg,2P1}\right),$$

where:

• UA_seg,2P1 is the weighted-average heat transfer conductance for two-phase fluid 1 in the segment.

• T_seg,2P1 is the weighted-average fluid temperature for two-phase fluid 1 in the segment.

The heat flow rate from the wall to the two-phase fluid 2 in the segment is

$$Q_{seg,2P2}=U{A}_{seg,2P2}\left(T_{seg,wall}-T_{seg,2P2}\right),$$

where:

• UA_seg,2P2 is the weighted-average heat transfer conductance for two-phase fluid 2 in the segment.

• T_seg,2P2 is the weighted-average fluid temperature for two-phase fluid 2 in the segment.

Two-Phase Fluid 1 Heat Transfer Correlation

The block calculates the heat transfer conductance in both two-phase fluids by using the same expressions.

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

$$U{A}_{seg,L,2P1}=a_{L,2P1}{\left({\mathrm{Re}}_{seg,L,2P1}\right)}^{b_{2P1}}{\left({\mathrm{Pr}}_{seg,L,2P1}\right)}^{c_{2P1}}{k}_{seg,L,2P1}\frac{G_{2P1}}{N},$$

where:

• a_L,2P1, b_2P1, and c_2P1 are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

• Re_seg,L,2P1 is the average liquid Reynolds number for the segment.

• Pr_seg,L,2P1 is the average liquid Prandtl number for the segment.

• k_seg,L,2P1 is the average liquid thermal conductivity for the segment.

• G_2P1 is the geometry scale factor for the two-phase fluid 1 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

$${\mathrm{Re}}_{seg,L,2P1}=\frac{{\dot{m}}_{seg,2P1}{D}_{ref,2P1}}{{\mu }_{seg,L,2P1}{S}_{ref,2P1}},$$

where:

• $${\dot{m}}_{seg,2P1}$$ is the mass flow rate through the segment.

• μ_seg,L,2P1 is the average liquid dynamic viscosity for the segment.

• D_ref,2P1 is an arbitrary reference diameter.

• S_ref,2P1 is an arbitrary reference flow area.

Note

The D_ref,2P1 and S_ref,2P1 terms are included in this equation for unit calculation purposes only, to make Re_seg,L,2P1 nondimensional. The values of D_ref,2P1 and S_ref,2P1 are arbitrary because the G_2P1 calculation overrides these values.

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

$$U{A}_{seg,V,2P1}=a_{V,2P1}{\left({\mathrm{Re}}_{seg,V,2P1}\right)}^{b_{2P1}}{\left({\mathrm{Pr}}_{seg,V,2P1}\right)}^{c_{2P1}}{k}_{seg,V,2P1}\frac{G_{2P1}}{N},$$

where:

• a_V,2P1, b_2P1, and c_2P1 are the coefficients of the Nusselt number correlation. These coefficients appear as block parameters in the Correlation Coefficients section.

• Re_seg,V,2P1 is the average vapor Reynolds number for the segment.

• Pr_seg,V,2P1 is the average vapor Prandtl number for the segment.

• k_seg,V,2P1 is the average vapor thermal conductivity for the segment.

The average vapor Reynolds number is

$${\mathrm{Re}}_{seg,V,2P1}=\frac{{\dot{m}}_{seg,2P1}{D}_{ref,2P1}}{{\mu }_{seg,V,2P1}{S}_{ref,2P1}},$$

where μ_seg,V,2P1 is the average vapor dynamic viscosity for the segment.

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

$$U{A}_{seg,M,2P1}=a_{M,2P1}{\left({\mathrm{Re}}_{seg,SL,2P1}\right)}^{b_{2P1}}CZ{\left({\mathrm{Pr}}_{seg,SL,2P1}\right)}^{c_{2P1}}{k}_{seg,SL,2P1}\frac{G_{2P1}}{N},$$

where:

• a_M,2P1, b_2P1, and c_2P1 are the coefficients of the Nusselt number correlation. These coefficients appear as block parameters in the Correlation Coefficients section.

• Re_seg,SL,2P1 is the saturated liquid Reynolds number for the segment.

• Pr_seg,SL,2P1 is the saturated liquid Prandtl number for the segment.

