On the mechanism of sinuous and varicose modes in three‐dimensional viscous secondary instability of nonlinear Görtler rolls

1994 ◽  
Vol 6 (2) ◽  
pp. 736-750 ◽  
Author(s):  
Xiuyang Yu ◽  
Joseph T. C. Liu
Keyword(s):  
Three Dimensional ◽  
Secondary Instability

Secondary instability and subcritical transition of the leading-edge boundary layer

2016 ◽  
Vol 792 ◽  
pp. 682-711 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
High Speed ◽  
Three Dimensional ◽  
Leading Edge ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Bypass Transition ◽  
Wall Suction ◽  
Transition Mechanism

The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as$Re\approx 175$, i.e. far below the linear critical Reynolds number$Re_{crit}\approx 583$of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above$Re_{tr}\approx 250$. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number$Re_{tr}\approx 250$at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

Mechanisms and passive control of crossflow-vortex-induced transition in a three-dimensional boundary layer

2002 ◽  
Vol 456 ◽  
pp. 49-84 ◽  
Author(s):  
PETER WASSERMANN ◽  
MARKUS KLOKER
Keyword(s):  
Boundary Layer ◽  
Passive Control ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Secondary Instability ◽  
Base Flow ◽  
Transition Control ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Underlying Mechanisms

Crossflow-vortex-induced laminar breakdown in a three-dimensional flat-plate boundary-layer flow is investigated in detail by means of spatial direct numerical simulations. The base flow is generic for an infinite swept wing, with decreasing favourable chordwise pressure gradient. First, the downstream growth and nonlinear saturation states initiated by a crossflow-vortex-mode packet as well as by single crossflow-vortex modes with various spanwise wavenumbers are simulated. Second, the secondary instability of the flow induced by the saturated crossflow vortices is scrutinized, clearly indicating the convective nature of the secondary instability and strengthening knowledge of the conditions for its onset. Emphasis is on the effect of crossflow-vortex-mode packets and of the spanwise vortex spacing on the secondary stability properties of the saturation states. Saturated uniform crossflow vortices initiated by single crossflow-vortex modes turn out to be less unstable than vortices initiated by a packet of vortex modes, and closely spaced saturated vortices are even stable. Third, we investigate the transition control strategy of upstream flow deformation by appropriate steady nonlinear vortex modes as applied in wind tunnel experiments at the Arizona State University. A significant transition delay is shown in the base flow considered here, and the underlying mechanisms are specified.

Secondary instability of crossflow vortices and swept-wing boundary-layer transition

1999 ◽  
Vol 399 ◽  
pp. 85-115 ◽  
Author(s):  
MUJEEB R. MALIK ◽  
FEI LI ◽  
MEELAN M. CHOUDHARI ◽  
CHAU-LYAN CHANG
Keyword(s):  
Experimental Data ◽  
Boundary Layer ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Secondary Instability ◽  
Boundary Layer Transition ◽  
Swept Wing ◽  
Layer Transition ◽  
Transition Prediction ◽  
Dimensional Boundary

Crossflow instability of a three-dimensional boundary layer is a common cause of transition in swept-wing flows. The boundary-layer flow modified by the presence of finite-amplitude crossflow modes is susceptible to high-frequency secondary instabilities, which are believed to harbinger the onset of transition. The role of secondary instability in transition prediction is theoretically examined for the recent swept-wing experimental data by Reibert et al. (1996). Exploiting the experimental observation that the underlying three-dimensional boundary layer is convectively unstable, non-linear parabolized stability equations are used to compute a new basic state for the secondary instability analysis based on a two-dimensional eigenvalue approach. The predicted evolution of stationary crossflow vortices is in close agreement with the experimental data. The suppression of naturally dominant crossflow modes by artificial roughness distribution at a subcritical spacing is also confirmed. The analysis reveals a number of secondary instability modes belonging to two basic families which, in some sense, are akin to the ‘horseshoe’ and ‘sinuous’ modes of the Görtler vortex problem. The frequency range of the secondary instability is consistent with that measured in earlier experiments by Kohama et al. (1991), as is the overall growth of the secondary instability mode prior to the onset of transition (e.g. Kohama et al. 1996). Results indicate that the N-factor correlation based on secondary instability growth rates may yield a more robust criterion for transition onset prediction in comparison with an absolute amplitude criterion that is based on primary instability alone.

Direct numerical simulations of laminar separation bubbles: investigation of absolute instability and active flow control of transition to turbulence

2014 ◽  
Vol 747 ◽  
pp. 141-185 ◽  
Author(s):  
Martin Embacher ◽  
H. F. Fasel
Keyword(s):  
Numerical Simulations ◽  
Three Dimensional ◽  
Secondary Instability ◽  
Direct Numerical Simulations ◽  
Absolute Instability ◽  
Two Dimensional ◽  
Periodic Forcing ◽  
Laminar Separation ◽  
Flow Response ◽  
Separation Bubbles

