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HX Air Solid

Heat exchanger between Air and Solid

	Description
	The HX Air Solid component models a generic heat exchanger between Fluid Air and Solid materials for the lumped thermal fluid simulation of Air. This component mainly calculates 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 Air Settings component.

	Type of flow = Linear and Dynamics of mass = Static
	Pressure difference is calculated with: $dp = \frac{1}{A \cdot α__linear} \cdot mflow$ Heat transfer coefficient is calculated with: $h__act = h$ Reynolds number is calculated with: $Re__h = \max (\frac{\frac{inStream (`port_a.rho`) + inStream (`port_b.rho`)}{2} \cdot \|v\| \cdot D__h}{μ}, 0.1)$ Prandtl is calculated with: $\Pr = \frac{vis \cdot c__p}{k}$

	Type of flow = Linear and Dynamics of mass = Dynamic
	Mass flow rate is calculated with: $mflow = A \cdot α__linear \cdot dp$ Heat transfer coefficient is calculated with: $h__act = h$ Reynolds number is calculated with: $Re__h = \max (\frac{\frac{inStream (`port_a.rho`) + inStream (`port_b.rho`)}{2} \cdot \|v\| \cdot D__h}{μ}, 0.1)$ Prandtl number is calculated with: $\Pr = \frac{μ \cdot c__p}{k}$

Type of flow = Square root and Dynamics of mass = Static

Pressure difference is calculated with:

$dp = \frac{1}{{(A \cdot α__sqrt)}^{2}} \cdot {mflow}^{2} \cdot sign (mflow)$

Heat transfer coefficient is calculated with:

$h__act = h$

Reynolds number is calculated with:

$Re__h = \max (\frac{\frac{inStream (`port_a.rho`) + inStream (`port_b.rho`)}{2} \cdot |v| \cdot D__h}{μ}, 0.1)$

Prandtl number is calculated with:

$\Pr = \frac{μ \cdot c__p}{k}$

Type of flow = Square root and Dynamics of mass = Dynamic

In theory, Mass flow rate is calculated with:

$mflow = A \cdot α__sqrt \cdot \sqrt{|dp|} \cdot sign (dp)$

In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation:

$mflow = A \cdot α__sqrt \cdot `HeatTransfer.Functions.regRoot` (dp, sharpness)$

Heat transfer coefficient is calculated with:

$h__act = h$

Reynolds number is calculated with:

$Re__h = \max (\frac{\frac{inStream (`port_a.rho`) + inStream (`port_b.rho`)}{2} \cdot |v| \cdot D__h}{μ}, 0.1)$

Prandtl number is calculated with:

$\Pr = \frac{μ \cdot c__p}{k}$

(*) $`HeatTransfer.Functions.regRoot`$ is the same function as $`Modelica.Fluid.Utilities.regRoot`$ . 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:

$dp = \frac{1}{2} \cdot λ \cdot \frac{L}{D__h \cdot A^{2} \cdot {\begin{array}{c} inStream (`port_a.rho`) & dp \geq 0 \\ inStream (`port_b.rho`) & others \end{array}} \cdot {mflow}^{2} \cdot sign (mflow)$

Heat transfer coefficient is calculated with:

$h__act = (1 - κ__h) \cdot h__lam + κ__h \cdot h__tur$

$h__lam = \frac{k}{D__h} \cdot 3.66$

$h__tur = {\begin{array}{c} \frac{k}{D__h} \cdot 0.023 \cdot {Re__h}^{0.8} \cdot \Pr^{0.4} & `solid.T` < \frac{`port_a.T` + `port_b.T`}{2} \\ \frac{k}{D__h} \cdot 0.023 \cdot {Re__h}^{0.8} \cdot \Pr^{0.3} & others \end{array}$

$κ__h = \frac{\tanh (\frac{IF__speed \cdot (Re__h - Re__CoT)}{2}) + 1}{2}$

Reynolds number is calculated with:

$Re__h_target = \max (\frac{\frac{inStream (`port_a.rho`) + inStream (`port_b.rho`)}{2} \cdot |v| \cdot D__h}{μ}, 0.1)$

$\frac{&DifferentialD; Re__h}{&DifferentialD; t} = \frac{(Re__h_target - Re__h)}{T__const}$

Prandtl number is calculated with:

$\Pr = \frac{μ \cdot c__p}{k}$

Type of flow = Darcy-Weisbach and Dynamics of mass = Dynamic

In theory, Mass flow rate is calculated with Darcy–Weisbach equation:

$mflow = \sqrt{\frac{2 \cdot D__h \cdot A^{2}}{λ \cdot L}} \cdot \sqrt{{\begin{array}{c} inStream (`port_a.rho`) & dp \geq 0 \\ inStream (`port_b.rho`) & others \end{array} \cdot |dp|} \cdot sign (dp)$

In the Heat Transfer Library, the following equation is used to resolve difficulties of the numerical calculation:

