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Heat Exchanger Interface (TL)

Thermal interface between a thermal liquid and its surroundings

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  • Simscape / Fluids / Fluid Network Interfaces / Heat Exchangers / Fundamental Components

  • Heat Exchanger Interface (TL) block

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

m˙A+m˙B=0,

where:

  • m˙A and m˙B 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

m˙A+m˙B=(dpdt1βdTdtα)ρV,

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

pAp=ΔpLoss,A,

while in the half volume between port B and the internal interface node it is computed as

pBp=ΔpLoss,B,

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

pApB=ΔpLoss,AΔpLoss,B.

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

ΔpLoss,A={m˙AμA(CP)LossReL14Dh,pρASMin,ReAReL(CP)Lossm˙A|m˙A|4ρASMin2,ReAReT,

while in the half volume adjacent to port B it is

ΔpLoss,B={m˙BμB(CP)LossReL14Dh,pρBSMin,ReBReL(CP)Lossm˙B|m˙B|4ρBSMin2,ReBReT,

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

ΔpLoss,A={m˙AμAλ(Lpress+Ladd)4Dh,pρASMin,ReAReLfT,A(Lpress+Ladd)4Dh,pm˙A|m˙A|ρASMin2,ReAReT,

while in the half volume adjacent to port B it is

ΔpLoss,B={m˙BμBλ(Lpress+Ladd)4Dh,pρBSMin,ReBReLfT,B(Lpress+Ladd)4Dh,pm˙B|m˙B|ρBSMin2,ReBReT,

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

fT,A=1[1.8log10(6.9ReA+r3.7Dh,p)1.11]2,

while in the half volume adjacent to port B it is

fT,B=1[1.8log10(6.9ReB+r3.7Dh,p)1.11]2,

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

ΔpLoss,A={m˙AμAλLpress4Dh,p2ρASMin,ReAReLf(ReA)Lpress4Dh,pm˙A|m˙A|ρASMin2,ReAReT,

while in the half volume adjacent to port B it is

ΔpLoss,B={m˙BμBλLpress4Dh,p2ρBSMin,ReBReLf(ReB)Lpress4Dh,pm˙B|m˙B|ρBSMin2,ReBReT,

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

ΔpLoss,A={m˙AμAEu(ReL)ReL14Dh,pρASMin,ReAReLEu(ReA)m˙A|m˙A|4ρASMin2,ReAReT,

while in the half volume adjacent to port B it is

ΔpLoss,B={m˙BμBEu(ReL)ReL14Dh,pρBSMin,ReBReLEu(ReB)m˙B|m˙B|4ρBSMin2,ReBReT,

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

dpdtdUdp+dTdtdUdT=ϕA+ϕB+QH,

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

dUdp=[1β(ρu+p)Tα]V

and

dUdT=[cpα(u+pρ)]ρV,

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

dEdt=ϕA+ϕB+QH,

where E is the total internal energy of the incompressible thermal liquid, or

E=ρuV.

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,

hLW=hConst,

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:

hLW=hA+hB2,

where:

  • hA and hB are the liquid-wall heat transfer coefficients at ports A and B.

The heat transfer coefficient at port A is

hA=NuAkADh,heat,

while at port B it is

hB=NuBkBDh,heat,

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

Dh,heat=4SMinLheatSheat,

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

NuA={NuL,ReAReL(fT,A8)(ReA1000)PrA1+12.7(fT,A8)1/2(PrB2/31),ReAReT,

while at port B it is

NuB={NuL,ReBReL(fT,B8)(ReB1000)PrB1+12.7(fT,B8)1/2(PrB2/31),ReBReT,

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

NuA=j(ReA,heat)ReA,heatPrA1/3,

while at port B it is

NuB=j(ReB,heat)ReB,heatPrB1/3,

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

    ReA,heat=m˙ADh,heatSMinμA,

    and at port B as

    ReB=m˙BDh,heatSMinμB.

If the heat transfer specification is set to Tabulated data — Nusselt number vs. Reynolds number & Prandtl number, the Nusselt number at port A is

NuA=Nu(ReA,heat,PrA),

while at port B it is

NuB=Nu(ReB,heat,PrB).

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

Dh,heat=4(π/4)(Do2Di2)πDi=Do2Di2Di,

while the hydraulic diameter for pressure calculations is

Dh,p=4(π/4)(Do2Di2)π(Di+Do)=DoDi,

where:

  • Do is the outer annulus diameter.

  • Di is the inner annulus diameter.

