Linear Stability Theory and the Problem of Supersonic Boundary- Layer Transition

Mack, Leslie M.

doi:10.2514/3.49693

Cited by 512 publications

(159 citation statements)

References 26 publications

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“…The wall heat flux is more influential in subsonic conditions and it affects the growth rate only slightly. As the TS waves we consider are of low frequency because they are induced by the Klebanoff modes through the triggering of the Lam-Rott modes, they are identified as compressible first modes, 5 for which wall cooling has been confirmed to be stabilizing, both numerically 35,[44][45][46][47] and experimentally. 48,49 In Fig.…”

Section: Tollmien-schlichting Waves For Z ™mentioning

confidence: 99%

Wall heat transfer effects on Klebanoff modes and Tollmien–Schlichting waves in a compressible boundary layer

Riccó

Tran

2009

Physics of Fluids

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The influence of wall heat transfer on fluctuations generated by free-stream vortical disturbances in a compressible laminar boundary layer is investigated. These disturbances are thermal Klebanoff modes, namely low-frequency, streamwise-elongated laminar streaks of velocity and temperature, and oblique Tollmien-Schlichting waves, induced by a leading-edge adjustment receptivity mechanism. The flow is governed by the linearized unsteady boundary-region equations, which properly account for the nonparallel and spanwise diffusion effects, and for the continuous forcing of the free-stream convected gusts. Wall cooling stabilizes the laminar streaks when their spanwise wavelength is much larger than the boundary-layer thickness. For these conditions, the disturbances confine themselves in the outer edge layer further downstream, where the compressibility effects are marginal. Klebanoff modes for which the spanwise diffusion is comparable with the wall-normal diffusion possess an asymptotic solution similar to the incompressible case, and are stabilized by wall heating. The unstable waves, which appear in high-Mach-number subsonic and supersonic conditions, are stabilized by wall cooling and destabilized by wall heating. Removing heat from the surface significantly shifts downstream the starting location of instability, while the streamwise wavelength and the growth rate are less affected by the wall heat flux. Perturbation methods, such as the WKBJ technique and the triple-deck theory, are used effectively to validate the numerical results and to explain the flow physics.

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Section: Tollmien-schlichting Waves For Z ™mentioning

confidence: 99%

Wall heat transfer effects on Klebanoff modes and Tollmien–Schlichting waves in a compressible boundary layer

Riccó

Tran

2009

Physics of Fluids

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“…They can cause locally increased pressure and thermal loads, cause separations and have a great influence onto the transition process. Most of the existing publications in this field deal with interactions of shock waves with turbulent boundary layers (Dupont et al 2006; Schülein 2006;Humble et al 2009; Helmer 2011;Grilli et al 2012), some handle the case of interactions of shock waves with laminar boundary layers (Boin et al 2006;Lüdeke and Sandham 2009;Brown and Boyce 2009) but investigations of the interaction between shock waves and transitional boundary layers are rare (Dolling 2001;Arnal and Delery 2004;Benay et al 2006;Vanstone et al 2013). In order to study these phenomena in detail within the framework of the ESA-TRP "laminar to turbulent transition in hypersonic flows," experiments in three different facilities using several measuring techniques have been carried out (Sandham et al 2014).…”

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confidence: 99%

Experiments on the effect of laminar–turbulent transition on the SWBLI in H2K at Mach 6

