Concentric Spheres with Radiation

Chapter 44: Concentric Spheres with Radiation

44 Concentric Spheres with Radiation

Summary 799

Introduction 800

Modeling Details 800

Material Modeling 807

Solution Procedure 807

Results 808

Modeling Tips 809

Pre- and Postprocess with SimXpert 810

Input File(s) 853

Video 854

799CHAPTER 44

Concentric Spheres with Radiation

SummaryTitle Chapter 44: Concentric Spheres with Radiation

Features Hemi-cube versus Gaussian Integration Methods

Geometry

Material properties

Analysis characteristics • Nonlinear steady state thermal analysis

Boundary conditions Inside sphere temperature fixed at 1000 K. The heat sink is ambient temperature at zero K where the radiation to space boundary condition is applied on the outer sphere. Stefan-Boltzmann constant is (above).

Element type 4-node QUAD4

FE results Outer sphere temperature using different radiation schemes and compared to an analytic solution

R = 1T = 1000

R = 1.5T = ?

Units: inch, watt, K

T = 0∞

εo2

1.0=

εo1

0.9=

t1

0.01=

t2

0.05=εi2

0.7=

k1 4.0W in K– = k2 6.0W in K– = 3.66x10 11– W in2

K4

– =

708.0

708.5

709.0

709.5

710.0

710.5

Hemi-cubeGaussian integrationAnalytic

Temperature K (Grid 367)Analytic 710.30Gaussian integration 709.85Hemi-cube 708.91

MD Demonstration Problems

CHAPTER 44800

IntroductionThis problem demonstrates the ability of the Nastran SOL 400 thermal nonlinear solution sequence to perform thermal radiation view factor calculations using the Hemi-cube and Gaussian integration methods. The Gaussian adaptive integration view factor calculation method has been with Nastran for many years. The view factor computed by the Gaussian method is extremely accurate. However, as the problems get big, computation time is roughly proportional to the number of surfaces squared. The introduction of Hemi-cube method in MD Nastran permits the solution of very large scale view factor problems where previously the use of the Gaussian method was overly time intensive. As compared to the adaptive Gaussian method, we have seen an improvement in CPU speed of 33 times in some problems. The CPU time increases linearly with the number of radiation surfaces because in Hemi-cube, the computation time is linearly proportional to the number of surfaces. In this problem, we have an analytical solution in which we compare both Hemi-cube and the Adaptive Gaussian integration methods to see which method offers the most accuracy.

Modeling Details

Figure 44-1 Concentric Spheres (top sector of outer sphere removed)

As shown in (Figure 44-1), the inner sphere with radius equal to 1 inch is subjected to a constant temperature of 1000°K (red). There is radiation exchange between the inner and the outer sphere (orange). The outer sphere radiates to space at an ambient temperature of zero K with view factors equal to 1.0.

Reference Solution

For these two diffuse isothermal concentric spheres, the view factors need to be determined. Since all of the energy leaving the inner sphere (1) will arrive at the outer sphere (2), . The reciprocity relation for view factors F1 2– 1.0=

801CHAPTER 44


gives , or . Since the inner sphere cannot see itself, . Finally since energy

must be conserved, the sum of all view factors of a closed cavity must be unity, which yields, .

Notice how the number of view factors grow as the square of the number of surfaces, i.e. two surfaces yield 4 view factors. Given the geometry of the spheres as and , the four view factors become:

. Below is an equation for calculation of outer sphere temperature where the outer sphere is

radiating to space at absolute zero and a view factor of 1. (Holman, Jack P. Holman Heat Transfer. McGraw-Hill, 2001).

This solution assumes perfect conduction (no resistance to heat flow) in the outer sphere.

While, in general, the view factors cannot be obtained from analytical solutions, in this simple problem, the view factors can be found analytically and we can use these view factors in a simple three grid model to check our analytic solution above. One grid represents the inner sphere, another represents the outer sphere, and the last grid represents the ambient temperature of the outer sphere.

