HX Water Solid - MapleSim Help

HX Water Solid

Heat exchanger between Water and Solid

 Description The HX Water Solid component models a generic heat exchanger between Fluid Water and Solid materials for the lumped thermal fluid simulation of Water. This component calculates mainly pressure difference, mass flow rate, and heat flow rate.

Equations

The calculation is changed based on parameter values of Type of flow and Dynamics of mass in the Water Settings component.

 Type of flow = Linear and Dynamics of mass = Static Pressure difference is calculated with: $\mathrm{dp}=\frac{1}{A\cdot \mathrm{α__linear}}\cdot \mathrm{mflow}$ Heat transfer coefficient is calculated with: $\mathrm{h__act}=h$ Reynolds number is calculated with: $\mathrm{Re__h}=\mathrm{max}\left(\frac{\frac{\mathrm{inStream}\left(\mathrm{port_a.rho}\right)+\mathrm{inStream}\left(\mathrm{port_b.rho}\right)}{2}\cdot \left|v\right|\cdot \mathrm{D__h}}{\mathrm{μ}},0.1\right)$ Prandtl is calculated with: $\mathrm{Pr}=\frac{\mathrm{vis}\cdot \mathrm{c__p}}{k}$
 Type of flow = Linear and Dynamics of mass = Dynamic Mass flow rate is calculated with: $\mathrm{mflow}=A\cdot \mathrm{α__linear}\cdot \mathrm{dp}$ Heat transfer coefficient is calculated with: $\mathrm{h__act}=h$ Reynolds number is calculated with: $\mathrm{Re__h}=\mathrm{max}\left(\frac{\frac{\mathrm{inStream}\left(\mathrm{port_a.rho}\right)+\mathrm{inStream}\left(\mathrm{port_b.rho}\right)}{2}\cdot \left|v\right|\cdot \mathrm{D__h}}{\mathrm{μ}},0.1\right)$ Prandtl number is calculated with: $\mathrm{Pr}=\frac{\mathrm{μ}\cdot \mathrm{c__p}}{k}$
 Type of flow = Square root and Dynamics of mass = Static Pressure difference is calculated with: $\mathrm{dp}=\frac{1}{{\left(A\cdot \mathrm{α__sqrt}\right)}^{2}}\cdot {\mathrm{mflow}}^{2}\cdot \mathrm{sign}\left(\mathrm{mflow}\right)$ Heat transfer coefficient is calculated with: $\mathrm{h__act}=h$ Reynolds number is calculated with: $\mathrm{Re__h}=\mathrm{max}\left(\frac{\frac{\mathrm{inStream}\left(\mathrm{port_a.rho}\right)+\mathrm{inStream}\left(\mathrm{port_b.rho}\right)}{2}\cdot \left|v\right|\cdot \mathrm{D__h}}{\mathrm{μ}},0.1\right)$ Prandtl number is calculated with: $\mathrm{Pr}=\frac{\mathrm{μ}\cdot \mathrm{c__p}}{k}$
 Type of flow = Square root and Dynamics of mass = Dynamic In theory, Mass flow rate is calculated with: $\mathrm{mflow}=A\cdot \mathrm{α__sqrt}\cdot \sqrt{\left|\mathrm{dp}\right|}\cdot \mathrm{sign}\left(\mathrm{dp}\right)$ In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation: $\mathrm{mflow}=A\cdot \mathrm{α__sqrt}\cdot \mathrm{HeatTransfer.Functions.regRoot}\left(\mathrm{dp},\mathrm{sharpness}\right)$ Heat transfer coefficient is calculated with: $\mathrm{h__act}=h$ Reynolds number is calculated with: $\mathrm{Re__h}=\mathrm{max}\left(\frac{\frac{\mathrm{inStream}\left(\mathrm{port_a.rho}\right)+\mathrm{inStream}\left(\mathrm{port_b.rho}\right)}{2}\cdot \left|v\right|\cdot \mathrm{D__h}}{\mathrm{μ}},0.1\right)$ Prandtl number is calculated with: $\mathrm{Pr}=\frac{\mathrm{μ}\cdot \mathrm{c__p}}{k}$ (*) $\mathrm{HeatTransfer.Functions.regRoot}$ is the same function as $\mathrm{Modelica.Fluid.Utilities.regRoot}$. To check the details of the package and view the original documentation, which includes author and copyright information, click here.
