Heat Exchanger Interface (TL)
Thermal interface between a thermal liquid and its surroundings
Library
Fluid Network Interfaces/Heat Exchangers/Fundamental Components
Description
The Heat Exchanger Interface (TL) block models the pressure drop and temperature change between the thermal liquid inlet and outlet of a thermal interface. Combine with the E-NTU Heat Transfer block to model the heat transfer rate across the interface between two fluids.
Mass Balance
The form of the mass balance equation depends on the dynamic
compressibility setting. If the Fluid dynamic compressibility parameter
is set to Off
, the mass balance equation
is
where:
and are the mass flow rates into the interface through ports A and B.
If the Fluid dynamic compressibility parameter
is set to On
, the mass balance equation
is
where:
p is the pressure of the thermal liquid volume.
T is the temperature of the thermal liquid volume.
α is the isobaric thermal expansion coefficient of the thermal liquid volume.
β is the isothermal bulk modulus of the thermal liquid volume.
ρ is the mass density of the thermal liquid volume.
V is the volume of thermal liquid in the heat exchanger interface.
Momentum Balance
The momentum balance in the heat exchanger interface depends
on the fluid dynamic compressibility setting. If the Fluid dynamic compressibility parameter is
set to On
, the momentum balance factors
in the internal pressure of the heat exchanger interface explicitly.
The momentum balance in the half volume between port A and the internal
interface node is computed as
while in the half volume between port B and the internal interface node it is computed as
where:
pA and pB are the pressures at ports A and B.
p is the pressure in the internal node of the interface volume.
ΔpLoss,A and ΔpLoss,B are the pressure losses between port A and the internal interface node and between port B and the internal interface node.
If the Fluid dynamic compressibility parameter
is set to Off
, the momentum balance in
the interface volume is computed directly between ports A and B as
Pressure Loss Calculations
The exact form of the pressure loss terms depends on the Pressure
loss parameterization setting in the block dialog box.
If the pressure loss parameterization is set to Constant
loss coefficient
, the pressure loss in the half volume
adjacent to port A is
while in the half volume adjacent to port B it is
where:
μA and μB are the fluid dynamic viscosities at ports A and B.
CPLoss is the Pressure loss coefficient parameter specified in the block dialog box.
ReL is the Reynolds number upper bound for the laminar flow regime.
ReT is the Reynolds number lower bound for the turbulent flow regime.
Dh,p is the hydraulic diameter for pressure loss calculations.
ρA and ρB are the fluid mass densities at ports A and B.
SMin is the total minimum free-flow area.
If the pressure loss parameterization is set to Correlations
for tubes
, the pressure loss in the half volume adjacent
to port A is
while in the half volume adjacent to port B it is
where:
Lpress is the flow path length from inlet to outlet.
Ladd is the aggregate equivalent length of local resistances.
fT,A and fT,B are the turbulent-regime Darcy friction factors at ports A and B.
The Darcy friction factor in the half volume adjacent to port A is
while in the half volume adjacent to port B it is
where:
r is the internal surface absolute roughness.
If the pressure loss parameterization is set to Tabulated
data — Darcy friction factor vs. Reynolds number
,
the pressure loss in the half volume adjacent to port A is
while in the half volume adjacent to port B it is
where:
λ is the shape factor for laminar flow viscous friction.
f(ReA) and f(ReB) are the Darcy friction factors at ports A and B. The block obtains the friction factors from tabulated data specified relative to the Reynolds number.
If the pressure loss parameterization is set to Tabulated data — Euler
number vs. Reynolds number
, the pressure loss in the half volume
adjacent to port A is
while in the half volume adjacent to port B it is
where:
Eu(ReL) is the Euler number at the Reynolds number upper bound for laminar flows.
Eu(ReA) and Eu(ReB) are the Euler numbers at ports A and B. The block obtains the Euler numbers from tabulated data specified relative to the Reynolds number.
