Heat Exchanger Interface (TL)

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The thermal boundary between a thermal liquid and its surroundings.

blockType: EngeeFluids.HeatExchangers.EffectivenessNTU.Interfaces.ThermalLiquid

Path in the library:

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

Description

Block Heat Exchanger Interface (TL) represents a boundary in a thermal liquid network for heat transfer between liquids. The block simulates the pressure drop and temperature change between the inlet and outlet of a thermal liquid and, in combination with the E-NTU Heat Transfer block, simulates the heat flow across the interface between the two liquids.

Mass conservation

The form of the mass conservation equation depends on the dynamic compressibility settings. If Thermal Liquid 1 dynamic compressibility is unchecked, the mass conservation equation will have the following form:

where is the mass flow rate. The subscripts denote ports A and B.

If the Thermal Liquid 1 dynamic compressibility, checkbox is selected, the mass conservation equation will have the following form:

where

- is the pressure of thermal liquid;
- temperature of thermal liquid;
- isobaric thermal expansion coefficient of thermal liquid;
- isothermal modulus of elasticity of thermal liquid;
- mass density of thermal liquid;
- volume of thermal liquid at the heat exchanger boundary.

Conservation of momentum

The momentum conservation at the heat exchanger boundary depends on the dynamic compressibility setting of the fluid. If the check box Thermal Liquid 1 dynamic compressibility, is selected, the momentum conservation depends on the internal pressure at the heat exchanger boundary explicitly. The momentum conservation equation for half of the volume in port A has the form:

The equation of conservation of momentum for half the volume in port B has the form:

where

and are pressures in ports A and B;
- pressure in the internal node;
and - pressure losses between port A and the internal node and between port B and the internal node.

If the checkbox is unchecked Thermal Liquid 1 dynamic compressibility, the momentum conservation is calculated directly between ports A and B:

Calculation of pressure losses

The pressure loss calculation depends on the value of the parameter Pressure loss model. If the parameter Pressure loss model is set to the value of `Pressure loss coefficient`then the pressure loss in the half volume adjacent to port A is:

and the pressure loss in the half volume adjacent to port B is:

where

and are dynamic viscosity of liquid in ports A and B;
- value of parameters Pressure loss coefficient;
- upper limit of Reynolds number for laminar flow;
- lower limit of Reynolds number for turbulent flow;
- hydraulic diameter for pressure loss calculations;
and - fluid density at ports A and B;
- total minimum free flow area.

If the parameters Pressure loss model are set to the value of Correlation for flow inside tubes, the pressure loss in half of the volume adjacent to port A is:

and the pressure loss in the half volume adjacent to port B is:

where

- is the length of the flow path from inlet to outlet;
- length of the pipe for calculation of equivalent losses;
and - Darcy friction coefficients in turbulent regime in ports A and B.

Darcy friction coefficient in half of the volume adjacent to the A port is equal to:

and the Darcy coefficient of friction in the half volume adjacent to port B is:

where is the absolute roughness of the inner surface.

If the parameter Pressure loss model is set to the value of Tabulated data - Darcy friction factor vs. Reynolds number, then the pressure loss in half of the volume adjacent to port A is:

and the pressure loss in the half volume adjacent to port B is:

where

- is the shape coefficient for viscous friction of laminar flow;
and are Darcy friction coefficients in ports A and B. The block obtains friction coefficients from tabular data specified with respect to Reynolds number.

If the parameter Pressure loss model is set to the value of Tabulated data - Euler number vs. Reynolds number, then the pressure loss in half of the volume adjacent to port A is:

and the pressure loss in the half volume adjacent to port B is:

where

- is the Euler number at the upper limit of the Reynolds number for laminar flows;
and are the Euler numbers at ports A and B. The block obtains the Euler numbers from tabular data specified with respect to the Reynolds number.

Energy conservation

The energy conservation at the heat exchanger boundary depends on the dynamic compressibility setting of the fluid. If the checkbox Thermal Liquid 1 dynamic compressibility, is selected, the energy conservation equation is of the form:

where

- is the internal energy of the liquid volume at the heat exchanger boundary;
and - energy fluxes at ports A and B, respectively;
- heat flux through port H, representing the thermal boundary, into the block.

The derivatives of the internal energy are defined as:

where is the specific internal energy of a thermal liquid, or the internal energy contained in a unit mass of that liquid.