Nastran test file: user1_point.dat

$Model concentric sphere with two nodes$ Length in Inches$! NASTRAN Control SectionNASTRAN SYSTEM(316)=19$! File Management Section$! Executive Control SectionSOL 400CENDECHO = NONE$! Case Control SectionTEMPERATURE(INITIAL) = 21 TITLE=MSC.Nastran job created on 05-Dec-03 at 13:33:05

A1F1 2– A2F2 1–= F2 1– R1 R2 2= F1 1– 0=

F2 2– 1 R1 R2 2–=

R1 1= R2 1.5=

F1 1– 0= F1 2– 1=

F2 1–49---= F2 2–

59---=

1 0.9= 2out1= 2inner

0.7=

T1 1000=

A1 4 R12 = A2 4 R2

2 =

A1 12.566= A2 28.274=

C 11-----

A1

A2------ 1

2inner

---------------- 1–

+= C 1.302=

D2

A1 T14

A1 C 2outA2 +

---------------------------------------------=

D2 2.545 1011= T2 D20.25= T2 710.299=


CHAPTER 44802

SUBCASE 1$! Subcase name : subcase_1$LBCSET SUBCASE1 lbcset_1 SUBTITLE=Default SPCFORCES(SORT1,PRINT,REAL)=ALL OLOAD(SORT1,PRINT,REAL)=ALL THERMAL(SORT1,PRINT)=ALL FLUX(PRINT)=ALL ANALYSIS = HSTAT SPC = 23 NLSTEP = 1BEGIN BULK$! Bulk Data Pre SectionPARAM SNORM 20.PARAM K6ROT 100.PARAM WTMASS 1.PARAM* SIGMA 3.6580E-11PARAM POST 1PARAM TABS 0.0$! Bulk Data Model SectionRADM 11 0.0 0.9 RadMat_1RADM 12 0.0 0.7 RadMat_1RADM 13 0.0 1. RadMat_1PHBDY 1 12.566 PHBDY_1_PHBDY 2 28.274 PHBDY_2_GRID 101 0.0 0.0 0.0 GRID 102 1. 0.0 0.0 $!SPOINT 777CHBDYP 1 1 point 10 101 + + 11 1. 0.0 0.0CHBDYP 2 2 point 10 102 + + 12 -1. 0.0 0.0CHBDYP 3 2 point 102 + + 13 -1. 0.0 0.0SPC 23 101 1 1000.SPC 23 777 1 0.0RADBC 777 1. 3

RADCAV 1 ++ VIEW 10 1 VIEW3D 10 RADSET 1RADMTX 10 1 0.012.56637RADMTX 10 215.70922RADLST 1 1 1 2TEMPD 21 900.TEMP 21 777 0.0TEMP 21 101 1000.NLSTEP 1 1. + + GENERAL 25 + + FIXED 1 1 + + HEAT PW 0.001 1.E-7AUTO 5

803CHAPTER 44


ENDDATA b1272084

Notice that the Stefan-Boltzmann constant (sigma) is 3.66e-11 W/in2/K4 and, the radiation matrix is define above by

the RADLST and RADMTX,

The radiation matrix must be symmetric to conserve energy (reciprocity relation ), and the

symmetric terms are not entered. Running this three node problem yields the output below with the temperature of the outer sphere of 710.31, agreeing to within 4-digits of our analytic solution of 710.3.

T E M P E R A T U R E V E C T O R

POINT ID. TYPE ID VALUE ID+1 VALUE ID+2 VALUE ID+3 VALUE ID+4 VALUE ID+5 VALUE

101 S 1.000000E+03 7.103098E+02

777 S 0.0

Solution HighlightsThe following are highlights of the Nastran input file necessary to model this problem using 700 elements to represent the inner and outer spheres with 1268 radiating surfaces:

$! NASTRAN Control SectionNASTRAN SYSTEM(316)=19$! File Management Section$! Executive Control SectionSOL 400CENDECHO = SORT$! Case Control SectionTEMPERATURE(INITIAL) = 33SUBCASE 1$! Subcase name : NewLoadcase$LBCSET SUBCASE1 DefaultLbcSet THERMAL(SORT1,PRINT)=ALL FLUX(PRINT)=ALL ANALYSIS = HSTAT SPC = 35 NLSTEP = 1BEGIN BULK$! Bulk Data Pre SectionPARAM WTMASS 1.PARAM GRDPNT 0 NLMOPTS HEMICUBE1 PARAM* SIGMA 3.6580E-11PARAM POST 1$! Bulk Data Model SectionPARAM OGEOM NO PARAM MAXRATIO 1e+8

