If Type of Branch is $\mathit{a}\mathbf{\Rightarrow }\mathit{b}\mathbf{\+}\mathit{c}\mathbf{\+}\mathit{d}$(Branching), Mass conservation is calculated with:

$\mathrm{NumOfRoute}\=\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}1.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}$

$\mathrm{`port\_x.mflow`}\=-\frac{1}{\mathrm{NumOfRoute}}\cdot \mathrm{`port\_a.mflow`}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.p`}\=p$

$\mathrm{`port\_x.p`}\=p$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

If Type of Branch is $\mathit{a}\mathbf{\+}\mathit{c}\mathbf{\+}\mathit{d}\mathbf{\Rightarrow }\mathit{b}\mathbf{ }$(Confluence), Mass conservation is calculated with:

$\mathrm{NumOfRoute}\=1.0\+\sum _{x\=\left\{c\,d\right\}}^{}\{\begin{array}{cc}1.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}$

$\mathrm{`port\_b.mflow`}\=-\(\mathrm{`port\_a.mflow`}\+\sum _{x\=\left\{c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}\)$ 

$\mathrm{`port\_a.p`}\=p$

$p\=-\frac{1}{\mathrm{NumOfRoute}}\cdot \sum _{x\=\left\{a\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.p`}& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}$

$\mathrm{`port\_b.p`}\=p$

Energy conservation is calculated with:

$$\begin{gathered} \mathrm{c\_\_p}\cdot M\cdot \frac{\ⅆT}{\ⅆ t}\=\mathrm{`port\_a.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_a.hflow`}\right) \\ \+\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_x.hflow`}\right)& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}\+\{\begin{array}{cc}\mathrm{`heat.Q\_flow`}& \mathrm{useHeatPort}\=\mathrm{true}\\ 0.0& \mathrm{useHeatPort}\=\mathrm{false}\end{array} \end{gathered}$$

State equation:

$p\=\mathrm{\ρ}\cdot \mathrm{R\_\_gas}\cdot T$

Relationship of mass:

$u\=\frac{U}{M}$

$M\=\mathrm{\ρ}\cdot V$

Definition of Enthalpy:

$\mathrm{hflow}\=\mathrm{Function\_\_hflow}\left(T\right)$

$u\=\mathrm{hflow}-\frac{p}{\mathrm{\ρ}}$

Port definitions:

$\mathrm{`port\_a.hflow`}\=\mathrm{hflow}$

$\mathrm{`port\_x.hflow`}\=\mathrm{hflow}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.rho`}\=\mathrm{\ρ}$

$\mathrm{`port\_x.rho`}\=\mathrm{\ρ}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.T`}\=T$

$\mathrm{`port\_x.T`}\=T$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$v\left[1\right]\=\frac{\mathrm{`port\_a.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_a.rho`}\right)\cdot A\left[1\right]}$

$v\left[i\right]\=\frac{\mathrm{`port\_x.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_x.rho`}\right)\cdot A\left[i\right]}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\,\mathrm{the} \mathrm{order} \mathrm{of} \mathrm{vector} \mathrm{is} b\=2\,c\=3\,d\=4\right)$

$\mathrm{`heat.T`}\=T$

(*) Regarding the value of properties, see more details in Air Settings.

Mass conservation is calculated with:

$\frac{\ⅆ\mathrm{\ρ}}{\ⅆ t}\=\frac{\mathrm{`port\_a.mflow`}\+\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}}{V}$

$\mathrm{`port\_a.p`}\=p$

$\mathrm{`port\_x.p`}\=p$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

Energy conservation is calculated with:

$$\begin{gathered} \frac{\ⅆU}{\ⅆ t}\=\mathrm{`port\_a.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_a.hflow`}\right) \\ \+\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_x.hflow`}\right)& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}\+\{\begin{array}{cc}\mathrm{`heat.Q\_flow`}& \mathrm{useHeatPort}\=\mathrm{true}\\ 0.0& \mathrm{useHeatPort}\=\mathrm{false}\end{array} \end{gathered}$$