Energy Balance
The energy balance in the heat exchanger interface depends on
the fluid dynamic compressibility setting. If the Fluid
dynamic compressibility parameter is set to On
,
the energy balance is
where:
U is the internal energy contained in the volume of the heat exchanger interface.
ΦA and ΦB are the energy flow rates through ports A and B into the volume of the heat exchanger interface.
QH is the heat flow rate through port H, representing the interface wall, into the volume of the heat exchange interface.
The internal energy derivatives are defined as
and
where u is the specific internal energy of the thermal liquid, or the internal energy contained in a unit mass of the same.
If the Fluid dynamic compressibility parameter is set to
Off
, the thermal liquid density is treated as a
constant. The bulk modulus is then effectively infinite and the thermal expansion
coefficient zero. The pressure and temperature derivatives of the compressible case
vanish and the energy balance is restated as
where E is the total internal energy of the incompressible thermal liquid, or
Heat Transfer Correlations
The block calculates and outputs the liquid-wall heat transfer
coefficient value. The calculation depends on the Heat transfer
coefficient specification setting in the block dialog box.
If the heat transfer coefficient specification is Constant
heat transfer coefficient
, the heat transfer coefficient
is simply the constant value specified in the block dialog box,
where:
hL-W is the liquid-wall heat transfer coefficient.
hConst is the Liquid-wall heat transfer coefficient value specified in the block dialog box.
For all other heat transfer coefficient parameterizations, the heat transfer coefficient is defined as the arithmetic average of the port heat transfer coefficients:
where:
hA and hB are the liquid-wall heat transfer coefficients at ports A and B.
The heat transfer coefficient at port A is
while at port B it is
where:
NuA and NuB are the Nusselt numbers at ports A and B.
kA and kB are the thermal conductivities at ports A and B.
Dh,heat is the hydraulic diameter for heat transfer calculations.
The hydraulic diameter used in heat transfer calculations is defined as
where:
Lheat is the flow path length used in heat transfer calculations.
Sheat is the total heat transfer surface area.
Nusselt Number Calculations
The Nusselt number calculation depends on the Heat
transfer coefficient specification setting in the block
dialog box. If the heat transfer specification is set to Correlations
for tubes
, the Nusselt number at port A is
while at port B it is
where:
NuL is the Nusselt number for laminar flow heat transfer value specified in the block dialog box.
PrA and PrB are the Prandtl numbers at ports A and B.
If the heat transfer specification is set to Tabulated
data — Colburn data vs. Reynolds number
, the
Nusselt number at port A is
while at port B it is
where:
j(ReA,heat) and j(ReB,heat) are the Colburn numbers at ports A and B. The block obtains the Colburn numbers from tabulated data provided as a function of the Reynolds number.
ReA,heat and ReB,heat are the Reynolds numbers based on the hydraulic diameters for heat transfer calculations at ports A and B. This parameter is defined at port A as
and at port B as
If the heat transfer specification is set to Tabulated
data — Nusselt number vs. Reynolds number & Prandtl number
,
the Nusselt number at port A is
while at port B it is
Hydraulic Diameter Calculations
The hydraulic diameter used in heat transfer calculations can differ from the hydraulic diameter employed in pressure loss calculations, and are different if the heated and friction perimeters are not the same. For a concentric pipe heat exchanger with an annular cross-section, the hydraulic diameter for heat transfer calculations is
while the hydraulic diameter for pressure calculations is
where:
Do is the outer annulus diameter.
Di is the inner annulus diameter.
