Average Skin Friction Coefficient Measurements in Constant Area Rectangular Ducts With Supersonic Flow

Internal supersonic duct flows with constant cross-sectional area are primarily encountered in scramjet isolators, wind-tunnel test sections and diffusers. For a given set of duct-entry conditions, predicting the flow properties at the exit of the duct requires an accurate estimate of the average skin-friction coefficient and average heat-transfer coefficient along the flow. The skin-friction coefficient is linked to the heat-transfer coefficient through the temperature-velocity relationship (Reynolds analogy). In a shock-free, constant-area rectangular duct, variations in the core-flow properties arise mainly from boundary-layer displacement thickness growth on all the walls. This confinement effect modifies the circulation per unit length within the boundary layer and thereby influencing the average skin-friction coefficient. In this work, the average skin-friction coefficient is measured using static-pressure differences between the duct inlet and exit. Existing measurement framework in the literature rely on a one-dimensional flow model to extract average skin friction coefficient using static pressure information at duct inlet and exit. The present study introduces a novel measurement framework using core-flow boundary-layer model that is more consistent with the physical flow characteristics of confined supersonic duct flows. A systematic experimental study is performed at Mach 2.0 inlet flow and by sweeping Reynolds number over a large range. The measurement from the one-dimensional flow model and core-flow boundary-layer model is compared. Furthermore, a detailed scaling relationship is developed for results obtained from core-flow boundary-layer model which captures the influence of duct confinement effects in addition to influence from Reynolds number, Mach number, Prandtl number, and wall temperature ratio.