Abstr:Shock/boundary-layer interaction (on airplanes)
Semi-Confined Flows
Underlying Flow Regime 3-05
Abstract
The interaction of a shock with a boundary layer developing on an aircraft wing can have an enormous impact on the subsequent development of the boundary layer and hence the performance characteristics of the aircraft. The main response to a shock is a thickening of the boundary layer possibly followed by flow separation. In order to predict this response with numerical simulation it is necessary that the numerical algorithm and mesh should be able to accurately resolve all the physical processes ocurring within the flow as it traverses the shock. In particular, for turbulent boundary layers, it is necessary that the model of turbulence provides a realistic representation of the interaction between the mean flow and the turbulence structure under conditions of rapid change in the mean flow. Typically the turbulence structure will respond to changes in the mean flow over a timescale much longer than that required to traverse the shock. Models which work well under conditions close to equilibrium between turbulence and the mean flow may respond in a totally inappropriate manner to a rapid change in the mean flow. In order to perform well, a model should be sensitised in an appropriate fashion to the ratio of timescales associated with the turbulence and changes in the mean flow.
Experimental investigations of shock/boundary layer interactions have been made for laminar and turbulent boundary layers as well as laminar boundary layers undergoing transition to turbulence following the shock/boundary-layer interaction. Most interest in CFD comparison exercises has been focussed on interactions with fully turbulent boundary layers although interactions with laminar boundary layers and boundary layers undergoing transition are also relevant to aerodynamic applications.
Comparison between CFD simulations for fully laminar boundary-layers and boundary layers induced to undergo transition were made in the ERCOFTAC workshop on shock/boundary layer interactions held at UMIST in 1997. The fully laminar test case was the experiment of Bristeau et al. involving flow through a double throated nozzle. Following an initial pressure induced separation, a smaller shock induced separation results from the impingement of an oblique shock on the boundary layer. Relatively small differences between the CFD solutions obtained by workshop participants for this test case were attributable to differences in the numerical schemes employed. The transition test case was Skebe’s case D in which an oblique shock impinges on laminar boundary layer flow over a flat plate. The problem of correctly predicting the transition made this a difficult test case in which to achieve good agreement with experiment.
In fully turbulent test cases the focus is on the performance of the turbulence model employed in the CFD simulation. Amongst turbulent boundary layer investigations the two-dimensional bump flow experiments of Delery have been widely used as test cases in CFD simulations. Delery performed three experiments known as cases A, B and C. In each of these flow is accelarated from subsonic to supersonic conditions through a constriction in a tunnel of rectangular cross section. In cases A and B the constriction is formed by a symmetric configuration of bumps mounted on the floor and ceiling of the tunnel whilst in case C a bump is mounted only on the floor. In each case a shock is formed in the divergent region of the flow and interacts with the turbulent boundary layer on the rearward facing side of the bump. In case A this results in an incipient separation whilst in case B there is an extended region of separation. In case C the separation is strongest and of greatest extent. In all three cases measurements were made of surface pressures along the mid-span line. Velocity turbulent kinetic energy and shear stress profiles were also measured at a number of mid span, streamwise locations.
Delery’s bumps A and C were used as test cases in the EUROVAL collaborative programme to validate turbulence models. More recently, case C was adopted as the fully turbulent test cases in the ERCOFTAC workshop on shock/boundary-layer interactions mentioned earlier. A shortcoming of using these test cases in these comparison exercises is the relatively close confinement of the flow in the spanwise direction resulting in 3d effects. The entrance to the test section has a width of only 120mm compared to a height of 100mm. Consequently non-negligible spanwise gradients of flow variables are observed casting doubt on the validity of comparisons with the 2d CFD simulations in EUROVAL and elsewhere. Whilst not really qualifying as 2d test cases these flows are not ideal as 3d test cases either due to the lack of relevant measurements for comparison with a 3d simulation.
An investigation of an intentionally 3d shock boundary layer interaction was made in the experiment of Pot, Delery and Quelin. This was similar to the transonic bump flows described above and was performed in the same test section. The difference in this case was that the bump was inclined at an angle of 60degrees to the flow direction resulting in strongly three-dimensional flow. The shock generated over the backward facing surface of the bump was sufficiently strong to provoke flow separation. Surface pressures were measured on all four walls and velocity and shear stress profiles were measured at a number of locations. This flow has a highly complex structure making it difficult to visualise and understand. This complexity makes it an unsuitable choice as a test case for the shock-boundary layer UFR.
An alternative to the complexity of fully 3d flow and the uncertainties associated with 2d planar flow is axisymmetric flow such as that in the bump flow experiment of Bachalo and Johnson. This experiment consists of flow over an annular bump mounted on a cylinder aligned with the flow direction. A shock above the rearward facing surface of the bump promotes flow separation. Measurements of surface pressures were made together with profiles of mean velocity, turbulent kinetic energy, shear and normal stresses. The axisymmetric character of the flow enables 2d numerical simulations to be performed in polar coordinates or 3d simulations on a thin wedge with appropriate symmetry conditions. This aspect together with the detailed high quality experimental data determined that this experiment should be selected as a fundamental test case within a collaborative research programme between UK universities and industry known as VoTMATA (Validation of Turbulence Models for Aerospace and Turbomachinery Applications). This programme sought to validate turbulence models and achieve some basic understanding of their strengths and failings. The uncomplicated character of the experiment together with the careful comparison with CFD available from VoTMATA has resulted in this being selected as the test case for the UFR.
Contributors: Antony Hutton - Qinetiq