Multi-element Airfoil Research Articles

A Jacobian-free Newton–Krylov algorithm for compressible turbulent fluid flows

Despite becoming increasingly popular in many branches of computational physics, Jacobian-free Newton–Krylov (JFNK) methods have not become the approach of choice in the solution of the compressible Navier–Stokes equations for turbulent aerodynamic flows. To a degree, this is related to some subtle aspects of JFNK methods that are not well understood, and, if poorly handled, can lead to inefficient and unreliable performance. These are described here, along with strategies for addressing them, leading to an efficient JFNK algorithm for turbulent aerodynamic flows applicable to multi-block structured grids and a one-equation turbulence model. Development of globalization strategies for field-equation turbulence models represents one of the key contributions of the paper. Numerous examples of subsonic and transonic flows over single and multi-element airfoils are presented in order to demonstrate the efficiency and reliability of the algorithm. In addition, a number of guidelines are presented to aid in diagnosing problems with JFNK algorithms.

Ice accretion simulation on multi-element airfoils using extended Messinger model

In the current article, the problem of in-flight ice accumulation on multi-element airfoils is studied numerically. The analysis starts with flow field computation using the Hess-Smith panel method. The second step is the calculation of droplet trajectories and droplet collection efficiencies. In the next step, convective heat transfer coefficient distributions around the airfoil elements are calculated using the Integral Boundary-Layer Method. The formulation accounts for the surface roughness due to ice accretion. The fourth step consists of establishing the thermodynamic balance and computing ice accretion rates using the Extended Messinger Model. At low temperatures and low liquid water contents, rime ice occurs for which the ice shape is determined by a simple mass balance. At warmer temperatures and high liquid water contents, glaze ice forms for which the energy and mass conservation equations are combined to yield a single first order ordinary differential equation, solved numerically. Predicted ice shapes are compared with experimental shapes reported in the literature and good agreement is observed both for rime and glaze ice. Ice shapes and masses are also computed for realistic flight scenarios. The results indicate that the smaller elements in multielement configurations accumulate comparable and often greater amount of ice compared to larger elements. The results also indicate that the multi-layer approach yields more accurate results compared to the one-layer approach, especially for glaze ice conditions.

Effect of Three-Dimensional Shear-Layer Structures on Slat Cove Unsteadiness

Numerical simulations are used to investigate the local and global dynamics of large-scale, three-dimensional vorticity structures within the free shear layer originating from the slat cusp of a multielement airfoil configuration. Results indicate that accounting for the local three-dimensionality of flow fluctuations leads to substantially improved agreement between the computed unsteady near-field solution and wind tunnel measurements based on particle image velocimetry. Analysis of simulation data indicates the potential significance of high intensity turbulent fluctuations near the reattachment location along the slat lower surface toward the generation of broadband slat noise. The computed acoustic characteristics, in terms of the frequency spectrum and spatial distribution within short distances from the slat, resemble the previously reported, subscale measurements of slat noise.

Analysis Method for Inertial Particle Separator

4Re 5 10 5 ).Alimitationsoftheanalysistoolisthatitlacksanappropriateparticlereboundmodelforthe treatment of particle-wall collisions. The usefulness of the analysis tool is its use in conjunction with a multipoint inverse design tool for the design of a multi-element airfoil based inertial particle separator system model in an inverse fashion as opposed to the direct design methods being employed currently for this task. With such a design andanalysistoolathand,thedesignspacecanbeexploredaswellastradeoffstudiescanbeperformedthatcanaidin the development of a more efficient design methodology for multi-element airfoil based inertial particle separator systems.

