Specific Dissipation Heat Exchanger Interface (TL)

Thermal interface between a thermal liquid and its surroundings

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Libraries:
Simscape / Fluids / Heat Exchangers / Fundamental Components

Description

The Specific Dissipation 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 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 Balance

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:

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

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.

• α 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 you clear the Thermal Liquid dynamic compressibility checkbox, 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 Balance

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.

Momentum Balance

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 $$\dot{m}$$_th is the mass flow rate threshold specified in the block dialog box. This threshold determines the width of the mass flow rate region over which to smooth the fluid density. The average mass flow rate is defined as:

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

Ports

Output

CP — Isobaric specific heat of the thermal liquid, kJ/(kg*K)

physical signal

Isobaric specific heat of the thermal liquid in the internal fluid volume of the thermal interface.

M — Mass flow rate of the thermal liquid, kg/s

physical signal

Mass flow rate of the thermal liquid in the interior of the thermal interface. The output signal is positive when the flow rate is directed from port A to port B and negative otherwise.

Conserving

A — Fluid opening

thermal liquid

Opening through which thermal liquid can enter and exit the thermal interface.

B — Fluid opening

thermal liquid

Opening through which thermal liquid can enter and exit the thermal interface.

H — Thermal condition at the fluid entrance

thermal

Thermal port used to set the thermal condition at the thermal liquid port serving as the thermal liquid entrance.

Parameters

Pressure Loss Tab

Mass flow rate vector — Mass flow rates at which to specify pressure-drop data

[.3, .5, 1, 1.5, 2, 2.5] kg/s (default) | K-element array with units of mass/time

Array of mass flow rates at which to specify the pressure drop tabulated data.

Pressure drop vector — Pressure-drop data corresponding to specified mass flow rates

[3, 5, 10, 25, 35, 50] * 1e-3 MPa (default) | K-element array with units of pressure

Array of pressure drops from inlet to outlet corresponding to the tabulated mass flow rate data.

Reference inflow temperature — Temperature at which pressure-drop data is specified

293.15 K (default) | scalar with units of temperature

Temperature at which the tabulated pressure-drop data is specified.

Reference inflow pressure — Pressure at which pressure-drop tabulated data is specified

0.101325 MPa (default) | scalar with units of pressure

Pressure at which the tabulated pressure-drop data is specified. The block uses this parameter to calculate a third reference parameter, the reference density. The reference that it uses to scale the tabulated pressure drop data for pressures and temperatures deviating from the reference conditions.

Mass flow rate threshold for flow reversal — Mass flow rate below which to smooth numerical data

1e-6 kg/s (default) | scalar with units of mass/time

Mass flow rate below which to initiate a smooth flow reversal to prevent discontinuities in the simulation data.

Thermal Liquid volume — Volume of thermal liquid inside the heat exchanger

0.01 m^3 (default) | scalar with units of volume

Volume of thermal liquid occupying the heat exchanger at any given time. The initial conditions specified in the Effects and Initial Conditions tab apply to this volume. The volume is constant during simulation.

Cross-sectional area at ports A1 and B1 — Flow area at the thermal liquid inlets

0.01 m^2 (default) | scalar with units of area

Flow area at the thermal liquid inlets. Inlets A1 and B1 are assumed to be identical in size.

Effects and Initial Conditions

Thermal Liquid dynamic compressibility — Option to model pressure dynamics inside the heat exchanger

On (default) | Off

Option to model the pressure dynamics inside the heat exchanger. If you select this parameter, the block removes the pressure derivative terms from the component energy and mass conservation equations. The pressure inside the heat exchanger is then reduced to the weighted average of the two port pressures.

Thermal Liquid initial temperature — Temperature inside the heat exchanger at the start of simulation

293.15 K (default) | scalar with units of temperature

Temperature of the internal volume of thermal liquid at the start of simulation.

Thermal Liquid initial pressure — Pressure inside the heat exchanger at the start of simulation

0.101325 MPa (default) | scalar with units of pressure

Pressure of the internal volume of thermal liquid at the start of simulation.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017b

R2024a: New block name

The block is now named Specific Dissipation Heat Exchanger Interface (TL). It was previously named Simple Heat Exchanger Interface (TL).