Supersonic Transition Physics

At the subsonic leading edges of the inner part of the wing. Attachment Line Transition (ALT) occurs as known from subsonic transports (Figure 109). It develops because on swept wings the flow at the attachment line does not start its contact with the surface there (with local Reynolds

number zero), but follows the attachment line and splits the flow to the upper and lower side of the wmg. For infinite swept wings a boundary-layer develops at the attachment line which is in an equilibrium between boundary layer material advected along the attachment line (increasing boundary-layer mass) and divergent flow by the removal of mass over the wing (reducing bound­ary-layer mass).

supersorwc leading edge

Figure 109 Transition Types

Downstiearn the round leading edge a strongly three dimensional flow region produces Cross Flow Instabilities (CFI). stronger than on transonic aircraft with moderately swept wings. Usually. CFI waves arc the ”stationary” vortical waves in the boundary layer, with the wave front direction along the stream line or the wave normal perpendicular to the stream line. Because they arc oriented on the streamline and do not move, the disturbances accumulate along the stream line.

Further downstream, wing geometry presents a large region with very low surface cur­vature Here nearly conical flow conditions prevail. Typical two-dimensional disturbances arc the Tollmicn-Schlichting-lnstability waves (TSI). At low speeds. TSI-wavcs have their wave front normal to the flow direction, but they move in flow direction. In supersonic flow. TSI waves arc inclined to the flow direction, so that the wave front direction is between normal and Mach angle, close to the Mach angle of the inviscid flow. In addition, instability waves of other orientations and wave speeds occur, but CFI (with nearly stream line orientation) and TSI usu­ally are the most important.

On SCTs the conical directions of nearly constant flow conditions do not coincide with the main flow direction, nor arc they orthogonal, but strongly inclined. This gives even in the nearly conical region on the wing 3D flow influences tending to a build-up of vortices. So. although Tollmien-Schlichting Instabilities (TSI) develop. CFI remain valid here. Strong inter­action must be expected.

Behind the sharp supersonic leading edges of the outer wing and empennage, the flow is only two-dimensional, if there is a flat surface behind the leading edge (wedge flow). ALT docs not exist, TSI develops, but as soon as there is curvature. CFI becomes important (3781.

In supersonic flow, in addition to CFI and TSI. Higher Mode Instabilities (HMI) may occur: These are waves travelling at supersonic speed relative to the undisturbed flow. For flat plates these HM1 occur only at free stream Mach numbers above 3 (379]. It is not expected that they become important for supersonic transport; although, at first, they must not be neglected for the more complicated 3D-llows.

TSI and HMI arc sensitive to changes in the boundary layer temperature profile: TS1 are damped by cooling (i. e. surface temperature lower than recovery temperature of the air flow), whereas HMI are amplified by cooling, for healing vice versa. All surfaces on a super­sonic transport being of any interest for laminansation do more or less cool the boundary layer flow Two cooling mechanisms arc important: capacity cooling by the heat sink of structure and fuel, and radiation cooling due to the elevated surface temperature. The latter has no big influ­ence at the relatively low temperatures of supersonic transports (mostly less than 450 K). but it prevents assumptions of adiabatic flow Heating surfaces only occur during deceleration periods or at the engines.

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