The Linear Stability of a Flat Plate Boundary-Layer Approaching a Cylindrical Obstacle

1992 ◽  
Vol 114 (3) ◽  
pp. 306-312 ◽  
Author(s):  
R. E. Spall ◽  
M. R. Malik
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Linear Stability ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Region Of Interest ◽  
Transition Process ◽  
Low Frequencies ◽  
Initial Separation ◽  
Tollmien Schlichting

The linear stability of the low-speed three-dimensional flow over a flat plate with an attached cylinder is studied. The region of interest is upstream of the initial separation point and includes the effects of both adverse and favorable pressure gradients, as well as crossflow. The resulting boundary-layer is subject to both the Tollmien-Schlichting (TS) and crossflow instabilities. Linear stability calculations, using N-factor correlations, indicate that the transition process would be dominated by TS instabilities, although for low frequencies crossflow-type disturbances are important.

scholarly journals A class of exact Navier–Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

2014 ◽  
Vol 752 ◽  
pp. 462-484 ◽  
Author(s):  
Michael O. John ◽  
Dominik Obrist ◽  
Leonhard Kleiser
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Linear Stability ◽  
Boundary Layers ◽  
Stokes Equations ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Transition Prediction ◽  
Neutral Curves ◽  
Tollmien Schlichting

AbstractWe introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Transition of streamwise streaks in zero-pressure-gradient boundary layers

2002 ◽  
Vol 472 ◽  
pp. 229-261 ◽  
Author(s):  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
High Speed ◽  
Plate Boundary ◽  
Transition Process ◽  
Free Stream Turbulence ◽  
Tollmien Schlichting ◽  
Streamwise Streaks ◽  
The Stability ◽  
Optimal Disturbances

A transition scenario initiated by streamwise low- and high-speed streaks in a flat-plate boundary layer is studied. In many shear flows, the perturbations that show the highest potential for transient energy amplification consist of streamwise-aligned vortices. Due to the lift-up mechanism these optimal disturbances lead to elongated streamwise streaks downstream, with significant spanwise modulation. In a previous investigation (Andersson et al. 2001), the stability of these streaks in a zero-pressure-gradient boundary layer was studied by means of Floquet theory and numerical simulations. The sinuous instability mode was found to be the most dangerous disturbance. We present here the first simulation of the breakdown to turbulence originating from the sinuous instability of streamwise streaks. The main structures observed during the transition process consist of elongated quasi-streamwise vortices located on the flanks of the low-speed streak. Vortices of alternating sign are overlapping in the streamwise direction in a staggered pattern. The present scenario is compared with transition initiated by Tollmien–Schlichting waves and their secondary instability and by-pass transition initiated by a pair of oblique waves. The relevance of this scenario to transition induced by free-stream turbulence is also discussed.

Numerical simulation of boundary-layer transition and transition control

1989 ◽  
Vol 199 ◽  
pp. 403-440 ◽  
Author(s):  
E. Laurien ◽  
L. Kleiser
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Transition Process ◽  
Numerical Results ◽  
Boundary Layer Transition ◽  
Two Dimensional ◽  
Layer Transition ◽  
Longitudinal Vortices ◽  
Tollmien Schlichting

The laminar-turbulent transition process in a parallel boundary-layer with Blasius profile is simulated by numerical integration of the three-dimensional incompressible Navier-Stokes equations using a spectral method. The model of spatially periodic disturbances developing in time is used. Both the classical Klebanoff-type and the subharmonic type of transition are simulated. Maps of the three-dimensional velocity and vorticity fields and visualizations by integrated fluid markers are obtained. The numerical results are compared with experimental measurements and flow visualizations by other authors. Good qualitative and quantitative agreement is found at corresponding stages of development up to the one-spike stage. After the appearance of two-dimensional Tollmien-Schlichting waves of sufficiently large amplitude an increasing three-dimensionality is observed. In particular, a peak-valley structure of the velocity fluctuations, mean longitudinal vortices and sharp spike-like instantaneous velocity signals are formed. The flow field is dominated by a three-dimensional horseshoe vortex system connected with free high-shear layers. Visualizations by time-lines show the formation of A-structures. Our numerical results connect various observations obtained with different experimental techniques. The initial three-dimensional steps of the transition process are consistent with the linear theory of secondary instability. In the later stages nonlinear interactions of the disturbance modes and the production of higher harmonics are essential.We also study the control of transition by local two-dimensional suction and blowing at the wall. It is shown that transition can be delayed or accelerated by superposing disturbances which are out of phase or in phase with oncoming Tollmien-Schlichting instability waves, respectively. Control is only effective if applied at an early, two-dimensional stage of transition. Mean longitudinal vortices remain even after successful control of the fluctuations.

