Combined method for solving an inverse boundary value problem of aerohydrodynamics for an axisymmetric body

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

“…An effective approach to solving the problem posed is the approach developed in [8], where an iterative process of solving the inverse problem for an axisymmetric body is constructed in accordance with the IIF model with the use of methods of solving the inverse problem for a plane contour and the direct problem for an axisymmetric body. The calculations performed revealed rapid convergence of the process (6-8 iterations on the average) with the accuracy reaching 10 −6 .…”

“…Expression (8) is a system of linear algebraic equations with respect to unknown q j , which is used to find the velocity distribution on the body surface. The sought velocity distribution on the surface of the fictitious airfoil U e (s) and the distribution δ 1 (s) depending on this velocity distribution are included into the right side of expression (8); hence, the following iterative process is constructed for determining U e (s).…”

“…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.…”

“…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.…”

Inverse boundary value problem of aerohydrodynamics for an axisymmetric body with blowing from an annular channel

“…In cases when a body shape is given, direct problems are solved by numerical methods such as widely applied panel method (see, e.g., [3,4]) and discrete vor tices method (see, e.g., [5]). Inverse boundary value problems are also solved by numerical (mainly itera tive) methods (see, e.g., [6,7]). …”