SummaryA method of predicting body drag in subcritical axisymmetric flow is outlined which requires only detailed body shape, free-stream conditions and transition point to be prescribed. Results of calculations for a range of body shapes are shown essentially to confirm information in Royal Aeronautical Society Data Sheets but clearly demonstrate that fineness ratio alone is not sufficient to characterise body shape. For example, at a fixed fineness ratio of 0.18, detailed changes in body contour are shown to produce 10 per cent changes in drag coefficient.
SummaryAn approximate analysis of conditions at separation produced by turbulent boundary-layer/shock-wave interaction is presented for swept, cylindrically symmetric flows. An integral boundary-layer prediction method is used, incorporating Johnston crossflow profiles. The results indicate a marked reduction in pressure rise required to produce separation as sweep is increased. At low Reynolds numbers the skin friction at separation is inferred to be small, whereas at higher Reynolds numbers the presence of a vigorous streamwise flow may be detected. In the limiting case of zero sweep, or two-dimensional flow, predictions using the approximate analysis are shown to compare well with experimental results of pressure rise to separation.
SummaryFor boundary layer flows over curved surfaces at moderately high supersonic speeds the existence of normal pressure gradients within the boundary layer becomes important even for small curvatures and they cannot be ignored. The describing equations are basically parabolic in form so that the simplifications inherent in hyperbolic flows would not at first sight seem to be relevant. However, the equations of motion for a two-dimensional, supersonic, rotational, viscous flow are analysed along the lines of a hyperbolic flow and the individual effects of viscosity and vorticity are examined with regard to the isobar distributions. It is found that these two properties have compensating effects and the experimental evidence presented confirms the conclusion that inside the boundary layer the isobars follow much the same rules as those which determine the isobars in the external hyperbolic flow. Since for turbulent boundary layers the fullness of the Mach number profile produces almost linear Mach lines in the boundary layer, this provides a simple extension to the methods of analysis, and the momentum integral equation is reformulated using a swept element bounded by linear isobars. The final equation is similar in form to the conventional one except that the momentum and displacement thicknesses are now defined by integrals along the swept isobars, and all normal pressure gradients due to centrifugal effects are accounted for.
SUMMARYAn inverse inviscid-boundary-layer interaction scheme is presented for the optimal design of axisymmetric ducts for subsonic, rotational flows. Distribution of the shape factor R on the duct wall, giving minimum total pressure loss and maximum static pressure rise, is used as boundary condition for the inverse integral boundary-layer solution, to obtain the velocity and displacement thickness distributions on the wall. Vector addition of the inviscid core radius, derived from the solution of the inverse inviscid flow equations, and the displacement thickness produces the desired duct shape.
A duct design algorithm is presented by which duct wall shapes are produced directly from prescribed wall friction velocity distributions. The method is based on matched axisymmetric core flow and integral boundary layer solutions in which the flow is assumed to be in viscid in the core, turbulent in the boundary layer and incompressible throughout. An inverse boundary layer analysis is based on Coles profiles coupled with momentum and entrainment equations. Wall friction velocity is used as the major boundary condition which leads to the calculation of the required core velocity at the boundary layer edge. This velocity distribution is simultaneously employed as the major boundary condition in an inverse core flow calculation which is based on an inverted form of the Stokes-Beltrami equation. The displacement surface method is used to match boundary layer and core solutions which together lead to a predicted duct shape. Numerical results are presented, some of which include separated boundary layer flows. An assessment of the influence of wall friction velocity distribution on duct shape and wall pressure field is included.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.