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Instantaneous, dynamic and time-averaged characteristics of the vortex structures which are shed from the dimples placed on one wall of a channel are described. The dimpled test surface contains 13 staggered rows of dimples in the streamwise direction, where each dimple has a print diameter of 5.08 cm, and a ratio of depth to print diameter of 0.2. Considered are Reynolds numbers (based on channel height) ReH from 600 to 11 000, and ratios of channel height to dimple print diameter H/D of 0.25, 0.50, and 1.00. For all three H/D, a primary vortex pair is periodically shed from the central portion of each dimple, including a large upwash region. This shedding occurs periodically and continuously, and is followed by inflow advection into the dimple cavity. The frequency of these events appears to scale on time-averaged bulk velocity and dimple print diameter, which gives nondimensional frequencies of 2.2–3.0 for all three H/D values considered. As H/D decreases, (i) the strength of the primary vortex pair increases, and (ii) two additional secondary vortex pairs (which form near the spanwise edges of each dimple) become significantly stronger, larger in cross section, and more apparent in flow visualization images and in surveys of time-averaged, streamwise vorticity. The locations of these primary and secondary vortex pairs near the dimpled surface coincide closely with locations where normalized Reynolds normal stress is augmented. This evidences an important connection between the vortices, Reynolds normal stress, and mixing. The large-scale unsteadiness associated with this mixing is then more pronounced, and encompasses larger portions of the vortex structure (and thus extends over larger volumes) as H/D increases from 0.25 to 1.0.

Randomly placed, nonuniform, three-dimensional roughness with irregular geometry and arrangement is analyzed. New correlations are presented for such roughness for determination of magnitudes of equivalent sand grain roughness size ks from a modified version of the Sigal and Danberg parameter Λs. Also described are the numerical procedures employed to determine Λs from three-dimensional profilometry data. The sand grain roughness values determined with this approach are then compared with and verified byks magnitudes determined using: (i) analytic geometry for uniformly shaped roughness elements arranged in a regular pattern on a test surface, and (ii) measurements made with nonuniform, three-dimensional, irregular roughness with irregular geometry and arrangement. The experiments to obtain these measurements are conducted using this latter type of roughness placed on the walls of a two-dimensional channel. Skin friction coefficients are measured in this channel with three different types of rough surfaces on the top and bottom walls, and agree very well with values determined using the numerical procedures and existing correlations. The techniques described are valuable because they enable the determination of equivalent sand grain roughness magnitudes, for similar three-dimensional roughness, entirely from surface geometry after it is characterized by three-dimensional optical profilometry data.

In this paper, the transonic flow pattern and its influence on heat transfer on a high-pressure turbine blade tip are investigated using experimental and computational methods. Spatially resolved heat transfer data are obtained at conditions representative of a single-stage high-pressure turbine blade (Mexit=1.0, Reexit=1.27×106, gap=1.5% chord) using the transient infrared thermography technique within the Oxford high speed linear cascade research facility. Computational fluid dynamics (CFD) predictions are conducted using the Rolls-Royce HYDRA/PADRAM suite. The CFD solver is able to capture most of the spatial heat flux variations and gives prediction results, which compare well with the experimental data. The results show that the majority of the blade tip experiences a supersonic flow with peak Mach number reaching 1.8. Unlike other low-speed data in the open literature, the turbine blade tip heat transfer is greatly influenced by the shock wave structure inside the tip gap. Oblique shock waves are initiated near the pressure-side edge of the tip, prior to being reflected multiple times between the casing and the tip. Supersonic flow within the tip gap is generally terminated by a normal shock near the exit of the gap. Both measured and calculated heat transfer spatial distributions illustrate very clear stripes as the signature of the multiple shock structure. Overall, the supersonic part of tip experiences noticeably lower heat transfer than that near the leading-edge where the flow inside the tip gap remains subsonic.