 Type of flow = Darcy-Weisbach and Dynamics of mass = Static Pressure difference is calculated with Darcy–Weisbach equation: $\mathrm{dp}=\frac{1}{2}\cdot \mathrm{λ}\cdot \frac{L}{\mathrm{D__h}\cdot {A}^{2}\cdot {\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_a.rho}\right)& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_b.rho}\right)& \mathrm{others}\end{array}}\cdot {\mathrm{mflow}}^{2}\cdot \mathrm{sign}\left(\mathrm{mflow}\right)$ Heat transfer coefficient is calculated with: $\mathrm{h__act}=\left(1-\mathrm{κ__h}\right)\cdot \mathrm{h__lam}+\mathrm{κ__h}\cdot \mathrm{h__tur}$ $\mathrm{h__lam}=\frac{k}{\mathrm{D__h}}\cdot 3.66$ $\mathrm{h__tur}={\begin{array}{cc}\frac{k}{\mathrm{D__h}}\cdot 0.023\cdot {\mathrm{Re__h}}^{0.8}\cdot {\mathrm{Pr}}^{0.4}& \mathrm{solid.T}<\frac{\mathrm{port_a.T}+\mathrm{port_b.T}}{2}\\ \frac{k}{\mathrm{D__h}}\cdot 0.023\cdot {\mathrm{Re__h}}^{0.8}\cdot {\mathrm{Pr}}^{0.3}& \mathrm{others}\end{array}$ $\mathrm{κ__h}=\frac{\mathrm{tanh}\left(\frac{\mathrm{IF__speed}\cdot \left(\mathrm{Re__h}-\mathrm{Re__CoT}\right)}{2}\right)+1}{2}$ Reynolds number is calculated with: $\mathrm{Re__h_target}=\mathrm{max}\left(\frac{\frac{\mathrm{inStream}\left(\mathrm{port_a.rho}\right)+\mathrm{inStream}\left(\mathrm{port_b.rho}\right)}{2}\cdot \left|v\right|\cdot \mathrm{D__h}}{\mathrm{μ}},0.1\right)$ $\frac{ⅆ\mathrm{Re__h}}{ⅆt}=\frac{\left(\mathrm{Re__h_target}-\mathrm{Re__h}\right)}{\mathrm{T__const}}$ Prandtl number is calculated with: $\mathrm{Pr}=\frac{\mathrm{μ}\cdot \mathrm{c__p}}{k}$
 Type of flow = Darcy-Weisbach and Dynamics of mass = Dynamic In theory, Mass flow rate is calculated with Darcy–Weisbach equation: $\mathrm{mflow}=\sqrt{\frac{2\cdot \mathrm{D__h}\cdot {A}^{2}}{\mathrm{λ}\cdot L}}\cdot \sqrt{{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_a.rho}\right)& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_b.rho}\right)& \mathrm{others}\end{array}\cdot \left|\mathrm{dp}\right|}\cdot \mathrm{sign}\left(\mathrm{dp}\right)$ In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation: $\mathrm{mflow}=\sqrt{\frac{2\cdot \mathrm{D__h}\cdot {A}^{2}}{\mathrm{\lambda }\cdot L}}\cdot \mathrm{HeatTransfer.Functions.regRoot2}\left(\mathrm{dp},\mathrm{dp_small},\mathrm{inStream}\left(\mathrm{port_a.rho}\right),\mathrm{inStream}\left(\mathrm{port_b.rho}\right),\mathrm{true},\mathrm{sharpness}\right)$ Heat transfer coefficient is calculated with: $\mathrm{h__act}=\left(1-\mathrm{κ__h}\right)\cdot \mathrm{h__lam}+\mathrm{κ__h}\cdot \mathrm{h__tur}$ $\mathrm{h__lam}=\frac{k}{\mathrm{D__h}}\cdot 3.66$ $\mathrm{h__tur}={\begin{array}{cc}\frac{k}{\mathrm{D__h}}\cdot 0.023\cdot {\mathrm{Re__h}}^{0.8}\cdot {\mathrm{Pr}}^{0.4}& \mathrm{solid.T}<\frac{\mathrm{port_a.T}+\mathrm{port_b.T}}{2}\\ \frac{k}{\mathrm{D__h}}\cdot 0.023\cdot {\mathrm{Re__h}}^{0.8}\cdot {\mathrm{Pr}}^{0.3}& \mathrm{others}\end{array}$ $\mathrm{κ__h}=\frac{\mathrm{tanh}\left(\frac{\mathrm{IF__speed}\cdot \left(\mathrm{Re__h}-\mathrm{Re__CoT}\right)}{2}\right)+1}{2}$ Reynolds number is calculated with: $\mathrm{Re__h_target}=\mathrm{max}\left(\frac{\frac{\mathrm{inStream}\left(\mathrm{port_a.rho}\right)+\mathrm{inStream}\left(\mathrm{port_b.rho}\right)}{2}\cdot \left|v\right|\cdot \mathrm{D__h}}{\mathrm{μ}},0.1\right)$ $\frac{ⅆ\mathrm{Re__h}}{ⅆt}=\frac{\left(\mathrm{Re__h_target}-\mathrm{Re__h}\right)}{\mathrm{T__const}}$ Prandtl number is calculated with: $\mathrm{Pr}=\frac{\mathrm{μ}\cdot \mathrm{c__p}}{k}$ (*) $\mathrm{HeatTransfer.Functions.regRoot2}$ is the same function as $\mathrm{Modelica.Fluid.Utilities.regRoot2}$. To check the details of the package and view the original documentation, which includes author and copyright information, click here.

