Transonic Flow Past Oscillating Airfoils

Tijdeman, H.; Seebass, R.

doi:10.1146/annurev.fl.12.010180.001145

Cited by 157 publications

(112 citation statements)

References 15 publications

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“…To determine the frequency of shock wave motion, figure 8 shows the power spectrum of the time-dependent lift force exerted on the aerofoil. The primary frequency corresponding to the highest peak is St = 0.148 approximately, or the reduced frequency, which is usually used in this problem (Tijdeman & Seebass 1980;Lee 2001), k = πSt ≈ 0.465, consistent with the previous experimental data, namely 0.44-0.49 (e.g. McDevitt et al 1976;Levy 1978;Marvin et al 1980).…”

Section: Shock Wave Motionsupporting

confidence: 87%

“…From the preceding description of the shock wave evolution, it is reasonably identified that the shock wave motion belongs to type C classified by Tijdeman & Seebass (1980), which is also confirmed by the previous experiments (McDevitt et al 1976;Levy 1978;McDevitt 1979;Marvin et al 1980). To determine the frequency of shock wave motion, figure 8 shows the power spectrum of the time-dependent lift force exerted on the aerofoil.…”

Section: Shock Wave Motionsupporting

confidence: 75%

“…A possible mechanism of self-sustained shock oscillation for type A during transonic buffeting with separated flow was first proposed by Lee (Lee 1990;Lee et al 1994). The classification of the type A shock motion by Tijdeman & Seebass (1980) states that the shock moves almost sinusoidally and exists during the complete cycle of oscillation even though its strength varies. We will try to extend this feedback model to the present type C shock wave motion.…”

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

“…In the type A motion, a shock wave is oscillating on the upper surface of a supercritical aerofoil (Tijdeman & Seebass 1980). Lee proposed that the formed pressure waves propagate downstream in the separated flow region over the aerofoil at speed V d , and the disturbances generate upstream-moving waves at speed V u as the waves reach the trailing edge (Lee 1990;Lee et al 1994).…”

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

“…The speed of upstream-propagating disturbances is described as (Tijdeman 1977;Lee 1990) where a loc is the local speed of sound; M s is the Mach number at the surface; and R is a relaxation factor and was experimentally determined as 0.7 (Tijdeman 1977). This equation can be reasonably simplified as (Deck 2005)…”

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

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Numerical investigation of the compressible flow past an aerofoil

Chen

2009

J. Fluid Mech.

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Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M∞ = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

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Section: Shock Wave Motionsupporting

confidence: 87%

Section: Shock Wave Motionsupporting

confidence: 75%

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

Section: Feedback Model Of Shock Wave Motionmentioning

confidence: 99%

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Numerical investigation of the compressible flow past an aerofoil

Chen

2009

J. Fluid Mech.

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CFD‐Based Nonlinear Computational Aeroelasticity

Farhat

2004

Encyclopedia of Computational Mechanics

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This chapter overviews a three‐field formulation of nonlinear aeroelastic problems, where the fluid is modeled by the arbitrary Lagrangian–Eulerian (ALE) form of either the Euler or Navier–Stokes equations; the structure is represented by a detailed finite element model, and the fluid‐mesh is unstructured, dynamic, and constructed by a robust structure‐analogy–based method. It also discusses recent advances in the computational algorithms associated with this approach for modeling nonlinear fluid/structure interaction problems. These include CFD schemes that are formally second‐order time‐accurate on moving grids, energy‐transfer–conserving methods for discretizing transmission conditions across nonmatching fluid and structure discrete interfaces, and state‐of‐the‐art loosely coupled algorithms for solving efficiently coupled systems of fluid and structural equations arising from the discretization of real aircraft configurations. A taste of the capabilities of such algorithms is provided by reporting on their validation for an F‐16 fighter aircraft configuration in various subsonic, transonic, and supersonic airstreams, and at various load factors. The chapter concludes with a discussion of the feasibility and merit of the overviewed computational technology for accurately extracting the flutter envelopes of civilian and military aircraft, and a perspective on future research in CFD‐based nonlinear computational aeroelasticity.

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Bibliography

1998

Theoretical Fluid Dynamics

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Transonic Flow Past Oscillating Airfoils

Cited by 157 publications

References 15 publications

Numerical investigation of the compressible flow past an aerofoil

Numerical investigation of the compressible flow past an aerofoil

CFD‐Based Nonlinear Computational Aeroelasticity

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