Mesh Generation for Airframe Noise Computations
As a company, one of Pointwise's goals is to be a good advocate of the meshing and computational fluid dynamics (CFD) communities. Being an advocate means participating in technical conferences and workshops and with other community members in a non-partisan way. Particular forums in which Pointwise regularly engages the community are the AIAA workshops. Earlier this year, Pointwise engineers began participating in the second workshop on benchmark problems for Airframe Noise Computations, (BANC-II). In addition to CFD, this workshop involves another CAE discipline called Computational Aero-Acoustics (CAA).
CAA, as the name indicates, concerns the numerical computation of aerodynamically generated noise. CAA is regarded as one of, if not, the most challenging areas of CAE. Why? Because the phenomena of sound propagation happens at much smaller time and length scales than the typical items of interest to an engineer, such as lift and drag. Consider the particular BANC-II case Pointwise engineers are working on, a multi-element wing in high-lift configuration (Figure 1).
Lift and drag are computed through the large scale behavior of the fluid – pressure for lift and friction plus pressure for drag. As a result, the Reynolds Averaged Navier-Stokes (RANS) approach has proven highly capable for efficiently computing lift and drag accurately. Recall that the RANS approach computes the large scale motion of the fluid and models the effect of the small scales, i.e. turbulence.
Sound is the propagation of pressure fluctuations – small, unsteady pulses in the pressure field – through the fluid. This introduces two aspects that the RANS approach ignores – small scales and unsteadiness. To get a better feel for the difference in scales, a practical comparison is helpful. To compute lift, one needs to know the pressure acting on the surface. A Boeing 747-8 has a maximum take-off weight of 442,000 kg and wing area of 554 m2 [Ref. 1] yielding a wing loading, or pressure, of 7882 Pa. Now consider the loud noise produced by a jackhammer. A jackhammer produces sound pressure levels of about 100 dBa at a distance 1 meter – enough to create some serious ringing in your ears. Yet, 100 dBa sound pressure level equates to only 2 Pa of pressure difference. This is a small value for such a loud noise.
Combine this with the inherently unsteady nature of sound and it is easy to understand the significant effort needed to compute aerodynamically generated noise and why RANS is ill-equipped.
Leading Edge Slat Noise
The NASA 30P30N multi-element high-lift airfoil, introduced above, is being used in the BANC-II to investigate the noise radiating from the leading slat region. The motivation for this case is to identify sources and mechanisms of the noise, as they are generally not well understood. Figure 2 illustrates some of the plausible sources and mechanisms of noise generation in the slat region. Thus, the goal of the BANC-II is to improve upon the description postulated in Figure 2.
Figure 2: Illustration of the possible mechanisms of aerodynamically generated noise in the leading edge slat region of a multi-element airfoil. Image courtesy BANC-II case 7 problem statement (http://ptwi.se/UaHFfw).
How does meshing factor into CAA?
Sufficiently resolving the flow field for aero-acoustics places two challenging requirements on the CFD preprocessor: a fine mesh and a high quality mesh. High resolution is obviously necessary to capture the small scales while high quality is needed to minimize the influence of numerical error. Correspondingly, structured meshes are preferred for high-fidelity CAA simulations.
While the computed flow field is 3D, the multi-element airfoil used for this case is essentially an extruded 2D airfoil without sweep. Therefore, the efforts in creating the mesh in Pointwise were carried out in 2D. When finished, the 2D mesh needs simply to be extruded in the spanwise direction to create the full 3D mesh. The fact that the mesh was 2D did not necessarily make the mesh generation easy. The barriers to creating multi-block structured meshes might be summarized by three main challenges:
The following describes how Pointwise was used to address these challenges for BANC-II multi-element airfoil case.
As the exact noise source mechanisms and locations are not known, it was important to create a highly resolved mesh in all areas of the leading edge region. Creating a local region of dense point clustering for multi-block structured meshes can unnecessarily introduce an excessive number of points into regions that do not require it. The dense point clustering in the slat cove region was propagated downstream on both the upper and lower surfaces of the main element to mitigate this issue, as seen in Figure 3. This serves two purposes. First, the dense point clustering created here can be somewhat contained and directed toward the outlet boundary. Second and more importantly, this helps to resolve the trailing edge regions, which are thought to be contributors to noise. The need to propagate the slat cove points in this manner greatly influenced the final topology, shown in Figure 4.