If the checkbox Thermal Liquid 1 dynamic compressibility, is not checked, the density of the thermal liquid will be treated as a constant. Then the Volumetric Modulus of Elasticity is effectively infinite and the coefficient of thermal expansion is zero. The pressure and temperature derivatives in the compressible case are not taken into account, and the energy conservation equation is represented in the following form:

where is the total internal energy of incompressible thermal liquid:

Relationships for heat transfer

This block calculates and outputs the value of the heat transfer coefficient between the fluid and the wall. The calculation method depends on the value of the parameters Heat transfer coefficient model.

If the parameter Heat transfer coefficient model is set to the value of Constant heat transfer coefficient, the heat transfer coefficient has a constant value set by the block parameters:

where

- is the heat transfer coefficient between the fluid and the wall;
- the value of parameters Liquid-wall heat transfer coefficient.

For all other parameter values Heat transfer coefficient model, the heat transfer coefficient is defined as the arithmetic mean of the port heat transfer coefficients:

where and are the heat transfer coefficients between liquid and wall in ports A and B.

The heat transfer coefficient in port A is equal to:

and the heat transfer coefficient in port B is:

where

and are Nusselt numbers at ports A and B;
and - thermal conductivities at ports A and B;
- hydraulic diameter for heat transfer calculations.

The hydraulic diameter used in heat transfer calculations is defined as:

where

- is the flow path length used in heat transfer calculations;
- is the total area of the heat transfer surface.

Calculation of Nusselt number

The method of calculating the Nusselt number depends on the value of the parameters Heat transfer coefficient model.

If the parameter Heat transfer coefficient model is set to the value of `Correlation for flow inside tubes`then the Nusselt number at port A will be:

and the Nusselt number at port B:

where

- is the value of parameters Nusselt number for laminar flow heat transfer;
and are the Prandtl numbers at ports A and B.

If for the parameters Heat transfer coefficient model is set to value `Tabulated data - Colburn factor vs. Reynolds number`then the Nusselt number at port A will be:

and the Nusselt number at port B is:

where

and are the Colburn factor at ports A and B. The block obtains the Colburn factor from tabulated data presented as a function of Reynolds number;
and are Reynolds numbers based on hydraulic diameters for heat transfer calculations at ports A and B. These values are defined at port A and B as:

и

If the parameters Heat transfer coefficient model are set to the value of `Tabulated data - Nusselt number vs. Reynolds number and Prandtl number`then the Nusselt number at port A will be:

and the Nusselt number at port B is:

Calculation of hydraulic diameter

The hydraulic diameter used in heat transfer calculations differs from the hydraulic diameter used in pressure loss calculations if the perimeter to be heated and the perimeter experiencing friction do not coincide. For a tube-in-tube heat exchanger with an annular cross-section, the hydraulic diameter for heat transfer calculations is:

and the hydraulic diameter for pressure calculations is:

where

- is the outer diameter of the ring shell;
- is the inner diameter of the ring.

heat exchanger interface tl 1

The difference between the outer and inner diameter, shown in orange, is the thermal liquid. The blue area inside the inner diameter is the liquid that exchanges heat with the thermal liquid.

Ports

Conserving

# A — thermal liquid port
thermal liquid

Details

Thermal liquid inlet port.

Program usage name

thermal_liquid_port_a

# B — thermal liquid port
thermal liquid

Details

Thermal liquid outlet port.

Program usage name

thermal_liquid_port_b

# H — inlet temperatures
`heat

Details

Port related to the inlet temperature of the thermal liquid.

Program usage name

thermal_port

Output

# C — flux heat capacity
scalar

Details

The value of the flow heat capacity of a thermal liquid.

Data types	`Float64`.
Complex numbers support	No

# HC — heat transfer coefficient
scalar

Details

The value of the heat transfer coefficient between a thermal liquid flow and a boundary, given as a scalar.

Data types	`Float64`.
Complex numbers support	No

Parameters

# Minimum free-flow area — cross-sectional area of the hole at the narrowest point
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

The total flow area free of obstructions based on the smallest pipe spacing or corrugation pitch.

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	`min_flow_area`
Evaluatable	Yes

# Hydraulic diameter for pressure loss — diameter or equivalent diameter of the channel
m | cm | ft | in | km | mi | mm | um | yd

Details

The hydraulic diameter of the tubes or channels that make up the heat exchange interface. The hydraulic diameter is the ratio of the cross-sectional area of the flow to the perimeter of the channel.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1 m`
Program usage name	`hydraulic_diameter_for_pressure_loss`
Evaluatable	Yes

# Thermal Liquid volume — total volume of thermal liquid in the channel
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

Total volume of thermal liquid contained in the flow channel.

