Two-Dimensional Viscous Flows with Large Distributed Surface Injection. Part I. Boundary Layer Flows with Large Injection and Heat Transfer. Part II. Experiments in Supersonic Turbulent Flow with Large Distributed Surface Injection. Part III. The Effect of Finite Plate Length

Citation

Fernandez, Fernando Lawrence (1969) Two-Dimensional Viscous Flows with Large Distributed Surface Injection. Part I. Boundary Layer Flows with Large Injection and Heat Transfer. Part II. Experiments in Supersonic Turbulent Flow with Large Distributed Surface Injection. Part III. The Effect of Finite Plate Length. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/TCCK-HT69. https://resolver.caltech.edu/CaltechETD:etd-10302003-155216

Abstract

This report is concerned primarily with the effect of surface injection on viscous two-dimensional flows. More precisely, the investigation centers on surface injection rates where the wall shear has been considerably reduced below the no-injection value, but where the momentum of the injectant is still negligible compared to that in the free stream. Three separate problems are investigated to try to obtain an understanding of the physical mechanisms which control the flow.

For the case of laminar boundary-layer flow, asymptotic solutions are obtained for large injection and heat transfer. It is found in this case that the boundary layer may be divided into two regions: (1) an inner region adjacent to the surface where viscous mixing plays a minor role; (2) a viscous layer where the transition occurs from the inner solution to the inviscid flow outside the boundary layer. In the case of the insulated wall the viscous layer contributes only small corrections to the boundary-layer properties. For the highly-cooled wall the boundary layer is strongly influenced by the viscous mixing between the inviscid outer flow and the high density low-speed gas adjacent to the wall.

For turbulent flow, experiments with constant distributed surface injection at M_∞=2.6 have been performed. These show that large injection leads to a constant pressure self-similar flow with linear growth. The experimental results are shown to be in good agreement with low Mach number experiments when the normal coordinate is stretched by using a Howarth-Dorodnitsyn transformation at the same value of the ratio of wall mass flow per unit area to that in the free stream.

Finally, the third part considers the upstream effect of the termination of injection on the flow in the "blown" layer. An analysis, using an integral approach is presented which agrees with the experimentally observed effects. In particular, as injection rates approaching the maximum value which can be entrained by a constant pressure mixing layer are approached, the analysis predicts that virtually the entire porous region experiences a falling pressure. It is postulated that this effect provides for a smooth transition from a boundary-layer flow to one where mixing is negligible, except in a thin layer near the streamline which divides the injected and freestream gas. Therefore, the analysis provides the step which gives a quantitative estimate for the range of injection rates in turbulent flow where the effect of mixing can be neglected and inviscid flow models utilized.

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