RADMTXA1F1 1– 0= A1F1 2– 12.566 1=

A2F2 1– 28.274 49---= A2F2 2– 12.566 5

9---=

0 12.56637

sym 15.70796= =

A1F1 2– A2F2 1–=


CHAPTER 44804

The use of a steady-state thermal analysis is indicated by ANALY=HSTAT. The NLMOPTS parameters indicate that we are using the Hemi-cube method as the view factor calculation method. If one desires to run the Gaussian integration method, then you do not need the NLMOPTS bulk data entry.

The inner sphere is composed of CHBDYG elements (see command details below) numbered from 6987 through 7214, and the outer sphere is from 7215 to 7734. The set1 ID option is used on the RADCAV bulk data entry to sum up all the view factors between the inner and outer spheres for comparisons against theory.

Loading and Boundary Conditions

Radiation- View Factor Calculation (CHBDYG Element)

The CHBDYG element is used in Nastran thermal analysis for any surface heat transfer phenomenon such as radiation or convection or imposing heat flux on these elements.

CHBDYG 6987 AREA4 2 3 3390 3389 3397 3398CHBDYG 6988 AREA4 2 3 3404 3403 3389 3390

RADM 3 0.9 0.9 Radm_3RADM 4 0.7 0.7 Radm_4RADM 5 1. 1. Radm_5RADSET 4RADCAV 4 YES 4 0.1VIEW3D 4 0 0 0 0.0 0.0 0.0$!VIEW 2 4 KSHD 1 1

805CHAPTER 44


In this case, we have CHBDYG element 6987 with TYPE='AREA4' bounded by grid 3390, 3389, 3397, 3398. The normal vector is defined by the grid connectivity and is directed from the inner sphere to the outer sphere (Figure 44-2

and Figure 44-3). The internal sphere has KSHD defined on the 4th field of the VIEW data entry, which means that this group of elements can shade the view of other elements. The external sphere has KBSHD defined which means that these elements can also be shaded by other elements. The reason that we have specified the shading flag is to speed up the sorting for these potential blockers in the view factor calculations. In general when the surface is very complex, the use of the flag called BOTH is recommended. The RADSET option tells us there is only 1 cavity in the model, and

the 2nd field on the VIEW points to the IVIEWF or IVIEWB on the CHBDYG field 5th or 6th, respectively. For a plate element, there is top and the bottom surface for view factor calculations. For a solid element, only the front side IVIEWF should be used. The inner sphere here is represented by number as 1 on the field 5 (IVIEWF) on the CHBDYG.

The 7th and 8th represent the ID for the RADM option where 7th field is the top surface RADM ID and the 8th field is the bottom surface RADM ID. The RADM specified the emissivity used for the sphere and, in this case, the emissivity for the inner sphere is equal to 0.7.

The RADCAV bulk data entry indicates that we will print the summary of view factor calculations. In this case, we have a complete enclosure and, therefore, the view factor summation should equal 1.0. The surface numbers 703, 704 are the ID numbers for the CHBDYG that has the radiation exchange.

*** VIEW FACTOR MODULE *** OUTPUT DATA *** CAVITY ID = 4 ***

ELEMENT TO ELEMENT VIEW FACTORS SURF-I SURF-J AREA-I AI*FIJ FIJ SCALE

6987 -SUM OF 5.19803E-02 9.99998E-01 6988 -SUM OF 6.14400E-02 9.99997E-01 6989 -SUM OF 4.30822E-02 9.99988E-01 6990 -SUM OF 4.36718E-02 1.00000E+00 6991 -SUM OF 5.08568E-02 1.00000E+00

The continuation field on the RADCAV is optional.

Radiation - RADBC (radiation to space)

On the outer sphere, we have a radiation to space using the view factor supplied on the 3rd field on the RADBC. (see

Example below) The 2nd field on the RADBC points to the ambient grid ID 100001 and, in this case, we have the grid fixed at 0° K.