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

# Laminar flow upper Reynolds number limit — beginning of transition between laminar and turbulent regimes

Details

The Reynolds number value corresponding to the beginning of the transition from laminar to turbulent regime. Above this value, inertial forces begin to dominate and the flow changes from laminar to turbulent. By default, this value corresponds to a round tube with a smooth inner surface.

Default value	`2000.0`
Program usage name	`Re_laminar`
Evaluatable	Yes

# Turbulent flow lower Reynolds number limit — end of transition between laminar and turbulent regimes

Details

The Reynolds number value corresponding to the end of the transition from laminar to turbulent regime. Below this value, viscous forces begin to dominate, resulting in a transition from turbulent to laminar flow. By default, this value corresponds to a round tube with a smooth inner surface.

Default value	`4000.0`
Program usage name	`Re_turbulent`
Evaluatable	Yes

# Pressure loss model — mathematical model for calculating pressure loss due to friction
Pressure loss coefficient | Correlation for flow inside tubes | Tabulated data - Darcy friction factor vs. Reynolds number | Tabulated data - Euler number vs. Reynolds number

Details

Mathematical model for pressure loss due to friction. This parameter determines which expressions to use for the calculation and which block parameters to specify as input.

For details, refer to [Pressure Loss Calculation]. Pressure Loss Calculation for details.

Values	`Pressure loss coefficient` \| `Correlation for flow inside tubes` \| `Tabulated data - Darcy friction factor vs. Reynolds number` \| `Tabulated data - Euler number vs. Reynolds number`
Default value	`Pressure loss coefficient`
Program usage name	`pressure_loss_type`
Evaluatable	No

# Pressure loss coefficient — total loss factor for all flow resistances between ports

Details

Total loss factor for all flow resistances in the channel, including wall friction (major losses) and local resistances due to bends, elbows and other geometry changes (minor losses).

The loss factor is an empirical dimensionless number used to express the pressure loss due to friction. It can be calculated from experimental data or derived from product specifications.

Dependencies

To use this parameter, set the parameters Pressure loss model to . Pressure loss coefficient.

Default value	`0.1`
Program usage name	`pressure_loss_coefficient`
Evaluatable	Yes

# Length of flow path from inlet to outlet — distance travelled from port to port
m | cm | ft | in | km | mi | mm | um | yd

Details

The total distance the flow must travel between ports. In multi-pass shell-and-tube heat exchangers, the total distance is the sum of all the passes of the shell. In tube bundles, corrugated plates and other ducts where the flow is divided into parallel branches, it is the distance travelled per branch. The longer the flow path, the greater the basic pressure loss due to wall friction.

Dependencies

To use this parameter, set the parameters Pressure loss model to the value of Correlation for flow inside tubes or Tabulated data - Darcy friction factor vs. Reynolds number.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`flow_path_length`
Evaluatable	Yes

# Aggregate equivalent length of local resistances — total local pressure loss expressed in length
m | cm | ft | in | km | mi | mm | um | yd

Details

Total local pressure losses expressed in length. The length of the straight duct results in equivalent losses equal to the sum of the existing local resistances of branches, tees and connections. The greater the equivalent length, the higher the pressure losses due to local resistances.

Dependencies

To use this parameter, set the parameter Pressure loss model to . Correlation for flow inside tubes.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`0.1 m`
Program usage name	`flow_path_length_add`
Evaluatable	Yes

# Internal surface absolute roughness — average height of roughnesses on the wall surface that cause friction losses
m | cm | ft | in | km | mi | mm | um | yd

Details

The average height of the roughnesses on the wall surface that result in friction losses. The greater the average height, the rougher the wall and the greater the pressure loss due to viscous friction. The surface roughness value is used to derive the Darcy friction coefficient from the Haaland relationship.

Dependencies

To use this parameter, set the parameter Pressure loss model to the value of Correlation for flow inside tubes.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`15e-6 m`
Program usage name	`roughness`
Evaluatable	Yes

# Reynolds number vector for Darcy friction factor — Reynolds number at each reference point in the Darcy friction coefficient look-up table

Details

A vector of Reynolds numbers at which the Darcy friction coefficient should be determined. The block uses this vector to create the Darcy friction coefficient lookup table.