Perhaps, the most time consuming of the challenges is devising an appropriate topology. Topology refers to the way blocks are connected to sub-divide the computational domain. A simple visual inspection of the geometry does not always reveal the most appropriate topology. The traditional way to uncover a suitable topology has been experimentation, sketching topologies with a paper and pencil. This is time consuming and difficult to visualize in 3D. However, Pointwise contains a comprehensive suite of easy-to-use curve drawing tools that makes the paper and pencil obsolete. By sketching block boundaries using the database curve drawing tools in Pointwise, the block topology surrounding the multi-element airfoil could be developed (Figure 5). The Bezier curve tool was found particularly useful because it allowed straightforward slope control, enabling the organic boundary shapes shown in Figure 4.
The block topology could have been created with connectors (grid) instead of database (geometry) curves, but using database curves served an additional purpose. Having database curves that define the block topology makes it trivial not only to create the mesh but recreate it if a portion or the entire grid needs to be restarted. Using the Connectors on Database toolbar button turns connector creation into a single mouse click action. Then, it is a matter of ensuring the dimensions are appropriately set to facilitate structured domain assembly. Dimensioning connectors is another feature directly accessible on the toolbar. A new feature introduced in Pointwise V17, copy and pasting spacing constraints, helps to achieve a smooth transition in spacing across adjacent connectors and domains.
In a complex block topology such as this multi-element airfoil, it is difficult to create domains of sufficient quality by adjusting the connector spacing and distribution alone. Pointwise's elliptic solver is a powerful tool to help improve grid quality for complex structured mesh topologies beyond what is possible through manual connector tweaking. Groups of domains can be smoothed simultaneously using the elliptic solver by allowing inter-block connectors to deform along with the other interior grid lines with the Float boundary condition in the solver's edge attributes. Another powerful but often overlooked feature of the elliptic solver is the Orthogonal boundary condition, which allows connector grid points to slide freely along boundaries to improve orthogonality in those regions. This particular boundary condition was used extensively in the slat region. This concept is illustrated in a close up of the mesh in the slat cove region (Figure 6).
The Grid, Dimension tool made adjusting the resolution of the multi-block grid system easy. This tool attempts to automatically detect and propagate changes made to a connector throughout the grid system such that the domains and/or blocks remain balanced. If it is unable to do so automatically, it highlights which connectors need to be modified to rebalance the domains. The benefit of this tool is that the user is not required to manually correct the dimensions if the grid system becomes unbalanced.
Using computational aided engineering tools is becoming ever more prevalent, not because they produce colorful images but because they allow engineers to tackle problems more efficiently or that were not otherwise possible. Aero-acoustics is a good example of the benefits CAE can provide. It is laborious and costly to experimentally measure aerodynamically generated noise. Benchmark case studies provide a forum in which CFD and CAA tools can be validated so they can be used as predictive tools.
Within these validation case studies, researchers are examining not only the physical mechanisms that cause noise but also the influence CFD and CAA models have on the predicted noise. And one of the key influences is the mesh. Recall that high-fidelity CAA is likely going to require better turbulence modeling than RANS provides. Detached Eddy Simulation and Large Eddy Simulation are the likely turbulence model approaches to be used. The turbulent viscosity computed by DES and LES is on the same order as the molecular viscosity. The repercussion of this is numerically generated errors due to discretization, convergence and mesh quality will play a much more important role in the accuracy of the DES and LES than they would in RANS. The mesh is where engineers have the most direct control of accuracy, so it is easy to understand why we are motivated to provide tools and solutions to help them meet their goals.
The mesh presented may not be the final mesh used in the analysis. Discussion of this problem is currently under way with BANC-II workshop technical leads that have previous experience with CFD analysis. Once a suitable point density and mesh quality are converged upon, the 3D mesh will be created. The final cell count for the preliminary mesh shown in the preceding images was approximately 750,000 points. Therefore, the point count for the full 3D mesh is anticipated to be 400-500 million. Results using the final mesh are expected to be presented at the third BANC workshop in Berlin, Germany, on 30-31 May 2013.