• k_seg,SL,2P1 is the saturated liquid thermal conductivity for the segment.

• CZ is the Cavallini and Zecchin term.

The saturated liquid Reynolds number is

$${\mathrm{Re}}_{seg,SL,2P1}=\frac{{\dot{m}}_{seg,2P1}{D}_{ref,2P1}}{{\mu }_{seg,SL,2P1}{S}_{ref,2P1}},$$

where μ_seg,SL,2P1 is the saturated liquid dynamic viscosity for the segment.

The Cavallini and Zecchin term is

$$CZ=\frac{{\left(\left(\sqrt{\frac{{\nu }_{seg,SV,2P1}}{{\nu }_{seg,SL,2P1}}}-1\right)\left(x_{seg,out,2P1}+1\right)\right)}^{1+b_{2P1}}-{\left(\left(\sqrt{\frac{{\nu }_{seg,SV,2P1}}{{\nu }_{seg,SL,2P1}}}-1\right)\left(x_{seg,in,2P1}+1\right)\right)}^{1+b_{2P1}}}{\left(1+b_{2P1}\right)\left(\sqrt{\frac{{\nu }_{seg,SV,2P1}}{{\nu }_{seg,SL,2P1}}}-1\right)\left(x_{seg,out,2P1}-x_{seg,in,2P1}\right)},$$

where:

• ν_seg,SL,2P1 is the saturated liquid specific volume for the segment.

• ν_seg,SV,2P1 is the saturated vapor specific volume for the segment.

• x_seg,in,2P1 is the vapor quality at the segment inlet.

• x_seg,out,2P1 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,2P1 to x_seg,out,2P1.

Two-Phase Fluid 1 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.

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

$$\begin{array}{l}{\Delta }_L=\left|\min \left(h_{seg,out,2P1},h_{seg,SL,2P1}\right)-\min \left(h_{seg,in,2P1},h_{seg,SL,2P1}\right)\right|\cdot U{A}_{seg,M,2P1}\cdot U{A}_{seg,V,2P1}\\ {\Delta }_M=\left|\min \left(\max \left(h_{seg,out,2P1},h_{seg,SL,2P1}\right),h_{seg,SV,2P1}\right)-\min \left(\max \left(h_{seg,in,2P1},h_{seg,SL,2P1}\right),h_{seg,SV,2P1}\right)\right|\cdot U{A}_{seg,L,2P1}\cdot U{A}_{seg,V,2P1}\\ {\Delta }_V=\left|\max \left(h_{seg,out,2P1},h_{seg,SV,2P1}\right)-\max \left(h_{seg,in,2P1},h_{seg,SV,2P1}\right)\right|\cdot U{A}_{seg,L,2P1}\cdot U{A}_{seg,M,2P1}\end{array}$$

where:

• h_seg,in,2P1 is the specific enthalpy at the segment inlet.

• h_seg,out,2P1 is the specific enthalpy at the segment outlet.

• h_seg,SL,2P1 is the saturated liquid specific enthalpy for the segment.

• h_seg,SV,2P1 is the saturated vapor specific enthalpy for the segment.

The weighted-average two-phase fluid 1 heat transfer conductance for the segment is therefore

$$U{A}_{seg,2P1}=w_L\left(U{A}_{seg,L,2P1}\right)+w_V\left(U{A}_{seg,V,2P1}\right)+w_M\left(U{A}_{seg,M,2P1}\right).$$

The weighted-average fluid 1 temperature for the segment is

$$T_{seg,2P1}=\frac{w_L\left(U{A}_{seg,L,2P1}\right)T_{seg,L,2P1}+w_V\left(U{A}_{seg,V,2P1}\right)T_{seg,V,2P1}+w_M\left(U{A}_{seg,M,2P1}\right)T_{seg,M,2P1}}{U{A}_{seg,2P1}},$$

where:

• T_seg,L,2P1 is the average liquid temperature for the segment.

• T_seg,V,2P1 is the average vapor temperature for the segment.

• T_seg,M,2P1 is the average mixture temperature for the segment, which is the saturated liquid temperature.