Finite element computation of turbulent flow past a multi-element airfoil

Flow past multi-element airfoil is studied via two-dimensional numerical simulations. The incompressible Reynolds averaged Navier–Stokes equations, in primitive variables, are solved using a stabilized finite element formulation. The Spalart–Allmaras and Baldwin–Lomax models are employed for turbulence closure. The implementation of the Spalart–Allmaras model is verified by computing flow over a flat plate with a specified trip location. Good agreement is seen between the results obtained with the two models for flow past a NACA 0012 airfoil at 5° angle of attack. Results for the multi-element airfoil, with the two turbulence models, are compared with experiments for various angles of attack. In general, the pressure distribution, from both the models matches quite well with the experimental results. However, at larger angles of attack, the computational results overpredict the suction peak on the slat. The velocity profiles from the Baldwin–Lomax model are, in general, more diffused compared to those from the Spalart–Allmaras model. The agreement between the computed and experimental results is not too good in the flap region for large angles of attack. Both the models are unable to predict the stall; the flow remains attached even for relatively large angles of attack. Consequently, the lift coefficient is over predicted at large α by the computations. Overall, compared to the Baldwin–Lomax model, the predictions from the Spalart–Allmaras model are closer to experimental measurements.

Active Boundary-Layer Separation Control on a Multi-ElementAirfoil

A fundamental and perennial motivation underlying research in fluid mechanics, especially in the field of aerodynamics, is the investigation of techniques that can be used to improve the high-lift performance of aircraft. Much research has been done in the area of modifying the design lines of various aircraft components to augment the total lift, most notably, the wings and other lifting surfaces. Advancements in this area have been aided mainly through the efforts of both experimentalists using wind tunnels and researchers applying computational fluid dynamics. Additionally, research has also proceeded along the path of employing variousflow control techniques for the purpose of improving the high-lift characteristics of aircraft. It is important now to capitalize on this knowledge and to add to the existing database by exploring and devising new and improved techniques of controlling the flow field affecting the performance of lifting surfaces. This should be done in an attempt to produce an improved lift capability of aircraft in an efficientmanner. The experimental investigation presently described is an attempt to do just that by employing a flow control technique to influence the flow field surrounding a standard, multielement airfoil geometry at a subsonic speed. The primary motivation behind the development of high-lift systems is to ensure that high aerodynamic lift at low aircraft speeds is maintained during the liftoff and landing phases of the flight. Of course, high-lift could simply be achieved by adding area to thewing, but this has the obvious disadvantage of increasing the weight and possible complexity of the lifting system. One option would be to employ conventional lift-augmenting devices such as leading-edge slats and trailing-edgeflaps.Over the years, various configurations of slats and flaps have been devised to achieve high-lift and yet the challenge has always been to minimize their adverse effects on the other aircraft systems due to aerodynamic interference. Active flow control can be applied to achieve a variety of objectives. This investigation was primarily concerned with flow control using piezoelectric devices as a means of achieving sizable increments in lift for aircraft, specifically at subsonic speeds by transferring turbulent kinetic energy and momentum into the boundary layer. Researchers have discovered that physicalmechanisms associated with the dynamics of vortices produce favorable effects with regards to the generation of high-lift [1]. Experiments have been conducted which have studied how vortex interactions in the shear layer of a separated boundary layer can contribute to the enhanced spreading rate of the shear layer [2]. Previous research results have shown that this phenomenon promotes boundary-layer reattachment. Bhattacharjee [3] observed that the process of “vortex pairing” increases the shear-layer-spreading rate. This phenomenon associated with vortices can be described as the amalgamation of neighboring vortex lumps into larger ones. The underlying premise is that vortex amalgamation reenergizes a separated boundary layer, which produces the favorable effect of an increment in aerodynamic lift. Experimental data from a previous study [4] have indicated that vortex amalgamation occurs when the forcing frequency is a subharmonic of the vortex passage frequency associated with the test article for a specified set of test conditions and model geometry.

Preliminary Parametric Study of Gurney Flap Dependencies

Introduction T HE Gurney flap1,2 is typically a small plate, which is attached at or near the trailing edge of an airfoil on the pressure side. The flap has been shown to be a highly effective small-scale (typically 0.5–1.5% of the chord) modification that can achieve significant lift and pitching-moment generation.1,2 The Gurney functions by essentially increasing the downward deflection of the trailingedge flow, facilitated through the formation of a series of counterrotating vortices similar to that of a von Karman vortex street. A subsequent effect is an apparent violation of the trailing-edge Kutta condition; experimental data show that finite loading is carried to the trailing edge. The Gurney flap increases the effective chord and camber of the airfoil, so by augmenting circulation. Liebeck3 suggested a flow pattern where a “virtual” cusped trailing edge is formed downstream of the Gurney from the shear layers merging downstream of the flap. The final pressure recovery would then occur off-surface, which is analogous to violation of the Kutta condition. Experimental and computational studies exploring the effect of Gurney flaps have been undertaken covering effects of flap height,4 angle,5 effects on multi-element airfoils,2 etc. In this Note, the database is increased through evaluation of the effects of flap porosity, inclination, and spacing from the surface. It would also be useful for experimental design and conceptual understanding to have correlations that relate Gurney-flap geometric parameters to performance. Consequently, such correlations are developed.

