Experimental Heat Transfer Behavior of a Turbulent Boundary Layer on a Rough Surface With Blowing

Abstract

Heat transfer measurements were made with a turbulent boundary layer on a rough, permeable plate with and without blowing. The plate was an idealization of sand-grain roughness, comprised of 1.25 mm spherical elements arranged in a most-dense array with their crests coplanar. Five velocities were tested, between 9.6 and 73 m/s, and five values of the blowing fraction, vo/u∞, up to 0.008. These conditions were expected to produce values of the roughness Reynolds number (Reτ = uτks/ν) in the “transitional” and “fully rough” regimes (5 ≤ Reτ, ≤ 70, Reτ > 70). With no blowing, the measured Stanton numbers were substantially independent of velocity everywhere downstream of transition. The data lay within ±7 percent of the mean for all velocities even though the roughness Reynolds number became as low as 14. It is not possible to determine from the heal transfer data alone whether the boundary layer was in the fully rough state down to Re = 14, or whether the Stanton number in the transitionally rough state is simply less than 7 percent different from the fully rough value for this roughness geometry. The following empirical equations describe the data from the present experiments for no blowing: Cf2=0.0036θr−0.25St=0.0034Δr−0.25 In these equations, r is the radius of the spherical elements comprising the surface, θ is the momentum thickness, and Δ is the enthalpy thickness of the boundary layer. Blowing through the rough surface reduced the Stanton number and also the roughness Reynolds number. The Stanton number appears to have remained independent of free stream velocity even at high blowing; but experimental uncertainty (estimated to be ±0.0001 Stanton number units) makes it difficult to be certain. Roughness Reynolds numbers as low as nine were achieved. A correlating equation previously found useful for smooth walls with blowing was found to be applicable, with interpretation, to the rough wall case as well: StSt0Δ=ln(1+B)B1.25(1+B).25 Here, St is the value of Stanton number with blowing at a particular value of Δ (the enthalpy thickness). St0 is the value of Stanton number without blowing at the same enthalpy thickness. The symbol B denotes the blowing parameter, vo/u∞ St. The comparison must be made at constant Δ for rough walls, while for smooth walls it must be made at constant ReΔ.