On aerodynamic forces for viscous compressible flow
type: Item
instance of: scholarly article
title: On aerodynamic forces for viscous compressible flow
zbMATH Open document ID: 0909.76085
author: Chien-Cheng Chang
author: Jeng-Yu Su
author: Sheng-Yuan Lei
published in: Theoretical and Computational Fluid Dynamics
publication date: 1999-04-12T00:00:00Z
review text: The paper is aimed at reviewing and adding some new results on a force theory for viscous compressible flows around a finite body. It has been proposed to analyse aerodynamic forces directly in terms of fluid elements of nonzero vorticity and density gradient. Let \(\rho\) denote the density, \({\mathbf u}\) the velocity, and \(\vec \omega\) the vorticity. It is demonstrated that for largely separated flows about bluff bodies, there are two major source elements: \(R_e ({\mathbf x}) =-{1\over 2} {\mathbf u}^2 \nabla \rho \cdot \nabla \varphi\) and \(V_e({\mathbf x}) =-\rho {\mathbf u} \times \vec \omega \cdot \nabla \varphi\), where \(\varphi\) is an acyclic potential, generated by the solid body moving with unit velocity in the negative direction of the force considered. In particular, under mild conditions, the (unique) choice of \(\varphi\) enforces that the elements \(R_e ({\mathbf x})\) and \(V_e ({\mathbf x})\) decay rapidly away from the body. Four kinds of finite bodies are considered: a circular cylinder, a sphere, a hemisphere-cylinder, and a delta wing of elliptic section -- all in transonic-to-supersonic regimes. From an extensive numerical study carried out for these bodies, it is found that these two elements contribute to \(95\%\) or more of the total drag or lift for all the cases under consideration.
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 76G25
Mathematics Subject Classification ID: 76H05
Mathematics Subject Classification ID: 76J20
zbMATH DE Number: 1174725
zbMATH Keywords: fluid elements of nonzero vorticity
zbMATH Keywords: density gradient
zbMATH Keywords: bluff bodies
zbMATH Keywords: acyclic potential
zbMATH Keywords: circular cylinder
zbMATH Keywords: sphere
zbMATH Keywords: hemisphere-cylinder
zbMATH Keywords: delta wing of elliptic section
zbMATH Keywords: total drag
zbMATH Keywords: lift
MaRDI profile type: Publication
full work available at URL: s001620050051
OpenAlex ID: W2016524883
DOI: 10.1007/S001620050051
description: scientific article; zbMATH DE number 1174725