Adjoint-based aerodynamic shape optimization including transition to turbulence effects

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

This paper presents a gradient-based aerodynamic shape optimization framework that utilizes a Graphics Processing Unit (GPU) for solving both flow and adjoint equations. It is built based on a GPU-accelerated flow solver that has been developed previously. Hence, the focus of this work is on how to solve the adjoint equations on the GPU and subsequently compute the gradients. The adjoint equations are right-preconditioned by a block Incomplete Lower Upper (ILU) preconditioner and solved by a restarted Generalized Minimum Residual (GMRES) method. The exact residual Jacobian matrix in the adjoint equations is computed using finite difference and a distance-2 graph coloring algorithm. With the adjoint-based gradients, the steepest descent method with momentum is employed for constrained aerodynamic shape optimization of a wing-body configuration at a transonic flow condition.

The present-day scenario of urbanization is mostly vertical densification that results in the building of super-tall structures in metropolitan areas with land shortage. In the process of going higher up, these buildings become part of the wind load rather than gravity acting on them. The combined action of turbulence wind flow and bluff bodies of high-rise buildings promotes the introduction of complex aerodynamic phenomena that include vortex shedding, buffeting, and galloping, all of which have a direct bearing on structural safety and occupant comfort. While traditional design techniques still focus on prismatic geometries, the recent architectural trends have moved to complex and irregular plan configurations, such as that of the Fish, Y, and Plus shapes, and also the globally twisted and tapered towers, which are mainly driven by aesthetic aspirations and functional optimization. Nevertheless, the current international design codes such as ASCE 7-16 and IS 875 (Part 3) do not provide many guidelines on these non-standard geometries and, consequently, performance-based wind engineering testing is commonly needed (ASCE, 2017; Bureau of Indian Standards, 2015). This is a review of the aerodynamic performance of complex plan-geometry high-rise buildings critically synthesized based on the peer-reviewed literature. It is conducted in a methodical assessment against the effectiveness of the Aerodynamic Shape Optimization (ASO) strategies by local geometric alterations including corner rounding, chamfering and recession against global morphological alterations including twisting and tapering. Additionally, the review examine the current analytical and numerical methods, find the drawbacks of Reynolds-Averaged Navier-Stokes (RANS) models regarding their inability to capture unsteady wake dynamics in comparison to Large Eddy Simulation (LES) and Delayed Detached Eddy Simulation (DDES) methods. The combined results illustrate the extent to which corner rounding and helical twisting lower the drag forces and the susceptibility to vibration caused by vortexes through disrupting the span-wise coherence of the vortices, while highly irregular configurations, like Fish-shaped plans, are very sensitive to the direction of the wind. Moreover, the review concludes with the identification of critical research gaps concerning the wind interference effects in dense urban clusters, and it positions the possible adoption of machine-learning-based surrogate models in the preliminary design phases as an attractive option to solve the problem of wind design codes currently having limitations.

Aerodynamic shape optimization of aircraft configurations often ignores stability considerations. To address this, a method for the computation of static, dynamic, and transient aircraft stability derivatives and their sensitivities for use in gradient-based optimization is introduced and evaluated. Computational fluid dynamics in the form of a three-dimensional structured-grid multiblock flow solver with both Euler and Reynolds-averaged Navier–Stokes equations is used. To compute the stability derivatives, a time-spectral formulation is used to compute an oscillating solution for the configuration of interest. From this oscillating solution, a series of linear regressions is performed to calculate the various stability derivatives. Because the solution is time dependent, it contains the information required to compute the transient, or “dot,” derivatives for the configuration. An adjoint method is used to compute the gradients of the stability derivatives of interest, enabling gradient-based stability-constrained aerodynamic shape optimization with respect to a large number of design variables. The computed stability derivatives are verified for an airfoil and validated for a generic unmanned combat aerial vehicle. The stability-constrained optimization of a wing demonstrates the viability and usefulness of the method for aircraft design optimization.

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.

