Aerodynamic Shape Optimization of an Adaptive Morphing Trailing-Edge Wing

This paper presents the fundamentals of a continuous adjoint method and the applications of this method to the aerodynamic design optimization of both external and internal flows. General formulation of the continuous adjoint equations and the corresponding boundary conditions are derived. With the adjoint method, the complete gradient information needed in the design optimization can be obtained by solving the governing flow equations and the corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. An inverse design of airfoil is firstly performed to study the accuracy of the adjoint gradient and the effectiveness of the adjoint method as an inverse design method. Then the method is used to perform a series of single and multiple point design optimization problems involving the drag reduction of airfoil, wing, and wing-body configuration, and the aerodynamic performance improvement of turbine and compressor blade rows. The results demonstrate that the continuous adjoint method can efficiently and significantly improve the aerodynamic performance of the design in a shape optimization problem.

An efficient aerodynamic topology optimization method was constructed based on the parameterized level set method (PLSM) and large neighborhood search algorithm. The traditional aerodynamic optimization design process is to optimize the shape of a basic shape, and the aerodynamic configuration is determined. The determination of the basic shape relies on the experience of human designers, making it difficult to obtain innovative aerodynamic configurations. To this end, the PLSM is used to obtain aerodynamic configurations of supersonic Busemann biplane with different topological structures. In response to the characteristics of large sample size and low computational efficiency in aerodynamic topology optimization design, a large neighborhood search algorithm is adopted as the optimization algorithm. Aerodynamic topology optimization design was carried out to achieve good drag reduction effect for the Busemann biplane. Compared with shape optimization design, aerodynamic topology design can generate airfoils with different topological structures, greatly improving the design freedom and making it possible to find different aerodynamic configurations in a wide design space.

Nowadays, one of the priorities of the European Commission is to reduce the environmental impact of aviation through the advanced design of novel aircraft configurations. This is of utmost importance in order to decrease the environmental footprint of aviation and to reduce fuel consumption and make airlines more profitable. This implies that new methods and tools for aerodynamic shape optimization will have to be developed, allowing aircraft configurations that cannot be obtained with traditional strategies. This paper focuses on the application of enhanced methods in aerodynamic shape design optimization to enable advanced aircraft configurations. In particular, this work aims to demonstrate the feasibility of the proposed strategy to reach optimal configurations that are far away from its baseline geometry. For this purpose, evolutionary algorithms are combined with support vector machines and applied to the optimization of a baseline geometry for different flow conditions. In particular, the selected application is based on the shape optimization problem of the landing gear master cylinder. Results pointed out the feasibility of the mentioned strategy to enable novel configurations within an aerodynamic shape optimization process.

Recently, we have proposed a robust and computationally efficient numerical algorithm for the optimization of 2-D and 3 -D catalysts distributions in Proton Exchange Membrane Fuel Cells (PEMFCs) using a gradient-based technique [1-3]. The algorithm is based on the computation of the catalyst sensitivity functions of the cell current and cell voltage by using the adjoint method. This method was initially developed by the applied mathematics community to solve optimization problems in fluid dynamics, climate, and heat transfer problems and, later, by other research groups to solve optimization problems in magnetics, model parameter determination, and semiconductor devices [4-6]. It was only recently that COMSOL, a popular finite element solver, has introduced the adjoint method, which has started to be used by the electrochemical community for calculation of sensitivities of platinum distribution in PEMFCs [7,8]. In this presentation we analyze the cell current, cell voltage, and spectral electrochemical impendence properties of PEMFCs by using the catalyst sensitivity functions of cell voltage, γPt(r). These functions show how much the cell voltage is increasing by adding 1 unit amount of platinum at a given location inside the catalyst layer (and assuming the cell is operating at the same current density). For instance, the figure below shows the 2-D catalysis sensitivity functions of the cell voltage for two cells with membrane thicknesses of 60 mm and 25 mm, in which the catalyst is distributed uniformly inside the cell. It is apparent from these figures that in order to increase the cell voltage and consequently the power of the cell, one needs to increase the concentration of Pt particles in the regions under the oxygen openings. As it will be shown at the conference the optimum catalyst distribution also depends on the operating temperature, catalyst and gas diffusion layers porosities, Nafion content, and cell current. In addition to the above analysis, we will also introduce a technique for the analysis of variability of polarization curves induced by the randomness of pore sizes and pore shapes in the catalyst and gas diffusion layers in PEMFCs. The technique is based on the evaluation of sensitivity functions of the cell voltage and can also be extended to the analysis of variability induced by the random platinum distribution in the catalyst layers (which is assumed to have a uniform random distribution). More details about the method for the analysis of variability effects, as well as about the numerical implementation of the adjoint method in the case of finite element simulations and its computational efficiency will be presented at the conference. [1] J. Lamb, G. Mixon, and P. Andrei, “Optimization of polymer electrolyte membrane fuel cells with a large number of degrees of freedom”, ECS 231Meeting, New Orleans, LA, 2017. [2] J. Lamb, G. Mixon, and P. Andrei, “Mathematical optimization of the spatial distribution of platinum particles in the catalyst layer of PEMFCs”, PRIME 2016 Meeting, Honolulu, HI, 2016. [3] P. Andrei, G. Mixon, M. Mehta, and V. Bevara, “Design of the catalyst layers in PEMFCs using an adjoint sensitivity analysis approach”, ECS Transactions 66(8), 91-128, 2015. [4] D. Cacuci, M. Ionescu-Bujor and M. N. Ionel, Sensitivity and Uncertainty Analysis, Volume 2: Applications to Large-Scale Systems, Chapman & Hall/CRC (2005) [5] W. K. Anderson and V. Venkatakrishnan, “Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation”, Computers & Fluids, 28, 443 (1999). [6] P. Andrei, I. Mayergoyz, “Quantum mechanical effects on random oxide thickness and random doping induced fluctuations in ultrasmall semiconductor devices”, Journal of Applied Physics, 94, 7163-7172 (2003). [7] COMSOL Multiphysics Software, https://www.comsol.com. [8] F. C. Cetinbas, S. G. Advani and A. K. Prasad, “Three dimensional proton exchange membrane fuel cell cathode model using a modified agglomerate approach based on discrete catalyst particles”, Electrochimica Acta, 174, 787 (2015). Figure 1