Two-Phase Fluid 2 Heat Transfer Correlation

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

$$U{A}_{seg,L,2P2}=a_{L,2P2}{\left({\mathrm{Re}}_{seg,L,2P2}\right)}^{b_{2P2}}{\left({\mathrm{Pr}}_{seg,L,2P2}\right)}^{c_{2P2}}{k}_{seg,L,2P2}\frac{G_{2P2}}{N},$$

where:

• a_L,2P2, b_L,2P2, and c_L,2P2 are the coefficients of the Nusselt number correlation. These coefficients are block parameters in the Correlation Coefficients section.

• Re_seg,L,2P2 is the average liquid Reynolds number for the segment.

• Pr_seg,L,2P2 is the average liquid Prandtl number for the segment.

• k_seg,L,2P2 is the average liquid thermal conductivity for the segment.

• G_2P2 is the geometry scale factor for the two-phase fluid 2 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

$${\mathrm{Re}}_{seg,L,2P2}=\frac{{\dot{m}}_{seg,2P2}{D}_{ref,2P2}}{{\mu }_{seg,L,2P2}{S}_{ref,2P2}},$$

where:

• $${\dot{m}}_{seg,2P2}$$ is the mass flow rate through the segment.

• μ_seg,L,2P2 is the average liquid dynamic viscosity for the segment.

• D_ref,2P2 is an arbitrary reference diameter.

• S_ref,2P2 is an arbitrary reference flow area.

Note

The D_ref,2P2 and S_ref,2P2 terms are included in this equation for unit calculation purposes only, to make Re_seg,L,2P2 nondimensional. The values of D_ref,2P and S_ref,2P2 are arbitrary because the G_2P2 calculation overrides these values.

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

$$U{A}_{seg,V,2P2}=a_{V,2P2}{\left({\mathrm{Re}}_{seg,V,2P2}\right)}^{b_{2P2}}{\left({\mathrm{Pr}}_{seg,V,2P2}\right)}^{c_{2P2}}{k}_{seg,V,2P2}\frac{G_{2P2}}{N},$$

where:

• a_V,2P2, b_V,2P2, and c_V,2P2 are the coefficients of the Nusselt number correlation. These coefficients appear as block parameters in the Correlation Coefficients section.

• Re_seg,V,2P2 is the average vapor Reynolds number for the segment.

• Pr_seg,V,2P2 is the average vapor Prandtl number for the segment.

• k_seg,V,2P2 is the average vapor thermal conductivity for the segment.

The average vapor Reynolds number is

$${\mathrm{Re}}_{seg,V,2P2}=\frac{{\dot{m}}_{seg,2P2}{D}_{ref,2P2}}{{\mu }_{seg,V,2P2}{S}_{ref,2P2}},$$

where μ_seg,V,2P2 is the average vapor dynamic viscosity for the segment.

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

$$U{A}_{seg,M,2P2}=a_{M,2P2}{\left({\mathrm{Re}}_{seg,SL,2P2}\right)}^{b_{2P2}}CZ{\left({\mathrm{Pr}}_{seg,SL,2P2}\right)}^{c_{2P2}}{k}_{seg,SL,2P2}\frac{G_{2P2}}{N},$$

where:

• a_M,2P2, b_L,2P2, and c_L,2P2 are the coefficients of the Nusselt number correlation. These coefficients appear as block parameters in the Correlation Coefficients section.

• Re_seg,SL,2P2 is the saturated liquid Reynolds number for the segment.

• Pr_seg,SL,2P2 is the saturated liquid Prandtl number for the segment.

• k_seg,SL,2P2 is the saturated liquid thermal conductivity for the segment.

• CZ is the Cavallini and Zecchin term.

The saturated liquid Reynolds number is

$${\mathrm{Re}}_{seg,SL,2P2}=\frac{{\dot{m}}_{seg,2P2}{D}_{ref,2P2}}{{\mu }_{seg,SL,2P2}{S}_{ref,2P2}},$$

where μ_seg,SL,2P2 is the saturated liquid dynamic viscosity for the segment.

