# 2D Airfoil: Multiparametric Optimization in Flow Simulation

In the Fall and Winter of 1901, Orville and Wilbur Wright completed the most comprehensive study of airfoils to-date in their experimental wind tunnel in Dayton, Ohio. They crafted a series of parametric experiments to explore the relationship between wing shape and aerodynamic performance. Specifically, they investigated 2D airfoil characteristics of camber (curvature) and thickness, as well as 3D wing parameters like planform aspect ratio and shape.

Wright Brothers example airfoil testing (http://wright.nasa.gov/airplane/models.html)

Today, we engineers have access to incredible software and computing power. You are probably aware of parametric studies that are available in SOLIDWORKS as part of a Design Study, a Parametric Optimization in Simulation Professional, and Parametric Study in Flow Simulation. With the release of SOLIDWORKS 2017, Flow Simulation introduces Multiparameter Optimization. This means we can set up a Design of Experiments in Flow, varying model or study characteristics and evaluating the performance of our design.

I decided to give this a try by optimizing a low-speed (M ~ 0.25) airfoil suitable for use on a small aircraft. I set up the base sketch to vary in airfoil thickness, camber, and position of max camber:

Varying thickness, camber, and position of max camber

The Flow Simulation was set up to match a Reynold’s Number of 3.1 x10^6. I used this because I had previously validated my meshing strategy by matching to NACA 2412 section lift and drag results with these same flow conditions. My study is a 2D domain and is a fixed 6 degree angle of attack. I am not going to dive in to meshing or much of the “windtunnel” study set up. There are good posts and forum discussions about this already. Some quick tips are to use equidistant mesh control and at least one Solution Adaptive mesh refinement to capture the complex pressure field that develops.

It’s a few simple clicks to select the dimensional parameters I want to vary, and the range they should vary within. We then specify how many Experiments to create. I chose 50 design points, because that seemed sufficient to get a good idea of response, but not enough that it wouldn’t solve overnight on my laptop. Before beginning this design study, I made sure to optimize my mesh and calculation controls to get an accurate enough answer in a minimum amount of time. For your studies, this might mean dialing back the mesh level or refinement controls from what you’d use in a single-point validation study.

Flow Simulation solver

Initial output I get is an Excel sheet with my three input parameters and my three selected goals: lift coefficient, drag coefficient, and lift-drag ration. You can interact with this plot and the data on plotly:

Results of 3-parameter DoE

So, in just a few hours I was able to create this response plot to understand how lift and drag varied against thickness, camber, and position of max camber. The airfoil geometry with the absolute highest lift-drag ratio is skinny, low-cambered, and max camber location near the leading edge. This makes sense, and resembles a section used on a glider.

The power of Flow Simulation’s new feature is that you can not only explore the design space automatically, but also ask it to find the optimum geometry based on a weighted response function. I might want an airfoil with higher lift coefficient, even though it might not be the simple highest lift-drag ratio. Instead, I asked Flow to give me the geometry that maximized the function: lift-drag ratio + 15*lift coefficient -5*drag coefficient:

Flow Simulation 2017 Multiparametric Optimization output

The output function can be defined as a linear weighted combination of any of your defined goals. The optimal airfoil in this case has a thickness of 2″, camber of 0.12 (% of chord length), and x/c of 0.26.

The resulting airfoil looks similar to the wing shape of the 1903 Wright Flyer – the first to achieve controlled, powered, manned flight. Of course there were more variables at play for the Wright Flyer than just airfoil, including the 3D wing shape (planform area and aspect ratio) and dihedral angle. In my next blog, I will explore a full 3D wing and reveal more of the power of Multiparameter Optimization in Flow 2017. Let me know below if you’d like more in-depth explanation of meshing or solving steps, or share how you could use Multiparameter Optimization.

#### Brian Zias

Senior Territory Technical Manager at Dassault Systemes SOLIDWORKS
Brian is a 10-year, expert SOLIDWORKS CAD, FEA, and CFD user and community advocate. His interests include engineering, simulation, business, and predictive analytics. Brian holds a BS in Aerospace Engineering and an MBA in Data Science.

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• Rob Jolly

Thank you, a very interesting read.

• David Maxham

Excellent article – very informative and the tie-ins to the Wright Bro’s make it even more interesting!