Annulus Schematic
Parameters
Parameters Tab
- Minimum free-flow area
Aggregate flow area free of obstacles based on the smallest tube spacing or corrugation pitch. The default value is
0.01
m^2.- Hydraulic diameter for pressure loss
Hydraulic diameter of the tubes or channels comprising the heat exchange interface. The hydraulic diameter is the ratio of the flow cross-sectional area to the channel perimeter . The default value is
0.1
m.- Laminar flow upper Reynolds number limit
Reynolds number corresponding to the upper bound of the laminar flow regime. The flow transitions to turbulent above this value. The default value is
2000
.- Turbulent flow lower Reynolds number limit
Reynolds number corresponding to the lower bound of the turbulent flow regime. The flow transitions to laminar below this value. The default value is
4000
.- Pressure loss parameterization
Parameterization used to compute the pressure loss between the inlet and outlet. You can assume a constant loss coefficient, use empirical correlations for tubes, or specify tabulated data for the Darcy friction factor or the Euler number. The default setting is
Constant loss coefficient
.- Pressure loss coefficient
Dimensionless number used to compute the pressure loss between the inlet and outlet. The pressure loss coefficient is assumed constant and the same for direct and reverse flows. This parameter is visible only if the Pressure loss parameterization parameter is set to
Constant loss coefficient
. The default value is.1
.- Length of flow path from inlet to outlet
Distance traversed by the fluid from inlet to outlet. This parameter is visible only if the Pressure loss parameterization parameter is set to
Correlations for tubes
orTabulated data — Darcy friction factor vs. Reynolds number
. The default value is1
m.- Aggregate equivalent length of local resistances
Pressure loss due to local resistances such as bends, inlets, and fittings, expressed as the equivalent length of those resistances. This parameter is visible only if the Pressure loss parameterization parameter is set to
Correlations for tubes
. The default value is0.1
m.- Internal surface absolute roughness
Average height of all surface defects on the internal surface of the pipe. The surface roughness enables the calculation of the friction factor in the turbulent flow regime. This parameter is visible only if the Pressure loss parameterization parameter is set to
Correlations for tubes
. The default value is15e-6
m.- Shape factor for laminar flow viscous friction
Proportionality constant between convective and conductive heat transfer in the laminar regime. The shape factor encodes the effects of component geometry on the laminar friction losses. This parameter is visible only if the Pressure loss parameterization parameter is set to
Correlations for tubes
. The default value is64
.- Reynolds number vector for Darcy friction factor
M-element vector of Reynolds numbers at which to specify the Darcy friction factor. The block uses this vector to create a lookup table for the Darcy friction factor. This parameter is visible only if the Pressure loss parameterization parameter is set to
Tabulated data — Darcy friction factor vs. Reynolds number
. The default vector is a 12–element vector ranging in value from400
to1e8
.- Darcy friction factor vector
M-element vector of Darcy friction factors corresponding to the values specified in the Reynolds number vector for Darcy friction factor parameter. The block uses this vector to create a lookup table for the Darcy friction factor. This parameter is visible only if the Pressure loss parameterization parameter is set to
Tabulated data — Darcy friction factor vs. Reynolds number
. The default vector is a 12-element vector ranging in value from0.0214
to0.2640
.- Reynolds number vector for Euler number
M-element vector of Reynolds numbers at which to specify the Euler number. The block uses this vector to create a lookup table for the Euler number. This parameter is visible only if the Pressure loss parameterization parameter is set to
Tabulated data — Euler number vs. Reynolds number
.- Euler number vector
M-element vector of Euler numbers corresponding to the values specified in the Reynolds number vector for Euler number parameter. The block uses this vector to create a lookup table for the Euler number. This parameter is visible only if the Pressure loss parameterization parameter is set to
Tabulated data — Euler number vs. Reynolds number
.- Heat transfer parameterization
Parameterization used to compute the heat transfer rate between the heat exchanger fluids. You can assume a constant loss coefficient, use empirical correlations for tubes, or specify tabulated data for the Colburn or Nusselt number. The default setting is
