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1、 Fluent Inc. 10/17/20217-1 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CHeat Transfer ModelingHeadlamp modeled withDiscrete OrdinatesRadiation Model Fluent Inc. 10/17/20217-2 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services COutlineuIntroductionuConjugate Hea

2、t TransferuNatural ConvectionuRadiationuPeriodic Heat Transfer Fluent Inc. 10/17/20217-3 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CIntroductionuEnergy transport equation:lEnergy source due to chemical reaction is included for reacting flows.lEnergy source due to species dif

3、fusion included for multiple species flows.nAlways included in coupled solver; can be disabled in segregated solver.lEnergy source due to viscous heating:nDescribes thermal energy created by viscous shear in the flow.sImportant when shear stress in fluid is large (e.g., lubrication) and/or in high-v

4、elocity, compressible flows.nOften negligiblesnot included by default for segregated solver; always included for coupled solver.lIn solid regions, simple conduction equation solved.nConvective term can also be included for moving solids.hjeffjjeffSVJhTkpEVEt)( Fluent Inc. 10/17/20217-4 Introductory

5、FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CConjugate Heat TransferuAbility to compute conduction of heat through solids, coupled with convective heat transfer in fluid.uCoupled Boundary Condition:lavailable to wall zone that separates two cell zones.GridTemperature contoursVelocity vecto

6、rsExample: Cooling flow over fuel rods Fluent Inc. 10/17/20217-5 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CNatural Convection - IntroductionuNatural convection occurswhen heat is added to fluidand fluid density varieswith temperature.uFlow is induced by force ofgravity acti

7、ng on densityvariation.uWhen gravity term isincluded, pressure gradientand body force term in themomentum equation are re-written as:gxpgxpo)(wheregxppoThis format avoids potential roundoff error when gravitational body force term is included. Fluent Inc. 10/17/20217-6 Introductory FLUENT Notes FLUE

8、NT v6.1 Feb 2003Fluent User Services CNatural Convection the Boussinesq ModeluBoussinesq model assumes the fluid density is uniform lExcept for the body force term in the momentum equation along the direction of gravity, we have:lValid when density variations are small (i.e., small variations in T).

9、uIt provides faster convergence for many natural-convection flows than by using fluid density as function of temperature.lConstant density assumptions reduces non-linearity.lSuitable when density variations are small.lCannot be used together with species transport or reacting flows.uNatural convecti

10、on problems inside closed domains:lFor steady-state solver, Boussinesq model must be used.nThe constant density, o, properly specifies the mass of the domain.lFor unsteady solver, Boussinesq model or ideal-gas law can be used.n Initial conditions define mass in the domain.()() 000gTTg Fluent Inc. 10

11、/17/20217-7 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CUser Inputs for Natural Convection1. Set gravitational acceleration.Define Operating Conditions.2. Define density model.lIf using Boussinesq model:nSelect Boussinesq as the Density method and assign constant value, o.Def

12、ine Materials.nSet Thermal Expansion Coefficient, .nSet Operating Temperature, To.lIf using temperature dependent model, (e.g., ideal gas or polynomial):nSpecify Operating Density or,nAllow Fluent to calculate o from a cell average (default, every iteration). Fluent Inc. 10/17/20217-8 Introductory F

13、LUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CRadiationuRadiation effects should be accounted for when is of equal or greater magnitude than that of convective and conductive heat transfer rates.uTo account for radiation, radiative intensity transport equations (RTEs) are solved.lLocal absor

14、ption by fluid and at boundaries links RTEs with energy equation.uRadiation intensity, I(r,s), is directionally and spatially dependent.uIntensity, I(r,s), along any direction can be modified by:lLocal absorptionlOut-scattering (scattering away from the direction)lLocal emissionlIn-scattering (scatt

15、ering into the direction)uFive radiation models are provided:lDiscrete Ordinates Model (DOM)lDiscrete Transfer Radiation Model (DTRM)lP-1 Radiation ModellRosseland ModellSurface-to-Surface (S2S)(4min4maxTTQrad Fluent Inc. 10/17/20217-9 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Servic