AbstractLaminar separation bubbles generated on a flat plate by an adverse pressure gradient are investigated using direct numerical simulations (DNSs). Two-dimensional periodic forcing is applied at a blowing/suction slot upstream of separation. Control of separation through forcing with various frequencies and amplitudes is examined. For the investigation of absolute instability mechanisms, baseflows provided by two-dimensional Navier–Stokes calculations are analysed by introducing pulse disturbances and computing the three-dimensional flow response using DNS. The primary instability of the time-averaged flow is investigated with a local linear stability analysis. Employing a steady flow solution as baseflow, the nonlinear and non-parallel effects on the self-sustained disturbance development are illustrated, and a feedback mechanism facilitated by the upstream flow deformation is identified. Secondary instability is investigated locally using spatially periodic baseflows. The flow response to pulsed forcing indicates the existence of an absolute secondary instability mechanism, and the results indicate that this mechanism is dependent on the periodic forcing. Results from three-dimensional DNS provide insight into the global instability mechanisms of separation bubbles and complement the local analysis. A forcing strategy was devised that suppresses the temporal growth of three-dimensional disturbances, and as a consequence, breakdown to turbulence does not occur. Even for a separation bubble that has transitioned to turbulence, the flow relaminarizes when applying two-dimensional periodic forcing with proper frequencies and amplitudes.

Three-dimensional secondary instability of a spatially developing von Kármán vortex street in a far wake

2010 ◽  
Vol 467 (2127) ◽  
pp. 675-694 ◽  
Author(s):  
J. T. C. Liu ◽  
X. Yu
Keyword(s):  
Nonlinear Interaction ◽  
Three Dimensional ◽  
Secondary Instability ◽  
Vortex Street ◽  
Wake Flow ◽  
Two Dimensional ◽  
Primary Flow ◽  
Von Karman ◽  
Von Karman Vortex Street ◽  
Far Wake

This paper presents studies of a three-dimensional secondary instability of a spatially developing von Kármán vortex street. It develops owing to the nonlinear interaction between a two-dimensional mean far-wake flow and its most unstable disturbances. This forms a nonlinear primary wake flow. Sections of this flow are selected to perform a temporal secondary stability study under the assumption of parallel flow. The eigenvalue characteristics of the secondary instability are compared with the results from the use of a linear primary flow comprising unmodified mean wake flow coexisting with a linear primary fundamental disturbance with an empirical amplitude as a parameter, resulting in a simpler Floquet analysis. The maximum amplification rates occur at about the same spanwise wavenumber for both the nonlinear and linear primary flows, in qualitative agreement. But the amplification rate versus the spanwise wavenumber spectrum are both qualitatively and quantitatively different, the nonlinear primary flow results in a lower magnitude of the amplification rates. Some interpretations of controlled experiments are made, and it is concluded that the two- and three-dimensional disturbances so obtained appeared to be from the primary instability, where the amplification mechanisms come from the unmodified mean flow. A general discussion of the nonlinear interaction between the primary two-dimensional flow and the three-dimensional secondary instability is given, which may well form the basis for further nonlinear studies.

Mixing enhancement via the release of strongly nonlinear longitudinal Görtler vortices and their secondary instabilities into the mixing region

2002 ◽  
Vol 468 ◽  
pp. 29-75 ◽  
Author(s):  
I. G. GIRGIS ◽  
J. T. C. LIU
Keyword(s):  
Steady Flow ◽  
Reynolds Stress ◽  
Three Dimensional ◽  
Secondary Instability ◽  
Mixing Enhancement ◽  
Reynolds Stresses ◽  
Trailing Edge ◽  
Mixing Properties ◽  
Longitudinal Vortices ◽  
Centrifugal Instability

Mixing enhancement in a mixing layer is considered in terms of a ‘vortex generator’ that uses fluid dynamically generated counter-rotating longitudinal vortices rather than explicit winglets or similar devices. This view is reached through considering the centrifugal instability of weak initial Görtler vortices on a slightly concave wall that are allowed to develop to their various nonlinear stages through selecting the cutoff lengths of the trailing edge prior to their release into the mixing region. These vortices are released from one side of the (say, upper) stream in the present work. The quantitative entrainment properties of the longitudinal vortices are studied to select an optimal trailing-edge cutoff for fixed upstream conditions. As the vortices develop along the wall, they are intensified because of the centrifugal instability mechanism and because of the work done by the Reynolds stress of the vortices against the local mean flow rate of strain; simultaneously, the region of strong streamwise vorticity moves away from the wall. This selection process is explained through a balance between the vorticity strength and proximity to the lower stream when the trailing edge is cut off: it is shown, therefore, that vortices of relatively modest strength and kinetic energy that are close to the interface separating the two streams provide mixing properties superior to stronger vortices located too far from the interface. Energy-balancing mechanisms and the stretching of the initial interface are studied, as are the effects of the velocity ratio and the spanwise wavelengths other than the fundamental. In order further to enhance mixing by exploiting the inherent secondary instability of primary steady longitudinal vortices, the most amplified secondary instability of the optimal-trailing-edge cutoff situation, which is the sinuous mode, is studied in detail in terms of the nonlinear development and modification of the steady vortical flow. Local energy-exchange mechanisms are studied, as are the mixing properties of the modified steady flow, which are shown to be significantly improved compared to the unmodified steady flow. Though the initiation of steady longitudinal vortices relies on centrifugal instability upstream, such vortices are able to develop self-sustaining and amplifying properties through the Reynolds stresses in the mixing region even without centrifugal instability reinforcement. The secondary instability is initiated and sustained entirely through its own three-dimensional Reynolds stress properties, which work against the three-dimensional rates of strain in the entire steady flow. This contrasts with initially generated potential-like vortices that decay downstream in the presence of dissipative mechanisms without the production mechanisms due to the Reynolds stresses.

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