SPOINT 6497SPC 5 6497 1 0.0TEMP 33 6497 0.0RADBC 6497 1. 0 -6467CHBDYG 6467 AREA4 5 5987 5975 5976 5986RADBC 6497 1. 0 -6468CHBDYG 6468 AREA4 5 5989 5976 5975 5988RADBC 6497 1. 0 -6469CHBDYG 6469 AREA4 5 5997 5996 5975 5987


CHAPTER 44806

Please note the negative EID represents that the radiation to space is effected from the back surface (opposite to the direction of normal) of the element.

Also, we have the temperature boundary conditions applied to all grids on the inner sphere at 1000 K via the SPC option.

SPC 1 1 1 1000.

Specifies an CHBDYi element face for application of radiation boundary conditions.

Format

Example

Remarks:

1. The basic exchange relationship is:

• if CNTRLND = 0, then

• if CNTRLND > 0, then

RADBC Space Radiation Specification

1 2 3 4 5 6 7 8 9 10

RADBC NODAMB FAMB CNTRLND EID1 EID2 EID3 -etc.-

1 2 3 4 5 6 7 8 9 10

RADBC 5 1.0 101 10

Field Contents Type Default

NODAMB Ambient point for radiation exchange. I > 0

FAMB Radiation view factor between the face and the ambient point. R > 0

CNTRLND Control point for radiation boundary condition. (Integer > 0; Default = 0) I > 0 0

EIDi CHBDYi element identification number. ( or “THRU” or “BY”)Integer 0

q = FAMB e Te4

Tamb4

–

q = FAMB uCNTRLND e Te4

Tamb4

–

807CHAPTER 44


Figure 44-2 Normal Vectors Point Outward from the Inner Sphere

Figure 44-3 Normal Vectors Point Inward for the Outer Sphere

Material ModelingThermal conductivity value is supplied on the MAT4 bulk data entry.

MAT4 1 4. Iso_1MAT4 2 6. Iso_2

Solution ProcedureThe nonlinear procedure used is defined using the following NLPARM entry:

NLSTEP 1 1. + + FIXED 1 + + HEAT UPW 0.001 0.001 1.E-7PFNT


CHAPTER 44808

In thermal analysis, the TEMPD bulk data entry specifies the initial temperature for the nonlinear radiation analysis. In this case, an initial guessed temperature of 800° was used. A casual selection of initial guessed temperature is not so important in a nonlinear conduction and convection thermal analysis. However, for nonlinear radiation analysis

where the thermal radiation transfer is given by , an initial guess is very helpful. The error (residual)

is proportional to the temperature to the 4th power. It is. therefore, recommended to specify a higher estimated temperature in a radiation dominant problem.

The default method for the NLPARM is the AUTO method in SOL 400 analyses. The convergence criterion is based on UPW. In this problem, you can achieve convergence by either the PFNT method (as above) or the AUTO method:

NLSTEP 1 1. + + FIXED 1 + + HEAT UPW 0.001 0.001 1.E-7AUTO

The U convergence criterion measures the error tolerance for the temperature. It has a recommended value of 1.0e-3 or smaller for thermal problem. The P and W convergence criteria measure the error tolerances for the load and work, respectively.

The number of increments is specified on the 3rd field of the NLPARM data entry (NINC). This should be set to 1 for steady-state thermal analyses since convergence can be achieved in one step only. This, typically, is not the case for structural analyses, where NINC is set to 10 by default. Generally, the PFNT or FNT methods are used for highly nonlinear mechanical analyses.

Results

Both methods yield temperatures very close to the analytical solution.

Q A T14

T24

– =

708.0

708.5

709.0

709.5

710.0

710.5



809CHAPTER 44


Figure 44-4 Hemi-cube Results

Modeling TipsThe current model uses 1268 surfaces to define the radiating surfaces of both spheres. The CPU run times for the Gaussian and Hemi-cube methods are nearly the same, at 27 seconds.

Figure 44-5, however, shows the dramatic increase in run time for the Gaussian model and the clear benefits of the Hemi-cube method as the number of surfaces increases.

At 20,000 surfaces, the Gaussian model takes 33 time longer to complete.

