Three-dimensional thermal boundary layer corrections for circular heat flux gauges mounted in a flat plate with a surface temperature discontinuity

Three-dimensional Navier–Stokes computational fluid dynamics (CFD) analysis has been performed in an effort to determine thermal boundary layer correction factors for circular convective heat flux gauges (such as Schmidt–Boelter and plug type) mounted flush in a flat plate subjected to a stepwise surface temperature discontinuity. Turbulent flow solutions with temperature-dependent properties are obtained for a freestream Reynolds number of 1E6, and freestream Mach numbers of 2 and 4. The effect of gauge diameter and the plate surface temperature have been investigated. The 3D CFD results for the heat flux correction factors are compared to quasi-2D results deduced from constant property integral solutions and also 2D CFD analysis with both constant and variable properties. The role of three-dimensionality and of property variations on the heat flux correction factors has been demonstrated.