Advanced Physical Models (Heat Transfer)
-
Upload
aminzargaran -
Category
Documents
-
view
221 -
download
6
description
Transcript of Advanced Physical Models (Heat Transfer)
-
ME469B/5/GI 1
Advanced Physical Models
Heat Transfer Buoyancy Combustion and reaction modeling Multiphase flows Solidification and melting
-
ME469B/5/GI 2
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
-
ME469B/5/GI 3
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
-
ME469B/5/GI 4
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)
-
ME469B/5/GI 5
Set-Up for Heat Transfer Calculations
Activate the energy equation
Define Models Energy
Specify material properties
Define Materials
-
ME469B/5/GI 6
Wall thermal boundary conditions
The options are:
1) Fixed temperature2) Fixed thermal flux (temperature gradient)
BC
wallthickness
computationaldomain
-
ME469B/5/GI 7
Flow-thermal simulations
For incompressible fluidsthe temperature andmomentum equations aredecoupled
For the energy equations all the numerical options (discretization, under-relaxation, etc.) are available
-
ME469B/5/GI 8
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
-
ME469B/5/GI 9
Wall heat transfer (temperature gradients) are strongly connectedto wall friction coefficients and therefore to turbulence modeling
Example of Heat Transfer Calculations
Ribbed Passages
-
ME469B/5/GI 10
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
-
ME469B/5/GI 11
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
-
ME469B/5/GI 12
x/e
Heat Transfer Predictions
-
ME469B/5/GI 13
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
-
ME469B/5/GI 14
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
-
ME469B/5/GI 15
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
-
ME469B/5/GI 16
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
-
ME469B/5/GI 17
Effect of the Thermal Wall Bc
-
ME469B/5/GI 18
Effect of the Thermal Wall Bc
-
ME469B/5/GI 19
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