Figure 44-5 CPU Run Times

0 5000 10000 15000 200000

2000

4000

6000

8000

10000

12000

Gaussian

Hemi-cube

CPU Time (s)

Number of Surfaces


CHAPTER 44810

Pre- and Postprocess with SimXpertThe same physical model will now be built, run and postprocessed with SimXpert. The Gaussian integration scheme will be used to compute the viewfactors. While the dimensions of length in the summary and nug*.dat files is inches, the model built here with SimXpert will use the same geometry but with units of meters. The only other change will be in the selection of the correct units of the Stefan-Boltzmann constant (p. 844).

Unitsa. Tools: Options

b. Observe the User Options window

c. Select Units Manager

d. For Basic Units, specify the model units:

e. Length = m, Mass = kg, Time = s, Temperature = Kelvin, and Force = N

a

b

c

d

e

811CHAPTER 44


Create First Hemispherical Surface

a. Geometry tab: Curve/Arc

b. Select Arc

c. Select 3 Points

d. For X,Y,Z, Coordinate, enter 0.0245, 0, 0; input, click OK

e. For X,Y,Z, Coordinate, enter 0, 0.0245, 0; input, click OK (not shown)

f. For X,Y,Z, Coordinate, enter -0.0245, 0, 0; click OK (not shown)

g. Click OK

h. Observe in the Model Browser tree: Part 1

l. Observe the curve arc

ab

c

h

i

d

g


CHAPTER 44812

Create First Hemispherical Surface (continued)

a. Geometry tab: Surface/Revolve

b. Select Vector

c. For X,Y,Z Coordinate, enter 0 0 0; click OK

d. Click OK

e. For Axis, select X; click OK

f. For Entities screen select the Curve arc

g. For Angel Of Spin (Degrees), enter 180; click OK

h. Observe the first hemispherical surface

-

ab

c

d

e

fg

j

h

813CHAPTER 44


Create Part for Second Hemispherical Surface

a. Assemble tab: Parts/Create Part

b. Use defaults of form

c. Click OK

d. Observe Part_2 in the Model Browser Tree

a

b

c

d


CHAPTER 44814

Create Second Hemispherical Surface

a. Geometry tab: Curve/Arc

b. Select Arc

c. Select 3 Points

d. For X,Y,Z, Coordinate, enter 0.0381, 0, 0; input, click OK

e. For X,Y,Z, Coordinate, enter 0, 0.0381, 0; input, click OK (not shown)

f. For X,Y,Z, Coordinate, enter -0.0381, 0, 0; click OK (not shown)

g. Click OK

h. Observe the curve arc

--

a

bc

h

d

g

815CHAPTER 44


Create Second Hemispherical Surface (continued)

a. Geometry tab: Surface/Revolve

b. Select Vector

c. For X,Y,Z Coordinate, enter 0 0 0; click OK

d. Click OK

e. For Axis, select X; click OK

f. For Entities screen select the Curve arc

g. For Angel Of Spin (Degrees), enter 180;

h. Click OK

i. Observe the second hemispherical surface

ab

c

f

kk

e

d

h

g

i


CHAPTER 44816

Create Third Hemispherical Surface

a. Tools: Transform/Reflect

b. Select X-Y Plane

c. Select Make Copy

d. Select Inner (smaller) hemispherical surface

e. Click Done; then click Exit

f. A third hemispherical surface is created that is the same color as the copied surface

g. Observe that there is another Part in the Model Browser tree

a

bc

e

f

g

817CHAPTER 44


Create Third Hemispherical Surface (continued)

a. In the Model Browser tree, right click on PART_1.COPY; select Change Color

b. Select a different color

c. Observe that the third hemispherical surface is now a different color

a

b

c


CHAPTER 44818

Create Fourth Hemispherical Surface

a. Tools: Transform/Reflect

b. Select X-Y Plane

c. Select Make Copy

d. Select outer (larger) hemispherical surface

e. Click Done; then click Exit

f. A fourth hemispherical surface is created that is the same color as the copied surface

g. Observe that there is another Part in the Model Browser tree

a

bc

e

f

g

f

819CHAPTER 44


Create Fourth Hemispherical Surface (continued)

