1.6.6 Axisymmetric elemental cavity radiation viewfactor calculations

Product: ABAQUS/Standard  

Relatively simple configurations were selected for these verification problems to ensure that analytical solutions or tabulated results could be found. In some cases certain parameters such as the distance between two surfaces or the number of elements on a surface were varied to illustrate the effects of these parameters on viewfactor calculations within ABAQUS. To duplicate the tabulated results for the cases where parameters were varied, the user can modify the input files provided with the ABAQUS release.

Parallel circular disks with centers along the same normal

Problem description

Analytical solution

where , , and .

Results and discussion

The number of elements along the bottom area can be varied to obtain the following results:

# of elements on bottom planeFF
ABAQUSAnalyticalABAQUSAnalytical
10.68530.68000.17130.1700
20.68360.68000.17090.1700
40.68200.68000.17050.1700

Input file

xrvda4n1.inp

DCAX4 elements are used to discretize the surfaces of the cavity; one element for the top surface and two elements for the bottom surface.

Reference

  • Siegel,  R., and J. R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 3rd, 1992.

  • Two concentric cylinders of same finite length

    Problem description

    Analytical solution

    and

    where for any argument , , and ; and where , , , and .

    Results and discussion

    FF
    ABAQUSAnalyticalABAQUSAnalytical
    0.17900.16260.10420.0925

    Input file

    xrvda4n2.inp

    One DCAX4 element is used to discretize each surface of the cavity.

    Reference

  • Siegel,  R., and J. R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 3rd, 1992.

  • Concentric cylinders of infinite length

    Problem description

    Analytical solution

    Results and discussion

    The number of elements on each face can be increased to obtain the additional results:

    # of elementsFFF
    ABAQUSAnalyticalABAQUSAnalyticalABAQUSAnalytical
    40.99831.00000.49910.50000.44090.5000
    80.99621.00000.49820.50000.45970.5000

    Input file

    xrvda4p3.inp

    Four DCAX4 elements are used to discretize each surface of the cavity. The infinite extent of the cavity is modeled by repeating the elements in the z-direction using periodic symmetry (NR = 10).

    Reference

  • Siegel,  R., and J. R. Howell, Thermal Radiation Heat Transfer, Hemisphere Publishing Corporation, Washington, 3rd, 1992.

  • Coaxial right circular cylinders of different radii, one on top of the other

    Problem description

    Analytical solution

    where , , and .

    If for , then receives no radiation from cylinder 1.

    Results and discussion

    F
    ABAQUSAnalytical
    0.50990.4793

    Input file

    xrvda4n4.inp

    DCAX4 elements are used to discretize the surfaces of the cavity; one element for the top area, and two elements for the bottom area.

    Reference

  • Howell,  J. R., A Catalog of Radiation Configuration Factors, McGraw-Hill Book Company, New York, 1982.