Constant loss coefficient
.- Heat transfer surface area
Aggregate surface area available for heat transfer between the heat exchanger fluids. This parameter is visible only when the Heat transfer parameterization parameter is set to
Correlation for tubes
,Tabulated data — Colburn factor vs. Reynolds number
, orTabulated data — Nusselt number vs. Reynolds number & Prandtl number
. The default value is0.4
m^2.- Liquid-wall heat transfer coefficient
Heat transfer coefficient between the thermal liquid and the heat-transfer surface. This parameter is visible only when the Heat transfer parameterization parameter is set to
Constant heat transfer coefficient
. The default value is100
.- Length of flow path for heat transfer
Distance traversed by the fluid along which heat exchange takes place. This parameter is visible only when the Heat transfer parameterization parameter is set to
Correlation for tubes
,Tabulated data — Colburn factor vs. Reynolds number
, orTabulated data — Nusselt number vs. Reynolds number & Prandtl number
. The default value is1
m.- Nusselt number for laminar flow heat transfer
Proportionality constant between convective and conductive heat transfer in the laminar regime. This parameter enables the calculation of convective heat transfer rates in laminar flows. The appropriate value to use depends on component geometry. This parameter is visible only when the Heat transfer parameterization parameter is set to
Correlation for tubes
. The default value is3.66
.- Reynolds number vector for Colburn factor
M-element vector of Reynolds numbers at which to specify the Colburn factor. The block uses this vector to create a lookup table for the Colburn number. This parameter is visible only when the Heat transfer parameterization parameter is set to
Tabulated data — Colburn factor vs. Reynolds number
. The default vector is[100.0, 150.0, 1000.0]
.- Colburn factor vector
M-element vector of Colburn factors corresponding to the values specified in the Reynolds number vector for Colburn number parameter. The block uses this vector to create a lookup table for the Colburn factor. This parameter is visible only when the Heat transfer parameterization parameter is set to
Tabulated data — Colburn factor vs. Reynolds number
. The default vector is[0.019, 0.013, 0.002]
.- Reynolds number vector for Nusselt number
M-element vector of Reynolds numbers at which to specify the Nusselt number. The block uses this vector to create a lookup table for the Nusselt number. This parameter is visible only when the Heat transfer parameterization parameter is set to
Tabulated data — Nusselt number vs. Reynolds number & Prandtl number
. The default vector is[100.0, 150.0, 1000.0]
.- Prandtl number vector for Nusselt number
N-element vector of Prandtl numbers at which to specify the Nusselt number. The block uses this vector to create a lookup table for the Nusselt number. This parameter is visible only when the Heat transfer parameterization parameter is set to
Tabulated data — Nusselt number vs. Reynolds number & Prandtl number
. The default vector is [1.0, 10.0].- Nusselt number table, Nu(Re,Pr)
M-by-N matrix of Nusselt numbers corresponding to the values specified in the Reynolds number vector for Nusselt number and Prandtl number vector for Nusselt number parameters. The block uses this vector to create a lookup table for the Nusselt factor. This parameter is visible only when the Heat transfer parameterization parameter is set to
Tabulated data — Nusselt number vs. Reynolds number & Prandtl number
. The default matrix is[3.72, 4.21; 3.75, 4.44; 4.21, 7.15]
.- Fouling factor
Empirical parameter used to quantify the increased thermal resistance due to dirt deposits on the heat transfer surface. The default value is
1e-4
m^2*K/W.
Effects and Initial Conditions
- Thermal Liquid dynamic compressibility
Option to model the pressure dynamics inside the heat exchanger. Setting this parameter to
Off
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 of the internal volume of thermal liquid at the start of simulation.
- Thermal Liquid initial pressure
Pressure of the internal volume of thermal liquid at the start of simulation.
Ports
A — Thermal liquid conserving port representing the thermal liquid inlet
B — Thermal liquid conserving port representing the thermal liquid outlet
C — Physical signal output port for the thermal capacity rate of the thermal liquid
H — Thermal conserving port associated with the thermal liquid inlet temperature
HC — Physical signal output port for the heat transfer coefficient between the thermal liquid and the interface wall