Thermal interface between a thermal liquid and its surroundings

**Library:**Simscape / Fluids / Fluid Network Interfaces / Heat Exchangers / Fundamental Components

The Simple Heat Exchanger Interface (TL) block models the pressure drop and temperature change in a thermal liquid as it traverses the length of a thermal interface such as that provided by a heat exchanger. Heat transfer across the thermal interface is ignored. See the composite block diagram of the Simple Heat Exchanger (TL-TL) block for an example showing how to combine the two blocks.

The pressure drop is calculated as a function of mass flow rate from tabulated data specified at some reference pressure and temperature. The calculation is based on linear interpolation if the mass flow rate is within the bounds of the tabulated data and on nearest-neighbor extrapolation otherwise. In other words, neighboring data points connect through straight-line segments, with those at the mass flow rate bounds extending horizontally outward.

**Linear interpolation (left) and nearest-neighbor extrapolation (right)**

The block calculations rely on the states and properties of the fluid—temperature, density, and specific internal energy—at the entrance to the thermal interface. The entrance changes abruptly from one port to the other during flow reversal, introducing discontinuities in the values of these variables. To eliminate these discontinuities, the block smooths the affected variables at mass flow rates below a specified threshold value.

**Smoothing of entrance temperature below mass flow rate threshold**

Mass can enter and exit the thermal interface through ports **A**
and**B**. The volume of the interface is fixed but the
compressibility of the fluid means that the mass inside the interface can change
with pressure and temperature. Whether compressibility is factored into the block
calculations depends on the setting of the **Thermal Liquid dynamic
compressibility** parameter in the **Effects and Initial
Conditions** tab:

$${\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}}=\{\begin{array}{ll}\left(\frac{dp}{dt}\frac{1}{\beta}-\frac{dT}{dt}\alpha \right)\rho V,\hfill & \text{if}ThermalLiquiddynamiccompressibility\text{isOn}\hfill \\ 0,\hfill & \text{otherwise}\hfill \end{array},$$

where:

*$$\dot{m}$$*are the mass flow rates in through the thermal liquid ports._{*}*p*is the internal fluid pressure.*T*is the internal fluid temperature.*ɑ*is the isobaric thermal expansion coefficient.*β*is the isothermal bulk modulus.*ρ*is the internal fluid density.*V*is the internal fluid volume.

If the **Thermal Liquid dynamic compressibility** parameter is
set to `Off`

, the fluid is treated as incompressible and
the mass flow rate in through one thermal liquid port must exactly equal that out
through the other thermal liquid port. The rate of mass accumulation is, in this
case, zero.

Energy can enter and exit the thermal interface in two ways: with fluid flow
through ports **A** and **B** and with heat flow
through port **H**. No work is done on or by the fluid inside the
interface. The rate of energy accumulation in the internal fluid volume of the
interface must therefore equal the sum of the energy flow rates through all three ports:

$$\frac{\partial E}{\partial p}\frac{dp}{dt}+\frac{\partial E}{\partial T}\frac{dT}{dt}={\varphi}_{\text{A}}+{\varphi}_{\text{B}}+{Q}_{\text{H}},$$

where:

*E*is the total energy in the internal fluid volume of the thermal interface.*ϕ*_{*}are the energy flow rates in through the thermal liquid ports.*Q*is the heat flow rate in through the thermal port.

The pressure drop calculation is based entirely on tabulated data that you specify. The causes of the pressure drop are ignored, except in the effects that they might have on the specified data. The overall pressure drop from one thermal liquid port to the other is calculated from the individual pressure drops from each thermal liquid port to the internal fluid volume:

$${p}_{\text{A}}-{p}_{\text{B}}=\Delta {p}_{\text{A}}-\Delta {p}_{\text{B}},$$

where:

*p*_{*}are the fluid pressures at the thermal liquid ports.*Δp*_{*}are the pressure drops from the thermal liquid ports to the internal fluid volume:$$\Delta {p}_{*}={p}_{*}-p,$$

with

*p*as the pressure in the internal fluid volume.

The tabulated data is specified at a reference pressure and temperature from which
a third reference parameter, the *reference density*, is
calculated. The ratio of the reference density to the actual port density serves as
a correction factor in the individual pressure drop equations, each defined as:

$$\Delta {p}_{*}=\Delta p({\dot{m}}_{*})\frac{{\rho}_{\text{R}}}{{\rho}_{*}},$$

where:

*Δp($$\dot{m}$$)*is the tabulated pressure drop function.*ρ*_{*}are the fluid densities at the thermal liquid ports.

The asterisk denotes the thermal liquid port (**A** or
**B**) at which a parameter or variable is defined. Subscript R
denotes a reference value. The density at the interface entrance is smoothed below
the mass flow rate threshold by introducing a hyperbolic term *ɑ*:

$${\rho}_{*,\text{smooth}}={\rho}_{*}\left(\frac{1+\alpha}{2}\right)+\rho \left(\frac{1-\alpha}{2}\right),$$

where *ρ*_{smooth} is the
smoothed density at the entrance port, *ρ*_{*}
is the unsmoothed density at the same port, and *ρ* is the density
in the internal fluid volume. The hyperbolic smoothing term is defined as:

$$\alpha =\text{tanh}\left(4\frac{{\dot{m}}_{\text{avg}}}{{\dot{m}}_{\text{th}}}\right),$$

where *$$\dot{m}$$ _{avg}* is the average of the
mass flow rates through the thermal liquid ports and

$${\dot{m}}_{\text{avg}}=\frac{{\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}}}{2}$$

Heat Exchanger (TL) | Heat Exchanger Interface (TL) | Simple Heat Exchanger Interface (G) | Specific Dissipation Heat Transfer