The prediction of turbulent boundary layer development in compressible flow

Abstract

Starting from Head's semi-empirical method for incompressible flow, two approaches to the prediction of turbulent boundary-layer development in compressible flow are explored. The first uses Head's incompressible method in conjunction with a compressibility transformation similar to Stewartson's transformation for laminar flow; the second carries over Head's physical arguments to treat the compressible flow directly. Measurements in supersonic flow, both on flat plates and downstream of an abrupt pressure rise, show broad agreement with the predictions of the second method but do not support the compressibility transformation. In particular, measurements on flat plates reveal that as Mach number increases the entrainment rate decreases to a lesser extent than the skin-friction coefficient. Whilst this result is consistent with the second treatment in this paper, it is difficult to reconcile with any of the compressibility transformations discussed, and the validity of these transformations in turbulent flow is therefore questioned.

Viscous-Inviscid Method for Airfoil Analysis and Design for Aviation and Windmills

“…In this study, the approach used is the concept of entrainment, 11 originally introduced by Head and later extended and improved by Green et al 14 Various modifications to improve its applicability under separated flow conditions have been used as the technical foundation of this work. 15,16 The entrainment-integral relationship is derived from Head's assumption that turbulent boundary layers grow by a process of entrainment from the free stream into the boundary layers of nonturbulent flow at the outer edge of the layer.…”

Improved design of subcritical and supercritical cascades using complex characteristics and boundary-layer correction

“…We follow the lag-entrainment method as developed by Green, Weeks and Brooman in reference [3]. This method contains less empirical factors than the classic of Nash and McDonald.…”

“…We refer to [3] for the definition and value of the others coefficients, which are function of the entrainment coefficient and the local free-stream magnitudes.…”

“…Of the three initial values necessary to numerically solve the system of ordinary differential equations (9), only the initial momentum thickness is specified as an input parameter. The other two are computed by means of the equilibrium relations established in [3].…”

Flowfield Analysis for Successive Oblique Shock Wave-Turbulent Boundary-Layer Interactions

“…S t a r t i n g w i t h conditions a t 3 as determined by the control volume analysis of t h e f i r s t i n t e r a c t i o n , changes i n the boundary layer properties t o Station 5 are computed using a turbulent boundary iayer program suggested by Paynter and Schuelle [ 4 ] . The program uses a wallwake p r o f i l e t o represent the velocity profile and the entrainment function concept proposed by Green [5] t o solve the boundary layer equations (see A.ppendix B ) . An inviscid flow solution i s used t o provide the wall s t a t i c pressure distribution needed for the boundary layer solution i n this region.…”