On boundary-layer transition in transonic flow
The authors study the boundary-layer transition in transonic external flow. The mechanisms are identified with three major factors: (a) substantial external-flow deceleration; (b) rapid boundary-layer thickening; (c) three-dimensional nonlinear interactions. After introduction of suitable scales depending on the Reynold's number, the governing equations are written in the form: \(U_ X+V_ Y+W_ Z=0\), \(U_ T+UU_ X+VU_ Y+WU_ Z=-P_ X+U_{YY}\), \(W_ T+UW_ X+VW_ Y+WW_ Z=0+W_{YY}\) with \(U=V=W=0\) at \(Y=0\) and \(U\sim Y+A\), \(W\to 0\), as \(Y\to \infty\) coupled with the unsteady linearized transonic small perturbation equation: \(\overline m \overline P_{XX}-\overline P_{ZZ}+2\overline P_{XT}=\overline {P}_{\bar y\bar y}\) subject to \(\overline P\to 0\) as \(\bar y\to \infty\) and \(\overline P\to P\), \(\overline P_{\overline y}\to A_{XX}\) as \(\bar y\to 0\). Here, in scaled terms, \(A\) is the unknown displacement caused by the disturbance in the boundary layer, while \(P,\overline P\) are the unknown wall pressure and external pressure, respectively, and \(P\), \(A\) depend on \(X,Z,T\) with \(U,V,W\) dependent on \(X,Y,Z,T\). The matching with the oncoming stream and between the upper and main decks, in turn, is ensured. A further transonic regime is considered, in which the flow structure is for local Mach numbers closer to unity than in the previous one, and which is able also to incorporate directly the presence of an external shock impinging on the boundary layer. The interactive flow structure, the small disturbance, and the effect of separation and shock oscillation are studied. After the above three-dimensional theory, certain of the extra two-dimensional effects arising in transonic transition are described. Strong nonlinear three-dimensional growth and nonlinear triad interactions effects are investigated.
scientific article; zbMATH DE number 469169
scientific article