The hypersonic laminar boundary layer near sharp compression and expansion corners

Abstract

The momentum integral method of Klineberg is shown to provide a good description of the major characteristics of two-dimensional laminar viscous-inviscid interactions a t hypersonic speeds. Surface pressure and heat-transfer-rate measurements were made for sharp compression and expansion corners at Mach 12.2 and are compared with the theoretical predictions. The agreement is found to be good for attached, incipient and fully separated flows.Some theoretical comparisons between methods based on the Klineberg formulation are made which suggest that the full boundary-layer equations are well described using integral methods that incorporate the energy equation. It is further shown that the properties associated with the stability of the governing differential equations are mathematical properties of the analytical model and should not be associated with any physical characteristics of the boundary layer.A correlation of hypersonic, cold-wall, incipient separation data is also presented.

Separation length in high-enthalpy shock/boundary-layer interaction

“…This has been confirmed numerous times both by experiments 1-15 and by computations, 2,[16][17][18][19][20] regardless of whether the interaction is laminar, transitional, or turbulent. L sep has also been shown without exception, both experimentally and computationally, to increase with decreasing M 1 .…”

“…Clearly, L sep should increase with increasing flap deflection w , or equivalently, with increasing reattachment pressure ratio p 3 /p 2 . This has been confirmed numerous times both by experiments 1-15 and by computations, 2,[16][17][18][19][20] regardless of whether the interaction is laminar, transitional, or turbulent.…”

Theory of Local Heat Transfer in Shock/Laminar Boundary-Layer Interactions

“…Needham 20 suggested that this feature would in fact serve as an incipient separation onset criterion: The present work now provides rm theoretical support for this empirical conclusion. Additional heat transfer data from several other investigators 21,22 also bear out these conclusions, as do numerical results obtained from interacting boundary-layer solutions on a rounded compression ramp. 23 Concerning the interaction zone downstream of the corner, it is seen from Fig.…”

“…Numerical studies of the effect of this term on the solution of Eqs. (21) and (22) con rm it to be small when S I ? I is small.…”

“…First, because the effective height of the inner deck (units of ŷ) is very small, we nd that the term «K u ŷ in Eq. (22) can still be neglected compared to unity even for rather cold walls; although H`/h w >> 1 for such walls, an estimate of ŷ max based on the inner deck theory of Lighthill 12 shows that «K u ŷ max is always small provided h w/ Hì s above the hypersonic threshold value of…”