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

Riccó, Pierre; Tran, Duc-Luan; Ye, Ganda

doi:10.1063/1.3054155

Cited by 24 publications

(14 citation statements)

References 40 publications

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“…A realistic streak profile along the whole wall-normal extent of the boundary layer was obtained by R9 and good agreement with the experimental data by Westin et al [56] was shown. Ricco & Dilib [43] employed R9's approach to show that the peak of the streak amplitude in the boundary-layer core may be completely suppressed if intense wall transpiration is applied and Ricco and co-authors [47,46,45] have studied the Klebanoff modes in compressible boundary layers.…”

Section: Theoretical Framework For the Laminar Streaksmentioning

confidence: 99%

Growth of boundary-layer streaks due to free-stream turbulence

Riccó

Walsh

Brighenti

et al. 2016

International Journal of Heat and Fluid Flow

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Section: Theoretical Framework For the Laminar Streaksmentioning

confidence: 99%

Growth of boundary-layer streaks due to free-stream turbulence

Riccó

Walsh

Brighenti

et al. 2016

International Journal of Heat and Fluid Flow

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“…Ricco & Wu (2007) showed that the growing disturbances evolved from the so-called quasi-three-dimensional Lam-Rott eigensolutions, which are excited by the free-stream disturbance and may be identified as highly oblique low-frequency T-S waves in the so-called first-mode family (Mack 1975(Mack , 1984. Ricco et al (2009) found that wall cooling suppresses the streaks and enhances the growth of the instability waves.…”

Section: Theoretical Workmentioning

confidence: 99%

“…Two types of different thermal boundary conditions at the wall may be imposed: the Dirichlet boundary condition,τ (0)=0, which was also employed by Ricco & Wu (2007), and the Neumann boundary condition, ∂τ /∂η| η=0 =0. The conditionτ (0)=0 is used herein as Ricco et al (2009) showed that there is no substantial difference in the development of the Klebanoff modes.…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

“…Ricco & Wu (2007) extended the incompressible analysis by Leib et al (1999) to the compressible case and explained the formation and growth of thermal streaks, which are thought to play a significant role in the secondary instability. Ricco et al (2009) and Ricco et al (2013) further studied the influence of wall heat transfer and wall suction, respectively, on the thermal streaks. The boundary-layer signature in the region relatively close to the leading edge corresponds to the inhomogeneous solution forced by the free-stream disturbance.…”

Section: Theoretical Workmentioning

confidence: 99%

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Nonlinear unsteady streaks engendered by the interaction of free-stream vorticity with a compressible boundary layer

Marensi

Riccó

2017

J. Fluid Mech.

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The nonlinear response of a compressible boundary layer to unsteady free-stream vortical fluctuations of the convected-gust type is investigated theoretically and numerically. The free-stream Mach number is assumed to be of O(1) and the effects of compressibility, including aerodynamic heating and heat transfer at the wall, are taken into account. Attention is focused on low-frequency perturbations, which induce strong streamwise-elongated components of the boundary-layer disturbances, known as streaks or Klebanoff modes. The amplitude of the disturbances is intense enough for nonlinear interactions to occur within the boundary layer. The generation and nonlinear evolution of the streaks, which acquire an O(1) magnitude, are described on a self-consistent and first-principle basis using the mathematical framework of the nonlinear unsteady compressible boundary-region equations, which are derived herein for the first time. The free-stream flow is studied by including the boundary-layer displacement effect and the solution is matched asymptotically with the boundary-layer flow. The nonlinear interactions inside the boundary layer drive an unsteady two-dimensional flow of acoustic nature in the outer inviscid region through the displacement effect. A close analogy with the flow over a thin oscillating airfoil is exploited to find analytical solutions. This analogy has been widely employed to investigate steady flows over boundary layers, but is considered herein for the first time for unsteady boundary layers. In the subsonic regime the perturbation is felt from the plate in all directions, while at supersonic speeds the disturbance only propagates within the dihedron defined by the Mach line. Numerical computations are performed for carefully chosen parameters that characterize three practical applications: turbomachinery systems, supersonic flight conditions and wind tunnel experiments. The results show that nonlinearity plays a marked stabilizing role on the velocity and temperature streaks, and this is found to be the case for low-disturbance environment such as flight conditions. Increasing the free-stream Mach number inhibits the kinematic fluctuations but enhances the thermal streaks, relative to the free-stream velocity and temperature respectively, and the overall effect of nonlinearity becomes weaker. An abrupt deviation of the nonlinear solution from the linear one is observed in the case pertaining to a supersonic wind tunnel. Large-amplitude thermal streaks and the strong abrupt stabilizing effect of nonlinearity are two new features of supersonic flows. The present study provides an accurate signature of nonlinear streaks in compressible boundary layers, which is indispensable for the secondary instability analysis of unsteady streaky boundary-layer flows.

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“…The most commonly investigated strategy for controlling the boundary-layer instability growth is the use of wall suction, which has been shown to reduce the growth of Tollmien-Schlichting waves (Bodonyi & Duck 1990, 1992Fransson & Alfredsson 2003), laminar streaks (Byström et al 2007;Davidsson & Gustavsson 2008;Ricco & Dilib 2010) and Görtler vortices (Floryan & Saric 1983;Balakumar & Hall 1999). Other techniques for controlling the growth of boundary-layer disturbances include wall cooling and heating (El-Hady 1992;Hubbard & Riley 1995;Ricco et al 2009) and wall forcing . In the present study the evolution and attenuation of laminar streaks are investigated above a spanwise oscillating plate.…”

Section: Introductionmentioning

confidence: 99%

Laminar streak growth above a spanwise oscillating wall

Hicks

Riccó

2015

J. Fluid Mech.

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Accepted for publication in Journal of Fluid MechanicsThe use of spanwise wall oscillations to attenuate the growth of laminar streaks within the incompressible Blasius boundary layer is investigated. As in the case of the flow above a stationary flat plate, studied by Leib et al. (J. Fluid Mech. vol. 380, 1999, p. 169), free-stream convected gusts interact with the boundary layer to drive the streak growth. Spanwise wall oscillations can either reduce or increase the total energy of the laminar streaks, depending upon the wall oscillation amplitude and frequency, as well as the free-stream gust properties. Reductions in streak energies of up to 90% are obtained, indicating that spanwise wall oscillations are an effective technique for attenuating the laminar streak growth. Therefore they may suppress secondary boundary-layer instabilities and delay transition.The laminar boundary-layer base flow matches the Blasius profile in the streamwise and wall-normal directions, while in the spanwise direction a generalized version of the classical Stokes layer profile (generated by a wall oscillating beneath a quiescent fluid) occurs, which evolves downstream due to non-parallel flow effects. Via a Wentzel-KramersBrillouin-Jeffreys (WKBJ) analysis this generalized Stokes layer is shown to approach the classical Stokes layer in the limit of large downstream distances or high-frequency plate oscillations. The laminar streaks forced by the generalized and the classical Stokes flows differ significantly, which implies that the choice of the spanwise base flow may affect the secondary instability and transition in this flow. The analysis also proves that the use of the classical Stokes layer as spanwise base flow, as employed by Hack & Zaki (Phys. Fluids. vol 24. 2012), is inappropriate.

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

Cited by 24 publications

References 40 publications

Growth of boundary-layer streaks due to free-stream turbulence

Growth of boundary-layer streaks due to free-stream turbulence

Nonlinear unsteady streaks engendered by the interaction of free-stream vorticity with a compressible boundary layer

Laminar streak growth above a spanwise oscillating wall

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