Hypersonic nonuniform gas flow past a beveled blunt leading edge

SummarySolutions to the problem of separated flow past slender delta wings for moderate values of a suitably defined incidence parameter have been calculated by Smith, using a vortex sheet model. By increasing the accuracy of the finite-difference technique, and by replacing Smith’s original nested iteration procedure, to solve the non-linear simultaneous equations that arise, by a Newton’s method, it is possible to extend the range of the incidence parameter over which solutions can be obtained. Furthermore for sufficiently small values of the incidence parameter, new and unexpected results in the form of vortex systems that originate inboard from the leading edge have been discovered. These new solutions are the only solutions, to the author’s knowledge, of a vortex sheet leaving a smooth surface.Interest has centred upon the shape of the finite vortex sheet, the position of the isolated vortex, and the lift, and variations of these quantities are shown as functions of the incidence parameter. Although no experimental evidence is available, comparisons are made with the simpler Brown and Michael model in which all the vorticity is assumed to be concentrated onto an isolated line vortex. Agreement between these two models becomes very close as the value of the incidence parameter is reduced.

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Flow past a square-section cylinder with a wavy stagnation face

Journal of Fluid Mechanics ◽

10.1017/s0022112000002299 ◽

2001 ◽

Vol 426 ◽

pp. 263-295 ◽

Cited By ~ 122

Author(s):

RUPAD M. DAREKAR ◽

SPENCER J. SHERWIN

Keyword(s):

Reynolds Number ◽

Cross Flow ◽

Leading Edge ◽

Reynolds Numbers ◽

Physical Structure ◽

Near Wake ◽

Hairpin Vortices ◽

Independent State ◽

Flow Past ◽

Edge Surface

Numerical investigations have been performed for the flow past square-section cylinders with a spanwise geometric deformation leading to a stagnation face with a sinusoidal waviness. The computations were performed using a spectral/hp element solver over a range of Reynolds numbers from 10 to 150.Starting from fully developed shedding past a straight cylinder at a Reynolds number of 100, a sufficiently high waviness is impulsively introduced resulting in the stabilization of the near wake to a time-independent state. It is shown that the spanwise waviness sets up a cross-flow within the growing boundary layer on the leading-edge surface thereby generating streamwise and vertical components of vorticity. These additional components of vorticity appear in regions close to the inflection points of the wavy stagnation face where the spanwise vorticity is weakened. This redistribution of vorticity leads to the breakdown of the unsteady and staggered Kármán vortex wake into a steady and symmetric near-wake structure. The steady nature of the near wake is associated with a reduction in total drag of about 16% at a Reynolds number of 100 compared with the straight, non-wavy cylinder.Further increases in the amplitude of the waviness lead to the emergence of hairpin vortices from the near-wake region. This wake topology has similarities to the wake of a sphere at low Reynolds numbers. The physical structure of the wake due to the variation of the amplitude of the waviness is identified with five distinct regimes. Furthermore, the introduction of a waviness at a wavelength close to the mode A wavelength and the primary wavelength of the straight square-section cylinder leads to the suppression of the Kármán street at a minimal waviness amplitude.

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Solution of Levi Civita’s Problem by Infinite Matrix Inversion

Journal of Applied Mechanics ◽

10.1115/1.3422968 ◽

1973 ◽

Vol 40 (1) ◽

pp. 31-36 ◽

Cited By ~ 1

Author(s):

M. Bentwich

Keyword(s):

Flow Pattern ◽

Flow Direction ◽

Leading Edge ◽

Arbitrary Cross Section ◽

Matrix Inversion ◽

Infinite Matrix ◽

Algebraic Equations ◽

Flow Past ◽

Linear Algebraic Equations ◽

Wet Surface

The author proposes a new method by which one can solve for the two-dimensional irrotational fully cavitating flow past a cylinder of arbitrary cross section. Unlike the available solutions, it is in the form of two expansions each valid in part of the complex potential plane w = Φ + iΨ. The a priori unknown coefficients in the two expansions are linked by infinitely many linear algebraic equations. By inverting the associated matrix and utilizing the boundary condition, that represent the geometry of the wet surface, the coefficients in the expansions are evaluated and the solution is completed. Cases in which the wet surface is circular, the pressure along the free streamlines is constant, and the entire flow pattern is symmetric with respect to flow direction at infinity are considered in detail. Also, the well-known solution for the flow past a flat plate is compared to that obtained by the method of matrix inversion. Judging from these results, the convergence of the series appears to be very rapid. The author finally discusses the applicability of the method to cases in which the obstacle has a sharp leading edge, the pressure in the cavity is not uniform, or the flow pattern is not symmetric.

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