a. In the Model Browser tree, right click on PART_2.COPY; select Change Color

b. Select a different color

c. Observe that the fourth hemispherical surface is now a different color

a

b

c


CHAPTER 44820

Create Material Properties

a. Materials and Properties tab: Material/Isotropic

b. For Name enter Inner_sphere

c. For Description enter a description

d. For Young’s Modulus enter 10e9 (needed for the software to run)

e. For Poisson’s Ratio enter 0.28 (needed for the software to run)

f. For Thermal Conductivity enter 157.48

g. Click OK

a

bc

f

h

d

e

g

f

821CHAPTER 44


Create Material Properties (continued)

a. Materials and Properties tab: Material/Isotropic

b. For Name enter Outer_sphere

c. For Description enter a description

d. For Young’s Modulus enter 10e9 (needed for the software to run)

e. For Poisson’s Ratio enter 0.28 (needed for the software to run)

f. For Thermal Conductivity enter 236.22

g. Click OK

a

bc

g

h

de

f


CHAPTER 44822

Create Inner Sphere Element Property

a. Create the element property for the inner sphere

b. Right click on PART_2; select HIDE to hide the outer hemispherical surfaces

c. Repeat Step b. for PART_2.COPY

d. Create the element property for the inner sphere

a

b

c

d

823CHAPTER 44


Create Inner Sphere Element Property (continued)

a. Materials and Properties tab: 2D Properties/Shell

b. For Name, enter Inner_sphere

c. For Entities screen, select the two inner hemispherical surfaces

d. For Material, select Inner_sphere from the Model Browser tree

e. For Part thickness, enter 2.54e-4

f. Click OK

a

b

cd

e c

f


CHAPTER 44824

Create Outer Sphere Element Property

a. Create the element property for the outer sphere

b. Right click on PART_1; select HIDE to hide the outer hemispherical surfaces

c. Repeat Step b. for PART_1.COPY

d. Right click on PART_2; select SHOW to show the outer hemispherical surfaces

e. Repeat Step d. for PART_2.COPY

f. Create the element property for the outer sphere

a

f

825CHAPTER 44


Create Outer Sphere Element Property (continued)

a. Materials and Properties tab: 2D Properties/Shell

b. For Name, enter Outer_sphere

c. For Entities screen, select the two outer hemispherical surfaces

d. For Material, select Outer_sphere from the Model Browser tree

e. For Part thickness, enter 1.27e-3

f. Click OK

a

b

cd

ec

f


CHAPTER 44826

Create Surface Mesh for Outer Sphere

a. Meshing tab: Automesh/Surface

b. For Surface to mesh screen, select both surfaces

c. For Element Size, enter 0.35

d. For Mesh type, select Quad Dominant

e. For Element property, select Outer_sphere from the Model Browser tree

f. Click OK

a

b

c

d

e

b

f

827CHAPTER 44


Create Surface Mesh for Outer Sphere (continued)

a. Display the geometric surfaces in wireframe

b. Display the elements as shaded

c. Observe resulting mesh for the outer sphere

d. Notice the elements at the geometric interface are congruent

e. Verify that the elements at the interface are connected

a

b

c

d

e

e


CHAPTER 44828

Create Surface Mesh for Inner Sphere

a. Display only the inner sphere using the picks in the Model Browser tree and those of the Render toolbar

for Geometry and FE.

a

829CHAPTER 44


Create Surface Mesh for Inner Sphere (continued)

a. Meshing tab: Automesh/Surface

b. For Surface to mesh screen, select both surfaces

c. For Element Size, enter 0.35

d. For Mesh type, select Quad Dominant

e. For Element property, select Inner_sphere from the Model Browser tree

f. Click OK

a

b

c

d

e

b

f


CHAPTER 44830

Create Surface Mesh for Inner Sphere (continued)

a. Display the geometric surfaces in wireframe

b. Display the elements as shaded

c. Observe resulting mesh for the inner sphere

d. The elements at the geometric interface are congruent

e. Verify that the elements ar the interface are connected

a

b

c

d

e

e

831CHAPTER 44


Equivalence All Nodes

a. Right Click Part_1 Show All

b. Nodes/Elements Modify/Equivalence

c. Select All

d. Observe Highlighted Nodes

e. OK

f. Observe 52 merged unreferenced nodes deleted

aa

c

b

e

d

f


CHAPTER 44832

Create Fixed Temperature LBC for Inner Sphere

a. LBCs tab: Heat Transfer/Temperature BC

b. For Name, enter Temperature_inner

c. For Entities screen, select the two inner hemispherical surfaces; best to have only the Pick Surfaces

icon active and pick near the center of an element away from the nodes.

