Infinite Swept Wing Research Articles

Improved Amplification Factor Transport Transition Model for Transonic Boundary Layers

Linear-stability-theory-based method plays an important role in boundary-layer transition prediction of aeronautical flows. Based on the simplification of linear stability theory (Drela and Giles, AIAA J, 1987), the amplification factor transport (AFT) equation for Tollmien–Schlichting waves using local variables was first proposed in 2013 (Coder and Maughmer, AIAA J, 2014). However, in transonic high-Reynolds-number flows, the AFT model seriously overestimates the value of . To fix this problem, we have conducted many linear stability analyses to rebuild the formulations of AFT model. Compressibility effect, which has a significant impact on the prediction of value, has been considered in the improved version. Coupled with the model for crossflow instabilities (Xu et al., CJA, 2020), the improved AFT model is established for transonic boundary layers. Several classic test cases are successfully employed to validate present AFT model, including a flat plate, an airfoil, an infinite swept wing, a sickled-shape wing, a 6:1 inclined prolate spheroid, the NASA Common Research Model, and ARA Transonic Swept Wing. Our prediction results show that both Tollmien–Schlichting instabilities and stationary crossflow instabilities can be captured and predicted well by the improved model in subsonic and transonic boundary layers.

A Comparison of Different Approaches for Predicting Transonic Buffet Onset on Infinite Swept Wings

A comparative study is performed on three different approaches for prediction of transonic buffet onset on infinite swept wings. All three approaches are based on the unsteady Reynolds-averaged Navier–Stokes (URANS) equations, and include: quasi-3D and fully-3D global stability analysis of the corresponding steady 2.5D RANS solutions and direct numerical solution of the 3D URANS equations. The results are presented for an infinite swept wing based on the ONERA OAT15A airfoil section. The quasi-3D stability analysis is shown to be accurate and most efficient and, thus, is best suited for this spanwise-uniform flow. The fully-3D stability analysis ensures the same accuracy, provided that the grid-step in the spanwise direction is sufficiently small. It is much more demanding in terms of computer memory but can be extended to more-general wing configurations. Good agreement is observed between the three approaches in terms of critical conditions for buffet onset and the instability growth characteristics, providing a cross-validation of the methods and an assessment of their computational demands.

Transition in an infinite swept-wing boundary layer subject to surface roughness and free-stream turbulence

The instability of an incompressible boundary-layer flow over an infinite swept wing in the presence of disc-type roughness elements and free-stream turbulence (FST) has been investigated by means of direct numerical simulations. Our study corresponds to the experiments by Örlü et al. (Tech. Rep., KTH Royal Institute of Technology, 2021, http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-291874). Here, different dimensions of the roughness elements and levels of FST have been considered. The aim of the present work is to investigate the experimentally observed sensitivity of the transition to the FST intensity. In the absence of FST, flow behind the roughness elements with a height above a certain value immediately undergoes transition to turbulence. Impulse–response analyses of the steady flow have been performed to identify the mechanism behind the observed flow instability. For subcritical roughness, the generated wave packet experiences a weak transient growth behind the roughness and then its amplitude decays as it is advected out of the computational domain. In the supercritical case, in which the flow transitions to turbulence, flow as expected exhibits an absolute instability. The presence of FST is found to have a significant impact on the transition behind the roughness, in particular in the case of a subcritical roughness height. For a height corresponding to a roughness Reynolds number $Re_{hh}=461$ , in the absence of FST the flow reaches a steady laminar state, while a very low FST intensity of $Tu =0.03\,\%$ causes the appearance of turbulence spots in the wake of the roughness. These randomly generated spots are advected out of the computational domain. For a higher FST level of $Tu=0.3\,\%$ , a turbulent wake is clearly visible behind the element, similar to that for the globally unstable case. The presented results confirm the experimental observations and explain the mechanisms behind the observed laminar–turbulent transition and its sensitivity to FST.

Fast Aerodynamic Calculations Based on a Generalized Unsteady Coupling Algorithm

An aerodynamic model for applications to external flows is formulated that provides a great tradeoff between computational cost and prediction accuracy. The novelty of the work is the ability to deal with any unsteady flow problem, irrespective of the frequency of motion and motion kinematics. The aerodynamic model, baptized FALCon, combines an in-house unsteady vortex lattice method with an infinite-swept wing Navier–Stokes solver. The two specialized methods are orchestrated by an unsteady coupling algorithm that represents our main research contribution. The paper gives the formulation and algorithmic implementation. FALCon is demonstrated on three test cases of increasing complexity in flow physics, up to flow conditions well outside its validity range. On average, FALCon achieves a computational speed-up of a factor of about 50, compared with a full Navier–Stokes run, while capturing relevant flow physics: three-dimensional, viscous, compressible, and unsteady phenomena.

