Base Pressure Associated With Incompressible Flow Past Wedges at High Reynolds Numbers

1979 ◽  
Vol 46 (3) ◽  
pp. 483-492 ◽  
Author(s):  
N. R. Warpinski ◽  
W. L. Chow
Keyword(s):  
Boundary Layer ◽  
Incompressible Flow ◽  
Inviscid Flow ◽  
The Body ◽  
Base Pressure ◽  
Jet Mixing ◽  
Flow Past ◽  
Wedge Surface ◽  
Surface Jet ◽  
High Reynolds

A model is suggested to study the viscid-inviscid interaction associated with steady incompressible flow past wedges of arbitrary angles. It is shown from this analysis that the determination of the nearly constant pressure (base pressure) prevailing within the near wake is really the heart of the problem and this pressure can only be determined from these interactive considerations. The basic free streamline flow field is established through two discrete parameters which should adequately describe the inviscid flow around the body and the wake. The viscous flow processes such as boundary-layer buildup along the wedge surface, jet mixing, recompression, and reattachment which occurs along the region attached to the inviscid flow in the sense of the boundary-layer concept, serve to determine the aforementioned parameters needed for the establishment of the inviscid flow. It is found that the point of reattachment behaves as a saddle point singularity for the system of equations describing the viscous recompression process. Detailed results such as the base pressure, pressure distributions on the wedge surface, and the wake geometry as well as the influence of the characteristic Reynolds number are obtained. Discussion of these results and their comparison with the experimental data are reported.

Introduction

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
The Body ◽  
Separation Theory ◽  
Wedge Surface ◽  
Classical Boundary ◽  
High Reynolds ◽  
Reynolds Number Flows

This book investigates high-Reynolds number flows, and analyses flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including Blasius’s boundary layer on a flat plate, Falkner–Skan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers the so-called ‘self-induced separation’ in supersonic flow, and which led to the ‘triple-deck model’. It also presents Sychev’s 1972 theory of the boundary-layer separation in an incompressible fluid flow past a circular cylinder. It discusses the triple-deck flow near the trailing edge of a flat plate, and then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It covers the Marginal Separation theory—a special version of the triple-deck theory—and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.

Fluid Dynamics

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Fluid Dynamics ◽  
Boundary Layer ◽  
Flat Plate ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
The Body ◽  
Separation Theory ◽  
Wedge Surface ◽  
Classical Boundary ◽  
High Reynolds

This is Part 3 of a book series on fluid dynamics. This is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture courses, and then progressing through more advanced material up to the level of modern research in the field. This book is devoted to high-Reynolds number flows. It begins by analysing the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory. These analyses include the Blasius boundary layer on a flat plate, the Falkner-Skan solutions for the boundary layer on a wedge surface, and other applications of Prandtl’s theory. It then discusses separated flows, and considers first the so-called ‘self-induced separation’ in supersonic flow that was studied in 1969 by Stewartson and Williams, as well as by Neiland, and led to the ‘triple-deck model’. It also presents Sychev’s 1972 theory of the boundary-layer separation in an incompressible fluid flow past a circular cylinder. It discusses the triple-deck flow near the trailing edge of a flat plate first investigated in 1969 by Stewartson and in 1970 by Messiter. It then considers the incipience of the separation at corner points of the body surface in subsonic and supersonic flows. It concludes by covering the Marginal Separation theory, which represents a special version of the triple-deck theory, and describes the formation and bursting of short separation bubbles at the leading edge of a thin aerofoil.

scholarly journals On transonic viscous–inviscid interaction

2002 ◽  
Vol 470 ◽  
pp. 291-317 ◽  
Author(s):  
E. V. BULDAKOV ◽  
A. I. RUBAN
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Body Surface ◽  
Inviscid Flow ◽  
Boundary Layer Separation ◽  
Viscous Sublayer ◽  
Interaction Region ◽  
The Body ◽  
Sonic Point ◽  
Similar Solutions

The paper is concerned with the interaction between the boundary layer on a smooth body surface and the outer inviscid compressible flow in the vicinity of a sonic point. First, a family of local self-similar solutions of the Kármán–Guderley equation describing the inviscid flow behaviour immediately outside the interaction region is analysed; one of them was found to be suitable for describing the boundary-layer separation. In this solution the pressure has a singularity at the sonic point with the pressure gradient on the body surface being inversely proportional to the cubic root dpw/dx ∼ (−x)−1/3 of the distance (−x) from the sonic point. This pressure gradient causes the boundary layer to interact with the inviscid part of the flow. It is interesting that the skin friction in the boundary layer upstream of the interaction region shows a characteristic logarithmic decay which determines an unusual behaviour of the flow inside the interaction region. This region has a conventional triple-deck structure. To study the interactive flow one has to solve simultaneously the Prandtl boundary-layer equations in the lower deck which occupies a thin viscous sublayer near the body surface and the Kármán–Guderley equations for the upper deck situated in the inviscid flow outside the boundary layer. In this paper a numerical solution of the interaction problem is constructed for the case when the separation region is entirely contained within the viscous sublayer and the inviscid part of the flow remains marginally supersonic. The solution proves to be non-unique, revealing a hysteresis character of the flow in the interaction region.