State equation:

$p\=\mathrm{\ρ}\cdot \mathrm{R\_\_gas}\cdot T$

Relationship of mass:

$u\=\frac{U}{M}$

$M\=\mathrm{\ρ}\cdot V$

Definition of Enthalpy:

$\mathrm{hflow}\=\mathrm{Function\_\_hflow}\left(T\right)$

$\left(\mathrm{c\_\_p}-\mathrm{R\_\_gas}\right)\cdot \frac{\ⅆT}{\ⅆ t}\=\frac{\frac{\ⅆU}{\ⅆ t}}{\mathrm{\ρ}\cdot V}-\frac{U\cdot }{{\mathrm{\ρ}}^2\cdot V}$

Port definitions:

$\mathrm{`port\_a.hflow`}\=\mathrm{hflow}$

$\mathrm{`port\_x.hflow`}\=\mathrm{hflow}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.rho`}\=\mathrm{\ρ}$

$\mathrm{`port\_x.rho`}\=\mathrm{\ρ}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.T`}\=T$

$\mathrm{`port\_x.T`}\=T$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$v\left[1\right]\=\frac{\mathrm{`port\_a.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_a.rho`}\right)\cdot A\left[1\right]}$

$v\left[i\right]\=\frac{\mathrm{`port\_x.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_x.rho`}\right)\cdot A\left[i\right]}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\,\mathrm{the} \mathrm{order} \mathrm{of} \mathrm{vector} \mathrm{is} b\=2\,c\=3\,d\=4\right)$

$\mathrm{`heat.T`}\=T$

(*) Regarding the values and equations of properties, see more details in Air Settings.

If Type of Branch is $\mathit{a}\mathbf{\Rightarrow }\mathit{b}\mathbf{\+}\mathit{c}\mathbf{\+}\mathit{d}$(Branching), Mass conservation is calculated with:

$\mathrm{NumOfRoute}\=\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}1.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}$

$\mathrm{`port\_x.mflow`}\=-\frac{1}{\mathrm{NumOfRoute}}\cdot \mathrm{`port\_a.mflow`}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.p`}\=p$

$\mathrm{`port\_x.p`}\=p$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

If Type of Branch is $\mathit{a}\mathbf{\+}\mathit{c}\mathbf{\+}\mathit{d}\mathbf{\Rightarrow }\mathit{b}\mathbf{ }$(Confluence), Mass conservation is calculated with:

$\mathrm{NumOfRoute}\=1.0\+\sum _{x\=\left\{c\,d\right\}}^{}\{\begin{array}{cc}1.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}$

$\mathrm{`port\_b.mflow`}\=-\(\mathrm{`port\_a.mflow`}\+\sum _{x\=\left\{c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}\)$ 

$\mathrm{`port\_a.p`}\=p$

$p\=-\frac{1}{\mathrm{NumOfRoute}}\cdot \sum _{x\=\left\{a\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.p`}& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}$

$\mathrm{`port\_b.p`}\=p$

Energy conservation is calculated with:

$$\begin{gathered} \mathrm{Function\_\_cp}\left(T\right)\cdot M\cdot \frac{\ⅆT}{\ⅆ t}\=\mathrm{`port\_a.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_a.hflow`}\right) \\ \+\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_x.hflow`}\right)& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}\+\{\begin{array}{cc}\mathrm{`heat.Q\_flow`}& \mathrm{useHeatPort}\=\mathrm{true}\\ 0.0& \mathrm{useHeatPort}\=\mathrm{false}\end{array} \end{gathered}$$

State equation:

$p\=\mathrm{\ρ}\cdot \mathrm{R\_\_gas}\cdot T$

Relationship of mass:

$u\=\frac{U}{M}$

$M\=\mathrm{\ρ}\cdot V$

Definition of Enthalpy:

$\mathrm{hflow}\=\mathrm{Function\_\_hflow}\left(T\right)$

$u\=\mathrm{hflow}-\frac{p}{\mathrm{\ρ}}$

Port definitions:

