UFR 3-08 Description
3D boundary layers under various pressure gradients, including severe adverse pressure gradient causing separation
Underlying Flow Regime 3-08 © copyright ERCOFTAC 2004
Boundary layers subject to an adverse pressure gradient are very often encountered in flows around bodies, and represent a severe test case for the numerical simulation methods. The prediction of the flow characteristics in the regions subject to an adverse pressure gradient, of the separation and of the subsequent flow development represent a real challenge for the modelling techniques used in the simulations.
Most of the studies that can be found in literature are for flows over a flat plate with an imposed pressure gradient and are usually either experiments or direct numerical simulations. An interesting test case is constituted by the flow around a 3D prolate spheroid. This flow has been investigated experimentally, for purpose of validation of CFD methodologies, in the NWG DLR and F1 ONERA wind tunnels, has been considered in the E. U. funded project ECARP  and is Test Case 74 in the ERCOFTAC database.
This document will focus mainly on the studies performed during the ECARP project.
Review of UFR studies and choice of test case
A boundary layer under an increasingly adverse pressure gradient without separation was investigated experimentally by Samuel and Jobert (1974) . They showed that the classical law of the wall for the mean velocity faces serious problems in the regions of the flow subject to strong adverse pressure gradient and does not hold near the separation points where the skin friction approaches zero. A law for the mean velocity near separation has been proposed by Perry and Schofield (1973)  and more recently by Castillo and George (2001) .
Experimental studies with measurements of boundary layer turbulence subject to an adverse pressure gradient upstream of the separation can be found in Simpson et al. (1981) [25,26] and Shiloh et al. (1981)  who investigated the physics of boundary layers separating from a smooth wall without downstream reattachment, and in Alving and Fernholz (1996)  who studied a boundary layer with a separation bubble and downstream recovery over an axisymmetric cylinder.
Scaling of Reynolds stresses in adverse pressure gradient boundary layers has been studied experimentally by Schofield (1981) , and Reynolds number effects have been studied by De Graaf and Eaton (1999)  and recently by Song and Eaton (2002) .
Numerical simulations of turbulent boundary layers subject to an adverse pressure gradient have been performed by Spalart (1986)  and Spalart and Leonard (1986) . They found satisfactory results in the favourable pressure gradient region but much less in the adverse pressure gradient region. Spalart and Watmuff (1993)  performed a direct numerical simulation of the flow over a flat plate subject to an adverse pressure gradient and compared their results to the experimental data by Watmuff (1989) .
Direct numerical simulations of flows over a flat plate with turbulent separation, due to an adverse pressure gradient, and reattachment have been performed by Na and Moin (1998)  and Spalart and Coleman (1997) . Hanjalic et al (1999)  reproduced the DNS of Spalart and Coleman (1997)  by using RANS with a low Reynolds number version of a second moment closure turbulence model.
Direct numerical simulations of flows with laminar separation and turbulent reattachment have been performed by Alam and Sandham (2000)  and Spalart and Strelets (2000) . RANS simulations of the DNS by Spalart and Coleman (1997)  have been carried out by Hadzic and Hanjalic (2000) by using a low Reynolds second moment closure model, and of the DNS by Alam and Sandham (2000)  by Howard et al. (2000)  by using several two equation turbulence models.
Most of the studies cited above do not present a comparison between numerical and experimental data, but are either experiments or numerical simulations. An interesting and well documented test case, involving a boundary layer subject to an adverse pressure gradient causing separation, is represented by the flow around a 3D prolate spheroid.This flow has been investigated experimentally, for purpose of validation of CFD methodologies, in the NWG DLR and F1 ONERA wind tunnels, has been considered in the E. U. funded project ECARP  and is Test Case 74 in the ERCOFTAC database.
© copyright ERCOFTAC 2004
Contributors: Pietro Catalano - CIRA