d. For Temperature, enter 1000

e. Click OK

a

b

d

e

cc

833CHAPTER 44


Create Fixed Temperature LBC for Inner Sphere (continued)

a. Observe the applied temperatures as values

b. Display temperature values; turn Detailed Rendering On/Off

c. Set Geometry and FE to Wireframe

d. Double click on Temperature_Inner under LBC in the Model Browser

e. Click on Visualization tab

f. Select Short under LBC Type and Value Labels

g. Select Associated Geometry under Display on Geometry / FEM

h. Click OK

a

b

e

f

g

h


CHAPTER 44834

Create Fixed Temperature LBC for Inner Sphere (continued)

a. Observe the applied temperatures (red dots)

b. Select FE Shaded

a

835CHAPTER 44


Create Radiation Enclosure LBC Between Spheres

a. Create two radiation enclosure faces (inner and outer spheres)

b. LBCs tab: Heat Transfer/Encl Rad Face

c. For Name, enter Encl Rad Face_Inner

d. For Entities screen, select both the inner hemispherical surfaces

e. Click on Advanced

f. For Shell surface option select, Front; direction of the element normals is found by

Quality tab: edit/fix Elements/Fix Elements/Normals

g. For Shell surface option, select Front

h. For Absorptivity, enter 0.9

i. For Emissivity, enter 0.9

j. Click OK

b

d

ef

hi

j

g

c


CHAPTER 44836

Create Radiation Enclosure LBC Between Spheres (continued)


b. Display only the outer sphere surfaces

c. Using the Model Browser tree, hide the inner surfaces and show the outer surfaces

d. Observe the outer surfaces

d

837CHAPTER 44




b. LBCs tab: Heat Transfer/Encl Rad Face

c. For Name, enter Encl Rad Face_outer

d. For Entities screen, select both the outer hemispherical surfaces

e. Click on Advanced

f. For Shell surface option select, Front; direction of the element normals is found by

Quality tab: edit/fix Elements/Fix Elements/Normals

g. For Shell surface option, select Back

h. For Absorptivity, enter 0.7

i. For Emissivity, enter 0.7

j. Click OK

b

c

d

e

fhi

j

g


CHAPTER 44838


a. Create a single radiation enclosure

b. LBCs tab: Heat Transfer/Radiation Enclosure

c. For Name, enter Rad Enclosure

d. For Shadowing Option, select NO

e. For Unused Enclosure Faces, select Encl Rad Face_outer

f. Click the > icon

g. For Unused Enclosure Faces, select Encl Rad Face_inner

h. Click the > icon

i. Click OK

b

c

d

ef

i

gh

839CHAPTER 44


Radiation Enclosure LBC Between Spheres (continued)

a. Create a single radiation enclosure; display created Radiation Enclosure LBS form

b. In the Model Browser tree under LBC, double click Radiation Enclosure

c. Observe the form for Rad Enclosure

b

c


CHAPTER 44840

Create Radiation to Space From Outer Sphere

a. Create radiation to space (ambient)

b. LBCs tab: Heat Transfer/Rad to Space

c. For Name, enter Rad to Space

d. For Entities screen, select the two outer surfaces

e. For Ambient temperature, enter 0.0

f. For View Factor, enter 1.0

g. For Absorptivity, enter 1.0

h. For Emissivity, enter 1.0

i. For Shell surface option, enter Front

j. Click OK

b

c

de

f

gh

i

j

d

841CHAPTER 44


Create SimXpert Analysis File

a. Specify parameter values for SOL 400 analysis

b. Right click on FileSet

c. Select Create new Nastran job

d. For Job Name, enter a title

e. For Solution Type, select SOL 400

f. For Solver Input File, specify the fine name and its path

g. Unselect Create Default Layout

h. Click OK

bc

d

e

f

g

h


CHAPTER 44842

Create SimXpert Analysis File (continued)


