Simulating Surface-to-Surface thermal radiation between objects in a vacuum environment
Problem
This article describes how to set up Surface-to-Surface (S2S) radiation energy exchange between objects in a vacuum environment using
STAR-CCM+ multi-physics CFD software. Specifically, a manufactured part
(Hot_Box) is placed on top of a cooling plate (Cold_Box) is contained within a
vacuum furnace, as shown in Figure 1. In this problem, we can think of a
cooling plate as a solid metal block with coolant flowing through internal
passages. The vacuum furnace is a fully enclosed vacuum (absence of air or
other gases) environment where the furnace walls are set to a specified
temperature.
Figure 1: Thermal
radiation of a manufactured part (Hot_Box) on top of a cooling plate (Cold_Box)
within a vacuum furnace
Assumptions
-
Internally facing furnace wall surfaces, except below the assembly, are set to a specified temperature of 1000 K.
-
Cold_Box bottom surface thermal specification is defined as adiabatic.
-
Steady state fluid flow and heat transfer.
Adopt
a
co-simulation
approach
if you want to examine
transient
phenomena to take advantage of the difference in timescales between the fluid
flow and thermal radiation heat transfer mechanisms.
Domain Considerations
We are interested in the S2S radiation
interaction between the interior furnace walls and exterior manufacture part
and cooling plate surfaces. The vacuum furnace walls are simplified to a thin
two-sided (front and back) solid shell region, as shown in Figure 2. One of the
main advantages of using shell elements is that it reduces the computational
time and resources required for simulations as fewer mesh elements are present.
In this case, the furnace wall shell Front and Back surfaces are oriented
outward and inward, respectively. Therefore, we can set the Furnace Wall
Default [Back] to a specified temperature 1000 K and Default [Front] set to
Adiabatic.
Figure 2: Vacuum
Furnace Walls Simplification
The front and back surfaces of the shell region appear as
different colors, as shown in Figure 3 and 4, respectively.
Figure 3: Shell front
surface appears dark blue
Figure 4: Shell back
surface appears light blue
Conceptually, the solid shell is a mathematical
simplification that reduces the computational time and resources required to
solve as there are fewer elements present in the model, as shown in Figure 5.
Figure 5: Shell
approximated as a thin 3D object with a front and back side
Methodology
S2S thermal radiation model was
selected for this problem to simulate energy exchange between the internally
facing furnace walls and assembly inside the furnace. S2S radiation
environmental boundary conditions must be configured at three different
locations within the simulation tree - solid physics continua, solid and solid
shell regions, and radiation exchanging boundaries, as shown in Figure 6.
Figure 6: Required simulation tree setting selections for
enabling S2S radiation environmental boundary condition
Solid Physics Continua
S2S radiation must be activated in the Solids
and Solid Shell physics continuums. Specify 1000 K as the environmental
radiation
temperature
– temperature of an open boundary that has a total radiant
emittance identical to that of a black body radiator (K).
The environmental radiation temperature setting is
excluded from this specific problem for two reasons. First, the furnace walls domain
is fully enclosed meaning the Hot_Box and Cold_Box were separated from the
environment. Second, the furnace walls region Radiation Transfer Option was set
to
Internal
meaning it did not receive radiation from external
sources, as discussed below.
Solid and Shell Regions
Region
Radiation
Transfer Option
enables S2S radiation at the region level. There are
four different selections to choose from – Internal, External, Internal and
External, or None. This application has two different selections based on their
respective position in the domain, as shown in Figure 7. The furnace walls
enclose the domain, so we select
Internal
. Internal activates S2S
radiation transfer in the region. The Hot_Box and Cold_Box regions are set to
External
.
External allows region boundaries to participate in S2S radiation exchange from
the external sides while deactivating S2S radiation transfer within the region.
Figure 7: Region Radiation
Transfer Option Selection
Radiation Exchanging Boundaries
So far, we have activated S2S radiation at the physics
continua and region levels, but we haven’t modeled the vacuum environment yet.
This is resolved in the simulation domain with the solid shell region treatment
of the furnace walls (vacuum region has no mesh), but now we need to specify
the appropriate thermal boundary condition for the Hot_Box and Cold_Box
regions. Set the Hot_Box and Cold_Box externally facing boundary called
Default
thermal specification to
Convection
, as shown in Figure 8. Then
set the Heat Transfer Coefficient to 0 W/m2-K. This selection will zero out the
convection computation and only solve for radiation heat transfer.
Figure
8: Hot_Box and Cold_Box Boundary Thermal Specification
Now set the Furnace Walls [Front] and [Back] boundary within
the Furnace Walls region thermal specification to Adiabatic and Temperature
1000 K, respectively.
Results
Enabling S2S radiation environmental boundary conditions at
the continua, region, and boundary levels enables radiation energy exchange
between the furnace walls set at a specified temperature and objects within the
furnace. Setting Box_1 and Box_2 exterior boundary thermal specification treats
the empty space as a vacuum environment.
Furnace Wall shell [back] surface is set to 1000 K, as shown
in Figure 9.
Figure 9: Specified Boundary Temperature 1000 K: Furnace
Walls Shell [Back]
Furnace Wall region radiation transfer option is set to
internal. Therefore, only S2S radiation transfer within the region is allowed,
as shown in Figure 10.
Figure 10: Radiation Transfer Option, Internal - Furnace
Walls Shell [Back] boundary irradiation
Hot_Box and Cold_Box solid regions radiation transfer option
set as external. This option allows only incoming radiation from external sides
of the region, as shown in Figure 11. This means no internal radiation within
these regions.
Figure 11: Radiation Transfer Option: External - Hot_Box and
Cold_Box Irradiation on External Side of Boundary
The external surface temperature profiles of both the Hot_Box
and Cold_Box are calculated, as shown in Figure 12.
Figure 12: Hot_Box and Cold_Box exterior surface temperature
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