The AIAA Aerodynamic Design Optimization Discussion Group developed a series of benchmark cases. (Martins & Hwang, 2013) present a broader overview of methods for computing derivatives, putting the adjoint method into context. (Martins et al., 2016) briefly describe other versions of the adjoint implementation that are more efficiently and are currently used in our aerodynamic shape optimization studies. This paper described an initial adjoint method that worked well but was not very efficient.
AIRFOIL SHAPE CODE
The overall approach is to selectively use automatic differentiation on parts of the CFD code to compute the partial derivative terms in the discrete adjoint equations. The adjoint method and our implementation is explained by (Mader et al., 2008). Gradient-based optimization requires the derivatives of the objective function (e.g., drag) and constraint functions (e.g., lift, moment) with respect to all the design variables (e.g., angle of attack, shape variables). Note that the adjoint method itself is not an optimization strategy, it is just a way to compute the gradients and it is independent of the specific gradient-based optimization algorithm that is used. The key enabler in aerodynamic shape optimization is the combination of gradient-based optimization, which is necessary to handle the hundreds of shape variables involved, with an adjoint method that computes the required gradients efficiently. The adjoint approach for computing derivatives The process is fully automatic and the final result is the re-invention of a modern supercritical airfoil. In the video below, we start from a circle and minimize the drag with respect to the shape while enforcing constraints on the area and chord (He et al., 2019). Example: From a circle to a supercritical airfoil This is not intended to be a comprehensive literature review for such reviews, you can see the introductions of our papers and the works they cite. In this page we summarize the work our lab has done in aerodynamic shape optimization.
The process is iterative: It starts with a given shape and then changes that shape to improve the performance while satisfying the specified constraints. The aerodynamic performance is usually evaluated using computer fluid dynamics (CFD) and the optimization can be done using a number of algorithms. As a result, the wings will produce more lift to keep the airplane in the air.Aerodynamic shape optimization, or aerodynamic design optimization consists in maximizing the performance of a given body (such as an airfoil or wing) by changing its shape. Air will move faster over the top section, and it will more slower under the bottom section. It’s designed to increase lift production by changing the speed at which air moves over the wings. In ConclusionĪirfoil is a shape used for airplane wings that consists of a curved top and a flat bottom. The difference in speed at which air moves over the top and bottom sections of an airplane’s wings allows it to generate more lift. This design means that air will travel faster over the top of section when compared to the bottom section. After all, the curved airfoil shape guides air downwards, thereby accelerating it. The curvature on the top section of an airplane’s wings means air will travel faster over it when compared to the bottom section. In turn, the wings will produce more lift.Īs previously mentioned, an airfoil shape consists of a curved top and a flat bottom. An airfoil shape, however, allows air to travel over the top of an airplane’s wings slower than the bottom. How exactly does an airfoil shape produce lift? If an airplane’s wings have the same shape on both the top and bottom, air will travel over the respective areas at the same speed. As a result, they are able to stay in the air more easily. Airplanes that use an airfoil shape for their wings produce more lift than their counterparts that use an alternative shape. Propulsion is generated by an airplane’s engine or engines, whereas lift is generated by an airplane’s wings and body. Along with propulsion, lift is one of the acting forces that allows airplanes to move from one point to another. An airfoil shape means that the top of an airplane’s wings is curved, whereas the bottom is flat and uncurved.Īirplanes use an airfoil shape for their wings to produce lift. What Is an Airfoil?Īlso known as an aerofoil, an airfoil is a specific wing shape that’s characterized by a curved top and a flat bottom. To learn more about wing airfoil and why it’s used, keep reading. With their use of an airfoil shape, the wings of an airplane can provide greater lift, thereby minimizing the energy needed to keep the airplane in the air. Known as an airfoil, it’s a common feature of nearly all commercial jets as well as propeller-driven airplanes. The wings of airplanes are designed in a specific shape to achieve the greatest amount of lift.
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