THERMAL PROBLEMS Chapter 6. Training Manual May 15, 2001 Inventory #001477 6-2 Types of Thermal...

THERMAL PROBLEMS

Chapter 6

May 15, 2001Inventory

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Training ManualTypes of Thermal Problems

• Constant Property

• Variable Property - Forced Convection

• Natural Convection

• Conjugate Heat Transfer

• Compressible Thermal Cases

• Algebraic Solver behavior


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Training ManualConstant Property

• Flow solution is not dependent on the energy solution

• Default choice: leave default settings in place and activate temperature solution.

• Alternate choice: Flow solution can be converged first, then solve the energy equation.

• Change relaxation factor from 0.8 to 1.0 and activate semi-direct solver.

– Check the performance for stall.

– Activate preconditioning option if memory is not a consideration.

– Increase the number of search directions if necessary.

• Constant property fluid only problems are usually well behaved.


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Training ManualSolver Notes - Conjugate Direction

• Conjugate Direction Solvers are the CR (Conjugate Residual) and the PCCR (Preconditioning of CR)

• A “semi-direct” solver is an iterative method that is guaranteed to produce the exact correct answer in the absence of round-off error.

• The conjugate direction methods construct a solution as a linear combination of independent vectors. A coefficient “alpha” is calculated for each vector.

• Stall is when this coefficient becomes essentially zero and the solution is no longer updated. This can happen with ill-conditioned problems.

• It also happens when the solver has found the answer.


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Training ManualMore Solver Notes

• A series of semi-direct solvers has been developed with an eye towards increasing the robustness when attacking conjugate heat transfer problems.

– PCCR

– PGMR

– PBCGM

• Sparse direct solver is available, and is recommended for 2D problems when you want an exact solution to the energy equation.

– Sometimes and approximate solution is more stable, particularly in the beginning of a natural convection problem.


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Training ManualVariable Property - Forced Convection

• Flow and energy solutions are coupled.

• Default choice: simply activate thermal solution and solve simultaneously.

• Thermal solution will generally converge with the flow solution.

• Default relaxation parameters for properties are 0.5.

• To check the energy solution after flow convergence, turn off FLOW and solve with the semi-direct approach with temperature relaxation at 1.0.


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Training ManualNatural Convection

• Variable Density must be activated

• Use of the buoyancy option will help prevent initial pressure fluctuations

• Specify a single value of pressure to anchor the solution (I.e. make it unique).

• Achieve initial pressure solutions with the TDMA algorithm.

• Some problems are more stable with the use of TDMA for both pressure and energy.

• Many problems benefit from relaxation factors of 1.0 for temperature and density.


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Training ManualNatural Convection Cells


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Training ManualConjugate Heat Transfer

• Problems will be ill-conditioned if there is wide variation among the properties of the fluid and non-fluid regions.

• The TDMA method may not produce a good solution even if the number of sweeps is increased significantly.

• PCCR Method (flda,meth,temp,3)

– Preconditioning and increase of the search vectors may be necessary to avoid stall with the conjugate residual method.

– Note that the PCCR solver may stall for difficult problems, but it will not “corrupt” the answer.

• For especially difficult problems it may be necessary to activate the PGMR Solver or PBCGM (3D)

• SPARSE DIRECT solver recommended for 2D problems


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Training ManualPGMR Solver

• Preconditioned Generalized Minimum residual method

• Storage Intensive

– LU Preconditioning with fill-in (Default is 6 elements/row)

– Uses minimum of 12 search vectors

• May require tight convergence criterion to avoid premature indication of convergence….

– Default is 1.E-10

– Typically, 1.E-16 is okay, perhaps try 1.E-20

• Each Global Iteration, PGMR starts with a zero guess. If convergence is premature, the answer is not accurate.

• If PGMR does not converge, it leaves the answer from the previous global iteration alone.


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Training Manual

• For adiabatic problems, the static temperature is calculated from the value input under Reference Conditions:

• The solution for non-adiabatic problems is in terms of total temperature, from which the static temperature is derived.

• The thermal option should be activated from the beginning of the run for thermal compressible problems.

• You can invoke artificial viscosity and/or velocity capping to help stabilize static temperature in the early stages of a compressible analysis.

postatic C

VTT

2

2

1

Compressible Problems


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Training Manual

Inlet

BLK1

BLK2

BLK3

The “Brick” Sample Problem Defined

• Consider the flow of air at 1 foot per second through a 1.0 inch gap between Three Thin Bricks…

• Total flow path length: 30 inches.


