Drag reduction of airplane fuselages through shaping by the inverse method

Abstract

The axial singularity solution for the axisymmetric inverse problem has been extended to utilize doublet elements with linear intensity distribution. The solution converges faster than the source-based method, and is therefore quite promising. A procedure based on this solution has been used to design low-drag laminar fuselage shapes for small aircraft applications with a volumetric Reynolds number range of 10-30 million. A profile with a fineness ratio of 6, transition at 40% of body length, and volumetric drag coefficient of 0.012 at a nominal /?v of 15 million, has been developed. The present inverse procedure was shown to be a powerful alternative to optimization methods. Several transition criteria were investigated in the course of the study. The Crabtree criterion appears to be the most consistent. Experimental transition data for axisymmetric bodies at high (flight) Reynolds numbers are urgently needed. Nomenclature CDV = volumetric drag coefficient based on V 2/3 as characteristic area /,. = fineness ratio, body length/maximum diameter H = boundary-layer shape factor, 8*/9 L = body length / = length of an axial-singularity element n = number of doublet elements q = local velocity on body surface (at the edge of the boundary layer) RL = length Reynolds number based on UM and L Rs = Reynolds number based on local velocity and s Rx = Reynolds number based on local velocity and jc Re = Reynolds number based on local velocity and 9 7?v = volumetric Reynolds number based on Ux and V1/3 r. — local body radius and radial coordinate 5 = length along body surface starting at nose Ux = freestream velocity u = axial component of q v = radial component of q X = nondimensional axial coordinate, x/L