Specific Dissipation Heat Exchanger Interface (TL)

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The thermal interface between a thermally conductive liquid and the environment.

blockType: EngeeFluids.HeatExchangers.SpecificDissipation.Interfaces.ThermalLiquid

Path in the library:

/Physical Modeling/Fluids/Heat Exchangers/Fundamental Components/Specific Dissipation Heat Exchanger Interface (TL)

Description

Block Specific Dissipation Heat Exchanger Interface (TL) simulates the pressure drop and temperature change of a heat-conducting liquid as it passes through a thermal interface, for example, through a heat exchanger. Heat transfer through the thermal interface is not taken into account. See the block diagram Heat Exchanger (TL-TL) for an example of combining two blocks.

The pressure drop is calculated as a function of mass flow based on tabular data set at a certain reference pressure and temperature. The calculation is based on linear interpolation if the mass flow rate falls within the limits of the tabular data, and on extrapolation to neighboring elements otherwise. In other words, adjacent data points are connected by rectilinear segments, with the segments at the boundaries of the mass flow extending horizontally outward.

Linear interpolation (left) and extrapolation by neighboring elements (right)

specific dissipation heat exchanger interface tl 1

The calculations of the unit are based on the states and properties of temperature, density, and specific internal energy of the liquid at the entrance to the thermal interface. The input changes abruptly from one port to another when a reverse flow occurs, which leads to gaps in the values of these variables. To eliminate these gaps, the unit smooths out the corresponding variables at mass flow values below the set threshold value.

Smoothing the input temperature below the mass flow threshold

specific dissipation heat exchanger interface tl 2

Mass balance

The mass can enter and exit the thermal interface via ports A and B. The volume of the interface is fixed, but the compressibility of the liquid means that the mass inside the interface can vary depending on pressure and temperature. Whether compressibility is taken into account in the block calculations depends on the parameter setting. Thermal Liquid dynamic compressibility in the parameter group Effects and Initial Conditions:

where

— mass flow through non-directional ports connected to a heat-conducting liquid;
— internal pressure of the liquid;
— internal temperature of the liquid;
— coefficient of isobaric thermal expansion;
— isothermal modulus of volumetric elasticity;
— internal density of the liquid;
— the internal volume of the liquid.

If you uncheck the option Thermal Liquid dynamic compressibility, the liquid will be considered incompressible, and the mass flow rate entering through one non-directional port connected to a heat-conducting liquid must be exactly equal to the mass flow rate exiting through another port connected to a heat-conducting liquid. In this case, the rate of mass accumulation is zero.

Energy balance

Energy can enter and exit the thermal interface in two ways: with liquid flow through ports A and B and with heat flow through port H. The liquid inside the interface does not do any work. Therefore, the rate of energy accumulation in the internal volume of the interface fluid should be equal to the sum of the energy flows through all three ports.:

where

— total energy in the internal volume of the thermal interface fluid;
— energy flow coming through non-directional ports connected to a heat-conducting liquid;
— the rate of heat flow coming through a non-directional port associated with heat.

Balance of impulses

The differential pressure calculation is based entirely on the tabular data you provided. The causes of the pressure drop are not considered, except for their possible effect on the indicated data. The total pressure drop between one non-directional port connected to a heat-conducting liquid and another is calculated based on the individual pressure drops between each non-directional port connected to a heat-conducting liquid and the internal volume of the liquid:

where

— the pressure of the liquid in the non-directional ports connected to the heat-conducting liquid;
— pressure difference between the non-directional ports connected to the heat-conducting liquid and the internal volume of the liquid:

where — pressure in the internal volume of the liquid.

Tabular data are provided for the reference pressure and temperature, on the basis of which the third reference parameter is calculated — the reference density. The ratio of the reference density to the actual density in the port serves as a correction factor in the individual differential pressure equations, each of which is defined as

where

— tabular differential pressure function;
— the density of the liquid in the non-directional ports connected to the heat-conducting liquid.

The asterisk indicates a non-directional port connected to a thermally conductive liquid (A or B) in which a parameter or variable is defined. Lower index indicates a reference value. The density at the interface entrance is smoothed below the threshold value of the mass flow due to the introduction of a hyperbolic term :

where — smoothed density at the entrance, — non-smoothed density at the same input and — the density in the internal volume of the liquid. The hyperbolic smoothing term is defined as

where — the average value of the mass flow rate through non-directional ports connected to a heat-conducting liquid, and — the threshold value of the mass flow rate set in the dialog box of the block. This threshold value determines the width of the mass flow area within which the density of the liquid is smoothed. The average mass flow rate is defined as

Ports

Conserving

# A — fluid port
thermal liquid

Details

The port through which the thermal liquid can enter and exit the thermal interface.

