cfx12_10_heattransfer

7/28/2019 CFX12_10_HeatTransfer

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Heat Transfer

Training Manual

Chapter 10

Heat Transfer

10-1ANSYS, Inc. Proprietary 2009 ANSYS, Inc. All rights reserved. April 28, 2009Inventory #002598


Introduction to CFX


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Heat Transfer

Training ManualGoverning Equations

Continuity

Momentum

Conservation Equations


Energy

where


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Heat Transfer

Training Manual

Heat transfer in a fluid domain is governed by the EnergyTransport Equation:

SourcesViscous workConvectionTransient Conduction

Governing Equations

Etottot

SUThUt

p

t

h

++=+

)()()(

)(


None: Energy Transport Equation not solved

Isothermal: The Energy Transport Equation is not solved but a temperature isrequired to evaluated fluid properties (e.g. when using an Ideal Gas)

Thermal Energy: An Energy Transport Equation is solved which neglects variabledensity effects. It is suitable for low speed liquid flow with constant specific heats.An optional viscous dissipation term can be included if viscous heating is significant.

Total Energy: This models the transport of enthalpy and includes kinetic energyeffects. It should be used for gas flows where the Mach number exceeds 0.2, and

high speed liquid flows where viscous heating effects arise in the boundary layer,where kinetic energy effects become significant.


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Heat Transfer

Training ManualGoverning Equations For multicomponent flows, reacting flows and radiation modeling

additional terms are included in the energy equation

Heat transfer in a solid domain is modeled using the followingconduction equation


SourceTransient Conduction


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Heat Transfer

Training ManualSelecting a Heat Transfer Model The Heat Transfer model is selected

on the Domain > Fluid Models panel

Enable the Viscous Workterm(Total Energy), or ViscousDissipationterm (Thermal Energy),


if viscous shear in the fluid is large

(e.g. lubrication or high speedcompressible flows)

Enable radiation model / submodels

if radiative heat transfer issignificant


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Heat Transfer

Training Manual

Radiation effects should be accounted for whenis significant compared to

convective and conductive heat transfer rates

To account for radiation, Radiative IntensityTransport Equations (RTEs) are solved

Local absorption by fluid and at boundaries couplesthese RTEs with the energy equation

Radiation

)(4

min

4

maxrad TTQ =


a at on ntens ty s rect ona y anspatially dependent

Transport mechanisms for radiation intensity: Local absorption

Out-scattering (scattering away fromthe direction)

Local emission

In-scattering (scattering into the direction)


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Heat Transfer

Training Manual

Several radiation models are available which provide approximate solutions

to the RTE

1) Rosseland Model (Diffusion Approximation Model)

2) P-1 Model (Gibbs Model/Spherical Harmonics Model)

3) Discrete Transfer Model (DTM) (Shah Model)

Radiation Models


Each radiation model has its assumptions, limitations, and benefits

on e ar o o e (not available in the ANSYS CFD-Flo product)


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Heat Transfer

Training ManualChoosing a Radiation Model The optical thickness should be determined before choosing a

radiation model

Optically thin means that the fluid is transparent to the radiation at

wavelengths where the heat transfer occurs The radiation only interacts with the boundaries of the domain

Optically thick/dense means that the fluid absorbs and re-emits theradiation


For optically thick media the P1 model is a good choice Many combustion simulations fall into this category since combustion

gases tend to absorb radiation

The P1 models gives reasonable accuracy without too muchcomputational effort


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Heat Transfer

Training ManualChoosing a Radiation Model For optically thin media the Monte Carlo or Discrete Transfer models

may be used

DTM can be less accurate in models with long/thin geometries

Monte Carlo uses the most computational resources, followed by DTM

Both models can be used in optically thick media, but the P1 model usesfar less computational resources


Available for Monte Carlo and DTM

Neglects the influence of the fluid on the radiation field (only boundariesparticipate)

Can significantly reduce the solution time

Radiation in Solid Domains

In transparent or semi-transparent solid domains (e.g. glass) only theMonte Carlo model can be used

There is no radiation in opaque solid domains


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Heat Transfer

Training Manual

Inlet Static Temperature

Total Temperature

Total Enthalpy

Outlet No details (except Radiation, see below)

