A univalent spiral-vortex model for separated flow past a polygonal obstacle

Bassanini, Piero; Elcrat, Alan R.

doi:10.1007/bf00948957

Cited by 5 publications

(12 citation statements)

References 10 publications

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“…In the inner iteration (iii), for each Zj, the parameters W, , . .. , in are determined, for fixed x,, x,, by the side lengths of the polygon as in [8], [5]. The determination of xs, xs, from equations (23) and (24), which we may think of as where 0 < o r < 2.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The two-dimensional inner solution in the Z-section is a modified version of the Tulin double spiral vortex model [7] which we have introduced in [8]. The relevant flow quantities are given in terms of a complex parameter x which varies over the upper half of an auxiliary plane.…”

Section: Inner Solutionmentioning

confidence: 99%

“…The vertices of the polygon are denoted by {Xk, 1 x e , (x) is the complex velocity, w the complex potential, dw/dz = , and co = In (). We have then, keeping the same notations as in [8]:…”

Section: Inner Solutionmentioning

confidence: 99%

“…If the near-wake free-streamline speed q, = (1 + ) 1 /2 and Xs, x,, are fixed, the parameters {k}, Ware determined in terms of the side lengths of the polygon by solving the associated system of equations [8,5]. Here the condition 4(oc) = 1 must be replaced by (oo) = exp (icxD) (see Section 3) where LD is the downwash angle, and this implies x -cos rn + D-…”

Section: Inner Solutionmentioning

confidence: 99%

“…The equations (23), (24) for x, Xs, and the side lengths in (iii) are solved using the iteration procedure of [8]. This is done on a finite number of sections after discretization in Z as discussed below.…”

Section: Iterations and Discretizationmentioning

confidence: 99%

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Separated flow past three-dimensional bodies as a singular perturbation problems

Bassanini¹,

Elcrat

1989

J Eng Math

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This paper proposes a method for computing steady wake flows of an inviscid fluid over a threedimensional body with polygonal cross-section and arbitrary plan-form. The method is based on the technique of matched asymptotic expansions, assuming a large "aspect ratio". The far-field velocity potential is given essentially by a lifting line and a line source. The near-field, treated as two-dimensional, is solved by a suitable version of Tulin's double spiral vortex model which incorporates a downwash correction and an underpressure in the near-wake. The latter is related to the Reynolds number of the corresponding real flow using recent results by Tulin and Hsu and the authors. Numerical results for a few prototype problems (flat-plate airfoil with separation at both the leading edge and the upper surface, flat-plate wing with full or partial spoiler) are presented. The method can be efficiently implemented on a parallel computer.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Inner Solutionmentioning

confidence: 99%

“…The vertices of the polygon are denoted by {Xk, 1 x e , (x) is the complex velocity, w the complex potential, dw/dz = , and co = In (). We have then, keeping the same notations as in [8]:…”

Section: Inner Solutionmentioning

confidence: 99%

Section: Inner Solutionmentioning

confidence: 99%

Section: Iterations and Discretizationmentioning

confidence: 99%

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Separated flow past three-dimensional bodies as a singular perturbation problems

Bassanini¹,

Elcrat

1989

J Eng Math

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Circular map for supercavitating flow in a multiply connected domain

Antipov

Silvestrov

2009

The Quarterly Journal of Mechanics and Applied Mathematics

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A nonlinear free boundary-value problem of supercavitating flow past n + 1 hydrofoils is analyzed. To describe the cavities' closure mechanism, the Tulin-Terent'ev single-spiral-vortex model is employed. The flow domain is considered as the image of an (n + 1)-connected circular domain. The conformal map is constructed in terms of the solutions to two Riemann-Hilbert problems of the theory of symmetric automorphic functions. One of the problems is homogeneous and its coefficients are continuous functions while the second problem is inhomogeneous and has discontinuous coefficients. The exact solutions to the problems are found by using quasiautomorphic and quasimultiplicative analogs of the Cauchy kernel. The case of a single plate is considered in detail and the numerical results are reported.

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Single- and double-spiral-vortex models for a supercavitating non-symmetric wedge in a jet

Antipov

Zemlyanova

2009

Proc. R. Soc. A.

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The problem of determining the free surface of a jet incident on a rigid wedge and the boundary of a cavity behind the wedge is considered. The single-and double-spiral-vortex models by Tulin are used to describe the flow at the rear part of the cavity. The location of the wedge in the jet and the sides lengths are arbitrary. This circumstance makes the flow domain doubly connected for the single-vortex model while it is simply connected for the double-vortex model. Both models are solved in closed form by the method of conformal mappings. The maps are expressed through the solutions to certain RiemannHilbert problems. For the former model, this problem is formulated on a genus-1 Riemann surface. The double-vortex model requires the solution to a standard Riemann-Hilbert problem on a plane. By comparative analysis of the numerical results for the two models, it is found that the drag and lift are practically the same while the jet surface, the cavity boundary at the rear part and the deflection angle of the jet at infinity are different. Also, the problem of determining the parameters for the conformal mapping in the single-vortex model has two solutions. It is shown that one of the solutions leads to a non-physical shape of the cavity and needs to be disregarded.

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A univalent spiral-vortex model for separated flow past a polygonal obstacle

Cited by 5 publications

References 10 publications

Separated flow past three-dimensional bodies as a singular perturbation problems

Separated flow past three-dimensional bodies as a singular perturbation problems

Circular map for supercavitating flow in a multiply connected domain

Single- and double-spiral-vortex models for a supercavitating non-symmetric wedge in a jet

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