Adjoint State of Nonlinear Vortex-Lattice Method for Aerodynamic Design and Control

The adjoint state of a nonlinear vortex-lattice method, coupled with sectional polars obtained with an infinite swept-wing (2.5D) Reynolds-averaged Navier–Stokes (RANS) solver, is presented as an interactive method for preliminary aerodynamic design and control of moderate-to-high aspect ratio wings in subsonic and transonic flows. First, the nonlinear vortex-lattice method is described, augmented with a Prandtl–Glauert compressibility correction and regularized so that poststall solutions can be recovered. The linearization of the coupled system of equations is formulated using a Newton method, and the adjoint state is obtained for lift, drag, and inverse design functionals. Numerical results show that the aerodynamic model approximates well the forces predicted by three-dimensional (3D) RANS simulations for the Common Research Model wing, and that the adjoint-state gradients agree well with finite difference tests for a plethora of test cases. More interesting examples are shown, ranging from the optimal unstalling of wings to the assimilation of 3D RANS data into the present model, as well as its ability to extrapolate.

Numerical study of a turbulent separation bubble with sweep

Direct numerical simulation (DNS) is used to study a separated and rapidly reattached turbulent boundary layer over an idealized $35^{\circ }$ infinite swept wing. The separation and reattachment are induced by a transpiration profile at fixed distance above the layer, with the pressure gradient applied to a well-defined, fully developed, zero-pressure-gradient (ZPG) collateral state. To isolate the influence of the sweep, results are compared with one of our earlier DNS of an unswept flow, with the same chordwise transpiration distribution and appropriate upstream momentum thickness. The independence principle (IP) traditionally proposed for swept wings, which is exact for laminar flows, is found to be close to valid in some regions (bridging the separation/reattachment zone) and to fail in others (in the ZPG layers upstream and downstream of the separation). This is assessed primarily through the skin friction and integral thicknesses. The regions in which the IP is approximately valid correspond to regions of diminished Reynolds-stress divergence, compared to the pressure-gradient magnitude. The mean-velocity profiles exhibit significant skewing as the flow develops, while the velocity magnitude departs only slightly from the ZPG logarithmic profile, even above the separation zone. Implications for Reynolds-averaged turbulence modelling are discussed.

Study on Riblet Drag Reduction Considering the Effect of Sweep Angle

This study computationally evaluates the riblet drag reduction effect considering the effect of sweep angle. An implicit large eddy simulation is performed on a channel flow and an infinite swept wing. First, three different inclined angles between the riblets and the flow direction are tested in the channel flow. The results show that with increases in the inclined angle, the friction drag decreases, while the pressure drag increases approximately quadratically. The riblets with a 30° inclined angle increase the total drag of the channel flow. Then, an infinite wing with a 30° swept angle with and without riblets is studied. The riblets demonstrate satisfactory drag reduction efficiency because the cross flow over most parts of the wing is mild. The lift and friction drag follow the relation of the cosine law of a swept wing. Moreover, the cross flow and the turbulence fluctuation are suppressed by the riblets.

Fully Local Amplification Factor Transport Equation for Stationary Crossflow Instabilities

The traditional linear stability analysis for transition prediction includes the following steps: solving velocity profiles using boundary-layer equations or a computational fluid dynamics solver, guessing and searching operations for the eigenvalues, computing the linear perturbation equations, and integrating the amplification factor . It is difficult to implement into modern computational fluid dynamics solvers with parallel computations because it requires many nonlocal variables and coordinate system transformations. In this Paper, an amplification factor transport equation, which can be coupled with a modern computational fluid dynamics parallel solver, is established based on the analysis results through linear stability theory for stationary crossflow instabilities. According to the analysis results of Falkner–Skan–Cooke similarity velocity profiles using linear stability theory analysis, the source term of the present transport equation is formulated locally to describe the growth of stationary crossflow waves in the laminar boundary layer. This new equation is added to the equation proposed by Coder and Maughmer for Tollmien–Schlichting instabilities. Finally, coupling of these two amplification factor transport equations and Menter’s shear stress transport turbulence model completes an effective transition turbulence model. Comparisons between the present predictions, wind tunnel experiments and the standard linear stability theory analysis on an NLF(2)-0415 infinite swept wing, Petzold’s sickle-shaped wing and 6:1 inclined prolate spheroid validate the reasonable establishment of the present amplification factor transport equation for stationary crossflow instabilities.

