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AG April 7, 2001 02:44

abbet's method/prandtl meyer relations
in the abbet's method we apply the prandtl-meyer isentropic expansion (or contraction) principle to impose flow tangency condition on a solid boundary. but what i need to know is that if the prandtl-meyer relation (ie between mach number and turning angle)is applicable in case of 3D problems (like for imposing surface tangency condition over an axisymmetric body...i have used it in case of a 2d wedge where results are okay. but in 3D it is not so.). What i need to know is that does the prandtl-meyer relations hold for axisymmetric bodies as well or it holds only for flows in 2D. can you please suggest some other methods used for imposing surface boundary conditions for flow over a two stepped cone (axisymmetric case).i am using a body fitted grid and applying finite difference technique (McCormack's pred cor scheme) i have to correct u,v,p,and density at the boundary points.

John C. Chien April 7, 2001 13:53

Re: abbet's method/prandtl meyer relations
(1). In the book "elements of gasdynamics" by Liepmann and Roshko, published by John Wiley & Sons, exercise of Chapter 12, problem 12.3, it says "Show that in the expansion over the shoulder of an axially symmetric body the pressure change is given by the two-dimensional, Prandtl-Meyer theory. Hint:Just at the shoulder,(1/w)*(dw/ds) is much greater than (sin(theta))/r." (2). The equation of motion for axially symmetric flow is given by equation-12.10. See Chapter-12, the method of characteristics. (3). In other words, 2-D Prandtl-Meyer theory (or approximation) is good for axially symmetric flow over the shoulder.

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