Annulus Schematic

The difference between the outer diameter and the inner diameter depicted in orange represents the thermal liquid. The blue region within the inner diameter is the fluid that exchanges heat with the thermal liquid.

Ports

Output

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Physical signal output port for the thermal capacity rate of the thermal liquid

Physical signal output port for the heat transfer coefficient between the thermal liquid and the interface wall

Conserving

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Thermal liquid conserving port representing the thermal liquid inlet

Thermal liquid conserving port representing the thermal liquid outlet

Thermal conserving port associated with the thermal liquid inlet temperature

Parameters

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Aggregate flow area free of obstacles based on the smallest tube spacing or corrugation pitch.

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.

Total volume of the fluid contained in the thermal liquid flow channel.

Start of the transition from the laminar regime to the turbulent regime. Above this number, inertial forces become increasingly dominant. The default value is given for circular pipes and tubes with smooth surfaces.

End of the transition from the laminar regime to the turbulent regime. Below this number, viscous forces become increasingly dominant.

Mathematical model for pressure loss due to friction. This setting determines which expressions to use for calculation and which block parameters to specify as input. See the Heat Exchanger Interface (TL) blocks for the calculations by parameterization.

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

The loss coefficient is an empirical, dimensionless number used to express the pressure losses due to friction. It can be calculated from experimental data or obtained from product data sheets.

Dependencies

To enable this parameter, set Pressure loss parameterization to Constant loss coefficient.

Total distance the flow must travel between the ports. In multi-pass shell-and-tube exchangers, the total distance is the sum over all shell passes. In tube bundles, corrugated plates, and other channels where the flow is split into parallel branches, it is the distance covered in a single branch. The longer the flow path, the steeper the major pressure loss due to friction at the wall.

Dependencies

To enable this parameter, set Pressure loss parameterization to Correlations for tubes or Tabulated data - Darcy friction factor vs Reynolds number.

Aggregate minor pressure loss, expressed as a length. The length of a straight channel results in equivalent losses to the sum of existing local resistances from elbows, tees, and unions. The larger the equivalent length, the steeper the minor pressure loss due to the local resistances.

Dependencies

To enable this parameter, set Pressure loss parameterization to Correlations for tubes.

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.

Dependencies

To enable this parameter, set Pressure loss parameterization to Correlations for tubes.

Pressure loss correction for laminar flow. This parameter is referred to as the shape factor, and can be used to derive the Darcy friction factor for pressure loss calculations in the laminar regime. The default value is for cylindrical pipes and tubes.

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

Dependencies

To enable this parameter, set Pressure loss parameterization to Correlations for tubes.

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.

Dependencies

To enable this parameter, set Pressure loss parameterization to Tabulated data - Darcy friction factor vs. Reynolds number.

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.

Dependencies

To enable this parameter, set Pressure loss parameterization to Tabulated data - Darcy friction factor vs. Reynolds number.

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.

Dependencies

To enable this parameter, set Pressure loss parameterization to Tabulated data - Euler number vs. Reynolds number.

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.

Dependencies

To enable this parameter, set Pressure loss parameterization to Tabulated data - Euler number vs. Reynolds number.

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.

Heat transfer coefficient between the thermal liquid and the heat-transfer surface.

Dependencies

To enable this parameter, set Heat transfer parameterization to Constant heat transfer coefficient.

Aggregate surface area available for heat transfer between the heat exchanger fluids.

Distance traversed by the fluid along which heat exchange takes place.

Dependencies

To enable this parameter, set Heat transfer parameterization to Tabulated data - Colburn factor vs. Reynolds number or Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

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.

Dependencies

To enable this parameter, set Heat transfer parameterization to Correlations for tubes.

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. The number of values in this vector must be equal to the size of the Colburn factor vector parameter to calculate tabulated breakpoints.

Dependencies

To enable this parameter, set Heat transfer parameterization to Tabulated data - Colburn factor vs. Reynolds number.

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.

Dependencies

To enable this parameter, set Heat transfer parameterization to Tabulated data - Colburn factor vs. Reynolds number.

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.

Dependencies

To enable this parameter, set Heat transfer parameterization to Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

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.

Dependencies

To enable this parameter, set Heat transfer parameterization to Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

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.

Dependencies

To enable this parameter, set Heat transfer parameterization to Tabulated data - Nusselt number vs. Reynolds number & Prandtl number.

Empirical parameter used to quantify the increased thermal resistance due to dirt deposits on the heat transfer surface.

Effects and Initial Conditions

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.

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

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 R2016a