Documentation

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

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|ρASMin2,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|ρBSMin2,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+ϕH,

where:

  • u is the specific internal energy in the internal interface volume.

  • ΦA and ΦB are the energy flow rates into the heat exchanger interface through ports A and B.

  • ΦH is the heat flow rate into the thermal liquid in the internal interface volume.

The specific internal energy derivative terms are

dudp=[1β(ρu+p)Tα]V

and

dudT=[cpα(u+pρ)]ρV.

If the Fluid dynamic compressibility parameter is set to Off, the energy balance is

dedt=ϕA+ϕB+Q,

where e is the total internal energy of the thermal liquid volume:

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 that used in pressure loss calculations. The two parameters are different if the heated and friction perimeters are different also. 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

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.

This parameter is visible only if the Pressure loss parameterization parameter is set to Correlations for tubes, Tabulated data — Darcy friction factor vs. Reynolds number, or Tabulated data — Euler number vs. Reynolds number.

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 or Tabulated data — Darcy friction factor vs. Reynolds number. The default value is 1 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 is 0.1 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 is 15e-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 is 64.

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 from 400 to 1e8.

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 from 0.0214 to 0.2640.

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, or Tabulated data — Nusselt number vs. Reynolds number & Prandtl number. The default value is 0.4 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 is 100.

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, or Tabulated data — Nusselt number vs. Reynolds number & Prandtl number. The default value is 1 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 is 3.66.

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

Introduced in R2016a

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