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Training ManualBrick Problem - Boundary Conditions

• Inlet temperature of 70F

• Laminar fully developed flow inlet profile

• Function describes inlet profile

• Thermal conditions at the base of the bricks

– Block1: Linear ramp up of temperature

• Tabular boundary condition

– Block2: Sinusoidally varying heat flux

• Function describes condition

– Block3: Radiation-to-Ambient Boundary condition


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Training Manual

Radiation with Ambient Temperature 340F

PRES=0

Inlet 70F constant, then ramp to 200F

Thermal Boundary Conditions

• Blk1 - 70F between 0<x<1.5, then ramp to 200F at x=6

• Blk2 - Sinusoidal Heat Flux (Qmax = 1.E-2)

• Blk3 - Radiation to an ambient temperature

)( 1max

xxSinQQ


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Training Manual

T = 70

Sample Problem - Overview of Steps

STEPS!! (for the student…)

• Interactive ANSYS execution

• Set up working plane

• Read input file that builds geometry and sets the simple flow and inlet boundary conditions (those shown below)

• Set up the remainder of the boundary conditions interactively

• Interactively set all properties and execution control

No Slip

P=0


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Training ManualSetup the Working Plane and Display

• Utility Menu > WorkPlane > Wp Settings

• Display Working plane

• Working Plane Settings Modified as indicated.

• Numbering… Set as below


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Training ManualCreate the Basic Model

• Execute the input file “brick.inp”:

• Utility Menu > File > Read Input From

• Result with working plane turned on with spacing set to 1, minimum to 1.0 and maximum to 30. The resulting picture areas should look as below (with Style >Color >Reverse Video)

• Note that the boundary condition symbols are turned on automatically.


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Training ManualThe Work of The Input File - Summary

• Input file Sets/Addresses the following:

– Geometry

• 3 areas for flow

• 3 areas for non-fluid regions

• Merging

– Size controls on for lines

• non-uniform spacing based on expected gradients

– Set material numbers for various areas

• AATT command (distinguish fluid and non-fluid regions)

– Basic boundary conditions

• Walls, Pressure outlet

• Inlet temperature, “3rd block” uniform temperature

– Creation of Mapped Mesh


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Training ManualThe Properties

• For the flowing air, use AIR-IN for the Properties in the FLOTRAN setup.

• Consult Appendix B for Sets of Consistent units

• Properties of the Brick (Material 2)

– Conductivity

• 0.4 (Btu)/(hr-ft-R) > 9.26E-6 (Btu)/(s-in-R)

– Density

• 100 (lbm)/(ft3) > 1.5E-4 (lbf-s2)/(in4)

– Specific Heat

• 0.2 (Btu)/(lbm-R) > 77.2 (Btu-in)/(lbf-s2-R)


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Training ManualSpecification of Non-Fluid Materials

• Preprocessor > Material Props > Material Models

• Choose a new model, since FLOTRAN demands that non-fluid materials have a material number > 1

Click on Thermal


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Training ManualNon-fluid materials

• Isotropic thermal conductivity (the density and specific heat are specified in similar fashion)


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Training ManualNon-Fluid Material

• You can verify the values by clicking on the property of interest


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Training ManualTabular Boundary Conditions

• Blk1: Temperature table

• Loads > Apply > Temperature > On Lines

– Pick the line of interest (OK).

Choose This!!(OK)


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Training ManualTabular Boundary Condition

• We are creating a new table, call it “blk1” (OK)

We will use 3 rows


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Training ManualThe Table...

What you are first shown…..

What you produce….Enter values and Apply/Quit


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Training ManualThe Sinusoidal Heat Flux

• Information on Function Boundary Conditions is contained in the Basic Analysis Procedures Guide…

– Loading

• How to Apply Loads

– Applying Loads Using Function Boundary Conditions

• Two basic steps

– Define function with Function Editor

– Load function as a table


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Training ManualFunction Editor

• Utility Menu > Parameters > Functions > Define Edit

Pull DownMenu ofIndependentVariables

INV toggles betweenthe two sets of functions (sin,asin)

Single regime(1 equation)

Radians….


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Training ManualCreation of the Function

• Point and click to enter function

• Save

• Choose name and note directory (not ones shown!!)