$\mathrm{`port\_a.hflow`}\=\mathrm{hflow}$

$\mathrm{`port\_x.hflow`}\=\mathrm{hflow}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.rho`}\=\mathrm{\ρ}$

$\mathrm{`port\_x.rho`}\=\mathrm{\ρ}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.T`}\=T$

$\mathrm{`port\_x.T`}\=T$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$v\left[1\right]\=\frac{\mathrm{`port\_a.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_a.rho`}\right)\cdot A\left[1\right]}$

$v\left[i\right]\=\frac{\mathrm{`port\_x.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_x.rho`}\right)\cdot A\left[i\right]}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\,\mathrm{the} \mathrm{order} \mathrm{of} \mathrm{vector} \mathrm{is} b\=2\,c\=3\,d\=4\right)$

$\mathrm{`heat.T`}\=T$

(*) The properties are defined with NASA polynomials and coefficients. For details, see Air Settings.

Mass conservation is calculated with:

$\frac{\ⅆ\mathrm{\ρ}}{\ⅆ t}\=\frac{\mathrm{`port\_a.mflow`}\+\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}}{V}$

$\mathrm{`port\_a.p`}\=p$

$\mathrm{`port\_x.p`}\=p$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

Energy conservation is calculated with:

$$\begin{gathered} \frac{\ⅆU}{\ⅆ t}\=\mathrm{`port\_a.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_a.hflow`}\right) \\ \+\sum _{x\=\left\{b\,c\,d\right\}}^{}\{\begin{array}{cc}\mathrm{`port\_x.mflow`}\cdot \mathrm{ActualStream}\left(\mathrm{`port\_x.hflow`}\right)& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}\\ 0.0& \mathrm{port\_\_x} \mathrm{on}\=\mathrm{false}\end{array}\+\{\begin{array}{cc}\mathrm{`heat.Q\_flow`}& \mathrm{useHeatPort}\=\mathrm{true}\\ 0.0& \mathrm{useHeatPort}\=\mathrm{false}\end{array} \end{gathered}$$

State equation:

$p\=\mathrm{\ρ}\cdot \mathrm{R\_\_gas}\cdot T$

Relationship of mass:

$u\=\frac{U}{M}$

$M\=\mathrm{\ρ}\cdot V$

Definition of Enthalpy:

$\mathrm{hflow}\=\mathrm{Function\_\_hflow}\left(T\right)$

$$\begin{gathered} \left(\mathrm{Function\_\_cp}\left(T\right)-\mathrm{R\_\_gas}\right)\cdot \frac{\ⅆT}{\ⅆ t} \\ \=\frac{\frac{\ⅆU}{\ⅆ t}}{\mathrm{\ρ}\cdot V}-\frac{U\cdot }{{\mathrm{\ρ}}^2\cdot V} \end{gathered}$$

Port definitions:

$\mathrm{`port\_a.hflow`}\=\mathrm{hflow}$

$\mathrm{`port\_x.hflow`}\=\mathrm{hflow}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.rho`}\=\mathrm{\ρ}$

$\mathrm{`port\_x.rho`}\=\mathrm{\ρ}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$\mathrm{`port\_a.T`}\=T$

$\mathrm{`port\_x.T`}\=T$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\right)$

$v\left[1\right]\=\frac{\mathrm{`port\_a.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_a.rho`}\right)\cdot A\left[1\right]}$

$v\left[i\right]\=\frac{\mathrm{`port\_x.mflow`}}{\mathrm{ActualStream}\left(\mathrm{`port\_x.rho`}\right)\cdot A\left[i\right]}$ $\mathbf{if} \mathrm{port\_\_x} \mathrm{on}\=\mathrm{true}$ $\left(x\=\left\{b\,c\,d\right\}\,\mathrm{the} \mathrm{order} \mathrm{of} \mathrm{vector} \mathrm{is} b\=2\,c\=3\,d\=4\right)$

$\mathrm{`heat.T`}\=T$

(*) The properties are defined with NASA polynomials and coefficients. For details, see Air Settings.