Development of a computational fluid dynamics compatible mathematical model for boundary layer transitional flows in low-disturbance environment

Because of the great influence of transition phenomena in aerodynamic property calculations, boundary layer transition has always been a hot research topic in the past few decades. Meanwhile, the prediction methods for boundary layer transition need to be established, researched and enhanced. In order to build a computational fluid dynamics (CFD) compatible transition model, the authors propose a two-equation transport transition model in this paper considering analysis results through linear stability theory (LST). This new transition model consists of one transport equation for laminar fluctuation kinetic energy and another for intermittency factor. Without boundary layer integration and other nonlocal operations, all the variables in this new transition model can be calculated locally so that present model is compatible with CFD parallel computation. Laminar separation bubble induced transition, Tollmien–Schlichting (T–S) instabilities and stationary crossflow instabilities (CF) dominated transition are modeled in the transport equation. The validation tests have been conducted on the classical Schubauer & Klebanoff flat plate, natural laminar airfoil NLF(1)-0416, NLF(2)-0415 infinite swept wing, classical sickle swept wing and 6:1 inclined prolate spheroid using this fully-local transition model. Since all the test cases are in accord with experimental data, the present transition model could be widely applied to aeronautical flows in low-disturbance environment.

Fast identification of transonic buffet envelope using computational fluid dynamics

PurposeThis paper aims to present a numerical method based on computational fluid dynamics that allows investigating the buffet envelope of reference equivalent wings at the equivalent cost of several two-dimensional, unsteady, turbulent flow analyses. The method bridges the gap between semi-empirical relations, generally dominant in the early phases of aircraft design, and three-dimensional turbulent flow analyses, characterised by high costs in analysis setups and prohibitive computing times.Design/methodology/approachAccuracy in the predictions and efficiency in the solution are two key aspects. Accuracy is maintained by solving a specialised form of the Reynolds-averaged Navier–Stokes equations valid for infinite-swept wing flows. Efficiency of the solution is reached by a novel implementation of the flow solver, as well as by combining solutions of different fidelity spatially.FindingsDiscovering the buffet envelope of a set of reference equivalent wings is accompanied with an estimate of the uncertainties in the numerical predictions. Just over 2,000 processor hours are needed if it is admissible to deal with an uncertainty of ±1.0° in the angle of attack at which buffet onset/offset occurs. Halving the uncertainty requires significantly more computing resources, close to a factor 200 compared with the larger uncertainty case.Practical implicationsTo permit the use of the proposed method as a practical design tool in the conceptual/preliminary aircraft design phases, the method offers the designer with the ability to gauge the sensitivity of buffet on primary design variables, such as wing sweep angle and chord to thickness ratio.Originality/valueThe infinite-swept wing, unsteady Reynolds-averaged Navier–Stokes equations have been successfully applied, for the first time, to identify buffeting conditions. This demonstrates the adequateness of the proposed method in the conceptual/preliminary aircraft design phases.

Extension of a Reynolds-Stress-Based Transition Transport Model for Crossflow Transition

Two crossflow transition prediction approaches, the local C1-based approach and the local helicity-based approach, have been implemented into a Reynolds-stress-based transition transport model of the modeling framework. The differential Reynolds stress model is the model that has been coupled with the model. The whole framework of the coupled model, including the crossflow extensions, is presented in detail. A grid sensitivity study for crossflow transition prediction was conducted. In addition, the influence of the numerical scheme on the computational results is discussed. The new Reynolds-stress-based transition model is compared with the model coupled to the SST two-equation eddy-viscosity turbulence model including the two crossflow extensions for the NLF (2)-0415 infinite swept wing, the DLR prolate spheroid and the DLR-F4 wing-body geometry. The comparisons show that the Reynolds-stress-based transition model can yield very accurate results, which, in terms of the predicted transition onset, are sometimes better than those of the in conjunction with the eddy-viscosity model.

