Transonic Aerofoil Research Articles

OpenSBLI v3.0: High-fidelity multi-block transonic aerofoil CFD simulations using domain specific languages on GPUs

OpenSBLI is an automatic code-generation framework for compressible Computational Fluid Dynamics (CFD) simulations on heterogeneous computing architectures (previous release: Lusher et al. (2021) [4]). OpenSBLI is coupled to the Oxford Parallel Structured (OPS) Domain Specific Language (DSL), which uses source-to-source translation to enable parallel execution of the code on large-scale supercomputers, including multi-GPU clusters. To date, OpenSBLI has largely been applied to compressible turbulence and shock-wave/boundary-layer interactions on very simple geometries comprised of single mesh blocks with essentially orthogonal grid lines. OpenSBLI has been extended in this new release to target strongly curvilinear cases, including transonic aerofoils using multi-block grids. In addition to multi-block mesh support, more efficient numerical shock-capturing methods and filters have been added to the codebase. Improvements to post-processing, reduced-dimension data output, and coupling to a modal decomposition library are also included. A set of validation cases are presented to showcase the new code features. Furthermore, state-of-the-art wide-span transonic aerofoil simulations on up to N=2.5×109 grid points demonstrate that wider aspect ratios can alter buffet predictions and increase the regularity of the low-frequency shock oscillations by accommodating fully-developed trailing edge flow separation. Spectral Proper Orthogonal Decomposition (SPOD) analysis showed that overly-narrow aerofoil simulations contain additional domain-dependent energy content at a Strouhal number of St≈3 associated with wake modes.

Assessment of implicit adaptive mesh‐free CFD modelling

SummaryThis work presents details and assesses implicit and adaptive mesh‐free CFD modelling approaches, to alleviate laborious mesh generation in modern CFD processes. A weighted‐least‐squares‐based, mesh‐free, discretisation scheme was first derived for the compressible RANS equations, and the implicit dual‐time stepping was adopted for improved stability and convergence. A novel weight balancing concept was introduced to improve the mesh‐free modelling on highly irregular point clouds. Automatic point cloud generations based on strand and level‐set points were also discussed. A novel, polar selection approach, was also introduced to establish high‐quality point collocations. The spatial accuracy and convergence properties were validated using 2D and 3D benchmark cases. The impact of irregular point clouds and various point collocation search methods were evaluated in detail. The proposed weight balancing and the polar selection approaches were found capable of improving the mesh‐free modelling on highly irregular point clouds. The mesh‐free flexibility was then exploited for adaptive modelling. Various adaptation strategies were assessed using simulations of an isentropic vortex, combining different point refinement mechanisms and collocation search methods. The mesh‐free modelling was then successfully applied to transonic aerofoil simulations with automated point generation. A weighted pressure gradient metric prioritising high gradient regions with large point sizes was introduced to drive the adaptation. The mesh‐free adaptation was found to effectively improve the shock resolution. The results highlight the potential of mesh‐free methods in alleviating the meshing bottleneck in modern CFD.

Morphing of an adaptive shock control bump using pressurized chambers

The dawn of research on shock and boundary layer interaction control dates back to the 1970s, when humped transonic aerofoils were first studied as a means to improve the performance of supercritical aerofoil technology at off-design conditions. Since then, shock control bumps have been found to be promising devices for such kind of flow control. They have a smearing effect on the shock wave structure achieved through isentropic pre-compression of the flow upstream of the main shock and can significantly lower wave drag without incurring unacceptable viscous losses. However, their performance is strongly dependent on a set of geometrical parameters which must be adjusted according to the ever-changing flight conditions. A concept for an adaptive shock control bump is therefore presented. The proposed actuation mechanism aims at a compact, lightweight and simple structure which could be integrated into the spoiler region of near-future aircraft without major design changes required. Numerical optimization of a simplified analytical model of the structure is used to investigate the shock control bump adaptation to various aerodynamic target shapes. Compromises between geometrical conformity and both structural and actuation related requirements are studied. Furthermore, an outlook is given on design issues related to three-dimensional effects on a finite span shock control bump.

