Shock buffet on wings encountered in edge-of-the-envelope transonic flight remains an unresolved and disputed flow phenomenon, challenging both fundamental fluid mechanics and applied aircraft aerodynamics. The question of global instability leading to flow unsteadiness is addressed herein. It is shown for the first time that incipient threedimensional shock buffet is governed by the dynamics of a single unstable linear eigenmode with its spatial structure describing previously reported buffet cells. An inner-outer Krylov approach is proposed to solve the arising large-scale eigenvalue problem iteratively using shift-and-invert spectral transformation and sparse iterative linear solver. The established numerical strategy with an industrial flow solver means that a practical noncanonical test case at high-Re flow condition can be investigated. A modern wing design with publicly available geometry and experimental data for code validation is studied. The numerical findings can be exploited for routes to flow control and model reduction. †

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This paper presents a numerical study of the transonic flow over a half wing-body configuration representative of a large civil aircraft. The Mach number is close to cruise conditions, while the high angle of attack causes massive separation on the suction side of the wing. Results indicate the presence of shock-wave oscillations inducing unsteady loads which can cause serious damage to the aircraft. Transonic shock buffet is found. Based on preliminary simulations using a baseline grid, the region relevant to the phenomenon is identified and mesh adaptation is applied to significantly refine the grid locally. Then, time-accurate Reynolds-averaged Navier-Stokes and delayed detached-eddy simulations are performed on the adapted grid. Both types of simulation reproduce the unsteady flow physics and much information can be extracted from the results when investigating frequency content, the location of unsteadiness and its amplitude. Differences and similarities in the computational results are discussed in detail and also analysed with respect to recent experimental data.

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SUMMARY An implicit meshless scheme is developed for solving the Euler equations, as well as the laminar and Reynolds‐averaged Navier–Stokes equations. Spatial derivatives are approximated using a least squares method on clouds of points. The system of equations is linearised, and solved implicitly using approximate, analytical Jacobian matrices and a preconditioned Krylov subspace iterative method. The details of the spatial discretisation, linear solver and construction of the Jacobian matrix are discussed; and results that demonstrate the performance of the scheme are presented for steady and unsteady two dimensional fluid flows. Copyright © 2012 John Wiley & Sons, Ltd.

Transonic buffet is commonly associated with self-sustained flow unsteadiness involving shock-wave/boundary-layer interaction over airfoils and wings. The phenomenon has been classified as either laminar or turbulent based on the state of the boundary layer immediately upstream of the shock foot, and distinct mechanisms for the two types have been suggested. The turbulent case is known to be associated with a global linear instability. Herein, large-eddy simulations are used for the first time to make direct comparisons of the two types by examining free- and forced-transition conditions. Corresponding simulations based on the Reynolds-averaged Navier–Stokes equations for the forced-transition case are also performed for comparison with the scale-resolving approach and for linking the findings with existing literature. Coherent flow features are scrutinized using both data-based spectral proper orthogonal decomposition of the time-marched results and operator-based global linear stability and resolvent analyses within the Reynolds-averaged Navier–Stokes framework. It is demonstrated that the essential dynamic features remain the same for the two buffet types (and for the two levels of the aerodynamic modeling hierarchy), suggesting that both types arise due to the same fundamental mechanism.

The physical mechanism governing the onset of transonic shock buffet on swept wings remains elusive, with no unequivocal description forthcoming despite over half a century of research. This paper elucidates the fundamental flow physics on a civil aircraft wing using an extensive experimental database from a transonic wind tunnel facility. The analysis covers a wide range of flow conditions at a Reynolds number of around 3.6 × 10 6 . Data at pre-buffet conditions and beyond onset are assessed for Mach numbers between 0.70 and 0.84. Critically, unsteady surface pressure data of high spatial and temporal resolution acquired by dynamic pressure-sensitive paint is analysed, in addition to conventional data from pressure transducers and a root strain gauge. We identify two distinct phenomena in shock buffet conditions. First, we highlight a low-frequency shock unsteadiness for Strouhal numbers between 0.05 and 0.15, based on mean aerodynamic chord and reference free stream velocity. This has a characteristic wavelength of approximately 0.8 semi-span lengths (equivalent to three mean aerodynamic chords). Such shock unsteadiness is already observed at low-incidence conditions, below the buffet onset defined by traditional indicators. This has the effect of propagating disturbances predominantly in the inboard direction, depending on localised separation, with a dimensionless convection speed of approximately 0.26 for a Strouhal number of 0.09. Second, we describe a broadband higher-frequency behaviour for Strouhal numbers between 0.2 and 0.5 with a wavelength of 0.2 to 0.3 semi-span lengths (0.6 to 1.2 mean aerodynamic chords). This outboard propagation is confined to the tip region, similar to previously reported buffet cells believed to constitute the shock buffet instability on conventional swept wings. Interestingly, a dimensionless outboard convection speed of approximately 0.26, coinciding with the low-frequency shock unsteadiness, is found to be nearly independent of frequency. We characterise these coexisting phenomena by use of signal processing tools and modal analysis of the dynamic pressure-sensitive paint data, specifically proper orthogonal and dynamic mode decomposition. The results are scrutinised within the context of a broader research effort, including numerical simulation, and viewed alongside other experiments. We anticipate our findings will help to clarify experimental and numerical observations in edge-of-the-envelope conditions and to ultimately inform buffet-control strategies.

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