Opening Opening Temperature

Opening Static Temperature

Heat Transfer Boundary Conditions

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April 28, 2009Inventory #002598

Wall Adiabatic

Fixed Temperature

Heat Flux

Heat Transfer Coefficient

Radiation Quantities

Local Temperature (Inlet/Outlet/Opening)

External Blackbody Temperature(Inlet/Outlet/Opening)

Opaque

Specify Emissivity and Diffuse Fraction


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Heat Transfer

Training ManualDomain Interfaces GGI connections are

recommended for Fluid-Solid andSolid-Solid interfaces

If radiation is modelled in onedomain and not the other, setEmissivity and Diffuse Fraction



radiation Set these on the boundary

condition associated with the

domain interface


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Heat Transfer

Training ManualThin Wall Modeling Using solid domains to model heat transfer through thin solids can present

meshing problems

The thickness of the material must be resolved by the mesh

Domain interfaces can be used to model a thin material Normal conduction only; neglects any in-plane conduction

Example: to model a baffle with heattransfer through the thickness



Create a Fluid-Fluid Domain Interface

On the Additional Interface Modelstab setMass and Momentumto No Slip Wall

This makes the interface a wall rather thanan interface that fluid can pass through

Enable the Heat Transfertoggle and pickthe Thin Material option

Specify a Material and Thickness

Other domain interface types (Fluid-Solidetc) can use the Thin Material option torepresent coatings etc.


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Heat Transfer

Training ManualThermal Contact Resistance

A Thermal Contact Resistance can bespecified using the same approach

as Thin Wall modeling Just select the Thermal Contact

Resistance option instead of the ThinMaterial option




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Heat Transfer

Training ManualNatural Convection Natural convection occurs

when temperature differences inthe fluid result in densityvariations

This is one-type of buoyancydriven flow



gravity acting on the densityvariations

As discussed in the Domains lecture, a source termSM,buoy= (ref) g is added to the momentum equations

The density difference (ref) is evaluated using either the FullBuoyancy model or the Boussinesq model

Depending on the physics the model is automatically chosen


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Heat Transfer

Training ManualSolution Notes When solving heat transfer

problems, make sure that you have

allowed sufficient solution time forheat imbalances in all domains to

become very small, particularlywhen Solid domains are included

Sometimes residuals reach the

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Inventory #002598

imbalances trend towards zero Create Solver Monitors showing

IMBALANCElevels for fluid andsolid domains

View the imbalance informationprinted at the end of the solver

output file

Use a Conservation Target whendefining Solver Control in CFX-Pre


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Heat Transfer

Training ManualHeat Transfer Variables The results file contains several variables related to heat transfer

Variables starting with Wall are only defined on walls

Mesh

Control Volumes

Temperature

This is the local fluid temperature

When plotted on a wall it is the temperature on the

wall, Twall

Wall Adjacent Temperature

This is the average temperature in the control


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April 28, 2009

Inventory #002598

)( refwallcw TThq =

Where Tref is the Wall AdjacentTemperatureor the tbulk for htctemperature if specified

Twallqw

volume next to the wall

Wall Heat Transfer Coefficient, hc

By default this is based on Twall and the WallAdjacent Temperature, not the far-field fluidtemperature

Set the expert parameter tbulk for htc to define

a far-field fluid temperature to use instead of theWall Adjacent Temperature

Wall Heat Flux, qw This is the total heat flux into the domain by all

modes convective and radiative (when modeled)


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Heat Transfer

Training ManualHeat Transfer Variables Heat Flux

This is the total convective heat flux into the domain

Does not include radiative heat transfer when a radiation model is used

Convective heat flux contains heat transfer due to both advection and diffusion

It can be plotted on all boundaries (inlets, outlets, walls etc)

At an inlet it would represent the energy carried with the incoming fluid relative to the fluidReference Temperature (which is a material property, usually 25 C)

Wall Radiative Heat Flux


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The net radiative energy leaving the boundary (emission minus incoming)

Heat Flux+ Wall Radiative Heat Flux= Wall Heat Flux

Only applicable when radiation is modeled

Wall Irradiation Flux

The incoming radiative flux Only applicable when radiation is modeled

cfx12_10_heattransfer

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