The boundary layer stability code they have developed, JoKHeR [1], analyzes the propagation and growth of boundary layer instabilities in a preexisting computed basic flow state. For stability analysis, it is important to create highquality grids to compute the basic state, since boundarylayer stability is extremely sensitive to minute details and perturbations of the basicstate solution. Pointwise provides them with various ways of controlling the quality of the meshes, such as using the spacing and growthrate functions and the elliptic PDE solver, which allows them to smooth domains and blocks.
Overset Grids Used for MicronSized Roughness Elements on Airfoil
In this study of stability and transition for subsonic aircraft, the effects of surface roughness and of roughness used for laminar flow control were examined. Discrete roughness elements (DRE) are applied as a passive control device to delay the onset of transition on swept wings [2]. An overset grid was constructed to model a windtunnel experiment featuring a laminarflow airfoil with micronsized roughness elements applied very near the leading edge.
The height of the DRE is 24 μm, the chord of the airfoil is 1.8 m, and the wing sweep angle is 45˚. The airfoil used is the ASU(67)0315 and the experimental conditions are provided by Hunt and Saric [3] (2011) from the KlebanoffSaric Wind Tunnel at Texas A&M University. The airfoil model and the computational domain are shown in Figure 1.
Figure 1: Airfoil geometry and grid location for discrete roughness element analysis
The grid geometry consists of three structured, overset blocks: an Ogrid around the circular DRE, a Cartesian path grid on top of the DRE, and a boundary layer grid. This construct is similar to that used by Rizzetta and Visbal [4] (2007) and Rizzetta et al [5] (2010), except the airfoil shape is no longer just an analytic shape but rather the actual coordinates of a windtunnel model. The DRE Ogrid block size is 505x63x76 points. The DRE Cartesian patch grid is 201x201x63, and the boundary layer grid is 681x106x204. The Ogrid and patch grid are shown in Figure 2, and the boundary layer grid is shown in Figure 3.
Figure 2: An Ogrid and a Cartesian grid form part of the overset grid near the DRE
Figure 3: The wing boundary layer grid surrounding the DRE
The overset grid was preprocessed with PEGASUS to compute the domain connectivity database. A highorder stencil code was used to model the flow and preliminary results have been obtained.
This work is ongoing, but preliminary results are promising. Figure 4 shows the boundary layer flow solution with DRE Ogrid and patch grids outlined. The flow is left to right and swept 45° from the chordline. Grid slices are presented with velocity magnitude contours where deep blue is zero and orange approaches U∞. A slice parallel to the airfoil surface is presented at the height of the 24 μm DRE and streaks of highervelocity fluid can be observed from the corner and downstream edge of the DRE. Vertical slices are also presented which show the boundarylayervelocity profiles as they develop with increasing chord position. Efforts are under way to produce fully developed DRE flow structures for input to JoKHeR. The result will be a physicsbased parabolized stability equation (PSE) model of the boundarylayer mode shapes to be validated with the experimental measurements of Hunt and Saric [3] (2011).
Figure 4: Flow velocity contours near one of the DREs
Boundary Layer Stability in Hypersonic Flows
The boundary layers over hypersonic vehicles are typically threedimensional (3D) and feature a variety of instability mechanisms, including viscous, acoustic, and crossflow instabilities. The Texas A&M research group studies a variety of representative geometries including straight cones, flared cones, and blunt capsules similar to the Apollo reentry capsule.
Results for the straight cone at angle of attack will be presented here. The straight cone was chosen as a verification case for JoKHeR as there is a vast amount of experimental and computational literature, including a direct numerical simulation (DNS), full NavierStokes computation of the instabilities by Balakumar & Owens [6] (2010). The cone model studied has a 7° halfangle, is 0.508 m (20 inches) in length, and has a nose radius of 0.05 mm.
Since there is no yaw in this case, only half of the cone needs to be modeled. To include the nose, a structured rectangular domain is projected onto the nose of the cone to create a domain on the surface. Figure 5 shows the mesh used in the current studies. There are two main sections in the wallnormal direction: a shock layer and a shock capture band. The shocklayer region is represented by the green color and the shock capture band is represented by the cyan color. The shockcapture band consists of 201 equally spaced points, while the shock layer contains 231 points. In the shock layer, cells are clustered toward the surface of the cone to capture the boundary layer and to the shockcapture band to ensure a smooth transition between domains. The mesh contains 274 points axially and 205 points circumferentially, totaling a mesh size of approximately 23 million cells.