• Close


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Training ManualCreation of the Function Table

• Utility Menu > Parameters > Functions > Read From File

• Highlight the function of interest and click “Open”

• Enter table name “blk2”

• Set constants…OK


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Training ManualApplication of flux Boundary Condition

• Now apply the table “blk2” to the line of interest

• (We are picking the back side of the second block…)

• Existing Table,OK

• Choose BLK2,OK


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Training ManualResult

• Model has all three blocks of boundary conditions…

– Temperature

– Heat flux

– Radiation to ambient


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Training ManualThird Block

• Solution> Loads-Apply>Ambient Rad>On lines

• Choose 3rd Block..


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Training ManualInlet Boundary Condition

• A fully developed laminar velocity profile will be applied to the inlet line.

• The coordinate of interest, Y, varies between 1.0 and 2.0 over the inlet. The resulting expression is:

– Build the function

– Establish table

– Apply table.

})2

3(41{ 2

max yVVx


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Training ManualCreating the inlet function

• Utilities>Parameter>Functions> Define/Edit

• File->Save Use “inletv” as the name, Save


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Training ManualApplying the Inlet Profile as a table

• The load is now an existing table, and set VY=0


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Training ManualCreation of the Table

• Utilities > Parameters > Functions > Read from file

• Highlight function of interest, OPEN

• Name the table “inlet”

• Set Vmax = 24

(Vmax known to be twice the average)


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Training ManualApply the Table to the inlet line

• Solid model boundary conditions - loads >apply>velocity>lines


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Training ManualPath plot of velocity across the inlet


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Training ManualChanging Default - FLOTRAN Settings

• Solution Options

– Activate Thermal Option

• Execution Control

– 100 global iterations

• Fluid Properties

– AIR - IN for all four properties

• Flow Environment - Reference Conditions

– Reference Pressure 14.7

– Nominal Temperature 70

– Offset Temperature 460


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Training ManualSolve - Graphical Convergence Monitor


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Training ManualExecution procedure

• Result indicates that the flow solution is converged

• The energy equation has been updated by 100 TDMA method sweeps every global iteration.

– Solution is still approximate

• To continue:

– Turn off flow solution

– Choose 5 global iteration

– Set temperature relaxation factor to 1.0

• Default was 0.8

– Activate sparse direct solver for temperature

• Default was TDMA


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Training ManualEnergy Equation Solution


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Training ManualFlow Results

• Laminar case - converges to default termination criteria

• Set Y Direction Scale factor to 3.0 to view results

• Select only fluid elements (and nodes)

• Pressure, VX

– VY will be very tiny...


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Training ManualThermal Results

• Problem was solved with default conditions

– TDMA solver for temperature (approximate)

• 100 sweeps per global iteration

– Relaxation factor of 0.8

• To Determine if further convergence is needed for the energy equation, turn on the PCCR Solver for Temperature and execute 5 global iterations…

– Use default parameters of PCCR Solver


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Training ManualThermal Solution - 105 global iterations

• This result obtained with default advection scheme… (MSU)


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Training ManualEnergy Balance information from .PFL


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Training ManualConvergence Monitors -

• Change to SUPG algorithm for temperature and execute 5 more global iterations


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Training ManualHeat Balance

• SUPG final result (not very different since we used fully developed flow conditions at the inlet….

What should match?...


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Training ManualHeat Balance

• Heat Transfer to Wall faces involves only the fluid.

– Postive: heat flow is into the fluid

• Positive Energy flow occurs where fluid is entering the system.

• Fluxes (and film coefficients) applied to solids and volumetric heat sources in solids do not directly influence the heat balance.

– Such heat is accounted for where it flows into the fluid.

– There is a separate tabulation of heat which is leaving solid regions.

• Energy flow in + heat transfer to wall faces + volumetric heat sources in fluids = Energy flow out

– Although normally small, one can account for the energy that due to conduction at the flow boundaries.


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Training ManualThe Numbers Game...

• Difference between energy flow in and energy flow out:

• 0.7847E-2

• This compares favorably with the net heat transfer to wall faces:

• 0.7855E-2

THERMAL PROBLEMS Chapter 6. Training Manual May 15, 2001 Inventory #001477 6-2 Types of Thermal...

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Transcript of THERMAL PROBLEMS Chapter 6. Training Manual May 15, 2001 Inventory #001477 6-2 Types of Thermal...