Program usage name

thermal_liquid_port_a

# B — fluid port
thermal liquid

Details

The port through which the thermal liquid can enter and exit the thermal interface.

Program usage name

thermal_liquid_port_b

# H — thermal regime at the fluid inlet
warmth

Details

A non-directional port used to adjust the thermal mode in a non-directional port connected to a thermal liquid.

Program usage name

thermal_port

Output

# CP — isobaric specific heat capacity of a thermal liquid, kJ/(kg·K)
scalar

Details

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

Data types	`Float64`
Complex numbers support	I don’t

# M — mass flow rate of thermal liquid, kg/s
scalar

Details

The mass flow rate of the thermal liquid in the internal volume for the interface liquid. The output signal is positive when the flow rate is directed from port A to port B, and negative otherwise.

Data types	`Float64`
Complex numbers support	I don’t

Parameters

Pressure Loss

# Mass flow rate vector — the mass flow rate at which it is necessary to specify the pressure drop data
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

An array of mass flow values for which tabular pressure drop data must be specified.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`[0.3, 0.5, 1.0, 1.5, 2.0, 2.5] kg/s`
Program usage name	`mdot_vector`
Evaluatable	Yes

# Pressure drop vector — pressure drop data corresponding to the specified mass flow values
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

An array of pressure drop values from the inlet to the outlet corresponding to the tabular mass flow data.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`[0.003, 0.005, 0.01, 0.025, 0.035, 0.05] MPa`
Program usage name	`delta_p_vector`
Evaluatable	Yes

Details

The temperature at which tabular pressure drop data is set.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_inflow_ref`
Evaluatable	Yes

# Reference inflow pressure — the pressure at which tabular pressure drop data is set
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The pressure at which tabular pressure drop data is set. The block uses this parameter to calculate the third reference parameter, the reference density. The reference value is used to scale the pressure drop tabular data for pressure and temperature values that differ from the nominal conditions.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_inflow_ref`
Evaluatable	Yes

# Mass flow rate threshold for flow reversal — the mass flow rate below which numerical data needs to be smoothed
kg/s | N*s/m | N/(m/s) | lbf/(ft/s) | lbf/(in/s)

Details

The mass flow rate, below which there is a smooth change in the flow direction to prevent discontinuities in the simulation data.

Units	`kg/s` \| `N*s/m` \| `N/(m/s)` \| `lbf/(ft/s)` \| `lbf/(in/s)`
Default value	`0.001 kg/s`
Program usage name	`mdot_threshold`
Evaluatable	Yes

# Thermal Liquid volume — the volume of heat-conducting liquid inside the heat exchanger
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

The volume of heat-conducting liquid in the heat exchanger at any given time. The initial conditions specified in the parameter group are applied to this volume. Effects and Initial Conditions. During the simulation, the volume remains constant.

Units	`l` \| `gal` \| `igal` \| `m^3` \| `cm^3` \| `ft^3` \| `in^3` \| `km^3` \| `mi^3` \| `mm^3` \| `um^3` \| `yd^3` \| `Nm/Pa` \| `Nm/bar` \| `lbfft/psi` \| `ftlbf/psi`
Default value	`0.01 m^3`
Program usage name	`V_liquid`
Evaluatable	Yes

# Cross-sectional area at ports A and B — the cross-sectional area of the flow at the heat-conducting fluid supply ports
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The cross-sectional area of the flow at the heat-conducting fluid supply ports. Ports A and B are assumed to be the same size.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.01 m^2`
Program usage name	`port_area`
Evaluatable	Yes

Effects and Initial Conditions

# Thermal Liquid dynamic compressibility — the ability to simulate the pressure dynamics inside the heat exchanger

Details

The ability to simulate the pressure dynamics inside the heat exchanger. When selecting this parameter, the unit excludes pressure derivatives from the equations of conservation of energy and mass of the components. The pressure inside the heat exchanger is then adjusted to a weighted average of the pressures in the two ports.

Default value	`true (switched on)`
Program usage name	`dynamic_compressibility`
Evaluatable	Yes

Details

The temperature of the internal volume of the heat-conducting liquid at the beginning of the simulation.

Units	`K` \| `degC` \| `degF` \| `degR` \| `deltaK` \| `deltadegC` \| `deltadegF` \| `deltadegR`
Default value	`293.15 K`
Program usage name	`T_start`
Evaluatable	Yes

# Thermal Liquid initial pressure — pressure inside the heat exchanger at the beginning of the simulation
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The pressure of the internal volume of the heat-conducting liquid at the beginning of the simulation.

Units	`Pa` \| `GPa` \| `MPa` \| `atm` \| `bar` \| `kPa` \| `ksi` \| `psi` \| `uPa` \| `kbar`
Default value	`0.101325 MPa`
Program usage name	`p_start`
Evaluatable	Yes