The Cavallini and Zecchin term is

$$CZ=\frac{{\left(\left(\sqrt{\frac{{\nu }_{seg,SV,2P2}}{{\nu }_{seg,SL,2P2}}}-1\right)\left(x_{seg,out,2P2}+1\right)\right)}^{1+b_{2P2}}-{\left(\left(\sqrt{\frac{{\nu }_{seg,SV,2P2}}{{\nu }_{seg,SL,2P2}}}-1\right)\left(x_{seg,in,2P2}+1\right)\right)}^{1+b_{2P2}}}{\left(1+b_{2P2}\right)\left(\sqrt{\frac{{\nu }_{seg,SV,2P2}}{{\nu }_{seg,SL,2P2}}}-1\right)\left(x_{seg,out,2P2}-x_{seg,in,2P2}\right)},$$

where:

• ν_seg,SL,2P2 is the saturated liquid specific volume for the segment.

• ν_seg,SV,2P2 is the saturated vapor specific volume for the segment.

• x_seg,in,2P2 is the vapor quality at the segment inlet.

• x_seg,out,2P2 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,2P2 to x_seg,out,2P2.

Two-Phase Fluid 2 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.

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

$$\begin{array}{l}{\Delta }_L=\left|\min \left(h_{seg,out,2P2},h_{seg,SL,2P2}\right)-\min \left(h_{seg,in,2P2},h_{seg,SL,2P2}\right)\right|\cdot U{A}_{seg,M,2P2}\cdot U{A}_{seg,V,2P2}\\ {\Delta }_M=\left|\min \left(\max \left(h_{seg,out,2P2},h_{seg,SL,2P2}\right),h_{seg,SV,2P2}\right)-\min \left(\max \left(h_{seg,in,2P2},h_{seg,SL,2P2}\right),h_{seg,SV,2P2}\right)\right|\cdot U{A}_{seg,L,2P2}\cdot U{A}_{seg,V,2P2}\\ {\Delta }_V=\left|\max \left(h_{seg,out,2P2},h_{seg,SV,2P2}\right)-\max \left(h_{seg,in,2P2},h_{seg,SV,2P2}\right)\right|\cdot U{A}_{seg,L,2P2}\cdot U{A}_{seg,M,2P2}\end{array}$$

where:

• h_seg,in,2P2 is the specific enthalpy at the segment inlet.

• h_seg,out,2P2 is the specific enthalpy at the segment outlet.

• h_seg,SL,2P2 is the saturated liquid specific enthalpy for the segment.

• h_seg,SV,2P2 is the saturated vapor specific enthalpy for the segment.

The weighted-average two-phase fluid 2 heat transfer conductance for the segment is therefore

$$U{A}_{seg,2P2}=w_L\left(U{A}_{seg,L,2P2}\right)+w_V\left(U{A}_{seg,V,2P2}\right)+w_M\left(U{A}_{seg,M,2P2}\right).$$

The weighted-average fluid 2 temperature for the segment is

$$T_{seg,2P2}=\frac{w_L\left(U{A}_{seg,L,2P2}\right)T_{seg,L,2P2}+w_V\left(U{A}_{seg,V,2P2}\right)T_{seg,V,2P2}+w_M\left(U{A}_{seg,M,2P2}\right)T_{seg,M,2P2}}{U{A}_{seg,2P2}},$$

where:

• T_seg,L,2P2 is the average liquid temperature for the segment.

• T_seg,V,2P2 is the average vapor temperature for the segment.

• T_seg,M,2P2 is the average mixture temperature for the segment, which is the saturated liquid temperature.

Pressure Loss

The pressure losses on the two-phase fluid 1 side are

$$\begin{array}{l}{p}_{A,2P1}-p_{2P1}=\frac{K_{2P1}}{2}\frac{{\dot{m}}_{A,2P1}\sqrt{{\dot{m}}^2{}_{A,2P1}+{\dot{m}}^2{}_{thres,2P1}}}{2{\rho }_{avg,2P1}}\\ p_{B,2P1}-p_{2P1}=\frac{K_{2P1}}{2}\frac{{\dot{m}}_{B,2P1}\sqrt{{\dot{m}}^2{}_{B,2P1}+{\dot{m}}^2{}_{thres,2P1}}}{2{\rho }_{avg,2P1}}\end{array}$$

where:

• p_A,2P1 and p_B,2P1 are the pressures at ports A1 and B1, respectively.

