Aerodynamic Optimization for Hypersonic Wing Design Based on Local Piston Theory

The suitability of local piston theory for modeling static loads on a deforming low-aspect-ratio wing in the presence of aerodynamic interference is investigated. Predictions using Euler-based local piston theory are compared to Euler solutions for the deformed geometry. Moderate to large deformations are investigated for the leeside wing on a cruciform wing/body configuration. It is shown that local piston theory is suitable even for large deformations, with the perturbation downwash/Mach number supersonic, provided that the loading induced by deformation is not dominated by interaction with body vortices or other sources of aerodynamic interference. Second-order local piston theory is recommended for deformations producing downwash/Mach numbers approaching sonic. The influence of the choice of piston theory coefficients is in producing an estimation band for the local piston theory load prediction, with insignificant influence on the load slope in the present investigation. In conclusion, local piston theory is put forward as a viable alternative to mesh deformation toward reduction of the computational cost of aerodynamic load prediction for static aeroelasticity, provided that perturbation loads are dominated by local twist and not by vortex interaction.

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.

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.

☞Introduction and Motivation➣While aerodynamic prediction methods based on CFD are now well established,accurate, and robust, the ultimate need in the design process is to find theoptimum shape which maximizes the aerodynamic performance.➣During the last decade aerodynamic shape optimization methods based oncontrol theory have been perfected for rigid wings with fixed planforms.➣Example: Redesign of the wing of a Boeing 747 with fuselage.

Numerical study on the nonlinear characteristics of shock induced two-dimensional panel flutter in inviscid flow

Generic aerodynamic shape optimization technology is presented, based on a domain element approach linked with global interpolation functions. This allows an efficient shape parameterization from which both the design surface geometry and corresponding computational fluid dynamics volume mesh can be deformed directly, in a high quality and robust fashion. The technique also provides a method that allows geometries to be parameterized at various levels, ranging from general planform alterations to detailed local surface changes. The global interpolation developed is totally independent of mesh type (structured or unstructured), and optimization independence from the flow solver is achieved by obtaining sensitivity information for an advanced gradient-based optimizer (feasible sequential quadratic programming) by finite differences. Results have been presented recently for two-dimensional aerofoil cases, and drag reductions of up to 45 per cent were demonstrated. Hence, this article presents initial extension of the method to three dimensions. Results are presented for highly constrained optimization of a modern aircraft wing in transonic cruise, using only planform parameters (design variables), i.e. wing sections can move but may not deform locally. This is done to test and validate the method before moving on to higher fidelity optimizations, and more computationally expensive applications. Even with this fidelity of parameterization, only 30 parameters are used, optimization produces an 8 per cent reduction in drag.

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.

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.

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.

In aerodynamic shape optimization, traditional static geometry control methods can produce suboptimal performance by introducing performance tradeoffs at various stages of optimization, enforcing arbitrary constraints on open-ended optimization, and necessitating foreknowledge of problem behavior to design an effective control scheme. These shortcomings can be mitigated through dynamic geometry control, which partly automates the geometry control design process by refining the geometry control topology throughout optimization. Such refinement can occur in a predetermined fashion (as in progressive control) or more automatically using sensitivity information to guide refinement (as in adaptive control). Both progressive control and adaptive control are implemented in the context of axial and free-form deformation geometry control, and novel contributions are made to the adaptive algorithm, including the treatment of active constraints and several novel “potential indicators” to rank candidate refinements. Application to a wide suite of aerodynamic shape optimization problems demonstrates that dynamic geometry control is effective, producing lower final drag than well-designed static schemes while reducing required iterations to convergence by 50% or more, and simultaneously reducing labor requirements on the user. These benefits are demonstrated across a wide variety of problems, representative of detailed and exploratory problems often encountered in both academia and industry.

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.

Adjoint-based aerodynamic shape optimization including transition to turbulence effects

An investigation is presented that considers various aspects of an aerodynamic shape optimization framework. A two-dimensional aerofoil transonic zero-lift drag minimization test case is used to investigate the effect of dimensionality, shape deformation parameters, and optimizer on the results from the shape optimization process. A flexible control point-based parameterization is implemented which decouples the design variables from the surface, such that control point deformations determine the surface and volume mesh deformations in a unified manner. A gradient-based optimizer (feasible sequential quadratic programming) and global search algorithm (gravitational search algorithm) are tested on the constrained optimization case. The results show, as expected, that an increase in the number of dimensions produces a greater design space coverage and better optimization results, and the gradient-based method is prone to terminating in local optima or at constraint boundaries, so the global search algorithm is more reliable at locating optima. Efficient, reduced, and orthogonal shape deformation parameters are defined here by singular value decomposition extraction, and are shown to be particularly effective, demonstrating a 99.7% drag reduction for the case considered.