Comparison of Point Design and Range-Based Objectives for Transonic Aerofoil Optimization

The most common aerofoil optimization problem considered is lift-constrained drag minimization at a fixed design point; however, shock-free solutions can result, which can lead to poor off-design performance. As such, this paper presents a study of the construction of the aerofoil optimization problem and its effect on the performance over a range of operating conditions. Single-point and multipoint optimizations of aerofoils in transonic flow are considered, and an improved range-based optimization problem subject to a constraint on fixed nondimensional wing loading with a varying design point is formulated. This problem is more representative of the aircraft design problem, though similar in cost to single-point drag minimization. An analytical treatment using an approximation of wave drag, which demonstrates that the optimum Mach number for a fixed shape is supercritical if the required loading is above a critical threshold, is also presented. This paper presents optimizations that show that to define an effective objective function three-dimensional effects modelled via an induced drag term must be introduced. The general trend is to produce solutions with higher Mach numbers and lower lift coefficients, and shocked solutions perform better when considering the performance in a range over the operating space. Furthermore, the resulting aerofoil shapes are supercritical in nature, a particularly promising result.

Optimisation of adaptive shock control bumps with structural constraints

This paper presents the results from a study to design an adaptive shock control bump for a transonic aerofoil. An optimisation framework comprising aerodynamic and structural computational tools has been used to assess the performance of candidate adaptive bump geometries based on a novel surface-pressure-based performance metric. The geometry of the resultant design is a unique feature of its adaptivity; being strongly influenced by the (passive) aerodynamic pressure forces on the flexible surface as well as the (active) displacement constraints. This optimal geometry bifurcates the shock-wave and carefully manages the recovering post-shock flow to maximise pressure-smearing in the shock-region with only a small penalty in L/D for the aerofoil. Short adaptive bumps (with small imposed displacements) generally perform better than taller ones, and maintain their performance advantage for a wide range of bump positions, suggesting good robustness to variations in shock position, which are an inevitable feature of a real-world flight application. Such devices may offer advantages over conventional (fixed geometry) shock control bumps, where optimal performance is achieved with taller devices, at the expense of poor robustness to variations in shock position.

Geometric Comparison of Aerofoil Shape Parameterization Methods

A comprehensive review of aerofoil shape parameterization methods that can be used for aerodynamic shape optimization is presented. Seven parameterization methods are considered for a range of design variables: class–shape transformations; B-splines; Hicks–Henne bump functions; a radial basis function domain element approach; Bèzier surfaces; a singular-value decomposition modal extraction method; and the parameterized sections method. Because of the large range of variables involved, the most effective way to implement each method is first investigated. Their performances are then analyzed by considering the geometric shape recovery of over 2000 aerofoils using a range of design variables, testing the efficiency of design space coverage with respect to a given tolerance. It is shown that, for all the methods, between 20 and 25 design variables are needed to cover the full design space to within a geometric tolerance, with the singular-value decomposition method doing this most efficiently. A set of transonic aerofoil case studies are also presented, with geometric error and convergence of the resulting aerodynamic properties explored. These results show a strong relationship between geometric error and aerodynamic convergence and demonstrate that between 38 and 66 design variables may be needed to ensure aerodynamic convergence to within one drag and one lift count.

Influence of the number and location of design parameters in the aerodynamic shape optimization of a transonic aerofoil and a wing through evolutionary algorithms and support vector machines

ABSTRACTSurrogate-based optimization (SBO) has recently found widespread use in aerodynamic shape design owing to its promising potential to speed up the whole process by the use of a low-cost objective function evaluation, to reduce the required number of expensive computational fluid dynamics simulations. However, the application of these SBO methods for industrial configurations still faces several challenges. The most crucial challenge nowadays is the ‘curse of dimensionality’, the ability of surrogates to handle a high number of design parameters. This article presents an application study on how the number and location of design variables may affect the surrogate-based design process and aims to draw conclusions on their ability to provide optimal shapes in an efficient manner. To do so, an optimization framework based on the combined use of a surrogate modelling technique (support vector machines for regression), an evolutionary algorithm and a volumetric non-uniform rational B-splines parameterization are applied to the shape optimization of a two-dimensional aerofoil (RAE 2822) and a three-dimensional wing (DPW) in transonic flow conditions.