Second-order boundary-layer effects in hypersonic flow past axisymmetric blunt bodies

1964 ◽  
Vol 20 (4) ◽  
pp. 593-623 ◽  
Author(s):  
R. T. Davis ◽  
I. Flügge-Lotz
Keyword(s):  
Boundary Layer ◽  
Mach Number ◽  
Free Stream ◽  
Practical Interest ◽  
Second Order ◽  
The Body ◽  
Specific Flow ◽  
Flow Past ◽  
Free Stream Mach Number ◽  
Stability And Accuracy

First- and second-order boundary-layer theory are examined in detail for some specific flow cases of practical interest. These cases are for flows over blunt axisymmetric bodies in hypersonic high-altitude (or low density) flow where second-order boundary-layer quantities may become important. These cases consist of flow over a hyperboloid and a paraboloid both with free-stream Mach number infinity and flow over a sphere at free-stream Mach number 10. The method employed in finding the solutions is an implicit finite-difference scheme. It is found to exhibit both stability and accuracy in the examples computed. The method consists of starting near the stagnation-point of a blunt body and marching downstream along the body surface. Several interesting properties of the boundary layer are pointed out, such as the nature of some second-order boundary-layer quantities far downstream in the flow past a sphere and the effect of strong vorticity interaction on the second-order boundary layer in the flow past a hyperboloid. In several of the flow cases, results are compared with other theories and experiments.

Second-order effects in free convection

1974 ◽  
Vol 62 (4) ◽  
pp. 793-809 ◽  
Author(s):  
I. C. Walton
Keyword(s):  
Boundary Layer ◽  
Free Convection ◽  
Equations Of State ◽  
Asymptotic Series ◽  
Inviscid Flow ◽  
Second Order ◽  
The Body ◽  
Order Effects ◽  
Boundary Layer Equations ◽  
Second Order Effects

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.

Prediction of Viscous Effects in Steady Transonic Flow Past an Aerofoil

1979 ◽  
Vol 30 (3) ◽  
pp. 485-505 ◽  
Author(s):  
M.R. Collyer ◽  
R.C. Lock
Keyword(s):  
Boundary Layer ◽  
Shock Waves ◽  
Transonic Flow ◽  
Lift Coefficient ◽  
Inviscid Flow ◽  
Viscous Effects ◽  
Flow Past ◽  
Boundary Layer Development ◽  
Transition Position ◽  
Realistic Representation

SummaryAn account is given of a numerical method for calculating transonic flow past an aerofoil with an allowance for viscous effects, providing that the boundary layer remains fully attached over the aerofoil surface. The method has been developed by combining, in an iterative manner, calculations of the inviscid flow with calculations of the compressible boundary layer and wake. The solution for the inviscid flow is obtained by an iterative scheme, originally established by Garabedian & Korn, which has been modified to give a more realistic representation of shock waves. The boundary-layer development is treated as laminar initially; at a certain transition position a turbulent boundary layer is assumed to develop, and this is determined by the lag-entrainment method of Green et al. Comparisons of the results from the numerical scheme with some experimental measurements are shown for various examples in which shock waves of moderate strength are present. The method predicts, with reasonable accuracy, both the detailed pressure distribution and the variation of drag coefficient with lift coefficient.

scholarly journals Prandtl–Batchelor flow past a flat plate with a forward-facing flap

1984 ◽  
Vol 143 ◽  
pp. 351-365 ◽  
Author(s):  
P. G. Saffman ◽  
S. Tanveer
Keyword(s):  
Flat Plate ◽  
Leading Edge ◽  
Vortex Sheet ◽  
Inviscid Flow ◽  
The Body ◽  
Two Dimensional ◽  
Rear Edge ◽  
Flow Past ◽  
Range Of Values ◽  
Streamline Method

Two-dimensional steady inviscid flow past an inclined flat plate with a forward-facing flap attached to the rear edge is considered for the case when a vortex sheet separates from the leading edge of the flat plate and reattaches at the leading edge of the flap, with uniform vorticity distributed between the vortex sheet and the body. Solutions are found for a particular geometry and a range of values of the vorticity. The method used to calculate the flow is an extension of a free-streamline method widely used in cases where the velocity is a constant on the separating streamline.

Two-Dimensional Boat-Tailed Bases in Supersonic Flow

1974 ◽  
Vol 25 (3) ◽  
pp. 210-224 ◽  
Author(s):  
P R Viswanath ◽  
R Narasimha
Keyword(s):  
Boundary Layer ◽  
Supersonic Flow ◽  
Free Stream ◽  
The Body ◽  
Base Pressure ◽  
Two Dimensional ◽  
Sharp Corner ◽  
Boundary Layer Effect ◽  
Pressure Distributions ◽  
Layer Effect

SummaryBoat-tailing of aft bodies may affect the base pressure through two mechanisms: firstly by changing the angle between the approaching flow at separation and the reattachment surface, and secondly by distorting the boundary layer through the favourable pressure gradient (which can be particularly severe in the presence of a sharp corner on the body). The first effect is isolated here by tests on inclined backward-facing steps with a fully developed turbulent boundary layer at separation, at free-stream Mach numbers of 1.75 and 2.4. It is found that the base pressure increases significantly with boat-tail angle; the data have been correlated taking explicit account of the boundary layer effect, modifying and extending the approach adopted by Nash. Charts are provided for quick estimation of base pressure in engineering calculations. Some of the earlier data on boat-tailed bases, on re-examination in the light of the present correlation, suggest that strongly distorted boundary layers at separation affect the base pressure appreciably. Several features of the measured reattachment pressure distributions, including their internal similarity, are also discussed.

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