This section shows how to reduce solution time for a model with symmetry using view factor condensation. The example problem described here models radiation within a U-shaped groove. It is an open enclosure, 3D solid body with planar symmetry. Similar calculations can be performed for a model with cyclic symmetry and models with extrusions. Efficiency gains using view factor condensation are larger for models with higher degrees of symmetry.
Figure 5.10: U-shaped Groove Modeled as an L-Shaped Solid with Symmetry illustrates the example problem, geometry, and the ambient and applied temperature at the bottom of the U-shaped groove as specified in the command input listing. To model radiation between the surfaces of the U-shaped bracket (A) and its ambient environment, the planar symmetry can be leveraged to reduce the problem to an L-shape with symmetry (B, C).
As can be seen in the front (B) and the oblique (C) views of the element
plot, the L-shape is modeled with:
| SOLID278 solid body elements (purple) that model the plates with radiating surfaces and a corner body element, and |
| surface elements (blue) overlain on the body elements with radiating surfaces to support radiation surface loads and calculate view factors using the radiosity solver method. The independent (blue in B) and dependent (red in B) facets are SURF252 elements created by defining the plane of symmetry via the RSYMM command and then issuing the RSURF command (See Commands for Building and Solving the Model). |
The view factor calculation for a symmetric geometry accounts for all radiating surfaces, including independent facets with underlying solid elements and dependent facets that are created from independent facets via the RSURF command based on RSYMM parameters. The concept of independent and dependent facets is illustrated in Figure 5.10: U-shaped Groove Modeled as an L-Shaped Solid with Symmetry (B and C).
View factor condensation significantly reduces solution time by leveraging model
symmetry. The level of condensation is set using the
LEVEL argument on the VFCO
command. For this example problem, LEVEL is set to 1,
which condenses the view factor matrix and solves only for independent facets to
achieve better efficiency than for LEVEL = 0 (no
condensation). A more aggressive view factor condensation could be achieved by
setting LEVEL = 2, but it requires more memory and loses
some information (See VFCO for details).
For a detailed description of the underlying theory used in view factor condensation see View Factor Matrix for a Model with Symmetry in the Theory Reference and Radiosity Equations Simplified for Models with Symmetry in the Theory Reference.
The following sequence of commands builds and solves the finite element model. Text preceded by an exclamation mark (!) is comment text.
/batch,list /title, L shape plate with reflection symmetry for radiosity L1 = 2 !plate length L2 = 3 !plate height th = 0.2 !plate thickness w1 = 1 !plate depth /prep7 et,1,278 !define SOLID278 3D thermal element block,0,th,th,th+L2,0,w1 block,0,th,0,th,0,w1 block,th,th+L1,0,th,0,w1 vglue,all esize,4 vmesh,all mp,kxx,1,4 !------------------------------------- nsel,s,loc,x,0 nsel,a,loc,y,0 d,all,temp,400 nsel,inve sf,all,rdsf,.3,1 !define radiosity surfaces nsel,all !--------------------------------------- stef,5.67e-8 toffst,273 spctemp,1,25 hemiopt,1000 local,11,0,th+L1 !define coordinate system csys,0 rsymm,define,11,x !define plane of symmetry rsymm,stat rsurf !create surf252 radiosity elements ( independent & dependent facets ) etlist elist /show,jpeg /view,1,1,1,1 eplot /show,close fini /aux12 mprint,1 vfco,,1,1 !condense dependent facets during vfopt,new command vfco,stat !list the enclosure number and level of view factor condensation vfopt,new,,,,,,on !compute viewfactors and write to file ( independent facets only ) rsymm,clear !remove plane of symmetry rsurf,clear,all !remove surf252 radiosity elements rsurf !create surf252 radiosity elements ( independent facets only ) vfopt,read !read in viewfactors ( independent facets only ) fini /solu allse radopt,,1.e-6,2 cnvtol,heat,-1 cnvtol,temp,,1.e-9 nsub,1 save solve fini /post1 set,last esel,s,type,,1 nsle,s prnsol,temp prrsol /show,jpeg plnsol,temp /show,close allse *get,radheat1,rad,1,nethf /com, /com, Net heat rate lost by enclosure: %radheat1% /com, esel,s,ename,,252 presol,nmisc,5 ! Temp presol,nmisc,7 ! Net radiation heat flux presol,nmisc,8 ! Emitted radiation heat flux presol,nmisc,9 ! Reflected radiation heat flux presol,nmisc,10 ! Incident radiant heat flux /show,jpeg plesol,nmisc,7 /show,jpeg esel,all fini /exit,nosave