This paper presents the design and wind tunnel testing of a morphing camber system and an estimation of performances on an unmanned aerial vehicle. The morphing camber system is a combination of two subsystems: the morphing trailing edge and the morphing leading edge. Results of the present study show that the aerodynamics effects of the two subsystems are combined, without interfering with each other on the wing. The morphing camber system acts only on the lift coefficient at a 0° angle of attack when morphing the trailing edge, and only on the stall angle when morphing the leading edge. The behavior of the aerodynamics performances from the MTE and the MLE should allow individual control of the morphing camber trailing and leading edges. The estimation of the performances of the morphing camber on an unmanned aerial vehicle indicates that the morphing of the camber allows a drag reduction. This result is due to the smaller angle of attack needed for an unmanned aerial vehicle equipped with the morphing camber system than an unmanned aerial vehicle equipped with classical aileron. In the case study, the morphing camber system was found to allow a reduction of the drag when the lift coefficient was higher than 0.48.

Natural laminar-flow wings are one of the most promising technologies for reducing fuel burn and emissions for commercial aviation. However, there is a lack of tools for performing shape optimization of wings based on computational fluid dynamics considering laminar-to-turbulent transition. To address this need, we develop a discrete adjoint-based optimization framework where transition is modeled. The core of this framework is a Reynolds-averaged Navier–Stokes solver that is coupled with a simplified method to predict Tollmien–Schlichting and laminar separation-induced transition that consists of a laminar boundary-layer code and a database method for flow stability analysis. The transition prediction is integrated with a Spalart–Allmaras turbulence model through a smoothed intermittency function, which makes it suitable for gradient-based optimization. A coupled-adjoint approach that uses transpose Jacobian-vector products derived via automatic differentiation computes the transition prediction derivatives. Lift-constrained drag minimizations of airfoils for a single-point design and a multipoint design problem are performed. The results show that the optimizer successfully reduces the drag coefficient by increasing the extent of laminar flow. The multipoint optimization formulation produces an airfoil with a significant amount of laminar flow that is maintained at several flight conditions. The proposed methods make it possible to perform aerodynamic shape optimization considering laminar-to-turbulent transition in airfoil optimization.

The adjoint method is used in this paper for the aerodynamic optimization of the nose shape of a train. This method has been extensively applied in aircraft or ground vehicle aerodynamic optimization, but is still in progress in train aerodynamics. Here we consider this innovative optimization method and present its application to reduce the aerodynamic drag when the train is subjected to front wind. The objective of this paper is to demonstrate the effectiveness of the method, highlighting the requirements, limitations and capabilities of it. Furthermore, a significant reduction of the aerodynamic drag in a short number of solver calls is aimed as well. The independence of the computational cost with respect to the number of design variables that define the optimal candidate is stressed as the most interesting characteristic of the adjoint method. This behavior permits a more complete modification of the shape of the train nose because the number of design variables is not a constraint anymore. The information obtained from the sensitivity field permits determining the regions of the geometry where a small modification of the nose shape might introduce a larger improvement of the train performance. A good agreement between this information and the successive geometry modifications is observed here.

