Determining the shape of an axisymmetric body in a viscous incompressible flow on the basis of the pressure distribution on the body surface

Abstract

A method is developed for determining the shape of an axisymmetric body on the basis of the pressure coefficient distribution specified along the meridional section of the body. Viscosity is taken into account within the framework of the boundary layer model. The method is based on an iterative process, which involves the solutions of the inverse problem in the plane case and of the direct problem for an axisymmetric body. A code implementing the iterative process is written, and examples of numerical results are given.Key words: inverse boundary-value problem of aerohydrodynamics, viscous incompressible fluid, boundary layer, axisymmetric body, iterative process, panel method.Introduction. Inverse boundary-value problems of aerohydrodynamics (IBPAs), which are incorporated into the general theory of inverse boundary-value problems, are used to determine the shape of an airfoil on the basis of the velocity or pressure distribution specified on the airfoil surface. In the case of spatial flows, inverse boundary-value problems can be used to design airships and to optimize the shapes of the fore and aft parts of flying vehicles.One of the basic idealizing models of aerodynamics, which simplify the calculations of aircraft wings, is the model of plane sections, where the body cross sections are considered instead of the body as a whole. Both direct problems of this kind (see, e.g., [1][2][3]) and inverse problems (see, e.g., [4]) were studied in detail. Methods that allow obtaining numerical-analytical solutions for various fluid models [ideal incompressible fluid (IIF) or viscous compressible fluid] were developed. If it is impossible to use analytical methods for airfoil calculations, then numerical methods are applied. The model of plane sections, however, is inapplicable for three-dimensional bodies with complicated geometry. In this case, direct problems are solved by numerical methods where a grid covering the entire body surface is constructed. Inverse spatial problems are also solved by numerical methods, which are mainly iterative methods and, therefore, can be applied in particular cases only. For instance, with the use of the model of meridional sections, the flow around axisymmetric bodies can be considered as a two-dimensional problem: construction of bodies of revolution on the basis of a specified chord diagram of the velocity distribution [5] or on the basis of a specified pressure distribution [6], determination of the shape of turbomachinery blades located on an axisymmetric stream surface [7], and construction of an axisymmetric body on the basis of a specified velocity distribution on the body surface [8].The present work deals with solving the problem of an axisymmetric viscous incompressible fluid (VIF) flow around an axisymmetric body, in contrast to [5,6,8] where the study is based on the IIF model. Viscosity is taken into account within the framework of the boundary layer (BL) model. The iterative process constructed for solving this problem includes methods of solving both inverse and direc...

Multi-Fidelity Design Optimization of Axisymmetric Bodies in Incompressible Flow

“…Numerous studies on underwater vehicle design and optimization have been reported which focus on the clean hull only, i.e., the appendages and the propulsion system are neglected and the flow is taken to be past an axisymmetric body at a zero angle of attack. Examples of such numerical studies include Goldschmied (1966), Parsons et al (1974), Myring (1976), Dalton and Zedan (1980), Lutz and Wagner (1998), Alvarez et al (2009), andSolov'ev (2009). Allen et al (2000), however, report an experimental investigation of propulsion system enhancements and drag reduction of an AUV.…”