Transonic Airfoil Research Articles

The application of the gradient-based adjoint multi-point optimization of single and double shock control bumps for transonic airfoils

A shock control bump (SCB) is a flow control method that uses local small deformations 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, we have used a multi-point adjoint optimization scheme to optimize shape and location of the SCB. Practically, this introduces transonic airfoils equipped with the SCB that are simultaneously optimized for different off-design transonic flight conditions. Here, we use this optimization algorithm to enhance and optimize the performance of SCBs in two benchmark airfoils, i.e., RAE-2822 and NACA-64-A010, over a wide range of off-design Mach numbers. All results are compared with the usual single-point optimization. We use numerical simulation of the turbulent viscous flow and a gradient-based adjoint algorithm to find the optimum location and shape of the SCB. We show that the application of SCBs may increase the aerodynamic performance of an RAE-2822 airfoil by 21.9 and by 22.8 % for a NACA-64-A010 airfoil compared to the no-bump design in a particular flight condition. We have also investigated the simultaneous usage of two bumps for the upper and the lower surfaces of the airfoil. This has resulted in a 26.1 % improvement for the RAE-2822 compared to the clean airfoil in one flight condition.

Design of adaptive transonic laminar airfoils using the [formula omitted] transition model

This paper examines the design of adaptive laminar airfoils in the transonic flow regime using the γ-Re˜θt model as a transition prediction method. A robust solution procedure for the transition model is described and a grid convergence study is presented. Predictions from the model are then compared to an extensive set of experimental results containing transition measurements on a morphing airfoil. It is shown that the sensitivity of the γ-Re˜θt transition model with respect to shape variations allows its use in a design framework. Using a multi-point optimization strategy, the model is then used to design transonic airfoils suitable for a range of flow conditions. The potential improvement in drag associated with the implementation of adaptive airfoil technology is then carefully quantified using single-point optimization with the multi-point designed airfoil as a reference. Structural design constraints are taken into account to obtain a realistic estimate of possible drag reduction through airfoil morphing using current wing construction technology. Airfoil drag improvements of up to 4.6% are obtained through morphing of the section of upper surface located between the wing spars with respect to the baseline multi-point design in flow conditions typical of large business jet operation.

Estimation of Wave Drag of Non-TransonicAirfoils Using Korn Equation

Approximation of Drag Divergence Mach number, Critical Mach Number and the Coefficient of Wave Drag of non-transonic airfoils using Korn equation are presented in this research paper. Due to the presence of the CFD factor which influences the aforementioned parameters heavily, transonic airfoils develop an undue advantage over non-transonic airfoils. A preliminary analysis of the behaviour of the airfoils is done using XFLR5 wherein the aerodynamic characteristics such as coefficient of lift, coefficient of drag, pitching moment, stall angle and aerodynamic efficiency of the airfoils are evaluated at low Reynolds Number. In order to observe the effect of camber and thickness on the performance of airfoils, airfoils of varying camber and thickness are chosen. The airfoils chosen for this research paper are NACA 0012, NACA 0018, MH 23, NLF 0115, FX 83 W108, FX 66 S196, UltraSport 1000 and Clark Y (smooth). The main objective of this paper is to computationally obtain an airfoil which can perform well under both transonic and low Reynolds number conditions.

Aerodynamic shape design using hybrid evolutionary computing and multigrid-aided finite-difference evaluation of flow sensitivities

Purpose – The purpose of this paper is to propose an accurate and efficient technique for computing flow sensitivities by finite differences of perturbed flow fields. It relies on computing the perturbed flows on coarser grid levels only: to achieve the same fine-grid accuracy, the approximate value of the relative local truncation error between coarser and finest grids unperturbed flow fields, provided by a standard multigrid method, is added to the coarse grid equations. The gradient computation is introduced in a hybrid genetic algorithm (HGA) that takes advantage of the presented method to accelerate the gradient-based search. An application to a classical transonic airfoil design is reported. Design/methodology/approach – Genetic optimization algorithm hybridized with classical gradient-based search techniques; usage of fast and accurate gradient computation technique. Findings – The new variant of the prolongation operator with weighting terms based on the volume of grid cells improves the accuracy of the MAFD method for turbulent viscous flows. The hybrid GA is capable to efficiently handle and compensate for the error that, although very limited, is present in the multigrid-aided finite-difference (MAFD) gradient evaluation method. Research limitations/implications – The proposed new variants of HGA, while outperforming the simple genetic algorithm, still require tuning and validation to further improve performance. Practical implications – Significant speedup of CFD-based optimization loops. Originality/value – Introduction of new multigrid prolongation operator that improves the accuracy of MAFD method for turbulent viscous flows. First application of MAFD evaluation of flow sensitivities within a hybrid optimization framework.

