Numerical solution of transonic stream function equation

Advances in research on inverse and hybrid problems of turbomachinery aerothermodynamics in China

“…Just recently, this moment function method has been extended by Liu and Guo [I91 to the inverse design of transonic cascadeslchannels by suggesting a new coefficient-upwinding technique which is a generalization of the artificial compressibility method [17]. Later, following the Liu and Tao's basic idea [4,5,8], a number of methods also employing the von Mises transformation, Eq.…”

“…(ii) the pressure p can be computed directly from Eq. (5), resulting in two advantages: first, no density ambiguity (double-valuedness) [17] appears; second, for the inverse problem the B.C. (i.e.…”

“…(17), where cijk is the permutation tensor. A similar method for solving 3-D hybrid problems was put forth by Chen et al [56], using, however, a second-order PDE formulation of @ including and Eqs.…”

Numerical simulations of transonic aerodynamic flows based on a hierarchical formulation

“…Alternative formulations to the standard Euler and Navier-Stokes equations can be based on generalized Cauchy=Riemann equations [9][10][11][12], stream functions [33,34], or potential functions with corrections to account for rotational ow ÿelds. In this paper, numerical results are presented based on a hierarchical approach, with the potential ow solver as a base for both inviscid and viscous ows.…”

Stream-function-coordinate (SFC) method for 2d and 3d aerodynamic inverse design in turbomachinery

“…(2),(8) and(9) the stream-function-coordinate equation can be obtained:where.3 A, = 2pr ($ ) R sin o / G o For transonic flow the artificial density technique 191 is used instead of the density in the momentum equation. It can be found by where the artificial density sensor p is pj,, = Max[O,(l -c/M2)] here,c is the user-specified constant.…”