Transient Method for Convective Heat Transfer Measurement With Lateral Conduction—Part II: Application to an Isolated Spherical Roughness Element

Abstract

The effect of lateral conduction on convective heat transfer measurements using a transient infrared technique over an isolated spherical roughness element (bump) is evaluated. Comparisons are made between a full 3D finite-volume analysis and a simpler 1D transient conduction model. The surface temperature history was measured with a high resolution infrared camera during an impulsively started hot-gas flow at a flow Reynolds number of 860,000. The boundary layer was turbulent with the bump heights equivalent to 0.75, 1.5, and 3 times the boundary layer momentum thickness. When considering transient conduction effects only in the bump wake, the 1D approximate method underestimates the actual Stanton number estimated with the 3D model. This discrepancy is only 10% for a 75% change in St number occurring over a surface distance of 10 mm (the half-width of the wake). When the actual bump topology is accounted for in estimating the Stanton number on the bump itself with the 3D analysis technique, the increased surface area of the finite-volume cells on the protruding bump actually decreases the predicted value of St locally. The net result is that the two effects can cancel each other, and in some cases the 1D approximate technique can provide a reasonably accurate estimate of the surface heat transfer without the added complexity of the 3D finite-volume method. For the case of the largest bump tested, with maximum surface angularity exceeding 60 deg, the correction for 3D topology yields a 1D St estimate that is within 20–30% of the 3D estimate over much of the bump surface. These observed effects are valid for transient measurement techniques while the opposite is true for steady-state measurement techniques.