A trended Kriging model with [formula omitted] indicator and application to design optimization

A trended Kriging model is known to improve the overall accuracy and efficiency of surrogate modeling; however, most studies have focused on a non-trended Kriging model because of the difficulty in the identification of a trend from an unknown data set. In the present study, an R2 indicator for a Kriging surrogate model has been developed to identify the trend from a training data set. Both linear and non-linear trends are identified with the R2 indicator using the function analytic values and the function derivatives of the Kriging predictor. The trends identified by the indicator are used to determine the order of the drift function in the trended Kriging model. A trend identification of the Kriging model was validated with various analytic test functions. Subsequently, more practical uses of the R2 indicator applied to actual responses from the Computational Fluid Dynamics (CFD) analysis of transonic airfoil. In conclusion, the trended Kriging model can improve overall accuracy of responses if the maximum order of drift function is properly adjusted to the trend of sample space identified by the R2 indicator.

Validation results for the LOGOS multifunction software package in solving problems of aerodynamics and gas dynamics for the lift-off and injection of launch vehicles

The paper discusses the applications of the LOGOS software package in the mathematical simulation of supersonic turbulent jets and transonic airfoil based on the Navier-Stokes equations with appropriate turbulence models. The calculation results are given for anisobaric flow streams. The theoretical and experimental results were compared for typical operation regimes of launch vehicle engines during lift-off. We give the results of the calculations for a transonic airfoil of a hammerhead payload fairing of a launch vehicle and compare them with the experimental data.

Aerodynamic shape optimization by variable-fidelity computational fluid dynamics models: A review of recent progress

A brief review of some recent variable-fidelity aerodynamic shape optimization methods is presented. We discuss three techniques that—by exploiting information embedded in low-fidelity computational fluid dynamics (CFD) models—are able to yield a satisfactory design at a low computational cost, usually corresponding to a few evaluations of the original, high-fidelity CFD model to be optimized. The specific techniques considered here include multi-level design optimization, space mapping, and shape-preserving response prediction. All of them use the same prediction–correction scheme, however, they differ in the way the low-fidelity model information it utilized to construct the surrogate model. The presented techniques are illustrated using three specific cases of transonic airfoil design involving lift maximization and drag minimization.

A GRADIENT-ENHANCED SPARSE GRID ALGORITHM FOR UNCERTAINTY QUANTIFICATION

Adjoint-based gradient information has been successfully incorporated to create surrogate models of the output of expensive computer codes. Exploitation of these surrogates offers the possibility of uncertainty quantification, optimization and parameter estimation at reduced computational cost. Presently, when we look for a surrogate method to include gradient information, the most common choice is gradient-enhanced Kriging (GEK). As a competitor, we develop a novel method: gradient-enhanced sparse grid interpolation. Results for two test functions, the Rosenbrock function and a test function based on the drag of a transonic airfoil with random shape deformations, show that the gradient-enhanced sparse grid interpolation is a reliable surrogate that can incorporate the gradient information efficiently for high-dimensional problems.

