fluent-boundary conditon basics

© Fluent Inc. 2/20/01F1

Fluent Software TrainingTRN-99-003

Heat Transfer and Thermal BoundaryConditions

Headlamp modeled withDiscrete OrdinatesRadiation Model



Outlineu Introductionu Thermal Boundary Conditionsu Fluid Propertiesu Conjugate Heat Transferu Natural Convectionu Radiationu Periodic Heat Transfer



Introductionu Energy transport equation is solved, subject to a wide range of thermal

boundary conditions.l Energy source due to chemical reaction is included for reacting flows.l Energy source due to species diffusion included for multiple species flows.

n Always included in coupled solver.n Can be disabled in segregated solver.

l Energy source due to viscous heating:n Describes thermal energy created by viscous shear in the flow.

s Important when shear stress in fluid is large (e.g., lubrication) and/or inhigh-velocity, compressible flows.

n Often negligibles not included by default for segregated solvers always included for coupled solver.

l In solid regions, simple conduction equation solved.n Convective term can also be included for moving solids.



User Inputs for Heat Transfer

1. Activate calculation of heat transfer.l Select the Enable Energy option in the Energy panel.

Define Õ Models Õ Energy...

l Enabling a temperature dependent density model, reacting flow model, or aradiation model will toggle Enable Energy on without visiting this panel.

2. Enable appropriate options:l Viscous Heating in Viscous Model panell Diffusion Energy Source option in the Species Model panel

3. Define thermal boundary conditions.Define Õ Boundary Conditions...

4. Define material properties for heat transfer.Define Õ Materials...

l Heat capacity and thermal conductivity must be defined.



Solution Process for Heat Transferu Many simple heat transfer problems can be successfully solved using

default solution parameters.u However, you may accelerate convergence and/or improve the stability

of the solution process by changing the options below:l Under-relaxation of energy equation.

Solve Õ Controls Õ Solution...

l Disabling species diffusion term.Define Õ Models Õ Species...

l Compute isothermal flow first, then add calculation of energy equation.Solve Õ Controls Õ Solution...



Theoretical Basis of Wall Heat Transfer

u For laminar flows, fluid side heat transfer is approximated as:

n = local coordinate normal to wall

u For turbulent flows:l Law of the wall is extended to treat wall heat flux.

n The wall-function approach implicitly accounts for viscous sublayer.

l The near-wall treatment is extended to account for viscous dissipationwhich occurs in the boundary layer of high-speed flows.

′′ = ≈q kTn

kTnwall

∂∂

∆∆



Thermal Boundary Conditions at Flow Inletsand Exits

u At flow inlets, must supplyfluid temperature.

u At flow exits, fluidtemperature extrapolatedfrom upstream value.

u At pressure outlets, whereflow reversal may occur,“backflow” temperature isrequired.



Thermal Conditions for Fluids and Solids

u Can specify an energy sourceusing Source Terms option.



Thermal Boundary Conditions at Walls

u Use any of following thermalconditions at walls:l Specified heat fluxl Specified temperaturel Convective heat transferl External radiationl Combined external radiation

and external convective heattransfer



u Fluid properties such as heat capacity, conductivity, and viscosity canbe defined as:l Constantl Temperature-dependentl Composition-dependentl Computed by kinetic theoryl Computed by user-defined functions

u Density can be computed by ideal gas law.u Alternately, density can be treated as:

l Constant (with optional Boussinesq modeling)l Temperature-dependentl Composition-dependentl User Defined Function

Fluid Properties



Conjugate Heat Transfer

u Ability to compute conduction of heat through solids, coupled withconvective heat transfer in fluid.

u Coupled Boundary Condition:l available to wall zone that

separates two cell zones. Grid

Temperature contours

Velocity vectors

Example: Cooling flow over fuel rods



Natural Convection - Introduction

u Natural convection occurswhen heat is added to fluidand fluid density varieswith temperature.

u Flow is induced by force ofgravity acting on densityvariation.

u When gravity term isincluded, pressure gradientand body force term is writtenas:

gxp

gxp

o )('

ρρρ −+∂∂

−⇒+∂∂

−

where gxpp oρ−='

• This format avoids potential roundoff errorwhen gravitational body force term is included.



Natural Convection - Boussinesq Modelu Makes simplifying assumption that density is uniform.

l Except for body force term in momentum equation, which is replaced by:

l Valid when density variations are small (i.e., small variations in T).

u Provides faster convergence for many natural-convection flows thanby using fluid density as function of temperature.l Constant density assumptions reduces non-linearity.l Use when density variations are small.l Cannot be used with species calculations or reacting flows.

u Natural convection problems inside closed domains:l For steady-state solver, Boussinesq model must be used.

n Constant density, ρo, allows mass in volume to be defined.l For unsteady solver, Boussinesq model or Ideal gas law can be used.

n Initial conditions define mass in volume.

( ) ( )ρ ρ ρ β− = − −0 0 0g T T g



User Inputs for Natural Convection1. Set gravitational acceleration.