Theoretical Aerodynamics in Today's Real World: Opportunities and Challenges

*† In spite of the CFD revolution, significant challenges still face aerodynamicists in predicting and controlling various classes of flows. These include three-dimensional separation, boundary layer transition, interaction of separation and transition such as on reentry capsules, multi-element airfoils and wings, UAV low Reynolds number flows and high angle of attack applications. Others include multi-body flows such as those occurring in store and stage separation, “stiff” combustion reacting and unsteady flows as well as plasma aerodynamics and turbulence, to name a few. In many cases, diverse multiple scales are involved and the proper identification and treatment of associated disparate length and time scales is critical in obtaining accurate prediction and effective control. The solution of such multi-scale problems can be a hurdle to effective domain decomposition, even overset, unstructured adaptive gridding and ultimately, solution accuracy. Theoretical insights can help make proper decisions on numerical pre-processing, solution, post-processing and interpretation. Opportunities for a combined theoretical, computational and experimental approach will be discussed. These will be illustrated by examples from the author’s experience. As compared to the limited “pen and paper” theoretical methods of the 50’s, illustrations will be given of the effectiveness of combined asymptotics, similitude, group invariance, approximate physics-based modeling and numerical methods for conceptual vehicle design, flow control innovation, identification of key parameters, leveraging of computational solutions, reducing the parameter space as well as providing added insight into the basic physical processes. These will be related to tradeoffs between accuracy and response speed in typical aerospace environments.

Zonal-Detached-Eddy Simulation of the Flow Around a High-Lift Configuration

A zonal hybrid Reynolds-averaged Navier-Stokes large-eddy simulation (RANS/LES) approach, called zonal-DES, used to handle a two-dimensional high-lift configuration with deployed slat and flap is presented. This method allows to reduce significantly the cost of an accurate numerical prediction of the unsteady flow around wings compared to a complete LES. Some issues concerning grid generation as well as the use of zonal-detached-eddy simulation for a multi-element airfoil are discussed. The basic planar grid has 250,000 points and the finest spanwise grid has 31 points with Az/c = 0.002. The effort is geared toward detailed comparison of the numerical results with the Europiv2 experimental particle image velocimetry data including both mean and fluctuating properties of the velocity field (Arnott and al)

A parallel viscous flow solver on multi-block overset grids

A multi-block overset grid method is presented to accurately simulate viscous flows around complex configurations. A combination of multi-block and overlapping grids is used to discretize the flow domain. A hierarchical grid system with layers of grids of varying resolution is developed to ensure inter-grid connectivity within a framework suitable for multi-grid and parallel computations. At each stage of the numerical computation, information is exchanged between neighboring blocks across either or both matched block boundaries and overlapping boundaries. Coarse-grain parallel processing is facilitated by the multi-block system. Numerical results of flows over multi-element airfoils and three-dimensional turbulent flows around wing–body aerodynamic configurations demonstrate the utility and efficiency of the method.

Efficient Optimization Design Method Using Kriging Model

The Kriging-based genetic algorithm is applied to aerodynamic design problems. The Kriging model, one of the response surface models, represents a relationship between the objective function (output) and design variables (input) using stochastic process. The kriging model drastically reduces the computational time required for objective function evaluation in the optimization (optimum searching) process. ‘Expected improvement (EI)’ is used as a criterion to select additional sample points. This makes it possible not only to improve the accuracy of the response surface but also to explore the global optimum efficiently. The functional analysis of variance (ANOVA) is conducted to evaluate the influence of each design variable and their interactions to the objective function. Based on the result of the functional ANOVA, designers can reduce the number of design variables by eliminating those that have small effect on the objective function. In this paper, the present method is applied to a two-dimensional airfoil design and the prediction of flap’s position in a multi-element airfoil, where the lift-to-drag ratio (L/D) is maximized.