Numerical Simulation and Investigation of Transonic & Symmetrical Airfoil for Helicopter Main Rotor Blade Application

Helicopter rotor aerodynamics is prognosticated to be one of the most perplexing and enigmatic affliction encountered by both researchers and aviators throughout the ages. The bewilderment of the flow field around the main rotor blade ceaselessly remains unrequited in tangible flight environments. Appalling calamities repeatedly befall owing to these unforeseen and equivocal instances. In order to extricate these impediments, one must go back to the brass tacks and apprehend the cause. However, it is every so often exceedingly disconcerting to obtain experimental data due to intricacy, perplexity and substantial price tag. Subsequently, computational simulation is progressively becoming more of a preferred choice in recent times. Bearing this in mind, this study intended to simulate and visualize the air flow configuration of the main rotor blade using symmetrical and transonic airfoils to demarcate their physiognomies and behavior. Results have revealed that the transonic airfoil has a higher lift coefficient (Cl) than the symmetrical airfoil. Contrariwise, if used in an actual rotorcraft, the transonic airfoil can cause stern apprehension in terms of stability and control.

Optimization of Airfoils for Minimum Pitching Moment and Compressibility Drag Coefficients

This paper concerns a numerical optimization method for designing airfoils based on adjoint method. The goal of present work is to reduce the compressibility drag or pitching moment of transonic airfoils without compromising on the lift coefficient. A new cost function based on this requirement is defined and the corresponding adjoint equations are discussed in details. At the end, by demonstrating some numerical results, we show that this technique is capable of converging to the optimum design point corresponding to the initial geometry of the airfoil.

Inverse airfoil design using variable-resolution models and shape-preserving response prediction

The paper presents a computationally efficient surrogate-based optimization algorithm for the inverse design of transonic airfoils. Our approach replaces the direct optimization of an accurate, but computationally expensive, high-fidelity airfoil model by an iterative re-optimization of two different surrogate models. Initially, for a few design iterations, a corrected physics-based low-fidelity model is employed, which is subsequently replaced by a response surface approximation model. The low-fidelity model is based on the same governing fluid flow equations as the high-fidelity one, but uses coarser mesh resolution and relaxed convergence criteria. The shape-preserving response prediction (SPRP) technique is utilized to predict the high-fidelity model response, here, the airfoil pressure distribution. In this prediction process, SPRP employs the actual changes of the low-fidelity model response (or the surface approximation model) due to the design variable adjustments. The SPRP algorithm is embedded into the trust region framework to ensure good convergence properties of the optimization procedure. Our algorithm is applied to constrained inverse airfoil design in inviscid transonic flow. A comparison with the basic version of the optimization algorithm, exploiting only a physics-based low-fidelity model, is carried out. While the performance of both versions is similar with respect to their ability to match the target pressure distribution, the improved algorithm offers substantial design cost savings, from 25 to 72 percent, depending on the test case.

On transonic flow models for optimized design and experiment

In the paper the near sonic flow theory for flows with small perturbations to sonic parallel flow is developed. This theory stands on the basis of potential flow of a compressible fluid and enables to receive an exact solution of the flow parameters past transonic cusped airfoils and their geometrical description. Generated airfoil shapes are tested using CFD ANSYS Fluent code to validate the results. Obtained numerical results from all-round commercial code show good accordance with the theory and confirm their value for future work in transonic design.

Linear-Frequency-Domain Predictions of Dynamic-Response Data for Viscous Transonic Flows

Determining the flutter boundaries for full aircraft configurations by time-accurately solving the Reynolds-averaged Navier–Stokes equations is prohibitive with respect to computational expense, as the unsteady aerodynamic loading must be predicted for a wide range of flight conditions, frequencies, and structural mode shapes. Nonetheless, there is an increasing demand to accurately predict flutter boundaries in the viscous transonic regime—a demand, which, until recently, could only be satisfied by high-fidelity Reynolds-averaged Navier–Stokes methods. Brought to application readiness over the last years, time-linearized/small-disturbance methods, however, have been shown to satisfy this demand as well. They retain the Reynolds-averaged Navier–Stokes method’s fidelity to a high degree, at a substantially reduced computational expense. Such a method is presented here on the basis of the TAU–Reynolds-averaged Navier–Stokes method. Denoted as the TAU linear-frequency-domain method, it is validated for both a standard transonic airfoil and a high-aspect-ratio-wing dynamic test case using rigid pitch modes. The response data obtained from the linear frequency domain are in good agreement with the experiment for a two-dimensional case. For the three-dimensional case, there are larger differences. More important, the linear-frequency-domain method is in excellent agreement to time-accurate Reynolds-averaged Navier–Stokes simulations. Depending on the linear-frequency-domain-employed-solution scheme, reductions in computational costs well beyond an order of magnitude are obtained. In addition, the limits of the so-called frozen-eddy-viscosity approach are established.