Definitions related to Mass flow rate and pressure:

$\mathrm{dp}=\mathrm{port_a.p}-\mathrm{port_b.p}$

$v=\frac{\mathrm{mflow}}{{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_a.rho}\right)& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_b.rho}\right)& \mathrm{others}\end{array}\cdot A}$

$\mathrm{port_a.mflow}=\mathrm{mflow}$

$\mathrm{port_b.mflow}=-\mathrm{mflow}$

Definitions related to Heat flow rate:

$\mathrm{Q_flow}=\mathrm{h__act}\cdot \mathrm{A__surface}\cdot \left(\mathrm{solid.T}-\frac{\mathrm{inStream}\left(\mathrm{port_a.T}\right)+\mathrm{inStream}\left(\mathrm{port_b.T}\right)}{2}\right)$

$\mathrm{q_flow}=\frac{\mathrm{Q_flow}}{\mathrm{max}\left(\left|\mathrm{mflow}\right|,0.00001\right)}$

If Dynamics of mass is Static, specific enthalpy is defined with:

$\mathrm{port_a.hflow}=\left\{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_b.hflow}\right)& \mathrm{mflow}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_b.hflow}\right)+\mathrm{q_flow}& \mathrm{others}\end{array}\right\$

$\mathrm{port_b.hflow}=\left\{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_a.hflow}\right)+\mathrm{q_flow}& \mathrm{mflow}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_a.hflow}\right)& \mathrm{others}\end{array}\right\$

If Dynamics of mass is Dynamic, specific enthalpy is defined with:

$\mathrm{port_a.hflow}=\left\{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_b.hflow}\right)& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_b.hflow}\right)+\mathrm{q_flow}& \mathrm{others}\end{array}\right\$

$\mathrm{port_b.hflow}=\left\{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_a.hflow}\right)+\mathrm{q_flow}& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_a.hflow}\right)& \mathrm{others}\end{array}\right\$

If Fidelity of properties = Constant, properties $\mathrm{μ}$ and $\mathrm{c__p}$ and $k$ are constants.

(*) Regarding the value of properties for Constant, see more in Water Settings.

If Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97), properties are calculated with:

$\mathrm{μ}=\mathrm{LUT__μ}\left(\frac{\left(\mathrm{port_a.p}\right)+\left(\mathrm{port_b.p}\right)}{2},\frac{\mathrm{solid.T}+\left(\frac{\mathrm{inStream}\left(\mathrm{port_a.T}\right)+\mathrm{inStream}\left(\mathrm{port_b.T}\right)}{2}\right)}{2}\right)$

$\mathrm{c__p}=\mathrm{LUT__c__p}\left(\frac{\left(\mathrm{port_a.p}\right)+\left(\mathrm{port_b.p}\right)}{2},\frac{\mathrm{solid.T}+\left(\frac{\mathrm{inStream}\left(\mathrm{port_a.T}\right)+\mathrm{inStream}\left(\mathrm{port_b.T}\right)}{2}\right)}{2}\right)$

$k=\mathrm{LUT__k}\left(\frac{\left(\mathrm{port_a.p}\right)+\left(\mathrm{port_b.p}\right)}{2},\frac{\mathrm{solid.T}+\left(\frac{\mathrm{inStream}\left(\mathrm{port_a.T}\right)+\mathrm{inStream}\left(\mathrm{port_b.T}\right)}{2}\right)}{2}\right)$

(*) The properties are defined with Liquid Water (Lookup table of IAPWS/IF97) and coefficients, see more in Water Settings.