Define Õ Operating Conditions...

2. Define density model.l If using Boussinesq model:

n Select boussinesq as the Density methodand assign constant value, ρo.

Define Õ Materials...n Set Thermal Expansion Coefficient, β.n Set Operating Temperature, To.

l If using temperature dependent model,(e.g., ideal gas or polynomial):n Specify Operating Density or,n Allow Fluent to calculate ρo from a cell

average (default, every iteration).

3. Set boundary conditions.



Radiationu Radiation intensity transport equations (RTE) are solved.

l Local absorption by fluid and at boundaries links energy equation with RTE.

u Radiation intensity is directionally and spatially dependent.l Intensity along any direction can be reduced by:

n Local absorptionn Out-scattering (scattering away from the direction)

l Intensity along any direction can be augmented by:n Local emissionn In-scattering (scattering into the direction)

u Four radiation models are provided in FLUENT:l Discrete Ordinates Model (DOM)l Discrete Transfer Radiation Model (DTRM)l P-1 Radiation Modell Rosseland Model (limited applicability)



Discrete Ordinates Model

u The radiative transfer equation is solved for a discrete number of finitesolid angles:

u Advantages:l Conservative method leads to heat balance for coarse discretization.l Accuracy can be increased by using a finer discretization.l Accounts for scattering, semi-transparent media, specular surfaces.l Banded-gray option for wavelength-dependent transmission.

u Limitations:l Solving a problem with a large number of ordinates is CPU-intensive.

( ) ')'()',(4

),(4

0

42 Ω⋅Φ+=++

∂∂

∫ dsssrIT

ansrIaxI s

si

isπ

πσ

πσ

σ

absorption emission scattering



Discrete Transfer Radiation Model (DTRM)

u Main assumption: radiation leaving surface element in a specific range ofsolid angles can be approximated by a single ray.

u Uses ray-tracing technique to integrate radiant intensity along each ray:

u Advantages:l Relatively simple model.l Can increase accuracy by increasing number of rays.l Applies to wide range of optical thicknesses.

u Limitations:l Assumes all surfaces are diffuse.l Effect of scattering not included.l Solving a problem with a large number of rays is CPU-intensive.

πσ

αα4T

IdsdI

+−=



P-1 Modelu Main assumption: radiation intensity can be decomposed into series of

spherical harmonics.l Only first term in this (rapidly converging) series used in P-1 model.l Effects of particles, droplets, and soot can be included.

u Advantages:l Radiative transfer equation easy to solve with little CPU demand.l Includes effect of scattering.l Works reasonably well for combustion applications where optical

thickness is large.l Easily applied to complicated geometries with curvilinear coordinates.

u Limitations:l Assumes all surfaces are diffuse.l May result in loss of accuracy, depending on complexity of geometry, if

optical thickness is small.l Tends to overpredict radiative fluxes from localized heat sources or sinks.



Choosing a Radiation Modelu For certain problems, one radiation model may be more

appropriate in general.Define Õ Models Õ Radiation...

l Computational effort: P-1 gives reasonable accuracy withless effort.

l Accuracy: DTRM and DOM more accurate.l Optical thickness: DTRM/DOM for optically thin media

(optical thickness << 1); P-1 better for optically thick media.l Scattering: P-1 and DOM account for scattering.l Particulate effects: P-1 and DOM account for radiation exchange between gas

and particulates.l Localized heat sources: DTRM/DOM with sufficiently large number of rays/

ordinates is more appropriate.



Periodic Heat Transfer (1)u Also known as streamwise-periodic or fully-developed flow.u Used when flow and heat transfer patterns are repeated, e.g.,

l Compact heat exchangersl Flow across tube banks

u Geometry and boundary conditions repeat in streamwise direction.

Outflow at one periodic boundaryis inflow at the other

inflow outflow



Periodic Heat Transfer (2)

u Temperature (and pressure) vary in streamwise direction.u Scaled temperature (and periodic pressure) is same at periodic

boundaries.u For fixed wall temperature problems, scaled temperature defined as:

Tb = suitably defined bulk temperature

u Can also model flows with specified wall heat flux.

θ =−−

T TT T

wall

b wall



Periodic Heat Transfer (3)u Periodic heat transfer is subject to the following constraints:

l Either constant temperature or fixed flux bounds.l Conducting regions cannot straddle periodic plane.l Properties cannot be functions of temperature.l Radiative heat transfer cannot be modeled.l Viscous heating only available with heat flux wall boundaries.

Contours of Scaled Temperature



Summary

u Heat transfer modeling is available in all Fluent solvers.u After activating heat transfer, you must provide:

l Thermal conditions at walls and flow boundariesl Fluid properties for energy equation

u Available heat transfer modeling options include:l Species diffusion heat sourcel Combustion heat sourcel Conjugate heat transferl Natural convectionl Radiationl Periodic heat transfer

fluent-boundary conditon basics

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