Aerodynamics of complex bodies of revolution

Abstract

The aerodynamics of five complex bodies of revolution are investigated experimentally and theoretically at a low Mach number (M f ^ 0.1) and over the range of angle of attack from 0 to 35 deg. The geometrical forms of the bodies are generally complex with the discontinuities in the slope of the body surface. The surface-flow visualization is performed by using the oil method. The balance measurements were made and the results compared with the potential theory and the method based on the crossflow analogy. It was observed that the discontinuities in the slope of the body surface make the flow separation and consequently the flowfield very complicated. It was also found that the method of crossflow analogy is applicable not only to simple-type bodies of revolution but also the complex ones. Nomenclatureof corresponding cylinder to body of revolution ( = S p /l) /(X) = normal force distribution / = total body length l r = reference length M^ = freestream Mach number M Coo = crossflow Mach number ( = M^ sina) q^ = freestream dynamic pressure (q^ = ^p R = local body radius Re d = Reynolds number based on the maximum body diameter d (Re d -V^d/v) R e cd s = crossflow Reynolds number based on d s ( = F^ sina ds/v) Re t -Reynolds number based on / S = local cross-sectional area ( = nR 2 ) S b = body base area S p = body planform area ( = Jo 2R d*) S r = reference area S, = body flat-nose area V^ = freestream velocity W = body volume ( = &nR 2 d*) x= body axis (axial distance from body nose) x c = axial distance from body nose to centroid of body planform area x cp = axial distance from body nose to center of pressure x m = pitching moment center (axial distance from body nose to pitching moment center) a = angle of attack p = density of air D = kinematic viscosity of air r\ -correction factor for influence of fineness ratio

Renormalized numerical simulation of flow over planar and non-planar fractal trees

“…The starting point for performing RNS analysis on trees with arbitrary orientations is the cross-flow principle [15][16][17][18]. In essence, this principle says that the force on an inclined object (e.g., cylinder or wire) in a given direction is determined by the projection of incoming velocity along that direction.…”