Multi-objective aerodynamic shape optimization using MOGA coupled to advanced adaptive mesh refinement

This paper demonstrates the big influence of the control of the mesh quality in the final solution of aerodynamic shape optimization problems. It aims to study the trade-off between the mesh refinement during the optimization process and the improvement of the optimized solution. This subject is investigated in the transonic airfoil design optimization using an Adaptive Mesh Refinement (AMR) technique coupled to Multi-Objective Genetic Algorithm (MOGA) and an Euler aerodynamic analysis tool. The methodology is implemented to solve three practical design problems; the first test case considers a reconstruction design optimization that minimizes the pressure error between a predefined pressure curve and candidate pressure distribution. The second test considers the total drag minimization by designing airfoil shape operating at transonic speeds. For the final test case, a multi-objective design optimization is conducted to maximize both the lift to drag ratio (L/D) and lift coefficient (Cl). The solutions obtained with and without adaptive mesh refinement are compared in terms of solution improvement and computational cost. Numerical results clearly show that the use of adaptive mesh refinement can improve the solution accuracy while reducing significant computational cost in both single- and multi-objective design optimizations.

Heat Transfer Coefficient Measurements on the Film-Cooled Pressure Surface of a Transonic Airfoil

This paper presents isoenergetic temperature and steady-state film-cooled heat transfer coefficient measurements on the pressure surface of a modern, highly cambered transonic airfoil. A single passage model simulated the idealized two-dimensional flow path between blades in a modern transonic turbine. This set up offered a simpler construction than a linear cascade but produced an equivalent flow condition. Furthermore, this model allowed the use of steady-state, constant surface heat fluxes. We used wide-band thermochromic liquid crystals (TLCs) viewed through a novel miniature periscope system to perform high-accuracy (±0.2 °C) thermography. The peak Mach number along the pressure surface was 1.5, and maximum turbulence intensity was 30%. We used air and carbon dioxide as injectant to simulate the density ratios characteristic of the film cooling problem. We found significant differences between isoenergetic and recovery temperature distributions with a strongly accelerated mainstream and detached coolant jets. Our heat transfer data showed some general similarities with lower-speed data immediately downstream of injection; however, we also observed significant heat transfer attenuation far downstream at high blowing conditions. Our measurements suggested that the momentum ratio was the most appropriate variable to parameterize the effect of injectant density once jet lift-off occurred. We noted several nonintuitive results in our turbulence effect studies. First, we found that increased mainstream turbulence can be overwhelmed by the local augmentation of coolant injection. Second, we observed complex interactions between turbulence level, coolant density, and blowing rate with an accelerating mainstream.

Shape optimization of airfoils in transonic flow using a multi-objective genetic algorithm

Shape optimization of transonic airfoils requires creating an airfoil that reduces the drag due to transonic shocks by either eliminating them or reducing their strength at a given transonic cruise speed while maintaining the lift. The RAE 2822 and NACA 0012 airfoils are most widely used test cases for validation of computational modeling in transonic flow. This study employs a multi-objective genetic algorithm for shape optimization of RAE 2822 and NACA 0012 airfoils to achieve two objectives, namely eliminating shock and maintaining or increasing the lift at a given transonic Mach number and angle of attack. The commercially available software FLUENT is employed for calculation of the flow field using the Reynolds-averaged Navier–Stokes equations in conjunction with a two-equation turbulence model. It is shown that the multi-objective genetic algorithm can generate superior airfoils compared with the original airfoils by achieving both the objectives.