Combined high-speed and high-lift wing aerodynamic optimization using a coupled VLM-2.5D RANS approach

The paper presents a numerical framework for the aerodynamic analysis of aircraft wings in transonic cruise and take-off/landing compatible with preliminary and conceptual design phase requirements based on the Non-Linear Vortex Lattice Method (NL-VLM). The purpose of this work is to demonstrate the applicability of the VLM-2.5D RANS approach for aircraft design optimization. The algorithm captures wing sweep effects, important in the transonic regime and near CLmax conditions, by a stripwise viscous-inviscid coupling strategy with an infinite-swept wing (2.5D) Reynolds-Averaged Navier–Stokes (RANS) solver. Aerodynamic forces are evaluated through spanwise integration of the 2.5D RANS solutions and a trefftz-plane analysis of the VLM solver. The framework allows calculations of single and multi-element configurations without modifying the VLM mesh. A novel CLmax criteria is proposed based on recently observed stall-cells patterns that captures CLmax, αmax and the spanwise location of the stall, which represent important design parameters. The applicability of the framework to aircraft design is demonstrated by embedding the analysis tools into a gradient-free Covariance Matrix Adaptation Evolution Strategy. After a verification phase, validation is performed on high-speed, high-lift and combined high-speed/high-lift optimizations cases. In particular, the capability of the numerical algorithms towards multi-topology optimization is demonstrated.

Efficient infinite-swept wing solver for steady and unsteady compressible flows

An efficient Navier–Stokes solver for the infinite-swept wing problem is presented. The new flow solution, that reproduces correctly the physics responsible for cross-flow effects, is obtained around a two-dimensional stencil. On the contrary, existing state-of-the-art methods rely on a three-dimensional stencil. Numerical details are followed by an extensive validation campaign, including steady and unsteady compressible flows. The test cases are for single and multi-element aerofoils in both laminar and turbulent regimes. Under identical conditions (numerical settings, grids, etc.), the computational cost of the proposed solver was reduced by at least 75% compared to that of existing state-of-the-art methods. This was also confirmed employing various turbulence models. With a limited effort required to enhance an existing computational fluid dynamics solver (either two or three-dimensional), the infinite-swept wing method was implemented in an industrial-grade package used across Europe for rapid engineering analysis.

Correlation-Based Transition Transport Modeling for Simulating Crossflow Instabilities

A correlation-based transition model has been developed by Langtry and Menter for modern computational fluid dynamics codes, which is widely used for transition prediction in the field of turbomachinery and aircraft. Langtry’s transition model could simulate bypass, laminar separation and streamwsie Tollmien–Schlichting wave transition. Even so, this model has no ability to predict the transition due to crossflow instabilities in three dimensional boundary layer. In this paper, a new correlation-based transport equation for the transition due to crossflow instabilities has been established based on the experiment data and self-similar equations. The new transport equation is introduced to describe the crosswise displacement thickness Reynolds number growth in boundary layer. This new equation is added to Langtry’s intermittency factor equation to improve the ability of predicting transition. Finally, coupling of these transport equations and Shear Stress Transport (SST) turbulence model completes the new improved transition turbulence model. Comparisons of predictions using the new model with wind tunnel experiments of NLF (2)-0415 infinite swept wing and 6:1 inclined prolate spheroid validate the predictive qualities of the new correlation based transport equation.

Boundary-layer receptivity to external disturbances using multiple scales

Non-homogeneous multiple scales are introduced to solve the resonant problem of non-parallel boundary-layer receptivity originating from the quadratic mixing of environmental disturbances. The resulting algorithm is computationally inexpensive and can be efficiently included in industrial codes for transition prediction. The mutual interactions between acoustic wave, vorticity wave, wall vibration and wall roughness are discussed in detail and the receptivity coefficient, which relates the amplitude of the excited wave to the amplitude of the exciting sources, is computed. The largest effect is found for the interaction between acoustic waves and wall roughness perturbations. Other coupling mechanisms are less effective. By comparing parallel and non-parallel results, it is found that flow non-parallelism can play a non-negligible role even in Blasius’ boundary layer, although the largest effects are evident for the three-dimensional boundary layer over an infinite swept wing. For the particular case of wall roughness—wall vibration mixing, the velocity disturbance is shown to be exactly equal to the velocity perturbation induced by wall roughness alone on a wall vibrating in the normal direction.