Application of the adjoint multi-point and the robust optimization of shock control bump for transonic aerofoils and wings

A shock control bump (SCB) is a flow control method which uses a local small deformation in a flexible wing surface to considerably reduce the strength of shock waves and the resulting wave drag in transonic flows. Most of the reported research is devoted to optimization in a single flow condition. Here, both equally and variably weighted multi-point optimization and a robust adjoint optimization scheme are used to optimize the SCB. The numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm are used to find the optimum location and shape of the SCB for two benchmark aerofoils. A multi-point optimization method under a constant-lift-coefficient constraint is implemented to find the optimum design of a two-dimensional (2D) SCB and it is observed that the general results are similar to other optimization algorithms. To show that these results are extendable to real three-dimensional (3D) cases, a 3D bump model with 11 parameters is introduced, and it is optimized using both single- and multi-point optimization procedures. Although the 3D flow structure involves much more complexity, the overall results are shown to be similar to the 2D case.

A REDUCED ORDER MODEL BASED ON BLOCK ARNOLDI METHOD FOR AEROELASTIC SYSTEM

A reduced-order model (ROM) based on block Arnoldi algorithm to quickly predict flutter boundary of aeroelastic system is investigated. First, a mass–damper–spring dynamic system is tested, which shows that the low dimension system produced by the block Arnoldi method can keep a good dynamic property with the original system in low and high frequencies. Then a two-degree of freedom transonic nonlinear aerofoil aeroelastic system is used to validate the suitability of the block Arnoldi method in flutter prediction analysis. In the aerofoil case, the ROM based on a linearized model is obtained through a high-fidelity nonlinear computational fluid dynamics (CFD) calculation. The order of the reduced model is only 8 while it still has nearly the same accuracy as the full 9600-order model. Compared with the proper orthogonal decomposition (POD) method, the results show that, without snapshots the block Arnoldi/ROM has a unique superiority by maintaining the system stability aspect. The flutter boundary of the aeroelastic system predicted by the block Arnoldi/ROM agrees well with the CFD and reference results. The Arnoldi/ROM provides an efficient and convenient tool to quick analyze the system stability of nonlinear transonic aeroelastic systems.

Transonic aerofoils admitting anomalous behaviour of lift coefficient

AbstractTransonic flow past a Boeing 737 Outboard aerofoil and Whitcomb one with a defected aileron is studied. The flow simulation is based on the system of Reynolds-averaged Navier-Stokes equations. The numerical study demonstrates the existence of free-stream conditions in which small perturbations produce abrupt changes of the lift coefficient. Also the simulation reveals adverse conditions in which aileron deflections have no influence on the lift.

Optimizing Rotor Blades with Approximate British Experimental Rotor Programme Tips

This work presents a framework for the optimization of certain aspects of a British Experimental Rotor Programme-like rotor blade in hover and forward flight so that maximum performance can be obtained from the blade. The proposed method employs a high-fidelity, efficient computational fluid dynamics technique that uses the harmonic balance method in conjunction with artificial neural networks as metamodels, and genetic algorithms for optimization. The approach has been previously demonstrated for the optimization of blade twist in hover and the optimization of rotor sections in forward flight, transonic aerofoils design, wing and rotor tip planforms. In this paper, a parameterization technique was devised for the British Experimental Rotor Programme-like rotor tip and its parameters were optimized for a forward flight case. A specific objective function was created using the initial computational fluid dynamics data and the metamodel was used for evaluating the objective function during the optimization using the genetic algorithms. The objective function was adapted to improve forward flight performance in terms of pitching moment and torque. The obtained results suggest optima in agreement with engineering intuition but provide precise information about the shape of the final lifting surface and its performance. The main computational cost was associated with the population of the genetic algorithms database necessary for the metamodel, especially because a full factorial method was used. The computational time of the optimization process itself, after the database has been obtained, is relatively insignificant. Therefore, the computational time was reduced with the use of the harmonic balance method as opposed to the time marching method. The novelty in this paper is two-fold. Optimization methods so far have used simple aerodynamic models employing direct “calls” to the aerodynamic models within the optimization loops. Here, the optimization has been decoupled from the computational fluid dynamics data allowing the use of higher-fidelity computational fluid dynamics methods based on Navier–Stokes computational fluid dynamics. This allows a more realistic approach for more complex geometries such as the British Experimental Rotor Programme tip. In addition, the harmonic balance method has been used in the optimization process.

