Simplified Treatment of the Turbulent Boundary Layer Along a Cylinder in Compressible Flow

1952 ◽  
Vol 19 (1) ◽  
pp. 23-28 ◽  
Author(s):  
HANS U. ECKERT
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Compressible Flow

scholarly journals Numerical investigation of the compressible flow past an aerofoil

2009 ◽  
Vol 643 ◽  
pp. 97-126 ◽  
Author(s):  
LI-WEI CHEN ◽  
CHANG-YUE XU ◽  
XI-YUN LU
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Compressible Flow ◽  
Complex Flow ◽  
Dynamical Processes ◽  
Vortical Structures ◽  
Boundary Layer Interaction ◽  
Flow Phenomena ◽  
Flow Evolution

Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M∞ = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

Transformations of the boundary-layer equations for rotating flows

1968 ◽  
Vol 33 (1) ◽  
pp. 113-126
Author(s):  
N. Rott ◽  
J. T. Ohrenberger
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Compressible Flow ◽  
Incompressible Flow ◽  
Flow Problem ◽  
Rotating Flows ◽  
Governing Equations ◽  
Boundary Layer Equations ◽  
Axis Of Symmetry ◽  
Semi Empirical

The boundary layer on an axisymmetric surface above which the flow is rotating about the axis of symmetry is considered. Transformations of the governing equations which permit the generalizations of a known solution for one meridian shape in incompressible flow to a family of meridian shapes are shown to exist. For compressible flow, a transformation of the Stewartson-Illingworth type was found which reduces a compressible flow problem to an incompressible case. Also, remarks are made concerning the invariance of the turbulent boundary-layer integral equations assuming particular semi-empirical shear laws.

The prediction of turbulent boundary layer development in compressible flow

1968 ◽  
Vol 31 (4) ◽  
pp. 753-778 ◽  
Author(s):  
J. E. Green
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Compressible Flow ◽  
Pressure Rise ◽  
Skin Friction Coefficient ◽  
Empirical Method ◽  
Entrainment Rate ◽  
Flat Plates ◽  
Boundary Layer Development ◽  
Layer Development

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.

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