On the Asymptotic Behaviour of Three-dimensional Compressible Fluid Flow at a Great Distance from a Body, I. (The Force and Moment on a Solid Body in a Stream of Compressible Fluid)

Abstract

The steady irrotational isentropic continuous subsonic flow of a perfect gas past an arbitary three-dimensional body with arbitary distribution of sources on its surface is considered. Based on the thing-wingexpansion method, the velocity potential Φ is expanded in the form Φ= U ( x + A 1 r -1 + A 2 r -2 +...), A 1 = a 0 f -1 , A 2 = f -3 [ a 10 cos θ+sin θ( a 11 cos ω+ a 1-1 sin ω)], f =(1- M 2 sin 2 θ) 1/2 , where U is the velocity of the undisturbed flow of Mach number M streaming in the positive direction of x -axis, and x = r cos θ, y = r sin θcos ω, Z = r sin θsin ω. Using this expression, the force ( X , Y , Z ) and moment ( M x , M y , M z ) experienced by the body are found to be: X =ρ ∞ Q ∞ U , Y = Z =0, M x =0, M y , z =± 4π a 1,±1 ρ ∞ U 2 /(1- M 2 ) -1 , where ρ ∞ Q ∞ is the total strength of sources, and ρ ∞ the density at infinity.