• p_2P1 is internal two-phase fluid 1 pressure at which the heat transfer is calculated.

• $${\dot{m}}_{A,2P1}$$ and $${\dot{m}}_{B,2P1}$$ are the mass flow rates into ports A1 and B1, respectively.

• ρ_avg,2P1 is the average two-phase fluid 1 density over all segments.

• $${\dot{m}}_{thres,2P1}$$ 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_2P1, so that p_A,2P1 – p_B,2P1 matches the nominal pressure loss at the nominal mass flow rate.

The pressure losses on the two-phase fluid 2 side are

$$\begin{array}{l}{p}_{A,2P2}-p_{2P2}=\frac{K_{2P2}}{2}\frac{{\dot{m}}_{A,2P2}\sqrt{{\dot{m}}^2{}_{A,2P2}+{\dot{m}}^2{}_{thres,2P2}}}{2{\rho }_{avg,2P2}}\\ p_{B,2P2}-p_{2P2}=\frac{K_{2P2}}{2}\frac{{\dot{m}}_{B,2P2}\sqrt{{\dot{m}}^2{}_{B,2P2}+{\dot{m}}^2{}_{thres,2P2}}}{2{\rho }_{avg,2P2}}\end{array}$$

where:

• p_A,2P2 and p_B,2P2 are the pressures at ports A2 and B2, respectively.

• p_2P2 is internal two-phase fluid 2 pressure at which the heat transfer is calculated.

• $${\dot{m}}_{A,2P2}$$ and $${\dot{m}}_{B,2P2}$$ are the mass flow rates into ports A2 and B2, respectively.

• ρ_avg,2P2 is the average two-phase fluid 2 density over all segments.

• $${\dot{m}}_{thres,2P2}$$ 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_2P2, so that p_A,2P2 – p_B,2P2 matches the nominal pressure loss at the nominal mass flow rate.

Two-Phase Fluid 1 Mass and Energy Conservation

The mass conservation equation for the overall two-phase fluid 1 flow is

$$\left(\frac{d{p}_{2P1}}{dt}{\displaystyle \sum _{segments}\left(\frac{\partial {\rho }_{seg,2P1}}{\partial p}\right)}+{\displaystyle \sum _{segments}\left(\frac{d{u}_{seg,2P1}}{dt}\frac{\partial {\rho }_{seg,2P1}}{\partial u}\right)}\right)\frac{V_{2P1}}{N}={\dot{m}}_{A,2P1}+{\dot{m}}_{B,2P1},$$

where:

• $$\frac{\partial {\rho }_{seg,2P1}}{\partial p}$$ is the partial derivative of density with respect to pressure for the segment.

• $$\frac{\partial {\rho }_{seg,2P1}}{\partial u}$$ is the partial derivative of density with respect to specific internal energy for the segment.

• u_seg,2P1 is the specific internal energy for the segment.

• V_2P1 is the total two-phase fluid 1 volume.

The summation is over all segments.

Note

Although the block divides the two-phase fluid 1 flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_2P1. Consequentially, p_2P1 is outside of the summation.

The energy conservation equation for each segment is

$$\frac{d{u}_{seg,2P1}}{dt}\frac{M_{2P1}}{N}+u_{seg,2P1}\left({\dot{m}}_{seg,in,2P1}-{\dot{m}}_{seg,out,2P1}\right)={\Phi }_{seg,in,2P1}-{\Phi }_{seg,out,2P1}+Q_{seg,2P1},$$

where:

• M_2P1 is the total two-phase fluid 1 mass.

• $${\dot{m}}_{seg,in,2P1}$$ and $${\dot{m}}_{seg,out,2P1}$$ are the mass flow rates into and out of the segment.

• Φ_seg,in,2p1 and Φ_seg,out,2p1 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 $${\dot{m}}_{A,2P1}$$ and $${\dot{m}}_{B,2P1}$$.