Robust active shock control bump design optimisation using hybrid parallel MOGA

The paper investigates a robust optimisation for detail design of active shock control bump on a transonic Natural Laminar Flow (NLF) aerofoil using a Multi-Objective Evolutionary Algorithm (MOEA) coupled to Computational Fluid Dynamics (CFDs) software. For MOEA, Robust Multi-Objective Optimisation Platform (RMOP) developed at CIMNE is used. For the active shock control bump design, two different optimisation methods are considered; the first method is a Pareto-Game based Genetic Algorithm in RMOP (denoted as RMOGA). The second method uses a Hybridised RMOGA with Game-Strategies and a parallel computation for high performance computation. Numerical results show not only how the concept of Shock Control Bump (SCB) coupled to CFD can improve aerodynamic performance of classic transonic aerofoil at the variability of flight conditions but also how high performance (parallel/distributed) computation with applying Hybrid-Game increases the efficiency of optimisation in terms of computational cost and results accuracy.

Double-shock control bump design optimization using hybridized evolutionary algorithms

This study investigates the application of two advanced optimization methods for solving active flow control (AFC) device shape design problem and compares their optimization efficiency in terms of computational cost and design quality. The first optimization method uses hierarchical asynchronous parallel multi-objective evolutionary algorithm and the second uses hybridized evolutionary algorithm with Nash-Game strategies (Hybrid-Game). Both optimization methods are based on a canonical evolution strategy and incorporate the concepts of parallel computing and asynchronous evaluation. One type of AFC device named shock control bump (SCB) is considered and applied to a natural laminar flow (NLF) aerofoil. The concept of SCB is used to decelerate supersonic flow on suction/pressure side of transonic aerofoil that leads to a delay of shock occurrence. Such active flow technique reduces total drag at transonic speeds which is of special interest to commercial aircraft. Numerical results show that the Hybrid-Game helps an EA to accelerate optimization process. From the practical point of view, applying a SCB on the suction and pressure sides significantly reduces transonic total drag and improves lift-to-drag ( L/ D) value when compared to the baseline design.

Origin of transonic buffet on aerofoils

Buffeting flow on transonic aerofoils serves as a model problem for the more complex three-dimensional flows responsible for aeroplane buffet. The origins of transonic aerofoil buffet are linked to a global instability, which leads to shock oscillations and dramatic lift fluctuations. The problem is analysed using the Reynolds-averaged Navier–Stokes equations, which for the foreseeable future are a necessary approximation to cover the high Reynolds numbers at which transonic buffet occurs. These equations have been shown to reproduce the key physics of transonic aerofoil flows. Results from global-stability analysis are shown to be in good agreement with experiments and numerical simulations. The stability boundary, as a function of the Mach number and angle of attack, consists of an upper and a lower branch – the lower branch shows features consistent with a supercritical bifurcation. The unstable modes provide insight into the basic character of buffeting flow at near-critical conditions and are consistent with fully nonlinear simulations. The results provide further evidence linking the transonic buffet onset to a global instability.

