Incipient Separation in Shock Wave Boundary Layer Interactions as Induced by Sharp Fin

The incipient separation induced by the shock wave turbulent boundary layer interaction at the sharp fin is the subject of present study. Existing theories for the prediction of incipient separation, such as those put forward by McCabe (1966) and Dou and Deng (1992), can have thus far only predicting the direction of surface streamline and tend to over-predict the incipient separation condition based on the Stanbrook's criterion. In this paper, the incipient separation is firstly predicted with Dou and Deng (1992)'s theory and then compared with Lu and Settles (1990)' experimental data. The physical mechanism of the incipient separation as induced by the shock wave/turbulent boundary layer interactions at sharp fin is explained via the surface flow pattern analysis. Furthermore, the reason for the observed discrepancy between the predicted and experimental incipient separation conditions is clarified. It is found that when the wall limiting streamlines behind the shock wave becomes\ aligning with one ray from the virtual origin as the strength of shock wave increases, the incipient separation line is formed at which the wall limiting streamline becomes perpendicular to the local pressure gradient. The formation of this incipient separation line is the beginning of the separation process. The effects of Reynolds number and the Mach number on incipient separation are also discussed. Finally, a correlation for the correction of the incipient separation angle as predicted by the theory is also given.Comment: 34 pages; 9 figure

Transition studies and skin friction measurements on an insulated flat plate at a hypersonic mach number

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. An investigation of transition and skin friction on an insulated flat plate, 5 x 26 inches, was made in the GALCIT 5 x 5 inch Hypersonic Wind Tunnel, Leg No. 1, at a nominal Mach number of 5.8. The phosphorescent lacquer technique was used for transition detection and was found to be in good agreement with total-head rake measurements along the plate surface and pitot boundary layer surveys. It was found that the boundary layer was laminar at Reynolds numbers of at least 5 x 10[superscript 6]. It was also observed that transverse contamination due to the turbulent boundary layer on the tunnel sidewall originated far downstream of the flat plate leading edge at Reynolds numbers of 1.5 to 2 x 10[superscript 6], and spread at a uniform angle of 5 1/2[degrees] compared with 9 1/2[degrees] in low speed flow. The effect of two-dimensional and local disturbances was investigated. The technique of air injection into the boundary layer as a means of stimulating transition was extensively used. It was observed that, although the onset of transition occurred at Reynolds numbers down to 10[superscript 6], a fully developed turbulent boundary layer was not obtained at Reynolds numbers much below 2 x 10[superscript 6] regardless of the amount of air injected. A qualitative discussion of these results is given with emphasis on the possibility of a greater stability of the laminar boundary layer in hypersonic flow than at lower speeds. Direct skin friction measurements were made by means of the floating element technique incorporating a null system using chain loading, over a range of Reynolds numbers (based on distance from leading edge) from 10[superscript 6] to 4 x 10[superscript 6]. Without artificial tripping, the boundary layer was verified as being laminar over the complete range. With air injection, turbulent shear was obtained only for Reynolds numbers greater than 2 x 10[superscript 6] , this value being in good agreement with earlier results of this investigation. The turbulent skin friction coefficient was found to be approximately 0.40 of that for incompressible flow for a constant value of R[subscript theta], and 0.46 for an effective Reynolds number between 5 and 6 x 10[superscript 6]

Determinants of transstenotic gradients observed during angioplasty: An experimental model

Pressure gradient measurement across a stenosis is used during angiopiasty to aid catheter positioning and estimate dilatation efficacy. The angiopiasty catheter itself, however, further reduces lumen size, and therefore augments the transstenotic gradient. To more precisely define the catheter influence on gradient, we derived a theoretical expression relating the measured gradient with the angiopiasty catheter in situ to the true gradient; that is, the gradient in the absence of the angiopiasty catheter. We then tested this theoretical construct in a canine femoral artery angiopiasty model. Fifty-four measurements were performed using 23 separate, 3-mm-long, 40 to 70% stenoses. As predicted by the theoretic model, true gradient is compounded by the angiopiasty catheter principally as a function of the angiopiasty catheter diameter (Dc) and the stenosis diameter (Ds). The best-fit curve of data points relating true and compounded gradients to various Dc and Ds combinations can be expressed as: Measured gradient = K × true gradient, where K = 0.25 (e)4.47 (Dc÷Ds and e = 2.718. Thus, the transstenotic gradient measured at angiopiasty overestimates true resting gradient in a predictable manner, which is dependent on the ratio of Dc to Ds. © 1983