Multi-objective aerodynamic optimization design of variable camber leading and trailing edge of airfoil

Variable camber is an effective method for improving the flight efficiency of large aircraft, and has attracted the attention of researchers. This work focused on the optimization of a variable camber airfoil. First, the influences of the variable camber of the leading and trailing edges on the airfoil aerodynamic performance were investigated using a computational fluid dynamics numerical simulation. An initial database was established for a deep neural network. Second, an iterative algorithm was constructed to optimize the variable camber airfoil in terms of the rotation angle of the leading edge, deflection position of the leading edge, rotation angle of the trailing edge, and deflection position of the trailing edge. A genetic algorithm was used in each iteration to maximize the lift coefficient and lift-to-drag ratio, as predicted using a deep neural network (DNN). The optimal results were validated using Fluent. If the DNN result approximated the Fluent results, the iterative process was stopped. Otherwise, the Fluent results were inserted into the database to update the DNN prediction model. The optimization results showed that the lift-to-drag ratio of the 2D airfoil could be increased by more than 14 when the angle of attack was less than 8° relative to the original airfoil. Furthermore, to validate the 2D optimal results, the optimized 2D airfoil was stretched into 3D, and it was discovered that the aerodynamic performance trend of the 3D airfoil with respect to the angle of attack was basically the same as that of the 2D airfoil. In addition, the corresponding 3D airfoil improved the aerodynamic performance and reduced the noise at a high frequency (by approximately 16 dB). In contrast, the noise in the low and medium frequencies remained unchanged. Therefore, the optimization method and results can provide a reference for the aerodynamic design and acoustic design of large civil aircraft wings.

CFD Comparative Study on Bended and 2D Airfoils on HAWT Performance

The design of a conventional horizontal axis wind turbine (HAWT) is based on the aerodynamic characteristics of a two-dimensional (2D) airfoil. The rotational motion and the consequent aerodynamic effects, of HAWT’s rotor, do not guarantee an optimal design point that matches the 2D airfoil characteristics. The present work studies the diversion of the flow due to the spanwise velocity component in a rotating reference frame. It suggests that a slight deviation in the flow away from the chordwise direction could alternate the characteristics of the airfoil profile. A bended profile with a circular arc was extracted from a baseline rotating blade, flattened, and modelled against the 2D S826 airfoil. The results show a substantial discrepancy in the airfoil characteristics which could influence the turbine efficiency. Therefore, it suggests using a pre-bended airfoil (3D) while modeling the blade, so the circular section will match the correct airfoil coordinates. The proposed bended-profile version was modeled against the baseline blade. This novel blade shows an augmentation in the power coefficient up to 5.4% starting from the design point to high tip speed ratios (TSR) and low wind speeds.

Inverse Design of 2D Airfoils using Conditional Generative Models and Surrogate Log-Likelihoods

This paper shows how to use conditional generative models in 2D airfoil optimization to probabilistically predict good initialization points within the vicinity of the optima given the input boundary conditions, thus warm starting and accelerating further optimization. We accommodate the possibility of multiple optimal designs corresponding to the same input boundary condition and take this inversion ambiguity into account when designing our prediction framework. To this end, we first employ the conditional formulation of our previous work BezierGAN---Conditional BezierGAN (CBGAN)---as a baseline, then introduce its sibling conditional entropic BezierGAN (CEBGAN), which is based on optimal transport regularized with entropy. Compared with CBGAN, CEBGAN overcomes mode collapse plaguing conventional GANs, improves the average lift-drag (C_l/C_d) efficiency of airfoil predictions from 80.8% of the optimal value to 95.8%, and meanwhile accelerates the training process by 30.7%. Furthermore, we investigate the unique ability of CEBGAN to produce a log-likelihood lower bound that may help select generated samples of higher performance (e.g., aerodynamic performance). In addition, we provide insights into the performance differences between these two models with low-dimensional toy problems and visualizations. These results and the probabilistic formulation of this inverse problem justify the extension of our GAN-based inverse design paradigm to other inverse design problems or broader inverse problems.

Exact pitch and heave flutter for the complex Theodorsen function

ABSTRACTConcepts of new fluttering wind and water mills led to general solution of flutter by a foil section free to pitch about an axis ahead of ${1}/{4}$ chord. The pitch damping of the vorticity being shed by lift change is negative singular via the imaginary part of the Theodorsen function. So a 2D airfoil can slowly flutter in pure pitch at a very high inertia with radian frequency and growth rate, reduced by windspeed/chord, resp. less than .087 and .01. At the frequency of nil net pitch damping, the binary inertia/damping cross determinant vanishes on a line in the imbalance vs inertia plane. The perturbed frequency contours just a bit above and below this ‘beab’ line spectacularly split to asymptote to the pure pitch inertia vertical of implied infinite heave stiffness. Higher frequency contours turn back towards the positive imbalance axis and then the origin, changing from hyperbolic to elliptical at exactly the same .087 and asymptoting to a line between the nexus and four times the nexus and a mode of effective pitch about ${3}/{4}$ chord. At .6 the pure pitch frequency the imaginary part dominates in the quadratic inertia and imbalance coefficients to bend the neutral contours down and across the quasi-steady line to even turn back to very large negative imbalance at small inertia, where kinematics then imply high mass. Diagonally mirror hyperbolae exist for greater than the pure pitch inertia with a different dynamic implication of very high foil mass.

AIRFOIL CONSIDERATIONS IN THE DESIGN OF HIGH PERFORMANCE, LOW REYNOLDS NUMBER PROPELLERS

A propeller was designed using 2D airfoil data obtained from a panel method numeric code. The propeller was designed to operate at 75% chord based Reynolds number of 20k. At low Reynolds numbers <40k, there are no publicly available 2D airfoil force data largely because of inherent difficulty in their measurement. Theoretical prediction of the propeller’s peak efficiency was 0.67 while experiment results was 0.58. To improve the propeller efficiency by using better performing airfoils, six (6) airfoils of varying thickness and camber were studied. Three of the six airfoils were chosen and used in the design of three propellers - a single airfoil for each propeller design. The propellers were designed to operate at Reynolds number of 30k at 0.75 radius and the 2D airfoil force data used for the designs were obtained from a numeric code. Theoretical predictions of efficiency were all > 81% in each of the designed propellers.