Sustainability has become one of the most significant considerations in everyday work, including energy production. The fast-growing trend of wind energy around the world has increased the demand for efficient and optimized airfoils, which has paved the way for energy harvesting systems. The present manuscript proposes an aerodynamically optimized design of the well-known existing NREL S809 airfoil for performance enhancement of the blade design for wind turbines. An integrated code, based on a genetic algorithm, is developed to optimize the asymmetric NREL S809 airfoil by class shape transformation (CST) and the parametric section (PARSEC) parameterization method, analyzing its aerodynamic properties and maximizing the lift of the airfoil. The in-house MATLAB code is further incorporated with XFOIL to calculate the coefficient of lift, coefficient of drag and lift-to-drag ratio at angles of attack of 0° and 6.2° by the panel technique and validated with National Renewable Energy Laboratory (NREL) experimental results provided by The Ohio State University (OSU). On the other hand, steady-state CFD analysis is performed on an optimized S809 airfoil using the Reynolds-averaged Navier–Stokes (RANS) equation with the K–ω shear stress transport (SST) turbulent model and compared with the experimental data. The present method shows that the optimized airfoil by CST is predicted, with an increment of 11.8% and 9.6% for the lift coefficient and lift-to-drag ratio, respectively, and desirable stability parameters obtained for the design of the wind turbine blades. These characteristics significantly improve the overall aerodynamic performance of new optimized airfoils. Finally, the aerodynamically improved results are reported for the design of the NREL Phase II, Phase III and Phase VI HAWT blades.

Surrogate models are used to dramatically improve the design efficiency of numerical aerodynamic shape optimization, where high-fidelity, expensive computational fluid dynamics (CFD) is often employed. Traditionally, in adaptation, only one single sample point is chosen to update the surrogate model during each updating cycle, after the initial surrogate model is built. To enable the selection of multiple new samples at each updating cycle, a few parallel infilling strategies have been developed in recent years, in order to reduce the optimization wall clock time. In this article, an alternative parallel infilling strategy for surrogate-based constrained optimization is presented and demonstrated by the aerodynamic shape optimization of transonic wings. Different from existing methods in which multiple sample points are chosen by a single infill criterion, this article uses a combination of multiple infill criteria, with each criterion choosing a different sample point. Constrained drag minimizations of the ONERA-M6 and DLR-F4 wings are exercised to demonstrate the proposed method, including low-dimensional (6 design variables) and higher-dimensional problems (up to 48 design variables). The results show that, for surrogate-based optimization of transonic wings, the proposed method is more effective than the existing parallel infilling strategies, when the number of initial sample points are in the range from Nv to 8Nv (Nv here denotes the number of design variables). Each case is repeated 50 times to eliminate the effect of randomness in our results.

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.

This work demonstrates the performance of Jetstream, a high-fidelity aerodynamic shape optimization methodology for three-dimensional turbulent flows. The geometry parameterization and mesh movement is accomplished using B-spline volumes and linear elasticity mesh movement. The Euler or Reynolds-averaged Navier-Stokes (RANS) equations are solved at each iteration using a parallel Newton-Krylov-Schur method. The equations are discretized in space using summation-by-parts operators with simultaneous approximation terms to enforce boundary and block interface conditions. The gradients are evaluated using the discrete-adjoint method to allow for gradient-based optimization using a sequential quadratic programming algorithm. The goal of this work is to investigate the performance of Jetstream for three test problems. The first problem is the drag minimization of a two-dimensional symmetric airfoil in transonic inviscid flow, under a geometric constraint that the airfoil have a thickness greater than or equal to that of a NACA 0012 airfoil. Although the shock waves are not quite eliminated, they are substantially weakened, such that the drag coefficient is reduced by 86% compared to the NACA 0012 airfoil. The second problem is drag minimization through optimizing the twist distribution of a three-dimensional wing characterized by NACA 0012 sections in subsonic inviscid flow, subject to a lift constraint. A nearly elliptical spanwise lift distribution is achieved by the optimized twist distribution, leading to a span efficiency factor of 0.98. The third problem is drag minimization through optimizing the sections and twist distribution of the blunt-trailing-edge Common Research Model wing in transonic turbulent flow, subject to lift and pitching moment constraints. For this case the optimization is performed based on the solution of the RANS equations, with the Spalart-Allmaras turbulence model fully coupled and linearized. The drag coefficient is reduced by eleven counts, or 6%, when analyzed on a fairly fine mesh.

