Effects of a Realistically Rough Surface on Vane Heat Transfer Including the Influence of Turbulence Condition and Reynolds Number

Heat transfer distributions are experimentally acquired and reported for a vane with both a smooth and a realistically rough surface. Surface heat transfer is investigated over a range of turbulence levels (low (0.7%), grid (8.5%), aerocombustor (13.5%), and aerocombustor with decay (9.5%)) and a range of chord Reynolds numbers (⁠$ReC=500,000$⁠, 1,000,000, and 2,000,000). The realistically rough surface distribution was generated by Brigham Young University’s accelerated deposition facility. The surface is intended to represent a TBC surface that has accumulated 7500 h of operation with particulate deposition due to a mainstream concentration of 0.02 ppmw. The realistically rough surface was scaled by 11 times for consistency with the vane geometry and cast using a high thermal conductivity epoxy $(k=2.1W/m/K)$ to comply with the vane geometry. The surface was applied over the foil heater covering the vane pressure surface and about 10% of the suction surface. The $958×573$ roughness array generated by Brigham Young on a $9.5×5.7mm2$ region was averaged to a $320×191$ array for fabrication. The calculated surface roughness parameters of this scaled and averaged array included the maximum roughness, $Rt=1.99mm$⁠, the average roughness, $Ra=0.25mm$⁠, and the average forward facing angle, $αf=3.974deg$⁠. The peak to valley roughness, Rz, was determined to be 0.784 mm. The sand grain roughness of the surface $(kS=0.466mm)$ was estimated using a correlation offered by Bons (2005, “A Critical Assessment of Reynolds Analogy for Turbine Flows,” ASME J. Turbomach., 127, pp. 472–485). Based on estimates of skin friction coefficient using a turbulence correlation with the vane chord Reynolds numbers representative values for the surface’s roughness Reynolds number are 23, 43, and 80 for the three exit condition Reynolds numbers tested. Smooth vane heat transfer distributions exhibited significant laminar region augmentation with the elevated turbulence levels. Turbulence also caused early transition on the pressure surface for the higher Reynolds numbers. The rough surface had no significant effect on heat transfer in the laminar regions but caused early transition on the pressure surface in every case.