b. Right click on Load Cases

c. Select Create Loadcase

d. For Name (Title), enter NewLoadcase

e. For Analysis Type, select Nonlinear Steady Heat Trans

f. Click OK

b

c

d

e

f

843CHAPTER 44




b. Right click on Load/Boundaries

c. Select Select Lbc Set

d. For Selected Lbc Set, select DefaultLbcSet in the Model Browser tree

e. Click OK

f. To see the contents of DefaultLbcSet, click on it in the Model Browser tree

b

c

d

e

d


CHAPTER 44844


Remember that our length unit is meter, so the correct Stefan-Boltzmann constant to pick will have units of W/M2/K4.


b. Select Solution 400 Nonlinear Parameters

c. For Default Init Temp, enter 750.0

d. For Absolute Temp Scale, select 0.0

e. For Stefan-Boltzmann, select 5.6696e-8 W/M2/K4 (Expert)

f. Click Apply

b

de

c

845CHAPTER 44


Create SimXpert Analysis File (continued)Finally let’s pick the hemicube viewfactor algorithm

a. Right Click Solver Control

b. Select Direct Input (BULK)

c.Enter nlmopts,hemicube,1

d. Check box Export this Section

e. Click Apply and Close

a

nlmopts,hemicube,1

b

c

de


CHAPTER 44846



b. Select Output File Properties

c. For Text Output, select Print

d. Click Apply

b

d

c

847CHAPTER 44



a. Specify parameter values for Sol 400 analysis

b. Double click on Loadcase Control

c. Select Subcase Steady State Heat

d. Click Temp Error

e. For Temperature Tolerance, enter 0.01

f. Click Load Error

g. For Load Tolerance, enter 1e-5

h. Click Apply

i. Click Close

b

d

c

ef

g


CHAPTER 44848


a. Specify parameter values for Sol 400 analysis

b. Right click on Output Requests

c. Select Nodal Output Requests

d. Select Create Temperature Output

e. Click OK

b

d

c

e

849CHAPTER 44


Perform SimXpert SOL 400 Thermal Analysis

a. Perform steady state heat transfer analysis Sol 400

b. Right click on rad_between_concentric_spheres

c. Select Run

d. After the analysis is complete, the shown files are created

b

d

c


CHAPTER 44850

Attach the Analysis Results File

a. Analysis complete, attach the .xdb results file

b. File: Attach Results

c. Select Results

d. Click OK

b

d

c

851CHAPTER 44


Display the Temperature Results

a. Create a fringe plot for the temperature results

b. Display just the two original surfaces (PART_1 and PART_2)

c. Results tab: Results/Fringe

d. For Result Cases, select Non-linear: 100. % of Load

e. For Result type, select Temperatures

f. Click Target entities

g. Screen select the elements for the two surfaces

c

d

e

f

g


CHAPTER 44852

Display the Temperature Results (continued)


b. Click Label attributes

c. Set color to black

d. Set format to Fixed

e. Click Update

b

cd

e

853CHAPTER 44


Display the Temperature Results (continued)

Input File(s)


b. Observe the fringe plot

File Description

nug_44a.dat MD Nastran input using Hemi-cube method

nug_44b.dat MD Nastran input using Gaussian integration method

nug_44c.datMD Nastran input with simple three grid model with user-defined radiation matrix

Ch_44b.SimXpert SimXpert model file

Ch_44c.SimXpert SimXpert model file

b709.3

1000

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch044/nug_44a.dat

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch044/nug_44b.dat

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch044/nug_44c.dat

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch044/Ch_44b.SimXpert

http://www.mscsoftware.com/doc/nastran/mdug/input_files/ch044/Ch_44c.SimXpert


CHAPTER 44854

VideoClick on the image or caption below to view a streaming video of this problem; it lasts approximately 24 minutes and explains how the steps are performed.

Figure 44-6 Video of the Above Steps

708.0

708.5

709.0

709.5

710.0

710.5



http://www.mscsoftware.com/training_videos/mdug/ch044/2010/ch044.swf

http://www.mscsoftware.com/training_videos/mdug/ch044/2010/ch044.swf

Documents

Concentric Spheres with Radiation