Dependencies

To use this parameter, set the Pressure loss model parameters to the value of Tabulated data - Darcy friction factor vs. Reynolds number.

Default value	`[400.0, 1000.0, 1500.0, 3e3, 4e3, 6e3, 1e4, 2e4, 4e4, 6e4, 1e5, 1e8]`
Program usage name	`Re_friction_vector`
Evaluatable	Yes

# Darcy friction factor vector — Darcy friction coefficient at each reference point in the Reynolds number look-up table

Details

A vector of Darcy friction coefficients corresponding to the values specified in the parameters Reynolds number vector for Darcy friction factor. The block uses this vector to create a Darcy friction coefficient lookup table.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Darcy friction factor vs. Reynolds number.

Default value	`[0.264, 0.112, 0.071, 0.0417, 0.0387, 0.0268, 0.0250, 0.0232, 0.0226, 0.0220, 0.0214, 0.0214]`
Program usage name	`friction_factor_vector`
Evaluatable	Yes

# Laminar friction constant for Darcy friction factor — pressure loss correction for the flow cross-section under laminar flow conditions

Details

Pressure loss correction for laminar flow. This parameter is called the shape coefficient and can be used to obtain the Darcy friction coefficient for laminar pressure loss calculations. The By default value corresponds to cylindrical pipes.

Some additional shape coefficients for non-circular cross sections can be determined from analytical solutions of the Navier-Stokes equations. A duct with a square cross-section has a shape factor of 56, a duct with a rectangular cross-section with an aspect ratio of 2:1 has a shape factor of 62, and a coaxial pipe has a shape factor of 96. A thin duct between parallel plates also has a shape factor of 96.

Dependencies

To use this parameter, set the parameter Pressure loss model to the value of Correlation for flow inside tubes.

Default value	`64.0`
Program usage name	`shape_factor`
Evaluatable	Yes

# Reynolds number vector for Euler number — Reynolds number at each reference point in the Euler number look-up table

Details

A vector of Reynolds numbers at which the Euler number should be determined. The block uses this vector to create the Euler number lookup table.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Euler number vs. Reynolds number.

Default value	`[50.0, 500.0, 1000.0, 2000.0]`
Program usage name	`Re_vector_Eu`
Evaluatable	Yes

# Euler number vector — Euler number at each reference point in the Reynolds number look-up table

Details

A vector of Euler numbers corresponding to the values specified in the parameters Reynolds number vector for Euler number. The block uses this vector to create the Euler number lookup table.

Dependencies

To use this parameter, set the Pressure loss model parameters to Tabulated data - Euler number vs. Reynolds number.

Default value	`[4.4505, 0.6864, 0.4791, 0.3755]`
Program usage name	`Eu_vector`
Evaluatable	Yes

# Heat transfer coefficient model — mathematical model for heat transfer between the coolant and the wall
Constant heat transfer coefficient | Correlation for flow inside tubes | Tabulated data - Colburn factor vs. Reynolds number | Tabulated data - Nusselt number vs. Reynolds number and Prandtl number

Details

A mathematical model used to calculate the heat flow between fluids in a heat exchanger. You can assume a constant heat transfer coefficient, use an empirical relationship for the flow inside the pipes, or specify tabular data for the Colburn number or Nusselt number.

For more information, see. Calculating the Nusselt number.

Values	`Constant heat transfer coefficient` \| `Correlation for flow inside tubes` \| `Tabulated data - Colburn factor vs. Reynolds number` \| `Tabulated data - Nusselt number vs. Reynolds number and Prandtl number`
Default value	`Constant heat transfer coefficient`
Program usage name	`heat_transfer_type`
Evaluatable	No

# Liquid-wall heat transfer coefficient — heat transfer coefficient by convection between the coolant and the wall
W/(m^2*K) | Btu_IT/(hr*ft^2*deltadegR)

Details

Heat transfer coefficient for convection between the heat transfer medium and the wall.

Dependencies

To use this parameter, set the parameters Heat transfer coefficient model to . Constant heat transfer coefficient.

Units	`W/(m^2K)` \| `Btu_IT/(hrft^2*deltadegR)`
Default value	`100.0 W/(m^2*K)`
Program usage name	`alpha_const`
Evaluatable	Yes

# Heat transfer surface area — effective surface area used in the heat transfer between the heat transfer medium and the wall
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Effective surface area used in heat transfer between heat transfer fluids in a heat exchanger.

