Computation of rotational transonic flows using a decomposition method

Abstract

Any vector field may be decomposed, in a unique way, into an irrotational and a rotational part, if appropriate boundary conditions are imposed to the scalar and vector potentials introduced by the above decomposition. In the present work, the transformation is applied to the mass flux vector, in order to calculate two-dimensional, steady, rotational, transonic flows in arbitrarily shaped ducts and plane cascades. The whole procedure is discussed from an analytical and a numerical point of view, while finite difference-finite volume schemes are used to derive numerical results. Nomenclaturea { = inlet flow angle a 2 = outlet flow angle c p -specific heat at constant pressure M = Mach number n = outward normal to the boundary vector p = pressure R g = universal gas constant S -entropy T = temperature (u,v) = velocity components in (x,y) coordinate system V = velocity vector x,y .= coordinates in physical space y = isentropic exponent £,ri = coordinates in computational space p = density O = scalar potential *p = vector potential co = relaxation factor Q = vorticity Subscripts and Superscripts t = total thermodynamic quantities n = normal to the boundary component n = number of current iteration (Note: Subscripting a variable with any of the coordinates indicates partial differentiation, whereas indices ij indicate the node point.)

Modelación de la distribución térmica en una tobera convergente-divergente utilizada en sistemas aeroespaciales

“…En [19] se desarrolla un método de descomposición para modelar el flujo transónico sobre ductos de cualquier forma, reduciendo el problema a una solución numérica de la ecuación diferencial de Poisson con condiciones de frontera tipo Dirichlet.…”

A dual-potential formulation of the Navier-Stokes equations

“…1.3.2.1 Applications of the dual potential method The dual potential method has been applied to inviscid and viscous flow problems. Inviscid flow applica tions include the work of Rao et al (1989) and Giannakoglou et al (1988). Rao et al (1987) developed a three-dimensional inviscid rotational flow solver based on the dual potential method.…”

“…They incorporated a boundary layer interaction scheme for viscous flow problems. Giannakoglou et al (1988) compute two-dimensional steady rotational transonic flows in arbitrarily shaped ducts and plane cascades. They decomposed the mass flux vector into two potentials.…”