This paper presents an aerodynamic shape optimization method based on a genetic algorithm with the compressible Euler or Navier-Stokes equations. A new algorithm to represent aerodynamic configurations is proposed to find optimum aerodynamic configurations efficiently. We solve three aerodynamic shape optimization problems. First, an inverse problem is solved to understand a basic character and to examine the possibility of the genetic algorithm. Second, a drag minimization problem is solved to find a streamlined body. Finally, L/D(ratio of lift to drag) maximization problem in a transonic flow is solved and the optimized configuration is compared with a supercritical airfoil. The results show that genetic algorithm is powerful and robust in solving aerodynamic shape optimization problems.

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

Aerodynamic shape design using stochastic optimization methods, such as simulated annealing method to optimize objective functions evaluated by modern state-of-the-art computational fluid dynamics solvers, normally requires enormous computation time to search for the global optimal design. Aerodynamic shape optimization of internal flow systems is studied using Euler/Navier-Stokes solvers and parallel simulated annealing algorithm, which is implemented on parallel computing platforms. A variety of inverse and direct design of internal flow systems are carried out to examine the efficiency and speedup of the parallel simulated annealing algorithms

In this paper, global optimization design of a transonic compressor 3D blade (Rotor 37) has been carried out by a self-developed aerodynamic shape optimization (ASO) platform based on improved parallel synchronous particle swarm optimization (PSPSO). To improve the performance of PSPSO, coefficient of variation (COV) based attenuation method with new parameters is proposed and then validated by optimization tests. Flow field of blade is calculated by an in-house computational fluid dynamic (CFD) code called PMB3D-Turbo, which is validated by Rotor 37. Choosing Rotor 37 as the case, optimization object is to maximize the peak adiabatic efficiency, meanwhile constraining mass flow and total pressure ratio. The solutions show that, the ASO platform is effective to transonic compressor blade and variations of thickness distribution near the trailing edge can help improve the adiabatic efficiency of a transonic compressor blade.

This paper presents an assessment of the potential fuel burn savings offered by the transonic strut-braced-wing configuration within the single-aisle class of aircraft relative to a modern conventional tube-and-wing aircraft through aerodynamic shape optimization based on the Reynolds-averaged Navier–Stokes equations. A representative strut-braced-wing aircraft is first developed through conceptual multidisciplinary design optimization based on the Airbus A320neo, with current technology levels assumed. A concept for the conventional tube-and-wing configuration is also developed to represent the Airbus A320neo as a performance baseline. Single-point aerodynamic shape optimization is then performed on wing–body–tail models of each aircraft to address aerodynamic design challenges and to provide more accurate performance estimates. Results indicate that shock formation can be mitigated from the wing–strut junction of the strut-braced wing at Mach 0.78 and a relatively high design lift coefficient of 0.750, providing an 8.2% reduction in block fuel over a 1000 n mile nominal mission when compared to the conventional tube-and-wing aircraft. Multipoint aerodynamic shape optimization is then performed to build toward a more credible estimate of fuel burn performance, with results showing a reduction in the fuel burn savings to 7.8% at the nominal design point relative to the conventional tube-and-wing aircraft to maintain a 7.6–8.0% improvement over the envelope of operating conditions, which includes design points at even higher Mach numbers and lift coefficients. These results demonstrate the viability of the transonic strut-braced-wing configuration for transport aircraft within the single-aisle class and its potential for reducing commercial fleet fuel burn.