2015

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than two and an increase in the heat flux by a factor of more than four. Therefore, big areas of laminar flow are desirable to increase the performance of a propelled vehicle and to reduce the weight of the necessary thermal protection systems of a propelled or re-entry vehicle. On the other hand, turbulent boundary layers have a lower tendency to separate and are preferred in regions of large pressure gradients. Hence, the correct prediction of the transition is essential for the design of future hypersonic vehicles and their thermal protection systems.Shock wave-boundary layer interactions (SWBLI) are inevitable for most of the practical applications. They can cause locally increased pressure and thermal loads, cause separations and have a great influence onto the transition process. Most of the existing publications in this field deal with interactions of shock waves with turbulent boundary layers (Dupont et al. 2006; Schülein 2006;Humble et al. 2009; Helmer 2011;Grilli et al. 2012), some handle the case of interactions of shock waves with laminar boundary layers (Boin et al. 2006;Lüdeke and Sandham 2009;Brown and Boyce 2009) but investigations of the interaction between shock waves and transitional boundary layers are rare (Dolling 2001;Arnal and Delery 2004;Benay et al. 2006;Vanstone et al. 2013). In order to study these phenomena in detail within the framework of the ESA-TRP "laminar to turbulent transition in hypersonic flows," experiments in three different facilities using several measuring techniques have been carried out (Sandham et al. 2014). This paper describes the results of the experiments performed in the hypersonic wind tunnel H2K at DLR in Cologne.The transition process of undisturbed hypersonic boundary layers is most likely driven by instabilities called second (Mack) modes (Mack 1975). These are acoustic waves trapped between the wall and the sonic line. Therefore, Abstract This paper presents the results of the experiments performed in the hypersonic wind tunnel H2K in the framework of the ESA technology research project "laminar to turbulent transition in hypersonic flows". The investigations include the free boundary-layer transition on a flat plate as well as the influence of a shock wave-boundary layer interaction on the transition. The shock is created by a wedge with a small angle of attack resulting in a moderate shock intensity. The experiments were performed at Mach 6.0, at three different unit Reynolds numbers and with a translational displacement of the shock generator. Besides the optical methods-Schlieren photography and infrared thermography-several intrusive sensors were used. High-speed measurements were carried out using PCB and atomic layer thermo pile sensors. Kulite sensors were used for low-and mid-speed pressure measurements. The data analysis includes the comparison of the absolute values, the frequency spectra and wavelets and their distributions in time and space.

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“…Mack [2] was the first to carry out extensive computations on the linear stability characteristics of compressible boundary layers. He used compressible linear stability theory (LST) to calculate the amplitude ratio (A=A 0 ) of constant-frequency disturbances as a function of Reynolds number, where A and A 0 were local disturbance amplitude and initial disturbance amplitude.…”

Section: Introductionmentioning

confidence: 99%

“…To predict and control boundary-layer transition, extensive studies have been carried out to investigate transition mechanisms [1][2][3][4][5]. It is recognized that the transition process of a boundary-layer flow strongly depends on the amplitude level of environmental perturbations [6], which is schematically shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Receptivity of a Hypersonic Flat-Plate Boundary Layer to Three-Dimensional Surface Roughness

Wang

Zhong

2008

Journal of Spacecraft and Rockets

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The laminar-turbulent transition of hypersonic boundary layers has a significant effect on drag calculation and aerothermal design of hypersonic vehicles. Recent research has shown that one possible explanation to roughnessinduced bypass transition is transient growth theory. However, it is not known how to generate the optimal disturbances computed by transient growth theory. Furthermore, there has not been any direct numerical simulation study on transient growth in hypersonic boundary layers. The objectives of this paper are to study the receptivity of a Mach 5.92 flow over a flat plate to three-dimensional surface roughness and the effect of spanwise wave number on the receptivity. Steady base flow is computed by solving compressible Navier-Stokes equations with a combination of a fifth-order shock-fitting method and a second-order total variation diminishing scheme. In receptivity simulations, small surface roughness is introduced on the plate. The numerical results show that counterrotating streamwise vortices and transient growth are induced by surface roughness, however, transient growth is generally weak due to the small height of roughness. For the six cases considered, surface roughness with the spanwise wave number being 0.0101 has the strongest excitation of transient growth.

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Linear Stability Theory and the Problem of Supersonic Boundary- Layer Transition

Cited by 512 publications

References 26 publications

Wall heat transfer effects on Klebanoff modes and Tollmien–Schlichting waves in a compressible boundary layer

Wall heat transfer effects on Klebanoff modes and Tollmien–Schlichting waves in a compressible boundary layer

Experiments on the effect of laminar–turbulent transition on the SWBLI in H2K at Mach 6

Receptivity of a Hypersonic Flat-Plate Boundary Layer to Three-Dimensional Surface Roughness

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