Axisymmetric-Harmonic 8-Node Thermal Solid
PLANE78 is used as an axisymmetric ring element with a 3-D thermal conduction capability. The element has one degree of freedom, temperature, at each node. PLANE78 is a generalization of PLANE77 in that it allows nonaxisymmetric loading. Various loading cases are described in Harmonic Axisymmetric Elements with Nonaxisymmetric Loads.
The 8-node elements have compatible temperature shapes and are well suited to model curved boundaries.
The element is applicable to an axisymmetric geometry for steady-state or transient thermal analyses. See PLANE78 in the Mechanical APDL Theory Reference for more details about this element. If the model containing the element is also to be analyzed structurally, the element should be replaced by the equivalent structural element (such as PLANE83).
The geometry, node locations, and the coordinate system for
this axisymmetric thermal solid element are shown in Figure 78.1: PLANE78 Geometry. The data input is essentially the same as
for PLANE77 and is described in "PLANE77 Input Data". The element input data also includes the
number of harmonic waves (
MODE on the MODE command) and the symmetry condition (
ISYM on the MODE command). If
MODE = 0 and
ISYM = 1, the
element behaves similarly to the axisymmetric case of PLANE77. If
MODE equals 1,
the temperature is assumed to be 0° along an entire diameter.
ISYM parameters describe the type of temperature distribution and are
discussed in detail in Harmonic Axisymmetric Elements with Nonaxisymmetric Loads.
Element loads are described in Nodal Loading. Harmonically varying bulk temperatures or heat fluxes (but not both) may be input as surface loads on the element faces as shown by the circled numbers on Figure 78.1: PLANE78 Geometry. Harmonically varying heat generation rates may be input as element body loads at the nodes. If the node I heat generation rate HG(I) is input and all others are unspecified, they default to HG(I). If all corner node heat generation rates are specified, each midside node heat generation rate defaults to the average heat generation rate of its adjacent corner nodes.
I, J, K, L, M, N, O, P
MP command: KXX, KYY, KZZ, DENS, C, ENTH
face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)
face 1 (J-I), face 2 (K-J), face 3 (L-K), face 4 (I-L)
HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P)
Number of harmonic waves around the circumference (MODE)
Symmetry condition (MODE)
Specific heat matrix:
Consistent specific heat matrix
Diagonalized specific heat matrix
The solution output associated with the element is in two forms:
Nodal temperatures included in the overall nodal solution
Additional element output as shown in Table 78.1: PLANE78 Element Output Definitions
Convection heat flux is positive out of the element; applied heat flux is positive into the element. The element output directions are parallel to the element coordinate system. The face area and the heat flow rate are on a full 360° basis. For more information about harmonic elements, see Harmonic Axisymmetric Elements with Nonaxisymmetric Loads. A general description of solution output is given in Solution Output. See the Basic Analysis Guide for ways to view results.
The Element Output Definitions table uses the following notation:
A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file Jobname.OUT. The R column indicates the availability of the items in the results file.
In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.
Table 78.1: PLANE78 Element Output Definitions
|NODES||Nodes - I, J, K, L, M, N, O, P||Y||Y|
|MODE||Number of waves in loading||Y||Y|
|XC, YC||Location where results are reported||Y||3|
|HGEN||Heat generations HG(I), HG(J), HG(K), HG(L), HG(M), HG(N), HG(O), HG(P)||Y||-|
|TG:X, Y, SUM, Z||Thermal gradient components and vector sum (X and Y) at centroid||1||1|
|TF:X, Y, SUM, Z||Thermal flux (heat flow rate/cross-sectional area) components and vector sum (X and Y) at centroid||1||1|
|TAVG, TBULK||Average of the two end nodal temperatures evaluated at peak value, fluid bulk temperature at peak value||2||2|
|HEAT RATE||Heat flow rate across face by convection||2||2|
|HEAT RATE/AREA||Heat flow rate per unit area across face by convection||2||2|
|HFAVG||Average film coefficient of the face||-||2|
|TBAVG||Average face bulk temperature||-||2|
|HFLXAVG||Heat flow rate per unit area across face caused by input heat flux||-||2|
|HFLUX||Heat flux at each node of face||2||2|
Available only at centroid as a *GET item.
Table 78.2: PLANE78 Item and Sequence Numbers lists output available through the ETABLE command using the Sequence Number method. See The General Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 78.2: PLANE78 Item and Sequence Numbers:
Table 78.2: PLANE78 Item and Sequence Numbers
The element must not have a negative or a zero area.
The element must lie in the global X-Y plane as shown in Figure 78.1: PLANE78 Geometry and the Y-axis must be the axis of symmetry for axisymmetric analyses.
An axisymmetric structure should be modeled in the +X quadrants.
A face with a removed midside node implies that the temperature varies linearly, rather than parabolically, along that face. See Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for more information about the use of midside nodes.
If the thermal element is to be replaced by the analogous structural element (PLANE83) with surface stresses requested, the thermal element should be oriented so that face IJ (and also face KL, if applicable) is a free surface. A free surface of the element (that is, not adjacent to another element and not subjected to a boundary constraint) is assumed to be adiabatic.
Thermal transients having a fine integration time step and a severe thermal gradient at the surface will also require a fine mesh at the surface.
Temperature-dependent material properties (including the film coefficient) are assumed to be axisymmetric even if the temperature varies harmonically.
MODE = 0, properties
are evaluated at the temperatures calculated in the previous substep
(or at TUNIF if for the first substep).
MODE > 0, properties
are evaluated at temperatures calculated from the previous
MODE = 0 substep; if no
MODE = 0 substep exists, then evaluation is done at 0.0 degrees.