Specific Dissipation Heat Exchanger Interface (G)

Thermal interface between a gas and its surroundings

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Libraries:
Simscape / Fluids / Heat Exchangers / Fundamental Components

Description

The Specific Dissipation Heat Exchanger Interface (G) block models the pressure drop and temperature change in a gas 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 (G-G) 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 andB. 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. The compressibility of the gas is always taken into account, with its value being that specified in the Gas Properties (G) block dialog box. The mass balance in the interface can then be expressed as:

$$\frac{\partial M}{\partial p}\frac{dp}{dt}+\frac{\partial M}{\partial T}\frac{dT}{dt}={\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}},$$

where:

• M is the mass of the internal fluid volume of the thermal interface.

• p is the internal fluid pressure.

• T is the internal fluid temperature.

• $$\dot{m}$$_* are the mass flow rates in through the gas ports.

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 gas 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 gas port to the other is calculated from the individual pressure drops from each gas 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 gas ports.

• Δp_* are the pressure drops from the gas 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 gas ports.

The asterisk denotes the gas 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 gas 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:

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

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables and Initial Conditions for Blocks with Finite Gas Volume.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Ports

Output

CP — Isobaric specific heat of gas, kJ/(kg*K)

physical signal

Isobaric specific heat of the gas 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 gas in the internal fluid volume of the 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

gas

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

B — Fluid opening

gas

Opening through which gas 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 gas port serving as the gas entrance.

Parameters

Pressure Loss

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.

Gas volume — Volume of gas inside the heat exchanger

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

Volume of gas 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 gas inlets

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

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

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 (G). It was previously named Simple Heat Exchanger Interface (G).