Figure 5: Structured grid used for flow over a straight cone at angle of attack
Once the mesh was created with Pointwise, it was imported into GASP, a general NavierStokes CFD code from Aerosoft, Inc.. The basic state was computed at the following conditions: freestream Mach number M∞ = 6, 6° angle of attack (AoA), freestream temperature T∞ = 5353.42 K, and freestream pressure P∞ = 11611.38 Pa abs, which results in a unit Reynolds number Re’ = 1010.09x106 per meter. An isothermal walltemperature condition, Twall = 300 K, was imposed. Figure 6 shows the basicstate Mach contour solution obtained from GASP.
Figure 6  Mach contours computed using GASP
In using PSE, a marching path must be specified in order to compute boundarylayer stability along that path. While inviscid streamlines provide a convenient marching path, they can be different from the true direction of disturbance propagation as defined by the group velocity. However, computing the group velocity requires a whole new set of stability calculations. On the straight cone at yaw, off the windward and leeward rays, the dominant instability is crossflow.
Stationary crossflow vortices do not follow inviscid streamlines, but if one is familiar with the physics of the problem, one can implement an approximate method to find the stationary crossflow vortices based solely on the undisturbed basicstate solution. Figure 7 shows JoKHeR computed Nfactors (natural log of integrated disturbance growth) along different computed crossflow stationary vortex paths compared to the DNS results. The red symbols represent Nfactors computed from the DNS of Balakumar & Owens [6] (2010). The black lines represent the Nfactors computed by using an eight million cell mesh without nose tip resolution for three different stationary crossflow vortices that correspond to the vortices in the DNS. The blue line represents the Nfactor results obtained with the current 23 million cell mesh. Good agreement was obtained between JoKHeR results and the DNS in the verification studies, as is evident by comparing the black lines and red symbols. The agreement improved when Nfactors were recomputed with the 23 million cell mesh basic state. This is significant because JoKHeR uses a fraction of the computational resources required for the DNS.
Figure 7: Instability growth rates predicted by DNS (black lines), coarse basicstate PSE (red symbols), and fine basicstate PSE (blue symbols)
Summary
Boundary layer stability prediction aids understanding of boundary layer transition in a variety of flow situations from very low speeds up to hypersonic speeds. The parabolized stability equation code, JoKHeR, developed at Texas A&M University provides an efficient way to make these predictions, but it does require an accurate basic flowfield state as a basis, and this in turn requires a good computational grid. Pointwise gives researchers the control they need to meet their demanding basicstate accuracy requirements and so predict how boundary layer disturbances will propagate and possibly cause a laminar flow to transition to turbulent.
References
 Kuehl, J., Perez, E., and Reed, H. 2012. JoKHeR: NPSE Simulations of Hypersonic Crossflow Instability. AIAA20120921.
 Saric, W., Carpenter, A., and Reed, H. 2011. Passive Control of Transition with Roughness in ThreeDimensional Boundary Layers. Philosophical Transactions of the Royal Society A, vol. 369, no. 1940, 13521364, April 2011.
 Hunt L. E., and Saric W. S. 2011. BoundaryLayer Receptivity of ThreeDimensional Roughness Arrays on a Swept Wing. AIAA20113881.
 Rizzetta, D. P., and Visbal, M. R., "Direct Numerical Simulation of Flow Past an Array of Distributed Roughness Elements," AIAA Journal vol. 45, no. 8, August 2007, pp. 19671976. doi: 10.2514/1.25916
 Rizzetta, D. P., Visbal, M. R., Reed, H. L., and Saric, W. S., "Direct Numerical Simulation of Discrete Roughness on a SweptWing Leading Edge," AIAA Journal vol. 48, no. 11, November 2010, pp. 26602673. doi: 10.2514/1.J050548
 Balakumar P, Owens LR. 2010. Stability of hypersonic boundary layers on a cone at angle of attack. AIAA20104718.