Two-Phase Fluid 2 Mass and Energy Conservation

The mass conservation equation for the overall two-phase fluid 2 flow is

$$\left(\frac{d{p}_{2P2}}{dt}{\displaystyle \sum _{segments}\left(\frac{\partial {\rho }_{seg,2P2}}{\partial p}\right)}+{\displaystyle \sum _{segments}\left(\frac{d{u}_{seg,2P2}}{dt}\frac{\partial {\rho }_{seg,2P2}}{\partial u}\right)}\right)\frac{V_{2P2}}{N}={\dot{m}}_{A,2P2}+{\dot{m}}_{B,2P2},$$

where:

• $$\frac{\partial {\rho }_{seg,2P2}}{\partial p}$$ is the partial derivative of density with respect to pressure for the segment.

• $$\frac{\partial {\rho }_{seg,2P2}}{\partial u}$$ is the partial derivative of density with respect to specific internal energy for the segment.

• u_seg,2P2 is the specific internal energy for the segment.

• V_2P2 is the total two-phase fluid 2 volume.

The summation is over all segments.

Note

Although the block divides the two-phase fluid 2 flow into N=3 segments for heat transfer calculations, it assumes all segments are at the same internal pressure, p_2P2. Consequentially, p_2P2 is outside of the summation.

The energy conservation equation for each segment is

$$\frac{d{u}_{seg,2P2}}{dt}\frac{M_{2P2}}{N}+u_{seg,2P2}\left({\dot{m}}_{seg,in,2P2}-{\dot{m}}_{seg,out,2P2}\right)={\Phi }_{seg,in,2P2}-{\Phi }_{seg,out,2P2}+Q_{seg,2P2},$$

where:

• M_2P2 is the total two-phase fluid 2 mass.

• $${\dot{m}}_{seg,in,2P2}$$ and $${\dot{m}}_{seg,out,2P2}$$ are the mass flow rates into and out of the segment.

• Φ_seg,in,2p2 and Φ_seg,out,2p2 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 $${\dot{m}}_{A,2P2}$$ and $${\dot{m}}_{B,2P2}$$.

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 1, W

physical signal

Rate of heat transfer to the first two-phase fluid network, 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 two-phase fluid 2, W

physical signal

Rate of heat transfer to the second two-phase fluid network, 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 on side 1

two-phase fluid

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

B1 — Two-phase fluid port on side 1

two-phase fluid

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

A2 — Two-phase fluid port on side 2

two-phase fluid

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

B2 — Two-phase fluid port on side 2

two-phase fluid

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

Parameters

Configuration

Flow arrangement at nominal operating conditions — Flow path alignment

Counter flow - Two-Phase Fluid 1 flows from A to B, Two-Phase Fluid 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, Two-Phase Fluid 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 1 to nominal operating conditions or Initialize two-phase fluid 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 two-phase fluid 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 two-phase fluid 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 two-phase fluid 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 two-phase fluid 2 port B2.

Two-Phase Fluid 1

Nominal operating condition — Nominal operating condition

Heat transfer from Two-Phase Fluid 1 to Two-Phase Fluid 2 (default) | Heat transfer from Two-Phase Fluid 2 to Two-Phase Fluid 1

Nominal operating condition:

• Heat transfer from Two-Phase Fluid 1 to Two-Phase Fluid 2 — Side 1 is cooled and side 2 is heated.

• Heat transfer from Two-Phase Fluid 2 to Two-Phase Fluid 1 — Side 2 is cooled and side1 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 fluid 1 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 fluid 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.

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 saturation temperature — Specify the nominal saturation temperature.

Nominal inlet pressure — Pressure at the two-phase fluid 1 inlet

1 MPa (default) | positive scalar

Pressure at the two-phase fluid 1 inlet of the heat exchanger during nominal operating condition.

Dependencies

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

Nominal saturation temperature — Use nominal saturation temperature to specify pressure

313.15 K (default) | positive scalar

Saturation temperature at the two-phase fluid 1 outlet of the heat exchanger during nominal operating condition. The pressure in the heat exchanger is the corresponding saturation pressure. The nominal saturation temperature must be less than the critical temperature.

Dependencies

To enable this parameter, set Pressure specification to Saturation pressure at specified saturation temperature.

