drjfloyd
commented
1 year ago To illustrate, the table below generates dx using a Biot number of 0.1 and dx using Sqrt(diffusivity). This is for an AST of 1000 C with h=50 W/m/K to a 20 C wall (~190 kW/m2). The effective h (radiation and convection) is ~200 W/m/K. The rows can roughly be thought of as an insulating material, something like wood, something like a plastic, a liquid pool with an effective k for convection, and a metal. At this high flux for wood like materials and insulating materials the diffusivity result is a bit large. For metals it smaller than we need. If we were at 10 % of the incident flux, the Biot dx would be 10 x bigger. We'd still be on the small side for insulating materials.
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rho | k | cp | dx Biot | dx Diff^0.5 | B / D -- | -- | -- | -- | -- | -- 100 | 0.01 | 1000 | 5.0E-06 | 3.2E-04 | 1.6E-02 1000 | 0.1 | 1000 | 5.0E-05 | 3.2E-04 | 1.6E-01 1000 | 1 | 1000 | 5.0E-04 | 1.0E-03 | 5.0E-01 1000 | 10 | 1000 | 5.0E-03 | 3.2E-03 | 1.6E+00 10000 | 100 | 1000 | 5.0E-02 | 3.2E-03 | 1.6E+01
Not for this release, but we have floated the idea of using a Biot number criterion to set the solid phase resolution near the surface. To me, this is more justifiable than assuming the time scale of 1 s applied to the thermal diffusivity. Jason has roughed out that they are reasonably similar in many cases. But I routinely find that I have to increase solid resolution to get grid converged results.