Thomas D. Economon, Francisco Palacios, Juan J. Alonso
Aeronautics & Astronautics Department
SU2 is an open-source collection of C++ and Python-based software for multi-physics simulation and design, and it is particularly well suited for computational fluid dynamics (CFD) and aerodynamic shape design. It is now under active development both by researchers at Stanford University and by individuals and groups at institutions all around the world. The project has received hundreds of thousands of web visits and tens of thousands of downloads since its release in January 2012. The goal of the SU2 team is to make CFD analysis and design freely available as open-source software, with worldwide collaboration in its creation, enhancement, verification, validation, and rapid development.
The SU2 team developed a SU2 Pointwise CAE plugin interface to write native SU2 grid and boundary conditions directly from Pointwise, and this plugin is now included with every Pointwise release. To make setting up optimization problems in SU2 easier, Pointwise, Inc. developed a Glyph script, CreateFFD, for creating Free-Form Deformation (FFD) boxes used in SU2 for shape optimization. The script is freely available for download from the Pointwise GitHub account.
This article discusses three design cases using SU2 and Pointwise together: transonic aircraft design with the NASA Common Research Model (CRM), supersonic aircraft design with the Lockheed Martin 1021 model, and design of the Stanford Solar Car in incompressible flow.
The NASA CRM, shown in Figure 1, is a generic, transonic airliner configuration that has been used for the AIAA Drag Prediction Workshop and is popular choice for verification and validation of CFD codes for such applications. The baseline grid was created in Pointwise. This problem was modeled with a 10 million cell mesh consisting of prism layers near the aircraft surface transitioning to a tetrahedral farfield grid with pyramid elements providing point-to-point connectivity between the prism cells and tetrahedral cells. For more information on the meshing process and to download the Pointwise project file for this grid, see the archive page for the Pointwise webinar How T-Rex Unstructured Meshing Aids Transonic Aircraft Drag Reduction.
One of the unique features of SU2 is its continuous adjoint methodology that provides sensitivity of any number of design parameters with respect to geometry changes. This can be displayed as surface sensitivity maps to give insight into design changes or used in conjunction with SU2's free-form deformation techniques to drive an automated shape optimization process. In this case, the wing shape is varied with the objective to minimize drag subject to constraints on lift coefficient and wing thickness.
The CreateFFD script mentioned earlier was used to create a free-form deformation box fitted around the wing of the CRM model as shown in Figure 2. The FFD box controls how the wing geometry can change in response to the adjoint sensitivity analysis. A total of 510 FFD variables were used around the wing for this optimization study.
The flow solution, adjoint solution, gradient calculations, and mesh deformations are all parallelized in SU2 and were run overnight across 960 cores. Figure 3 shows surface pressure coefficient from the flow solution and sensitivity of drag to surface displacement from the adjoint solution. The adjoint drag sensitivity is used to drive geometry deformations in the optimization loop. Gradient information for additional constraints, such as lift, can be easily provided to the optimizer by solving an additional adjoint problem for that objective.
After 15 optimization iterations, the drag is reduced by 2.2 percent while satisfying the lift and wing thickness constraints. Surface pressure coefficients from the optimized design and the original geometry are compared in Figure 4. In the original geometry, there is a shock wave at approximately the mid-chord location over much of the wing's span, while in the optimized geometry the pressure rise on the upper surface is much more gradual.
SU2 can also be applied to supersonic flows. SU2 and Pointwise were applied to reduce the supersonic drag of the Lockheed Martin 1021 aircraft model subject to constraints on the lift and pitching moments generated. This model is one of the test cases from the 1st AIAA Sonic Boom Prediction Workshop. The meshing, solution, and optimization process for this case are described in a recorded joint Pointwise-SU2 webinar, Supersonic Aircraft Shape Design Powered by SU2 and Pointwise. The surface mesh for this geometry is shown in Figure 5.
A hybrid mesh with tetrahedral cells in a core block near the aircraft and Mach-aligned hexahedral cells in the farfield was generated with Pointwise. Using tetrahedral cells near the body simplifies the mesh generation process when treating complex geometry, such as the LM 1021. The Mach-aligned hexahedral cells in the farfield have two faces aligned with the freestream Mach angle and the other faces aligned with the freestream flow direction. This alignment scheme helps to reduce numerical diffusion and using hexahedral cells helps to bring down the cell count without compromising accuracy. This grid topology is often used to accurately predict sonic boom characteristics, since this typically requires the extraction of pressure signatures at off-body locations. The overall layout of the volume grid is shown in Figure 6.
Pointwise was used to create FFD boxes around the outboard portion of the wing as shown in Figure 7. For this case, 264 FFD control point variables were used to control the wing shape deformation during the optimization process.
The original and optimized surface pressure distributions are shown in Figure 8 for the upper surface of the aircraft and in Figure 9 for the lower surface. Since the outboard portion of the wing is the only part of the geometry that changed, that is where the biggest differences in the solutions are located. On the upper surface, the optimized wing has less pressure drop than the original geometry.
On the lower surface, the optimized wing features higher pressures near the aft portion of the wing and slightly modified shock wave characteristics as compared to the original geometry. While appearing subtle, the resulting changes to the geometry have helped to trim the aircraft by reducing the pitching moment, and the net result is a reduction of 3 drag counts less than the baseline geometry while meeting the lift and pitching moment constraints.
The final test case is for incompressible flow around the Stanford Solar Car. The Stanford Solar Car Project aerodynamics team consists of approximately 10 undergraduate students. During the design of the new solar car for the 2015 cycle, they ran full design iterations that included the generation of CAD models, creation of unstructured, boundary layer resolved meshes using T-Rex in Pointwise, and the execution of incompressible SU2 calculations on hundreds of cores with turnaround times on the order of one day.
Figure 10 shows a cut through a T-Rex volume mesh for their Luminos vehicle, and Figure 11 shows surface pressure coefficient distribution.
SU2 is a freely downloadable suite of open-source software tools for CFD and shape optimization. When used in conjunction with Pointwise for mesh generation and FFD set up, it can handle a wide range of industrial problems from incompressible through transonic and supersonic flows.
Pointwise and the SU2 team conducted a joint workshop in September to introduce new users to setting up CFD and optimization problems. An archived recording of the workshop is available for anyone wanting to learn more.
For more information about SU2, including how to download and install it, please visit the SU2 team website.
If you would like to generate your meshes using Pointwise request a free evaluation today.