Units	`m^2` \| `cm^2` \| `ft^2` \| `in^2` \| `km^2` \| `mi^2` \| `mm^2` \| `um^2` \| `yd^2`
Default value	`0.4 m^2`
Program usage name	`heat_transfer_area`
Evaluatable	Yes

# Nusselt number for laminar flow heat transfer — constant value of Nusselt number for laminar flow

Details

Constant value of Nusselt number for laminar flows. This parameter allows the calculation of convective heat fluxes in laminar flows. The Nusselt number value depends on the geometry of the component. The value by default corresponds to a cylindrical pipe.

Dependencies

To use this parameter, set the parameters Heat transfer coefficient model to . Correlation for flow inside tubes.

Default value	`3.66`
Program usage name	`Nu_laminar`
Evaluatable	Yes

# Reynolds number vector for Colburn factor — Reynolds number at each reference point of the Colburn factor look-up table

Details

A vector of Reynolds numbers at which the Colburn factor should be determined. The block uses this vector to create the Colburn factor lookup table. The number of values in this vector must be equal to the dimensionality of the parameter Colburn factor vector to calculate the table reference points.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameter to Tabulated data - Colburn factor vs. Reynolds number.

Default value	`[100.0, 150.0, 1000.0]`
Program usage name	`Re_vector_colburn`
Evaluatable	Yes

# Colburn factor vector — Colburn factor at each reference point in the Reynolds number look-up table

Details

A vector of Colburn factors corresponding to the values specified in the parameters Reynolds number vector for Colburn factor. The block uses this vector to create the Colburn factor lookup table.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameters to the value of Tabulated data - Colburn factor vs. Reynolds number.

Default value	`[0.019, 0.013, 0.002]`
Program usage name	`colburn_factor_vector`
Evaluatable	Yes

# Reynolds number vector for Nusselt number — Reynolds number at each reference point in the Nusselt number look-up table

Details

A vector of Reynolds numbers at which the Nusselt number is to be determined. The block uses this vector to create the Nusselt number lookup table.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameters to the value of Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[100.0, 150.0, 1000.0]`
Program usage name	`Re_vector_Nu`
Evaluatable	Yes

# Prandtl number vector for Nusselt number — Prandtl number at each reference point of the Nusselt number look-up table

Details

A vector of Prandtl numbers at which the Nusselt number should be determined. The block uses this vector to create the Nusselt number lookup table.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameters to Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[1.0, 10.0]`
Program usage name	`Pr_vector_Nu`
Evaluatable	Yes

# Nusselt number table, Nu(Re,Pr) — Nusselt number at each reference point of the Reynolds-Prandtl number search table

Details

A matrix of Nusselt numbers corresponding to the values specified in the parameters Reynolds number vector for Nusselt number and Prandtl number vector for Nusselt number. The block uses this matrix to create the Nusselt number lookup table.

Dependencies

To use this parameter, set the Heat transfer coefficient model parameters to the value of Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Default value	`[3.72 4.21; 3.75 4.44; 4.21 7.15]`
Program usage name	`Nu_matrix`
Evaluatable	Yes

# Length of flow path for heat transfer — characteristic length travelled during heat transfer between the heat transfer medium and the wall
m | cm | ft | in | km | mi | mm | um | yd

Details

Characteristic length for heat transfer between the heat transfer medium and the wall.

Dependencies

To use this parameter, set the parameters Heat transfer coefficient model to the value of Tabulated data - Colburn factor vs. Reynolds number or Tabulated data - Nusselt number vs. Reynolds number and Prandtl number.

Units	`m` \| `cm` \| `ft` \| `in` \| `km` \| `mi` \| `mm` \| `um` \| `yd`
Default value	`1.0 m`
Program usage name	`length_for_heat_transfer`
Evaluatable	Yes

Effects and Initial Conditions

# Thermal Liquid 1 dynamic compressibility — compressibility of the fluid in the heat exchanger

Details

Option for modelling pressure changes inside the heat exchanger. If this box is unchecked, pressure derivatives are not considered in the energy and mass conservation equations. The pressure inside the heat exchanger is defined as the average of the two port pressures.

Default value	`true (switched on)`
Program usage name	`dynamic_compressibility`
Evaluatable	No

Details

The temperature of the thermal 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 — initial pressure of thermal liquid
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

Thermal liquid pressure 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