Turbulence Model Behavior in Low Reynolds Number Regions of Aerodynamic Flowfields

The behaviors of the widely used Spalart-Allmaras and Menter shear-stress transport turbulence models at low Reynolds numbers and under conditions conducive to relaminarization are documented. The flows used in the investigation include 2-D zero-pressure-gradient flow over a flat plate from subsonic to hypersonic Mach numbers, 2-D airfoil flow from subsonic to supersonic Mach numbers, 2-D subsonic sink flow, and 3-D subsonic flow over an infinite swept wing (particularly its leading-edge region). Both models exhibit a range over which they behave transitionally even with inflow values set to cause immediate growth of the turbulence quantities, in the sense that the flow is neither laminar nor fully turbulent, but these behaviors are different: the shear-stress transport model typically has a well-defined transition location, whereas the Spalart-Allmaras model does not. Both models are predisposed to delayed activation of turbulence with increasing freestream Mach number. Also, both models can be made to achieve earlier activation of turbulence by increasing their freestream levels, but too high a level can disturb the turbulent solution behavior. The technique of maintaining freestream levels of turbulence without decay in the shear-stress transport model, introduced elsewhere, is shown here to be useful in reducing grid dependence of the model's transitional behavior. Both models are demonstrated to be incapable of predicting relaminarization; eddy viscosities remain weakly turbulent in accelerating or laterally strained boundary layers for which experiment and direct simulations indicate turbulence suppression. The main conclusion is that these models are intended for fully turbulent high Reynolds number computations, and using them for transitional (e.g., low Reynolds number) or relaminarizing flows is not appropriate. Competing models which fare better in these areas have not been identified.

Shape Optimization for Delay of Laminar-Turbulent Transition

A method using gradient-based optimization is introduced for the design of wing profiles with the aim of natural laminar flow, as well as minimum wave drag. The Euler equations of gasdynamics, the laminar boundary-layer equations for compressible flows on infinite swept wings, and the linear parabolized stability equations (PSE) are solved to analyze the evolution of convectively unstable disturbances. Laminar‐turbulent transition is assumed to be delayed by minimizing a measure of the disturbance kinetic energy of a chosen disturbance, which is computed using the PSE. The shape gradients of the disturbance kinetic energy are computed based on the solutions of the adjoints of the state equations just named. Numerical tests are carried out to optimize the RAE 2822 airfoil with the aim to delay simultaneously the transition, reduce the pressure drag coefficient, and maintain the coefficients of lift and pitch moments. Constraints are also applied on the geometry. Results show a reduction of the total amplification of a large number of disturbances, which is assumed to represent a delay of the transition in the boundary layer. Because delay of the transition implies reduction of the viscous drag, the present method enables shape optimization to perform viscous drag reduction.

Infinite Swept-Wing Navier-Stokes Computations with eN Transition Prediction.

The flow around infinite swept wings is computed using a Reynolds-averaged Navier-Stokes method coupled to a boundary layer and a transition prediction method based on the e N approach. This approach applies the two N factor e N strategy, which allows the differentiation between excited Tollmien-Schlichting waves of constant frequency and stationary crossflow waves of constant spanwise wave number. The applicability is documented by comparing computations with infinite swept-wing experiments on four configurations, where one configuration was tested in two different wind tunnels. The limiting N factors for both types of waves are a priori unknown. Hence, firstly the limiting N factors, which represent the stability limit, are deduced from the measured transition locations. Subsequently, iterative computations are executed to determine the transition location using the coupled system, Navier-Stokes, boundary-layer, and two N factor e N method in combination with the stability limit

Subcritical instability on the attachment-line of an infinite swept wing

The leading-edge contamination (LEC) problem of an infinite swept wing is shown here as vortex-induced instability. The governing equation for receptivity is presented for LEC in terms of disturbance energy based on the Navier-Stokes equation. The unperturbed shear layer given by the swept Hiemenz boundary-layer solution is two-dimensional and an exact solution of incompressible the Navier-Stokes equation. Thus, the LEC problem is solved numerically by solving the full two-dimensional Navier-Stokes equation. The contamination at the attachment-line is shown by solving a receptivity to a convecting vortex moving outside the attachment-line boundary layer, which triggers subcritical spatio-temporal instability

Transition prediction in infinite swept wings using Navier–Stokes computations and linear stability theory

The coupling of Navier–Stokes computations with e N method for transition prediction in infinite swept wings is demonstrated. In the present paper, results are presented illustrating the successful coupling of these methods for a 45° swept wing operating at four different Reynolds numbers. Moreover, the main issues involved in the generation of adapted meshes and in the computation of the mean flow by a Navier–Stokes method are documented. In all studied cases, the subsequent linear stability analysis of the mean flow has shown that the transition process was dominated by cross-flow instability. The transition prediction results have been validated against experimental transition data from the literature.