This paper presents an approach for the rapid implementation of an adjoint solver for the ReynoldsAveraged Navier–Stokes equations with a Spalart–Allmaras turbulence model. Automatic differentiation is used to construct the partial derivatives required in the adjoint formulation. The resulting adjoint implementation is computationally efficient and highly accurate. The assembly of each partial derivative in the adjoint formulation is discussed. In addition, a coloring acceleration technique is presented to improve the adjoint efficiency. The RANS adjoint is verified with complex-step method using a flow over a bump case. The RANS-based aerodynamic shape optimization of an ONERA M6 wing is also presented to demonstrate the aerodynamic shape optimization capability. The drag coefficient is reduced by 19% when subject to a lift coefficient constraint. The results are compared with Euler-based aerodynamic shape optimization and previous work. Finally, the effects of the frozenturbulence assumption on the accuracy and computational cost are assessed.

Aerodynamic shape optimisation technology is presented, comprising an efficient variable fidelity shape parameterisation method, an efficient andhigh quality mesh deformation scheme, and a parallel optimisation algorithm. The objective of the research presented here is the comparison of truly three-dimensional optimisations of aircraft wings in both aerodynamic and aeroelastic environments. The novel shape parameterisation technique allows various fidelities of design parameters, ranging from detailed surface changes to novel truly three-dimensional planform adjustments. An efficient interpolation scheme, using radial basis functions, transfers domain element movements into direct deformations of the design surface and corresponding CFD mesh, thus allowing total independence from the grid generation package and type (structured or unstructured). Optimisation is independent from the CFD flow solver by obtaining sensitivity information for an advanced parallel gradient-based optimiser by finite-differences. This ‘wrap-around’ optimisation technique is applied to a modern large transport aircraft wing in the cruise flight condition for minimum drag with stringent constraints in lift, volume, and two root moments. The objective of all optimisations is aerodynamic, however the static aeroelastic deflection provided by an aeroelastic solver will give that particular optimisation increased accuracy and real world relevance. The result of a constrained inviscid aerodynamic optimisation is presented and has a significant reduction in drag when compared to the initial wing with no violation of any constraints. The shape parameterisation method demonstrates that only a low number of design variables are necessary to achieve innovative planform and surface geometries with dramatically improved performance. Computational fluid dynamics (CFD) methods are now commonplace in aerospace industries, and at the forefront of analysis capabilities, providing a fast and effective method of predicting a design’s aerodynamic performance. However, with ever increasing complexity of designs, engineers can often struggle to interpret the intricacies of the CFD results sufficiently to be able to manually alter the geometry to improve performance. Hence, there has been an increase in demand for intelligent and automatic shape optimisation schemes. This requires combining geometry control methods with numerical optimisation algorithms, to provide a mechanism to mathematically seek improved and optimum designs, using CFD as the analysis tool. Optimisation requires consideration of three issues, each of which have numerous solutions: shape parameterisation including CFD surface and volume mesh deformation, computation of design variable derivatives, and effective use of these derivatives to improve design. Geometry parameterisation is critical for effective shape optimisation. This is the method of representing the design surface, and defines the degrees of freedom in which the geometry can be altered and, ideally, this should be linked with an effective method of deforming the CFD surface and volume mesh in a corresponding fashion. Parameterising complex shapes is a problem that remains a serious obstacle to both manual and automatic CFD-based optimisation. A wide variety of shape control and morphing methods have been developed, but many do not allow sufficiently

The efficiency of analytical asymptotic flow solution is demonstrated in application to the aerodynamic design optimization. The asymptotic solution method is formulated in natural streamline coordinate system, wherein the governing equations are transformed into non-homogeneous Cauchy-Riemann system. A sequence of coordinate transformation, mapping, and asymptotic expansion places the governing equations in a form suitable for classical mathematical techniques. The method has particularly strong potential in aerodynamic design optimization because the objective function can be evaluated at a very low cost. In this paper, the accuracy and the efficiency of this design approach, which uses the asymptotic flow solution for objective function evaluation, are evaluated with examples of inverse airfoil designs. The asymptotic flow solver has been coupled to Genetic Algorithm as well as gradient-based optimization algorithm to demonstrate the advantages in computational efficiency. The asymptotic flow solution coupled with Genetic Algorithm has produced robust design results at reasonable computational costs.

