Numerical prediction of incompressible separation bubbles

Abstract

A method is presented for performing detailed computations of thin incompressible separation bubbles on smooth surfaces. The analysis consists of finite-difference solutions to the time-dependent boundary-layer or Navier-Stokes equations for the flow in the immediate vicinity of the bubble. The method employs the McDonald-Fish turbulence model, to predict the development of the time-mean flow field, as influenced by the free-stream turbulence level. It also employs a viscous-inviscid interaction model, which accounts for the elliptic interaction between the shear layer and inviscid free stream. The numerical method is based on an alternating-direction implicit scheme for the vorticity equation. It employs transformations, to allow the free-stream boundary to change in time with the shape of the computed shear layer, and to ensure an adequate resolution of the sublayer region. Numerical solutions are presented for transitional bubbles on an NACA 663-018 airfoil at zero angle of incidence with chordal Reynolds numbers of 2·0 × 106 and 1·7 × 106. These have a qualitative behaviour similar to that observed in numerous experiments; they are also in reasonable quantitative agreement with available experimental data. Little difference is found between steady solutions of the boundary-layer and Navier-Stokes equations for these flow conditions. Numerical studies based on mesh refinement suggest that the well-known singularity at separation, which is present in conventional solutions of the steady boundary-layer equations when the free-stream velocity is specified, is effectively removed when viscous-inviscid interaction is allowed to influence the imposed velocity distribution.

Analysis of airfoil leading-edge separation bubbles

“…Sj-e (13) where '" * 6 8 : 8 -8 re f (14) and (15) With the source strength, d/d~ (u ~o*) assumed to vary linearly over each subinterval, Sj_l to Sj' Eq. (13) is analytically integrated to give (16) ImaX-1 ++l:…”

Prediction of Separating Turbulent Boundary Layers Including Regions of Reversed Flow.

“…Gerhart and Chima [16] Nreported that an attempt to apply an integral boundary layer scheme in an interaction procedure for treating subsonic turbulent separation had, to date, been unsuccessful. Differential solutions to the boundary layer equations were used in the interaction schemes applied to subsonic 4turbulent flow by Briley and McDonald [17], Carter [18], and Kwon and…”

“…The Briley and McDonald study utilized a time-dependent analysis, whereas both Carter and Kwon and Pletcher employed inverse 4 boundary layer procedures. Carter [18] computed the separated flow on an axisymmetric body-sting juncture, whereas the other two studies [17,19] treated transitional midchord separation bubbles. Only [17] and [19] included comparisons with experimental data.…”

Direct Numerical Simulation of Unsteady Separated Boundary-Layer Flows over Smooth Backward-Facing Steps

“…For larger Reynolds numbers the numerical methods often fail to converge or are otherwise unable to yield meaningful solutions. Attempts have been made to apply these methods for the calculation of transitional separation bubbles [9,10] using empirical transition models to switch the solution from laminar to turbulent flow. However, these calculations have shown that the numerical solution is strongly dependent on the transition criteria used.…”