Transition Prediction on the Slat of a High-Lift System

In this paper, a transition prediction approach for the slat of a high-lift system is presented. Accurate mean flows over a multi-element airfoil at various angles of attack have been calculated by using a Navier‐Stokes code. Linear parabolized stability equations have been used to analyze these mean flows and to generate the database for simplified transition prediction correlations. The slat transition prediction module, constituting these correlations, is then used to analyze low-disturbance wind-tunnel data for transition onset in the slat boundary layer. Good agreement is found when Ntr =9 is used as the transition criterion for the two-dimensional flow on the slat of a three-element high-lift system for a range of angle of attack. Comparison of velocity profiles from Navier‐Stokes and boundary-layer computations indicates significant departure from the assumptions associated with the first-order boundary-layer theory.

Multi-Element High-Lift Configuration Design Optimization Using Viscous Continuous Adjoint Method

An adjoint-based Navier‐Stokes design and optimization method for two-dimensional multi-element high-lift configurations is derived and presented. The compressible Reynolds-averaged Navier‐Stokes equations are used as a flow model together with the Spalart‐Allmaras turbulence model to account for high Reynolds number effects. When a viscous continuous adjoint formulation is used, the necessary aerodynamic gradient information is obtained with large computational savings over traditional finite difference methods. The high-lift configuration parallel design method uses a point-to-point matched multiblock grid system and the message passing interface standard for communication in both the flow and adjoint calculations. Airfoil shape, element positioning, and angle of attack are used as design variables. The prediction of high-lift flows around a baseline three-element airfoil configuration, denoted as 30P30N, is validated by comparison with available experimental data. Finally, several design results that verify the potential of the method for high-lift system design and optimization are presented. The design examples include a multi-element inverse design problem and the following optimization problems: lift coefficient maximization, lift-to-drag ratio maximization, and the maximum lift coefficient maximization problem for both the RAE2822 single-element airfoil and the 30P30N multi-element airfoil.

Multipoint and Multi-Objective Aerodynamic Shape Optimization

A Newton‐Krylov algorithm is presented for the aerodynamic optimization of singleand multi-element airfoil configurations. The flow is governed by the compressible Navier‐Stokes equations in conjunction with a one-equation turbulence model. The preconditioned generalized minimum residual method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. Design examples include lift-enhancement and multi-point lift-constrained drag minimization problems. Furthermore, the new algorithm is used to compute a Pareto front for a multi-objective problem, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an ecient and robust approach for addressing the issues of complex aerodynamic

Nonet-Cartesian Grid Method for Shock Flow Computations

A nonet-Cartesian grid method, based on anisotropic/isotropic refinement, is presented for solving the Euler equations in gas dynamic problems. Grids are generated automatically, by the recursive subdivision of a single cell into nine subcells for isotropic nonet-Cartesian grids and into three subcells independently in each direction for anisotropic nonet-Cartesian grids, encompassing the entire flow domain. The grid generation method is applied here to steady inviscid shock flow computation. A finite difference formulation for the Euler equation using nonet-Cartesian grids is used to treat complex two-dimensional configuration. Results using this approach are shown to be competitive with other methods. Further, it is demonstrated that this method provides a simple and accurate procedure for solving flow problems involving multielement airfoils.

Transitional Flow Modeling and Application to High-Lift Multi-Element Airfoil Configurations

To enhance its capabilities to handle e ows with transition, a Reynolds averaged Navier ‐Stokes solver has been extended with regard to the modeling of transitional e ow regions based on transition length models and the intermittency function. Because the full coupling of the solver to an e N -method that predicts the locations of transitiononsethasnotyetbeencompleted,thepointsoflaminarseparationaresupposedtorepresentthetransition locations in a e rst step. A method and an algorithm for detecting the laminar separation points are derived, and the intermittency function and two transition length models are implemented and validated for a selected high-lift multi-element test case. The background of the implementation work and the testing of the functionalities of the algorithms are focused on. Details of the implementation, which are consequences of an underlying transition prediction strategy, are outlined. The testing is described and then documented. Nomenclature cd = drag coefe cient c f = skin-friction coefe cient cl = lift coefe cient cp = pressure coefe cient FLGlt = laminar‐ turbulent e ag for the code internal eddy