Genetic algorithm-based design of transonic aerofoils using Euler equations

The paper describes the adaptation of genetic algorithms (GA) to the design of inviscid transonic aerofoils. GA is effective in optimization strategies for designing transonic aerofoils where the non-linear aerodynamic phenomenon of shock wave results in flow discontinuity. The Euler equations are discretized through the flux-vector splitting method with Poisson's equation-based grid generation. Advanced strategies in the GA such as directed crossover and multi-stage searches are employed in the context of function-based global optimization. The objective is to determine the best combination of weighted parameters of a analytic function for the aerofoil surface, by maximizing the L/ D ratio. The paper first covers the optimization of transonic aerofoils to enhance the baseline design of NACA0012. A two-point design problem is also conducted to accommodate both transonic and subsonic regimes represented by the Mach number and angle of attack. The optimized aerofoils have shown improved aerodynamic performance for both flight regimes.

Shock-Wave/Boundary-Layer Interaction Control Using Three-Dimensional Bumps for Transonic Wings

Three-dimensional bumps have been developed and investigated on transonic wings, aiming to fulfill two major objectives of shock-wave/boundary-layer interaction control, that is, drag reduction and buffet delay. An experimental investigation has been conducted for a rounded bump in channel flow at the University of Cambridge and a computational study has been performed for a spanwise series of rounded bumps mounted on a transonic aerofoil at the University of Stuttgart. In both cases wave drag reduction and mild control effects on the boundary layer have been observed. Control effectiveness has been assessed for various bump configurations. A double configuration of narrow rounded bumps has been found to perform best, considerably reducing wave drag by means of a well-established X-shock structure with little viscous penalty and thus achieving a maximum overall drag reduction of about 30%, especially when significant wave drag is present. Counter-rotating streamwise vortex pairs have been produced by some configurations as a result of local flow separation. On the whole a large potential of three-dimensional control with discrete rounded bumps has been demonstrated both experimentally and numerically.

A method for solving compressible flow equations in an unsteady free stream

The paper presents a method to increase the computational accuracy by preserving additional constraints on the numerical solution. The new technique can noticeably increase the precision of a standard finite-volume flow solver by a modification to the flux computation procedure without changing its essential features. The efficiency of this method is demonstrated by application to the prediction of sound from high-speed helicopter blades. Several open domain boundary conditions for this application are also developed and compared for a model problem of a two-dimensional transonic aerofoil in an unsteady free stream.

Evaluation of wave drag reduction by flow control

An analytical expression is proposed to estimate the wave drag of an aerofoil equipped with shock control. The analysis extends the conventional approach for a single normal shock wave in the absence of control, based on the knowledge that all types of successful shock control on transonic aerofoils cause bifurcated λ-shock structures. The influence of surface curvature on the λ-shock structure has been taken into account. The extended method has been found to produce fairly good agreement with the results obtained by CFD methods while requiring negligible computational effort. This new formulation is expected to be beneficial in the industrial design process of transonic aerofoils and wings where a large number of computational simulations have to be performed.

Numerical study of active shock control for transonic aerodynamics

In this paper, the effectiveness of a number of active devices for the control of shock waves on transonic aerofoils is investigated using numerical solutions of the Reynolds‐averaged Navier‐Stokes equations. A brief description of the flow model and the numerical method is presented including, in particular, the boundary condition modelling and the numerical treatment for surface mass transfer. Comparisons with experimental data have been made where possible to validate the numerical study before some systematic numerical simulations for a parametric study. The effects of surface suction, blowing, and local modification of the surface contour (bump) on aerofoil aerodynamic performance have been studied extensively regarding the control location, the mass flow strength and the bump height. The numerical simulations highlight the benefits and drawbacks of the various control devices for transonic aerodynamic performance and identify the key design parameters for optimisation.

A variational model for a symmetric transonic aerofoil

By the semi‐inverse method proposed by He, a variational principle is established for steady flow over a thin, symmetric, non‐lifting aerofoil. The nonlinear, small‐disturbance, velocity‐potential equation is obtained by minimizing the obtained functional, and all boundary conditions are converted into natural boundary conditions, resulting in much convenience when incorporating the finite element method.