Effects of compressibility on design of subsonic fuselages for natural laminar flow

Abstract

At high subsonic speeds, density gradients in compressible laminar boundary layers provide increased damping of the two-dimensional and axisymmetric Tollmien-Schlichting instability waves. The favorable influence of flow compressibility provides a unique opportunity to attain natural laminar flow over portions of high-speed subsonic fuselages for drag-reduction purposes. For bodies of moderate fineness ratios (e.g., 5 to 9), the generally destabilizing effect of increasing length-Reynolds number on laminar stability is overpowered by the damping effect of compressibility. Compressible linear stability analyses (based on the e n method) are presented for the laminar boundary layer on axisymmetric body shapes for length-Reynolds numbers up to 86.6 million and Mach numbers up to 0.80. At a fixed Reynolds number, based on body length, it is predicted that the transition-length Reynolds number triples as the Mach number increases from near zero to 0.80. The favorable effects of flow compressibility on laminar stability might be exploited in the design of external fuel tanks, engine nacelles, and fuselages of business or commuter transports. Attainment of natural laminar flow on the forebodies of larger transport fuselages could provide significant reductions in total drag of transport aircraft. NomenclatureA/A 0 = ratio of local disturbance amplitude to amplitude at point of neutral stability for fixed disturbance frequency C D = body drag coefficient (based on frontal area) C Dref = drag coefficient for boundary-layer transition location fixed at x/L = 0.05 at given Mach numberfineness ratio (body length/maximum body diameter) L = body length, ft M = local surface Mach number MO,, = freestream Mach number n = logarithmic exponent of amplitude-growth ratio of unstable Tollmien-Schlichting wave, n = &i(A/A 0 ) R L = Reynolds number based on freestream conditions and body length R TR = Reynolds number based on freestream conditions and transition length T.S. = Tollmien-Schlichting x = axial coordinate starting at nose, ft

Aircraft Design with Active Load Alleviation and Natural Laminar Flow

“…For low sweep wings, the incompressible approach is likely conservative because compressibility tends to stabilize the streamwise boundary layer [53][54][55]. To simplify surface discretization and numerical integration, we use the single-step H − R x criteria of Wazzan et al to predict flow transition [56]:…”