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Advanced Physical Models

Heat Transfer Buoyancy Combustion and reaction modeling Multiphase flows Solidification and melting

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Heat Transfer

Thermal analysis are crucial in many industrial applications

Turbulence is enhanced is internalturbine cooling passages to improveheat transfer

Roughness elements (ribs) areplaced in the channels

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Heat Transfer Modeling

An energy equation must be solved together with the momentum and thecontinuity equations

For incompressible flows the energy equation is decoupled from the others(r is NOT a function of the temperature)

For laminar flows the energy equation can be solved directly; for turbulentflows after Reynolds-averaging the equation contains an unclosedcorrelation:

Momentum

Energy

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Heat Transfer Modeling

Momentum

Energy

The Prandtl number is the measure of the momentum diffusivity vs. thethermal diffusivity

Pr=cp m/k

Pr is order 1 for gases (typically 0.7 for air)

Prt is an additional parameter in the turbulence model (typically 0.9)

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Set-Up for Heat Transfer Calculations

Activate the energy equation

Define Models Energy

Specify material properties

Define Materials

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Wall thermal boundary conditions

The options are:

1) Fixed temperature2) Fixed thermal flux (temperature gradient)

BC

wallthickness

computationaldomain

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Flow-thermal simulations

For incompressible fluidsthe temperature andmomentum equations aredecoupled

For the energy equations all the numerical options (discretization, under-relaxation, etc.) are available

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Periodic flows

Many heat-transfer devices are characterized by geometrically periodicconfigurations (ribbed passages)

Temperature behaves like the pressure: it varies in the streamwise direction butits variation (gradient) is periodic

The energy equations can be rewritten in terms of a scaled temperature:

And the modified energy equation can be solved with periodic BC

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Wall heat transfer (temperature gradients) are strongly connectedto wall friction coefficients and therefore to turbulence modeling

Example of Heat Transfer Calculations

Ribbed Passages

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Problem set-up Solver Set-Up

Material Properties:r = 1kg/m3

m = 0.0001kg/msCp = 1000 J/Kg/oKk = 0.142 W/m oK

Reynolds number:h = 1m, L=10m, H=LReh = rUbh/m = 10,000

Boundary Conditions: Periodicity m=rUbH=10Kg/s No-slip walls

Initial Conditions:u = 1; v = p = 0

Turbulence model:k-e

Segregated Solver

Discretization:2nd order upwindSIMPLE

MultigridV-Cycle

Example: Ribbed Channel Flow

H

Periodic boundaries

L

h

h

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Grid points are clustered at thewalls and in the shear layers

Grids in Ribbed Channel Flows

Unstructured gridding allows to separate the bottom and top BLshaving different resolutions in the streamwise direction

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x/e

Heat Transfer Predictions

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In many cases the correct prediction of the thermal field in a devicerequires the inclusion of conduction effects in solids

Conjugate simulations are referred to coupled fluid-solidtemperature calculations

Conjugate Heat Transfer

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Set-Up Conjugate Heat Transfer

We need to specify two zones (fluid and solid) in the grid generationAnd then specify the material properties

Define Materials Fluid Define Materials Solid

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Wall thermal boundary conditions

The boundary between the two zones is ALWAYS a wall and a shadowzone is created automatically by Fluent

wallthickness

Fluidzone

shadowwall

thickness

Solidzone

couplingcondition

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The temperature field is affected by the treatment of the rib walls

Conjugate Heat Transfer

The rib is insulated

The rib is heated from the base

The rib is uniformly heated

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Effect of the Thermal Wall Bc

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Effect of the Thermal Wall Bc

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Comments on Thermo-fluid simulations

In incompressible flows the energy equation is decoupled from themomentum equations and can be solved a posteriori with the velocityfield frozen

Additional modeling is involved for the solution of thermal equation inthe RANS context (therefore additional approximations and errors)

Wall quantities (temperature and heat flux) are very sensitive to themodeling of near-wall turbulence

Conjugate heat transfer (coupled fluid/solid) are often necessary todescribe accurately a physical device