This study investigates the factors influencing the aerodynamic performance enhancement of the rear wing of the joined‐wing configuration UAVs by analyzing the flow field structure and flow mechanisms before and after airfoil optimization. Correspondingly, an optimization design concept tailored to joined‐wing aircraft is proposed. Focusing on the rear wing, a three‐dimensional design framework integrating geometric parameterization, aerodynamic simulation, and radar performance analysis was developed. The accuracy of the surrogate model was enhanced through multiround updating and optimization, and the optimal solution was derived using a genetic algorithm. The results demonstrate that the lift–drag ratio of the rear wing has been improved by approximately 9.7%. Specifically, the optimization outcomes confirm that adjusting the airfoil geometry and introducing a spanwise variation in the installation angle of control surfaces mitigates the adverse effects of front‐wing downwash on the rear wing, thereby improving the overall aerodynamic characteristics. By fully accounting for the interference of Frt‐wing downwash, this framework addresses the core challenges in rear‐wing aerodynamic optimization and provides an effective solution for enhancing the high‐altitude flight efficiency of UAVs.

Roughness Based Crossflow Transition Control for a Swept Wing Airfoil Design

The recent volatility of fuel prices and the potential of explicit CO2 emission control regulations have caused aerodynamic performance to become a critical component of heavy vehicle development. The use of traditional computational fluid dynamics (CFD) simulation for aerodynamic drag prediction on fully complex production geometries has not been adopted for a number of key reasons: the high level of expertise required, simulation time-to-completion, and accuracy versus experiment. This paper demonstrates that the proprietary, Lattice-Boltzmann based simulation method of EXA Corporation delivers valuable results on fully complex geometry, allowing aerodynamic optimization in the concept and design phase. Included is an overview of the simulation method and results for two fully detailed open grille Kenworth models: the T603 and T2000. Comparisons are made to full scale drag meter testing. Additional results are provided for several trailer drag reduction devices including a full gap seal, side skirts, boat tail, and wake boards. Advanced post-processing of the simulation results is used to study transient flow structures and highlight the physics involved with the drag reduction of these devices.

Active flow control of surface dielectric barrier discharge (SDBD) plasma is a technology that converts electrical energy into kinetic energy to achieve flow control. Its main application areas are concentrated in the aviation field. Undoubtedly, few studies have applied it in the field of automobile flow control. Meanwhile, during high-speed driving, there is a serious airflow separation phenomenon at the rear of notch-back cars, which brings a large area of negative pressure to the back of the cars. Due to the huge pressure difference between the front and end of the cars, it will increase the driving drag and fuel cost of the car. In this context, we seek to discuss the control effect on the airflow separation at the rear of the notch-back by using the phenomenological numerical simulation method of plasma flow control. Firstly, the plasma actuator is arranged separately on the rear end of the roof, c-pillar, upper and side of the trunk to study the control effect of airflow separation. After that, the plasma actuators at each position are combined and actuated simultaneously. We try to observe the control effect of airflow separation and select the combination with the best drag reduction effect. In the third stage, an efficient global optimization (EGO) algorithm based on kriging response surface is applied to optimize the supply voltage of the best combination that has been obtained before and obtain the driving voltage parameter of each actuator optimized under this combination. The results show that when plasma actuation is applied at four locations, only the actuation applied to the side of the luggage compartment has a significant drag reduction effect, while in other cases, the drag coefficient will increase. Specifically, drag reduction is better when the actuation is applied at four positions simultaneously. The maximum drag reduction coefficient of the car is reduced by 13.17%.

ABSTRACTIn this article, a Virtual Stackelberg Game (VSG) is proposed for aerodynamic shape optimization, where the design variables are divided into two categories to optimize the same objective function, one acts as a leader, and the other ones as followers react independently and selfishly relative to the leader's strategy. During each Stackelberg strategy cycle, the Gradient-Based Method (GBM) with the adjoint method in Stanford University Unstructured (SU2) is applied in the optimization of each player. Firstly, parametric studies of VSG by two simple cases are conducted to assess the impact of critical parameters on aerodynamic shape optimization, including the design cycle, the split of design variables and role (leader and follower) assignment. Based on the criterion from parametric studies, two typical numerical cases under transonic flow are applied—the drag reduction design of a 2D airfoil and a 3D wing. It is found that, compared to the original GBM method, VSG can provide better optimization results with less computational cost.