The effect of non-equilibrium condensation on the coefficients of force with the angle of attack in the transonic airfoil flow of NACA0012

A transonic flow with a non-equilibrium condensation past NACA0012 profile whose aspect ratio AR is 1.0 with the angle of attack was analyzed by numerical analysis using a TVD scheme, and investigated using an intermittent indraft type supersonic wind tunnel. Transonic flows of 0.70–0.90 in free stream Mach number with variations of Φ0 and α were tested. For the same M∞ and α, the increase in stagnation relative humidity Φ0 caused a decrease in the drag coefficient of profile (that is total) which is composed of the components of form, viscous, wave and condensation; however, the lift coefficient up to Φ0 = 50% increased in the opposite direction. As an example, in the case of M∞ = 0.83, Φ0 = 50%, α = 3○ and T0 = 298 K, the decreasing rate of the coefficient of profile drag and the increasing rate of the lift coefficient compared to the case of Φ0 = 0% caused by non-equilibrium condensation amounted to 65% and 52%, respectively. In addition, for the same Φ0 and α, as the free stream Mach number M∞ increased, at first, the lift coefficient increased slightly, and then suddenly severely dropped, and finally remained nearly constant. The suddenly dropped free stream Mach number in CL became larger with an increase of Φ0. It turned out that the drag coefficients of form and viscous were almost independent of Φ0. The contribution of wave drag to the coefficient of profile drag for M∞ = 0.83, Φ0 = 30%, α = 3° and T0 = 298 K amounted to approximately 79%, and in the case of Φ0 = 60%, the contribution of the non-equilibrium condensation to the reduction in the coefficient of the profile drag compared to the case without condensation amounted to 75%. Especially, for the case of Φ0 = 0% and α = 0°, there was an oscillatory flow region around M∞ = 0.87.

Subsonic and transonic airfoil inverse design via Ball-Spine Algorithm

Inverse design in external flow regimes usually involves finding the wall shape associated with a prescribed distribution of wall pressure or velocity. In this research, a novel iterative inverse design method is developed for inviscid subsonic and transonic external flow regimes. The method links up a novel inverse design algorithm, called Ball-Spine Algorithm (BSA), and a 2D inviscid analysis code. The Euler equations are solved for a physical domain of which some unknown boundaries are iteratively modified via BSA until a prescribed pressure distribution is reached. In BSA, the unknown walls are composed of a set of virtual balls that move freely along the specified directions called spines. The difference between target and current pressure distributions causes to deform the flexible boundary at each modification step. Some validation test cases and design examples in subsonic and transonic regimes are presented here which show the robustness and flexibility of the method in handling the complex geometries in various flow regimes.

An Improved Parallel Optimization Framework for Transonic Airfoil Design

Variable Fidelity Optimization (VFO) is used to obtain a minimum drag transonic airfoil, at constant lift, subject to thickness and pitching moment constraints using several low fidelity solvers. VFO has emerged as an attractive method of performing, both, high-speed and high-fidelity optimization. VFO uses computationally inexpensive low-fidelity models, complemented by a surrogate to account for the difference between the high- and low-fidelity models, to obtain the optimum of the function efficiently and accurately. The authors’ original Variable Fidelity (VF) framework is modified for increased efficiency and accuracy by incorporating parallel evaluation and more constraints to the optimization problem. The method is found to be efficient and capable of finding the optimum that closely agrees with the results of high-fidelity optimization alone.

Convergence behaviours of genetic algorithms for aerodynamic optimisation problems

The convergence behaviour of genetic algorithms (GAs) applied to aerodynamic optimisation problems for transonic flows of ideal and dense gases is analysed using a statistical approach. To this purpose, the concept of GA-hardness, i.e., the capability of converging more or less easily toward the global optimum for a given problem, is introduced, as well as a statistical GA-hardness indicator. For GA-hard problems, reduced convergence rate and high sensitivity to the choice of the starting population are observed. The validity of the proposed framework is initially verified for a reference optimisation problem, namely, minimisation of drag over a transonic airfoil. Numerical examples allow to identify sources of GA-hardness for aerodynamic problems. Numerical errors in the representation of the objective function contribute to increase GA-hardness. A simple and effective strategy based on Richardson extrapolation is proposed as a cure to this problem.