The effects of small-scale surface roughness on laminar airfoil-scale trailing edge separation bubbles

In this study, an interacting boundary-layer algorithm is used to investigate the effects of small-scale surface roughness on airfoil-scale laminar separation bubbles. Steady, laminar trailing-edge separation bubbles are computed for two-dimensional flow past a symmetric biconvex airfoil. Results from this work show that small-scale roughness configurations can significantly alter the characteristics of a laminar separation bubble in low speed flows. Introduction This study investigates the effects of small-scale surface roughness on laminar separation bubbles in low speed subsonic flow. Currently, there is little data available on small-scale roughness interaction with globalseparation bubble characteristics. An interacting boundary-layer algorithm, based on the one developed by Rothmayer, is used to analyze this interaction for a laminar trailing-edge separation bubble. Airfoil surface roughness can take many forms ranging from bug contamination to ice build-up on a surface. The detrimental effects of surface roughness on aerodynamic performance have been well documented over the years. Surface roughness has been shown to decrease lift, increase drag, and alter stall characteristics. It is also well known that the characteristics (i.e., position and size) of laminar separation bubbles and trailing-edge separation have a significant impact on the aerodynamic performance of an airfoil in low speed subsonic flow. Therefore, it is important to obtain an understanding of how these two phenomena may interact with each other. There are a limited number of experiments suggest*. Graduate research assistant, member AIAA f. Professor, member AIAA Copyright © 1998 by authors. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. All rights reserved. ing that such an interaction is possible. For example, Bloch and Mueller conducted an experimental investigation on the effects of small-scale (sand grit) roughness on leading-edge and trailing-edge separation bubbles at low Reynolds numbers. Their results show that smallscale surface roughness, placed at the leading edge of an airfoil, has the ability to alter the location and size of separation bubbles. This included both the leading-edge separation bubble as well as the trailing edge separation. Cronin, et. al. also conducted an experiment in which it was shown that small-scale roughness significantly effected the leading-edge suction spike of the airfoil. The small-scale roughness in this case was various sized grits of sandpaper placed at the leading edge of the airfoil. These results showed that the performance degradation produced with contamination present was dependent on roughness size, Reynolds number and angle-of-attack. The combination of large leading-edge roughness and a large angle-of-attack had the strongest influence on the performance drop. Rothmayer also conducted a numerical simulation similar to our study. His work investigated surface roughness effects on breakaway laminar separation for supersonic flow in the immediate vicinity of the separation point. These results indicated that small-scale roughness would not have any significant local effect on the overall laminar breakaway separation. However, as Rothmayer suggests, the outcome may be different in the subsonic flows. Various parameters have been investigated in the present study to determine how the small-scale roughness interacts with the larger scale separation. This includes roughness height, wavelength, and distribution. The roughness elements used in this study have a maximum height of approximately 1% 5% of the airfoil half-thickness and are all contained within the laminar boundary layer. This study also investigates several other aspects of this phenomenon, including the differences between "sharp" and "smooth" roughness elements. It is hoped that this work will lend itself to further 1 American Institute of Aeronautics and Astronautics Copyright© 1997, American Institute of Aeronautics and Astronautics, Inc. applications in the area of roughness interaction with leading-edge short bubbles, which is relevant to the study of airfoil ice accretion at early growth stages. While the trailing-edge bubbles being investigated do not account for transition to turbulent flow, they are representative of the starting laminar separations in many leading-edge bubbles. Interacting Boundary-Layer Method The algorithm used in this study is essentially the quasi-simultaneous interacting boundary-layer (IBL) method developed by Davis and Werle5 (see also Veldman). It is well established that a steady interacting boundary-layer method can produce results for small separation regions that are in good agreement with both Navier-Stokes calculations and experimental results (see McDonald7). The problem considered here is an incompressible, laminar flow past a thin twodimensional symmetric biconvex airfoil aligned with the oncoming flow, i.e. Semi-infinite Splitter-plate Fig. 1 Biconvex airfoil geometry. The body shape is given by: 1/2 /(*) = Re 4&x(l-x), (1) where Q is half of the actual thickness-to-chord ratio. The chord length of the airfoil is set to a value of 1. A splitter plate is used in the downstream region. Small-scale surface roughness is added to the top and bottom surfaces of the airfoil. The roughness is modeled as a sine wave and classified as sharp-edged roughness (Geometry A), smooth roughness (Geometry B), and inverted sharp-edged roughness (Geometry C), respectively. These three forms of roughness geometry are shown below: A.) Sharp-edged roughness B.) Smooth roughness C.) Inverted sharp-edged roughness Fig. 2 Typical roughness element configurations used to simulate the small-scale surface roughness. The smooth roughness is formed from a continuous sine wave, while the sharp roughness consists of a truncated sine wave. The geometries (A-C) given in Figure 2. are not shown to scale. The vertical scale is greatly exaggerated to help visualize the form of the surface roughness. Governing Equations The form of the interacting boundary-layer equations used in this study closely follows those given by Davis and Werle. There are three basic classes of IBL methods: the inverse, semi-inverse, and quasi-simultaneous method. This study uses the quasi-simultaneous method. For brevity, only the main equations of the interacting boundary-layer method are presented. For a more detailed discussion of the full derivation, the reader is referred to [1], [5], [6], and [8]. The interacting boundary-layer method is composed of two regions: a viscous boundary-layer flow near the body and an inviscid flow outside the boundary layer. These two regions are solved in a fully implicit, coupled manner to retain the strong interaction between the viscous and inviscid flows. The viscous flow near the airfoil and in the wake is governed by the two-dimensional, incompressible boundary layer equations, which have been written in boundary-layer scaled variables (i.e. y = Re~ Y). A Prandtl transposition is used to produce a body fitted coordinate system. New coordinates s and N are defined as follows: s = x , N = Y-f(x) . (2) The governing equation variables are further transformed using Gortler variables, f Ue N E, = \ Ue (s)ds and TI = —2= , Jo ° ./7F M (3) where Ue0 is the inviscid surface speed over a baseline curve, taken here to be the x-axis (see Davis and Werle5). The transformed velocities, in Gortler variables, are defined by