Modeling Unsteady Surface Pressure Autospectra for Turbulent Boundary-Layer Flow over Small Dense Roughness

Abstract

This work concentrates on analyzing and modeling the unsteady surface pressure autospectra beneath zero-pressure gradient, turbulent boundary-layer flowfields with variably rough flow surfaces. These surface conditions are qualitatively described as being for small, dense, rigid, spatially homogeneous roughness topologies, along with corresponding quantitative parameters. Turbulent boundary-layer velocity and unsteady surface pressure data from a new wind tunnel test with multiple surface conditions are analyzed in conjunction with the compiled results from five, distinct, additional references. These compiled results are utilized to develop and propose a new empirical model for the unsteady surface pressure autospectra for a range of variably rough surfaces. This new modeling framework is approached as an extension of the Goody model, which pertains to smooth-wall flows. The variable character of the newly proposed model is controlled by parameters based on viscous scaling of the effective roughness height and friction velocity such that the surface pressure model inputs are based on readily available mean properties of the turbulent boundary-layer flowfield. For the data utilized in this analysis the approximate values of viscous scaled effective roughness height range between approximately 100 and 2000. Finally, this newly proposed model is used to compare to the unsteady surface pressure data of two additional and separate experimental references for rough-wall flows, yielding further positive comparisons as well as isolated examples of the sensitivity of analysis and modeling to the determined friction velocity for a flow configuration.