The effect of surface roughness on breakaway separation

The supersonic breakaway-separation eigensolution of Neiland (1969a) and Stewartson & Williams (1969) is extended to include breakaway separation past distributed surface roughness. Laminar, steady, two-dimensional breakaway separations are computed for flow past a wavy wall, and geometries simulating entry into patches of roughness, using a quasi-simultaneous, alternating-direction-implicit (ADI) method. A mechanism is proposed whereby flow past small scale surface roughness can effect the much larger scale separations within which it is embedded. Numerical computations show that this mechanism is not triggered to any significant degree for the problems considered here. Introduction The adverse effect of surface contamination on aerodynamic performance has been well documented over the years. For example, Abbott & Doenhoff (1959) show a decrease in maximum lift coefficient due to surface roughness near the leading edge of an airfoil. More recently, Bloch & Mueller (1986) have argued that distributed surface roughness can effect the position and size of separation bubbles. Surface roughness can clearly impact a number of aerodynamic phenomenon, including the laminar flow, three-dimensionality, unsteadiness and transition. While such problems have been extensively studied on a local scale using analytical and computational methods (i.e. for flow about an individual roughness element), not much has been done to connect the local solutions to global separation bubble behavior. * Professor, member AIAA t Copyright ©1996 by author. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. All rights reserved In this study, a possible mechanism for such an interaction will be examined, in the context of steady, two-dimensional, laminar flow past surface roughness in supersonic flow. This analysis is based on the triple-deck theory of Neiland (1969a) and Stewartson & Williams (1969), as shown in the figure on the next page. A Proposed Mechanism Whereby Near Wall Roughness and Transition Can Effect Global Separation Properties The central question is how can small scale surface distortions which are embedded within the boundary layer effect a much larger scale separation. One possible answer is largely contained in the existing literature. It has been known for some time now that both subsonic and supersonic external separations start from a viscous sublayer embedded within the main boundary layer, and controlled by a localized viscous-inviscid interaction. When the separation bubble is on the same scale as the airfoil, or some other geometry, the initial breakaway separation is often a local eigensolution, or free-interaction, centered at the separation point. This free-interaction, in turn, fixes some condition in the larger scale separation. In a supersonic flow, the breakaway eigensolution sets the shear layer slope at separation (see Stewartson & Williams (1969)), while in subsonic flow the breakaway eigensolution effectively sets the curvature of the breakaway shear layer at separation (actually it sets the coefficient in an X ' breakaway shear layer, see Sychev (1972) and Smith (1977), as well as Korolev (1980) and Van-Dommelen & Shen (1983)). This local condition acts much like the well known Kutta-condition of classical aerodynamics it simply sets a boundary condition or "separation criterion" on the larger scale separation. In fact, for subsonic flows this boundary condition is found to control body-scale separations (see Cheng & Smith (1982)). The separation criterion emerging from both the subsonic and supersonic separations are generally believed to be effected by the local nonlinear viscous solution within the triple-deck free-interaction (see Stewartson & Williams (1969)). Any mechanism which could modify that solution via the viscous sublayer could effect the separation criterion, thereby modifying the larger scale separation. Mechanisms other than the one discussed in this study are also possible. The sublayer could be modified by three-dimensional and/or unsteady effects. If low-level near-wall turbulence is present then it could also influence the laminar separation via the sublayer. potential slope change ^eriodic^Re" solution TM<r sublayer breakaway separation It is clear that such an effect could lead to enhanced separation. For example, in a subsonic separation if the action of the local mechanism, say roughness, is to retard the rate of breakaway of the shear layer, then the theory of Cheng & Smith (1982) suggests that the separation point will move towards an inviscid smooth separation — which generally corresponds to forward motion and an increase in the size of the separation bubble. The Smith & Khorrami Breakdown It should be noted that supersonic triple-deck separations can terminate in a finite position singularity as some controlling parameter in the problem is varied (see Smith & Khorrami (1991)). This does not happen in the Stewartson & Williams free-interaction. Some of the more extreme cases computed in this study (such as Figs. 16 and 23) do show glitches which may be an indication of the Smith & Khorrami singularity, though it is more likely that they are simply numerical in origin. The less severe cases which could be grid refined did not exhibit any such behavior. The Central Triple-Deck Problem The above mechanism is examined here for steady, two-dimensional, laminar supersonic flow past a wavy wall and related geometries using triple-deck theory. The main assumptions are that the Reynolds number is large, the Mach number is finite and supersonic, and the wall is adiabatic or approximately constant temperature. The triple-deck equations consist of boundary layer equations in a viscous sublayer and an interaction with a local supersonic external flow which is given by Ackerets law. The reader may consult Stewartson (1974) for further details. The triple-deck equations are Ux + VY = 0 (1) and UUX + VUY = PX(X) + UYY , (2) with the boundary conditions U -* Y + A(X) + F(X) as Y (3) and U(X,0) = V(X,0) = 0 . The interaction law for supersonic flows is = ~ A (4) Numerical Methods for the Boundary Layer Equations A number of different algorithms will be used throughout this study to solve the triple-deck problem. They all follow well-known methods developed for the boundary layer equations and implemented by a number of other authors. The algorithms used here closely parallel those by Veldman (1981) and Davis & Werle (1982) for the interacting boundary layer equations. The main one is a pressure gradient based algorithm for the boundary layer differential equations with a streamwise ADI acceleration of the boundary condition. The various algorithms are summarized below.