If Fidelity of properties = IAPWS/IF97 standard, properties are calculated with:

(*) The properties are defined with IAPWS/IF97 standard and coefficients, see more in Water Settings.



Port's variables are defined with:

$\mathrm{port_a.rho}=\mathrm{inStream}\left(\mathrm{port_b.rho}\right)$

$\mathrm{port_b.rho}=\mathrm{inStream}\left(\mathrm{port_a.rho}\right)$

$\mathrm{port_a.T}=\mathrm{inStream}\left(\mathrm{port_b.T}\right)$

$\mathrm{port_b.T}=\mathrm{inStream}\left(\mathrm{port_a.T}\right)$

Variables

 Symbol Units Description Modelica ID $\mathrm{dp}$ $\mathrm{Pa}$ Pressure difference p $\mathrm{mflow}$ $\frac{\mathrm{kg}}{s}$ Mass flow rate mflow $v$ $\frac{m}{s}$ Velocity of flow v $\mathrm{h__act}$ $\frac{W}{{m}^{2}\cdot K}$ Heat transfer coefficient used for Fluid simulation h_act $\mathrm{Re__h}$ $-$ Reynolds number for Heat transfer coefficient calculation Re_h $\mathrm{Re__h_target}$ $-$ Targeted Reynolds number for Heat transfer coefficient calculation, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid. Re_h_target $\mathrm{Pr}$ $-$ Prandtl number Pr $\mathrm{κ__h}$ $-$ Intermittency factor to calculate Transition zone, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid. kappa_h $\mathrm{h__lam}$ $\frac{W}{{m}^{2}\cdot K}$ Heat transfer coefficient for Laminar flow, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid. h_lam $\mathrm{h__tur}$ $\frac{W}{{m}^{2}\cdot K}$ Heat transfer coefficient for Turbulent flow, if Fidelity of properties = Liquid Water (Lookup table of IAPWS/IF97) or IAPWS/IF97 standard is valid. h_tur $\mathrm{Q_flow}$ $W$ Heat flow rate between solid materials and fluid Water. Q_flow $\mathrm{q_flow}$ $\frac{W}{\mathrm{kg}}$ Specific energy between solid materials and fluid Water. q_flow $\mathrm{μ}$ $\mathrm{Pa}\cdot s$ Dynamic viscosity vis $\mathrm{c__p}$ $\frac{J}{\mathrm{kg}\cdot K}$ Specific heat capacity at the constant pressure cp $k$ $\frac{W}{m\cdot K}$ Thermal conductivity k

Connections

 Name Description Modelica ID $\mathrm{port__a}$ Water Port $\mathrm{port_a}$ $\mathrm{port__b}$ Water Port $\mathrm{port_b}$ $\mathrm{solid}$ Heat Port $\mathrm{solid}$

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{WaterSettings1}$ $-$ Specify a component of Water simulation settings Settings $\mathrm{Linear}$ $-$ Select Flow calculation type  - Linear  - Square root  - Darcy-Weisbach TypeOfFlow $\mathrm{α__linear}$ $30$ $-$ Flow coefficient for Linear type alpha_lin $\mathrm{α__sqrt}$ $3000$ $-$ Flow coefficient for Square root type alpha_sqrt $L$ $0.5$ $m$ Pipe length (Only for Darcy-Weisbach) L $\mathrm{D__h}$ $0.01$ $m$ Internal hydraulic diameter (Only for Darcy-Weisbach) Dh $A$ $\frac{\mathrm{Pi}}{40000}$ ${m}^{2}$ Flow area A $\mathrm{A__surface}$ $\frac{\mathrm{Pi}}{200}$ ${m}^{2}$ Surface area for Heat exchange A_surface $\mathrm{λ}$ $0.000015$ $-$ Friction coefficient for Darcy-Weisbach equation lambda $\mathrm{dp__small}$ $0.1$ $\mathrm{Pa}$ Approximation of function for |dp| <= dp_small dp_small $\mathrm{sharpness}$ $1.0$ $-$ Sharpness of approximation for sqrt(dp) and sqrt(rho * dp) sharpness $h$ $10$ $-$ Coefficient of heat transfer h $\mathrm{T__const}$ $0.001$ $s$ Time constant for Reynolds number calculation T_const $\mathrm{Re__CoT}$ $3500$ $-$ Reynolds number of the center of Transition zone Re_CoT $0.007$ $-$ Changing rate of Intermittency factor IF_spread