$mflow = \sqrt{\frac{2 \cdot D__h \cdot A^{2}}{λ \cdot L}} \cdot `HeatTransfer.Functions.regRoot2` (dp, dp_small, inStream (`port_a.rho`), inStream (`port_b.rho`), true, sharpness)$

Heat transfer coefficient is calculated with:

$h__act = (1 - κ__h) \cdot h__lam + κ__h \cdot h__tur$

$h__lam = \frac{k}{D__h} \cdot 3.66$

$κ__h = \frac{\tanh (\frac{IF__speed \cdot (Re__h - Re__CoT)}{2}) + 1}{2}$

Reynolds number is calculated with:

$Re__h_target = \max (\frac{\frac{inStream (`port_a.rho`) + inStream (`port_b.rho`)}{2} \cdot |v| \cdot D__h}{μ}, 0.1)$

$\frac{&DifferentialD; Re__h}{&DifferentialD; t} = \frac{(Re__h_target - Re__h)}{T__const}$

Prandtl number is calculated with:

$\Pr = \frac{μ \cdot c__p}{k}$

(*) $`HeatTransfer.Functions.regRoot2`$ is the same function as $`Modelica.Fluid.Utilities.regRoot2`$ . 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 :

$dp = `port_a.p` - `port_b.p`$

$v = \frac{mflow}{{\begin{array}{c} inStream (`port_a.rho`) & dp \geq 0 \\ inStream (`port_b.rho`) & others \end{array} \cdot A}$

$`port_a.mflow` = mflow$

$`port_b.mflow` = - mflow$

Definitions related to Heat flow rate:

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

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

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

$`port_a.hflow` = \{\begin{array}{c} inStream (`port_b.hflow`) & mflow \geq 0 \\ inStream (`port_b.hflow`) + q_flow & others \end{array}$

$`port_b.hflow` = \{\begin{array}{c} inStream (`port_a.hflow`) + q_flow & mflow \geq 0 \\ inStream (`port_a.hflow`) & others \end{array}$

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

$`port_a.hflow` = \{\begin{array}{c} inStream (`port_b.hflow`) & dp \geq 0 \\ inStream (`port_b.hflow`) + q_flow & others \end{array}$

$`port_b.hflow` = \{\begin{array}{c} inStream (`port_a.hflow`) + q_flow & dp \geq 0 \\ inStream (`port_a.hflow`) & others \end{array}$

If Fidelity of properties = Constant, properties $μ$ and $c__p$ and $k$ are constants.

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

If Fidelity of properties = Ideal Gas (NASA Polynomial), properties are calculated with:

$μ = Function__vis (\frac{inStream (`port_a.T`) + inStream (`port_b.T`)}{2})$

$c__p = Function__cp (\frac{inStream (`port_a.T`) + inStream (`port_b.T`)}{2})$

$k = Function__k (\frac{inStream (`port_a.T`) + inStream (`port_b.T`)}{2})$

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

Port's variables are defined with:

$`port_a.rho` = inStream (`port_b.rho`)$

$`port_b.rho` = inStream (`port_a.rho`)$

$`port_a.T` = inStream (`port_b.T`)$

$`port_b.T` = inStream (`port_a.T`)$

Variables

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

Connections

Name	Description	Modelica ID
$port__a$	Air Port	$port_a$
$port__b$	Air Port	$port_b$
$solid$	Heat Port	$solid$

Parameters

Symbol	Default	Units	Description	Modelica ID
$Air simulation settings$	$AirSettings1$	$-$	Specify a component of Air simulation settings	Settings
$Type of flow$	$Linear$	$-$	Select Flow calculation type - Linear - Square root - Darcy-Weisbach	TypeOfFlow
$α__linear$	$10$	$-$	Flow coefficient for Linear type	alpha_lin
$α__sqrt$	$60$	$-$	Flow coefficient for Square root type	alpha_sqrt
$L$	$0.1$	$m$	Pipe length (Only for Darcy-Weisbach)	L
$D__h$	$0.1$	$m$	Internal hydraulic diameter (Only for Darcy-Weisbach)	Dh
$A$	$\frac{Pi}{400}$	$m^{2}$	Flow area	A
$A__surface$	$\frac{Pi}{100}$	$m^{2}$	Surface are for Heat exchange	A_surface
$λ$	$0.000015$	$-$	Friction coefficient for Darcy-Weisbach equation	lambda
$dp__small$	$0.1$	$Pa$	Approximation of function for \|dp\| <= dp_small	dp_small
$sharpness$	$1.0$	$-$	Sharpness of approximation for sqrt(dp) and sqrt(rho * dp)	sharpness
$T__const$	$0.001$	$s$	Time constant for Reynolds number calculation	T_const
$Re__CoT$	$3500$	$-$	Reynolds number of the center of Transition zone	Re_CoT
$Spread of Intermittency factor$	$0.007$	$-$	Changing rate of Intermittency factor	IF_spread

	See Also
	Heat Transfer Library Overview Air Overview Air Basic Overview

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