Vortex Panel Method in Axisymmetric Cylindrical Coordinates: Inviscid Formulation

IF 1.8 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Suguru Shiratori, Kosuke Kimata, Masaya Katoh, Hideaki Nagano, Kenjiro Shimano
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引用次数: 0

Abstract

This study addresses the vortex panel method, which is an efficient solution for inviscid flow around a body. For Cartesian coordinates, the panel method has been developed and widely applied. However, a formulation has not been proposed for axisymmetric cylindrical coordinates. This study derives a Green's function corresponding to the governing equation of the potential flow in axisymmetric cylindrical coordinates by modifying the Green's function provided by Cohl and Tohline [doi:10.1086/308062]. The derived Green's function G $$ G $$ is significantly compact and is composed of a single term of the half-integer degree Legendre function of the second type. The derivation of Green's function G $$ G $$ is confirmed by analytically evaluating the requirement G = 0 $$ \mathit{\mathcal{L}G}=0 $$ , where $$ \mathcal{L} $$ is a linear operator of the governing equation. Under the derived G $$ G $$ , the vortex panel method is formulated by discretizing the vorticity distribution along the body surface. The validity of the constructed panel method is confirmed through calculations of the flow past a sphere, an ellipsoid, a torus, and a teardrop-like object by comparison with analytical or numerical solutions.

Abstract Image

轴对称柱坐标下的涡盘法:无粘公式
涡流面板法是求解物体无粘绕流的一种有效方法。对于直角坐标系,面板法得到了发展并得到了广泛应用。然而,对于轴对称柱坐标,还没有提出一个公式。本文通过对Cohl和Tohline [doi:10.1086/308062]给出的格林函数进行修正,推导出轴对称柱坐标系下势流控制方程对应的格林函数。导出格林函数G $$ G $$ 是非常紧凑的,由半整数次的第二类勒让德函数的单项组成。格林函数G的求导 $$ G $$ 通过对需求的解析求出,得到了确认 $$ \mathit{\mathcal{L}G}=0 $$ ,其中; $$ \mathcal{L} $$ 是控制方程的线性算子。在导出的G下 $$ G $$ ,通过对车身表面涡度分布的离散化,建立了涡盘法。通过对球体、椭球体、环面和水滴状物体的流动计算,并与解析解和数值解进行比较,证实了构造面板方法的有效性。
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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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