Airfoils have been studied extensively in steady cases to understand the effects on the performance of varying airfoil shapes. This has led to an understanding of what airfoil shapes are most efficient for given flow regimes. In this research, we extend that work to include air/hydrofoils undergoing a flapping motion, thus opening the door for future engineers to make better design decisions about airfoil shapes and give biologists another tool to analyze the flapping hydrofoils commonly seen in fish and other aquatic animals. In this research, we study the effects of variable airfoil thickness at different points along the chord has on efficiency through a pitching and heaving motion.The parametric study begins by using the class shape transformation (CST) parameterization method to create airfoil geometries. Through this method, we break down the airfoil into six coefficients that correspond to thickness at different points along the chord of the airfoil. The CST maintains the core airfoil shape and allows us to change the thickness in specific regions of the airfoil with a few inputs. The Reynolds number is chosen to be 10000, and the Strouhal number is 0.3. These were chosen to be within the range of natural swimmers, such as fish. The pitching and heaving motion is also set up to be within the natural domain. Also, in consideration of natural features, we study only symmetric airfoils. For the base case, the NACA0012 airfoil shape is used. After finding the CST coefficients for the base case, we use the results of a gradient-based optimization for efficiency published in Han et al. as a guide for the range of the coefficients. In this study, we vary each coefficient from the NACA0012 value to 1.5 × (A-B), where A is the optimized shape value and B is the NACA 0012 value. Within the range we test five values, along with testing the limits, giving us a total of 37 cases run. To solve the cases, we use an immersed boundary method-based incompressible flow solver. In this solver, the Navier-Stokes equations are discretized using a cell-centered, collocated arrangement of the primitive variables and are solved using a finite difference-based Cartesian grid immersed boundary method.The results of the simulations will be shown through the power coefficient (P), thrust coefficient (T), and propulsive efficiency (T/P) of the airfoil motion. From this, we expect to see that the optimized CST coefficients produce the highest efficiency, but we will also be able to see more specifically what regions of the airfoil thickness have a greater impact on power, thrust, and efficiency. From the results, we will see the changes in wake structure that are caused by changing the airfoil shape. The results will allow engineers to make more informed decisions on specific hydrofoil design features for flapping cases, such as trailing edge sharpness and location of maximum thickness. Also, the results may serve as an additional tool for biologists to better understand the shapes that are seen in animals as a result of evolution.

Wake Structures and Effect of Hydrofoil Shapes in Efficient Flapping Propulsion

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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