Uncertainty Analysis of Coaxial Thermocouple Calorimeters used in Arc Jets

Recent introduction of Coaxial Thermocouple type calorimeters into the NASA Ames arc jet facilities has inspired an analysis of 2D conduction effects internal to this type of calorimeter. Lateral conduction effects violate the 1D finite slab inverse analysis which is typically used to deduce the heat transfer to such calorimeters. The spherical shaped nose associated with most calorimeters (rather than flat) leads to a bias error that over-estimates the stagnation heating. Non-uniform heating on the face of spherically shaped calorimeters leads to conduction losses to the colder rim of the calorimeter which causes an underestimate of the stagnation heating. These two effects come into play at different times of the calorimeter's exposure to the arc jet, so they do not cancel. The spherical body effects come into play in the early stages of exposure, while the non-uniform heating effect becomes most severe at the later stages of exposure. The bias associated with spherical effects can be avoided by rewriting the 1D finite slab inverse analysis code to solve for 1D conduction in spherical coordinates. However, reducing the bias error associated non-uniform heating requires a somewhat ad hoc modification to the 1D finite element inverse analysis.