Radiation simulation: external temperature below 50

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Roy
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Joined: 05 Dec 2017, 04:34
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Radiation simulation: external temperature below 50

Post by Roy »

Hi everyone,
I was running a simulation of heat radiation of 1m * 1m * 0.5m cube. I wanted to know what would happen if the cube had one side emitting to deep space (external temperature: 15 K) but the result was crazy. The following list indicated different results I got from different external temperatures on the emitting side:

external temperature, temperature on BC with idealized radiation with emissivity 0.8

50 ,216.84

75 ,217.46

100 ,219.103

150 ,228.179

500 ,504.352

600 ,602.535



30 ,219.804

15 ,1227.83

10 ,4143.02


As you see, if the external temperature is above 50 K then the results make sense. However, for cases with temperature 30, 15 (the deep space) and 10 K, the numbers are crazy. Could any tell me what happened?

This is the sif file:
Note: The BC of heat flux 100 was applied on a 1 m * 1 m side and the BC of radiation with external temperature was on the opposite 1 m * 1 m side.

Header
CHECK KEYWORDS Warn
Mesh DB "." "."
Include Path ""
Results Directory ""
End

Simulation
Max Output Level = 5
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Simulation Type = Steady state
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Solver Input File = case_50.sif
Post File = case_50.ep
End

Constants
Gravity(4) = 0 -1 0 9.82
Stefan Boltzmann = 5.67e-08
Permittivity of Vacuum = 8.8542e-12
Boltzmann Constant = 1.3807e-23
Unit Charge = 1.602e-19
End

Body 1
Target Bodies(1) = 1
Name = "Body Property 1"
Equation = 1
Material = 1
End

Solver 1
Equation = Heat Equation
Procedure = "HeatSolve" "HeatSolver"
Variable = Temperature
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-7
Nonlinear System Max Iterations = 20
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Iterative
Linear System Iterative Method = BiCGStab
Linear System Max Iterations = 500
Linear System Convergence Tolerance = 1.0e-10
BiCGstabl polynomial degree = 2
Linear System Preconditioning = ILU2
Linear System ILUT Tolerance = 1.0e-3
Linear System Abort Not Converged = False
Linear System Residual Output = 1
Linear System Precondition Recompute = 1
End

Equation 1
Name = "Heat Equation"
Active Solvers(1) = 1
End

Material 1
Name = "Aluminium (generic)"
Heat expansion Coefficient = 23.1e-6
Heat Conductivity = 237.0
Sound speed = 5000.0
Heat Capacity = 897.0
Mesh Poisson ratio = 0.35
Density = 2700.0
Poisson ratio = 0.35
Youngs modulus = 70.0e9
End

Boundary Condition 1
Target Boundaries(1) = 6
Name = "Heat_100"
Heat Flux = 100
End

Boundary Condition 2
Target Boundaries(1) = 7
Name = "Radiation"
Radiation = Idealized
External Temperature = 50
Emissivity = 0.8
End
raback
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Re: Radiation simulation: external temperature below 50

Post by raback »

Hi

Are you getting convergence or just running out the number of nonlinear iterations?

To improve convergence you could have some initial condition (default is zero) and use nonlinear relaxation in range 0.5-0.7. Usually the initial guess is not required but in radiation the effective heat transfer coefficient will depend on both temperatures. Hence the first iteration overshoots the temperature and it is never recovered.

-Peter
Roy
Posts: 9
Joined: 05 Dec 2017, 04:34
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Re: Radiation simulation: external temperature below 50

Post by Roy »

Hi Peter,
Thank you very much. Your suggestion really works :D
The attached is what I tried based on your suggestion. Thanks a lot.
Attachments
Trial of the initial temp and nonlinear relaxation factor
Trial of the initial temp and nonlinear relaxation factor
01_MasterThesis_Notes_20180319.png (60.93 KiB) Viewed 2677 times
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