Sketch highlighting major features of the curved ramp models.
(a) Model of the vortex generator strip mounted in the flat plate. (b) Model of a single vortex generator element.
Sketch of experimental setup and flow features over a concave curved surface.
Baseline measurements of heat transfer for a laminar boundary layer over a flat plate section of the full length of the models. Experimental data are compared with predictions based on the model of Hayne 33 and are in reasonable agreement.
A representative heat transfer trace highlighting the effect of including a correction to remove the establishment time on the calculated mean heat transfer value.
Schlieren images and measured visual boundary layer thickness (δ) over (a) flat plate and (b) Curved30.
Measurements of visual boundary layer thickness over the large curved models. (a) Curved10, (b) Curved16, (c) Curved25, and (d) Cubic32.
Experimental heat transfer data for boundary layers developing over the different surface geometries. The solid line is a optimal curve fit to the heat transfer data, while the dashed line is the surface equation of the model with a linear scaling applied. (a) Curved10, (b) Curved16, (c) Curved25, (d) Curved30, and (e) Cubic32.
Comparison of experimental heat flux data over the Curved16 model with approximate methods of Cohen and Reshotko, 4 Bertram and Feller, 9 and Crawford. 10 Agreement near the leading edge is reasonable, but the predictions diverge sharply from the experimental data around 150 mm (θ = 11°) downstream from the leading edge.
(a) Model surface equations. (b) Pressure profiles for each model geometry calculated using the method of characteristics. (c) Mach number profiles for each geometry calculated with method of characteristics. (d) Experimental heat transfer measurements (symbols) and curve fits (solid lines) generated based on the model surface equations as described in the text.
Heat transfer data for laminar boundary layers over all models versus the local turning angle. The solid line is the pressure distribution calculated using the method of characteristics.
(a) Comparison of nondimensional heat transfer data to results from a previous study in a different facility. 14 Good agreement is observed when all data are plotted against the local turning angle of the curved surface. Each point represents the average of repeat experiments. Non-dimensionalization calculated using freestream quantities. (b) Nondimensional heat transfer data recalculated using edge quantities rather than freestream. Reasonable estimates of heat transfer indicate freestream quantities were most likely used.
Pressure sensitive paint visualization of streaks behind the vortex generators for the baseline flat plate model. The white region corresponds to location of heat transfer gages where no paint data were collected. The bottom of the image corresponds to 10 mm above the model centerline.
Comparison of heat flux distributions over a flat plate both with (⋄) and without (⧫) imposed streamwise vortices. Each point represents the average of repeat experiments.
Pressure sensitive paint visualization of the evolution of streaks on over a concave surface (Curved16). The bottom of the image corresponds to 10 mm above the model centerline.
Spanwise pressure distributions at 187 mm behind the leading edge extracted from PSP images of Curved16 model. Solid line is data taken with the vortex generator array installed, while the dashed line is data taken with no vortex generator array installed.
Comparison of heat transfer distributions over all four large models both with (○) and without (•) imposed streamwise vorticity. Each point represents the average of repeat experiments. (a) Curved16, (b) Curved10, (c) Curved25, and (d) Cubic32.
Comparison of heat transfer distributions as a function of local turning angle for all surface geometries for boundary layers with imposed streamwise vortex structures. Each data point represents the average of repeat experiments.
Theoretical parameters for HET test conditions used in this study.
Model specifications. G is the Goertler number at the initiation of curvature.
Vortex generator parameters.
Curve fit parameters used to scale the model geometry surface equations to compare with curve fits to the heat transfer data. R is the regression coefficient.
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