Simulating Surface-to-Surface thermal radiation between objects in a vacuum environment

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.

       CFD simulation of vacuum furnace, thermal radiation of a manufactured part (Hot_Box) on top of a cooling plate (Cold_Box) within a vacuum furnace
      Figure 1: Thermal radiation of a manufactured part (Hot_Box) on top of a cooling plate (Cold_Box) within a vacuum furnace

Assumptions

  1. Internally facing furnace wall surfaces, except below the assembly, are set to a specified temperature of 1000 K. 
  2. Cold_Box bottom surface thermal specification is defined as adiabatic.
  3. 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.

       Vacuum Furnace Walls Simplified as a Shell Region
       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.

       Shell front surface appears dark blue
       Figure 3: Shell front surface appears dark blue

       Shell back surface appears light 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.

       Shell diagram, Shell approximated as a thin 3D object with a front and back side
       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.

       Simulation tree, Required simulation tree setting selections for enabling S2S radiation environmental boundary condition
      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.

       Vacuume furnace regions, Region Radiation Transfer Option Selection
      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.


       Simulation tree, setting exterior boundary thermal specification to Convection (Vacuum)
       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.

       furnace walls temperature
       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.

       furnace walls boundary irradiation
       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.


       parts boundary irradiation on external side

       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.


       Hot_Box and Cold_Box exterior surface temperature
       Figure 12: Hot_Box and Cold_Box exterior surface temperature

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