On Modeling of Transitional Flow and its Application to a High Lift Multi-element Airfoil Configuration

In order to enhance its capabilities to handle flows with transition a RANS solver has been extended with regard to the modeling of transitional flow regions based on transition length models and the intermittency function. As the full coupling of the solver to an e*-method that predicts the locations of transition onset has not yet been completed the points of laminar separation are supposed to represent the transition locations in a first step. A method and an algorithm for detecting the laminar separation points are derived, the intermittency function and two transition length models are implemented and validated at a selected high lift multi-element test case. The paper focuses on the background of the implementation work and the testing of the functionalilites of the algorithms. Details of the implementation, which are consequences of an underlying transition prediction strategy are outlined. The testing is described and documented by a number of commented plots.

Low-Mach-Number Preconditioning Applied to Turbulent Helicopter Fuselage Flowfield Computation

HIS paper deals with the problems encountered in simulating low-Mach-number e ows encountered in applied aerodynamics. Typical examples are e ows over external aerodynamic bodies such as helicopter fuselages, road vehicles, submarines, and multielement airfoils at high angles of attack. Low-speed e ows may be compressible because of surface heat transfer or volumetric heat addition. Classical numerical methods for the simulation of compressible viscous e ows using the Reynolds averaged Navier‐ Stokes (RANS)equationsperformsatisfactorilyinmoste owregimes(from mediumsubsonice owtohypersonice ow).However,inthelowsubsonic e ow regime, that is, for Mach numbers lower than about 0.1, these methods give poor results in terms of convergence rate and solution accuracy. The dife culty in solving the compressible equations for low Mach numbers is associated with the large ratios that exist between the acoustic and convective wave speeds. Two approaches are currently considered to solve this problem. The e rst is a perturbation method. It is based on a perturbed form of the equations where the physical acoustic waves are replaced

Two-Dimensional Unstructured Navier-Stokes Simulation of Multi-Element Airfoils Using Spalart-Allmaras One-Equation Model

A high-lift system is a crucial part of aircraft design because it influences takeoff and landing performance. Computational fluid dynamics as well as wind tunnel test has been recently incorporated into high-lift design and a multi-element airfoil is used to optimize high-lift performance. To estimate the high-lift aerodynamics of multi-element airfoils, two-dimensional compressible unstructured Navier-Stokes code with Spalart-Allmaras one-equation turbulence model is presented. For this validation, subsonic flows over a two-element configuration, NASA Model-B airfoil, and a three-element configuration, RAE 2815 airfoil, are computed. On surface pressure coefficient distributions and boundary-layer velocity profiles, the present computed results show good agreement with the wind-tunnel testing data. Also performed are the computations of subsonic flows over a five-element configuration, NASA Model-D airfoil, to demonstrate the possibility for more complex geometry. The present code is expected to be powerful tool for high-lift design.

Bubble Bursting and Laminar Separation Unsteadiness on a Multi-Element High Lift Configuration

The purpose of this work is to gain insight into the problem of the bursting of a laminar separation bubble in the nose region of a slotted flap on a multi-element airfoil configuration. The interest in bubble bursting, which, especially on multi-element configurations has not been thoroughly investigated yet, was raised by the experimental results obtained while testing a computer designed flap in the low speed low Turbulence wind tunnel of the Delft University of Technology. A sudden and dangerous stall was found to occur on the flap surface due to the bursting of a bubble in its nose region. CFD calculations, both laminar and RANS, were first performed on a single element configuration, namely the Eppler E387 airfoil (Re = 105) and then on the multi-element configuration tested in the wind tunnel (Re = 2 ·106). The results show that a strong vortex shedding can potentially originate from the separated shear layer, both on the flap and on the single element airfoil, suggesting a close connection between the two cases. The effect of transition on the structure of the bubble was investigated by imposing and then varying the transition point. The computational results suggest that the unsteady behavior of the laminar bubble has to be regarded as a major issue in order to find an effective bursting predictor method for airfoil design.