Inlet condition specification — Select quantity to describe the inlet condition of the two-phase fluid 1

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 1 inlet

440 kJ/kg (default) | positive scalar

Specific enthalpy at the two-phase fluid 1 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 1 inlet

313.15 K (default) | positive scalar

Temperature at the two-phase fluid 1 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 1 inlet

1 (default) | positive scalar

Vapor quality, defined as the mass fraction of vapor in a liquid-vapor mixture, at the two-phase fluid 1 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 two-phase fluid 1

Rate of heat transfer (default) | Outlet condition

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

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 Heat transfer from two-phase fluid 1 to two-phase fluid 2, this parameter is the rate of the heat transfer from the two-phase fluid side 1 to side 2 during the nominal operating condition.

• If Nominal operating condition is Heat transfer from two-phase fluid 2 to two-phase fluid 1, this parameter is the rate of the heat transfer from the two-phase fluid side 2 to side 1 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 Heat transfer from two-phase fluid 1 to two-phase fluid 2.

• Superheating — Specify the nominal superheating. This option is available if you set Nominal operating condition to Heat transfer from two-phase fluid 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 1 outlet

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

Specific enthalpy at the two-phase fluid 1 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 1 outlet

5 deltaK (default) | positive scalar

Degree of temperature below the liquid saturation temperature at the two-phase fluid 1 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 1 outlet

5 deltaK (default) | positive scalar

Degree of temperature above the vapor saturation temperature at the two-phase fluid 1 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 1 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 1 outlet of the heat exchanger during the nominal operating condition.

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

Dependencies

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

Two-phase fluid 1 volume — Total volume of two-phase fluid 1

0.001 m^3 (default) | positive scalar

Total volume of two-phase fluid 1 inside the heat exchanger.

Initialize two-phase fluid 1 to nominal operating conditions — Option for initializing two-phase fluid 1

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 1

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

Quantity used to describe the initial state of the side 1 fluid: temperature, vapor quality, vapor void fraction, specific enthalpy, or specific internal energy.

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 1 to nominal operating conditions check box.

Initial two-phase fluid 1 pressure — Fluid 1 pressure at start of simulation

0.101325 MPa (default) | positive scalar

Two-phase fluid 1 pressure at the start of the simulation.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid 1 to nominal operating conditions check box.

Initial two-phase fluid 1 specific enthalpy — Enthalpy per unit mass at start of simulation

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

Two-phase fluid 1 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 1 to nominal operating conditions check box and set Initial fluid energy specification to Specific enthalpy.

Initial two-phase fluid 1 temperature — Temperature at start of simulation

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

Two-phase fluid 1 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 1 to nominal operating conditions check box and set Initial fluid energy specification to Temperature.

Initial two-phase fluid 1 vapor quality — Vapor mass fraction at start of simulation

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

Two-phase fluid 1 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 1 to nominal operating conditions check box and set Initial fluid energy specification to Vapor quality.

Initial two-phase fluid 1 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 1 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 1 to nominal operating conditions check box and set Initial fluid energy specification to Vapor void fraction.

Initial two-phase fluid 1 specific internal energy — Internal energy per unit mass at start of simulation

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

Two-phase fluid 1 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 1 to nominal operating conditions check box and set Initial fluid energy specification to Specific internal energy.

Two-Phase Fluid 2

Nominal mass flow rate — Mass flow rate between two-phase fluid 2 ports during nominal operating condition

0.001 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 two-phase fluid 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.

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 saturation temperature — Specify the nominal saturation temperature.

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

1 MPa (default) | positive scalar

Pressure at the two-phase fluid 2 inlet of the heat exchanger during nominal operating condition.

Dependencies

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

Nominal saturation temperature — Use nominal saturation temperature to specify pressure

243.15 K (default) | positive scalar

Saturation temperature at the two-phase fluid 2 outlet of the heat exchanger during nominal operating condition. The pressure in the heat exchanger is the corresponding saturation pressure. The nominal saturation temperature must be less than the critical temperature.

Dependencies

To enable this parameter, set Pressure specification to Saturation pressure at specified saturation temperature.

Inlet condition specification — Select quantity to describe inlet condition of the two-phase fluid 2

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 2 inlet

250 kJ/kg (default) | positive scalar

Specific enthalpy at the two-phase fluid 2 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 2 inlet

237.15 K (default) | positive scalar

Temperature at the two-phase fluid 2 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 2 inlet

0.1 (default) | positive scalar

Vapor quality, defined as the mass fraction of vapor in a liquid-vapor mixture, at the two-phase fluid 2 inlet of the heat exchanger during the nominal operating condition.