16、es CDiscrete Ordinates ModeluThe radiative transfer equation is solved for a discrete number of finite solid angles, si:uAdvantages:lConservative method leads to heat balance for coarse discretization.nAccuracy can be increased by using a finer discretization.lMost comprehensive radiation model:nAcc

17、ounts for scattering, semi-transparent media, specular surfaces, and wavelength-dependent transmission using banded-gray option.uLimitations: lSolving a problem with a large number of ordinates is CPU-intensive.) () ,(4),(4042dsssrITansrIaxIssii sabsorptionemissionscattering Fluent Inc. 10/17/20217-

18、10 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CDiscrete Transfer Radiation Model (DTRM)uMain assumption: radiation leaving surface element in a specific range of solid angles can be approximated by a single ray.uUses ray-tracing technique to integrate radiant intensity along

19、each ray:uAdvantages:lRelatively simple model.lCan increase accuracy by increasing number of rays.lApplies to wide range of optical thicknesses.uLimitations:lAssumes all surfaces are diffuse. lEffect of scattering not included.lSolving a problem with a large number of rays is CPU-intensive. Fluent I

20、nc. 10/17/20217-11 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CP-1 ModeluMain assumption: Directional dependence in RTE is integrated out, resulting in a diffusion equation for incident radiation. uAdvantages:lRadiative transfer equation easy to solve with little CPU demand.

21、lIncludes effect of scattering. nEffects of particles, droplets, and soot can be included.lWorks reasonably well for combustion applications where optical thickness is large.uLimitations:lAssumes all surfaces are diffuse. lMay result in loss of accuracy, depending on complexity of geometry, if optic

22、al thickness is small.lTends to overpredict radiative fluxes from localized heat sources or sinks. Fluent Inc. 10/17/20217-12 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CSurface-to-Surface Radiation ModeluThe S2S radiation model can be used for modeling enclosure radiative tr

23、ansfer without participating media.le.g., spacecraft heat rejection system, solar collector systems, radiative space heaters, and automotive underhood coolinglView-factor based modellNon-participating media is assumed.uLimitations: lThe S2S model assumes that all surfaces are diffuse. lThe implement

24、ation assumes gray radiation. lStorage and memory requirements increase very rapidly as the number of surface faces increases.nMemory requirements can be reduced by using clusters of surface faces.sClustering does not work with sliding meshes or hanging nodes. lNot to be used with periodic or symmet

25、ry boundary conditions. lCannot be used for models with multiple enclosures geometry. Fluent Inc. 10/17/20217-13 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CChoosing a Radiation ModeluFor certain problems, one radiation model may be more appropriate in general.Define Models R

26、adiation.lComputational effort: P-1 gives reasonable accuracy with less effort.lAccuracy: DTRM and DOM more accurate.lOptical thickness: DTRM/DOM for optically thin media (optical thickness 1); P-1 better for optically thick media.lScattering: P-1 and DOM account for scattering.lParticulate effects:

27、 P-1 and DOM account for radiation exchange between gas and particulates.lLocalized heat sources: DTRM/DOM with sufficiently large number of rays/ ordinates is more appropriate. Fluent Inc. 10/17/20217-14 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CPeriodic Heat Transfer (1)u

28、Also known as streamwise-periodic or fully-developed flow.uUsed when flow and heat transfer patterns are repeated, e.g.,lCompact heat exchangerslFlow across tube banksuGeometry and boundary conditions repeat in the streamwise direction.Outflow at one periodic boundary is inflow at the otherinflowout

29、flow Fluent Inc. 10/17/20217-15 Introductory FLUENT Notes FLUENT v6.1 Feb 2003Fluent User Services CPeriodic Heat Transfer (2)uTemperature (and pressure) vary in the streamwise direction.uScaled temperature (and periodic pressure) is same at periodic boundaries. uFor fixed wall temperature problems, scaled temperature defined as: Tb = suitably defined bulk temperatureuCan also model flows with specified wall heat flux.TTTTwallbwa

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