Dependencies

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

Two-phase fluid 2 volume — Total volume of two-phase fluid 2

0.001 m^3 (default) | positive scalar

Total volume of two-phase fluid 2 inside the heat exchanger.

Initialize two-phase fluid 2 to nominal operating conditions — Option for initializing two-phase fluid 2

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 2

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

Quantity used to describe the initial state of the side 2 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 2 to nominal operating conditions check box.

Initial two-phase fluid 2 pressure — Fluid 2 pressure at start of simulation

0.101325 MPa (default) | positive scalar

Two-phase fluid 2 pressure at the start of the simulation.

Dependencies

To enable this parameter, clear the Initialize two-phase fluid 2 to nominal operating conditions check box.

Initial two-phase fluid 2 specific enthalpy — Enthalpy per unit mass at start of simulation

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

Two-phase fluid 2 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 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 two-phase fluid 2 to nominal operating conditions check box and set Initial fluid energy specification to Specific enthalpy.

Initial two-phase fluid 2 temperature — Temperature at start of simulation

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

Two-phase fluid 2 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 two-phase fluid 2 to nominal operating conditions check box and set Initial fluid energy specification to Temperature.

Initial two-phase fluid 2 vapor quality — Vapor mass fraction at start of simulation

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

Two-phase fluid 2 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 A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

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 2 to nominal operating conditions check box and set Initial fluid energy specification to Vapor quality.

Initial two-phase fluid 2 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 2 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 A2 and B2, with the first element corresponding to port A2 and the second element corresponding to port B2.

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 2 to nominal operating conditions check box and set Initial fluid energy specification to Vapor void fraction.

Initial two-phase fluid 2 specific internal energy — Internal energy per unit mass at start of simulation

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

Two-phase fluid 2 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 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 two-phase fluid 2 to nominal operating conditions check box and set Initial fluid energy specification to Specific internal energy.

Correlation Coefficients

a in Nu = a*Re^b*Pr^c for two-phase fluid 1 liquid — Correlation coefficient for subcooled liquid in two-phase fluid 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 subcooled liquid in two-phase fluid 1. The default value is based on the Colburn equation.

a in Nu = a*Re^b*Pr^c for two-phase fluid 1 mixture — Correlation coefficient for liquid-vapor mixture in two-phase fluid 1

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 1. The default value is based on the Cavallini and Zecchin correlation.

a in Nu = a*Re^b*Pr^c for two-phase fluid 1 vapor — Correlation coefficient for superheated vapor in two-phase fluid 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 superheated vapor in two-phase fluid 1. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for two-phase fluid 1 — Reynolds number exponent in correlation for two-phase fluid 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 two-phase fluid 1. 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 1 — Prandtl number exponent in correlation for two-phase fluid 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 two-phase fluid 1. The same value applies to subcooled liquid, liquid-vapor mixture, and superheated vapor.

a in Nu = a*Re^b*Pr^c for two-phase fluid 2 liquid — Correlation coefficient for subcooled liquid in two-phase fluid 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 subcooled liquid in two-phase fluid 2. The default value is based on the Colburn equation.

a in Nu = a*Re^b*Pr^c for two-phase fluid 2 mixture — Correlation coefficient for liquid-vapor mixture in two-phase fluid 2

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 2. The default value is based on the Cavallini and Zecchin correlation.

a in Nu = a*Re^b*Pr^c for two-phase fluid 2 vapor — Correlation coefficient for superheated vapor in two-phase fluid 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 superheated vapor in two-phase fluid 2. The default value is based on the Colburn equation.

b in Nu = a*Re^b*Pr^c for two-phase fluid 2 — Reynolds number exponent in correlation for two-phase fluid 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 two-phase fluid 2. 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 2 — Prandtl number exponent in correlation for two-phase fluid 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 two-phase fluid 2. The same value applies to subcooled liquid, liquid-vapor mixture, and superheated vapor.

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 R2021b

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.