On the Criterion for the Determination Transition Onset and Breakdown to Turbulence in Wall-Bounded Flows1

2004 ◽  
Vol 126 (4) ◽  
pp. 626-633 ◽  
Author(s):  
J. Jovanovic´ ◽  
M. Pashtrapanska
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Local Equilibrium ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Correlation Technique ◽  
Equilibrium Solutions ◽  
Onset Of Turbulence ◽  
Transition Criterion ◽  
Flat Plate Boundary Layer

Starting from the basic conservation laws of fluid flow, we investigated transition and breakdown to turbulence of a laminar flat plate boundary layer exposed to small, statistically stationary, two-component, three-dimensional disturbances. The derived equations for the statistical properties of the disturbances are closed using the two-point correlation technique and invariant theory. By considering the equilibrium solutions of the modeled equations, the transition criterion is formulated in terms of a Reynolds number based on the intensity and the length scale of the disturbances. The deduced transition criterion determines conditions that guarantee maintenance of the local equilibrium between the production and the viscous dissipation of the disturbances and therefore the laminar flow regime in the flat plate boundary layer. The experimental and numerical databases for fully developed turbulent channel and pipe flows at different Reynolds numbers were utilized to demonstrate the validity of the derived transition criterion for the estimation of the onset of turbulence in wall-bounded flows.

Studies of Wake-Induced Bypass Transition of a Flat-Plate Boundary Layer: Comparisons Between Two Transition Modes Induced by Small Sphere Wake and Thin Wire Wake

2005 ◽  
Author(s):  
Ken-ichi Funazaki ◽  
Takahiro Otsuki
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Plate Boundary ◽  
Transition Process ◽  
Bypass Transition ◽  
Velocity Data ◽  
Turbulent Spot ◽  
Transition Modes ◽  
The Wire ◽  
Flat Plate Boundary Layer

This study aims at deepening the understanding of wake-induced bypass transition process of a flat-plate boundary layer using two types of wake generating objects, which are small spheres and thin wires. Main focus is on emergence of isolated turbulent spots from the influence of the wake passage over the boundary layer. Precursors of the wake-induced turbulent spot, which have not been observed in an explicit manner in any other previous studies, are also of concern in this study. It is expected that wakes from the wires are so weak that an isolated turbulent spot may be induced by the wire wake, while the position of the spot emergence varies randomly along the wire. A multi-channel sensor with 7 hot-wire probes acquires the velocity data of the flow over the flat plate subjected to the wake passage. These velocity data reveal the spot shape and spot generation rate. In addition, the existence of Klebanoff mode in this wake-affected boundary layer is examined.

Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge

2010 ◽  
Vol 653 ◽  
pp. 245-271 ◽  
Author(s):  
L.-U. SCHRADER ◽  
L. BRANDT ◽  
C. MAVRIPLIS ◽  
D. S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Three Dimensional ◽  
Low Frequency ◽  
Leading Edge ◽  
Sound Waves ◽  
Streamwise Vorticity ◽  
Low Frequencies ◽  
Free Stream Turbulence

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien–Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

Computation of Laminar-Turbulent Transition in Turbumachinery Using the Correlation Based γ-Reθ Transition Model

2010 ◽  
Author(s):  
M. E. Kelterer ◽  
R. Pecnik ◽  
W. Sanz
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Transition Process ◽  
Boundary Layer Transition ◽  
Correct Prediction ◽  
Test Cases ◽  
Transition Model ◽  
Algebraic Models ◽  
Plate Test

The accurate numerical simulation of the flow through turbomachinery depends on the correct prediction of boundary-layer transition phenomena. Especially heat transfer and skin friction investigations demand a reliable simulation of the transition process. Many models have been developed to simulate the transition process, ranging from simple algebraic models to very sophisticated transport models. But nearly all models suffer from the need to determine boundary layer parameters and from their difficult application in three-dimensional flows. Therefore, in this work the correlation based γ-Reθ transition model developed by Menter and Langtry is implemented into the in-house Reynolds-averaged Navier-Stokes solver. This model avoids the calculation of non-local parameters and is thus very suitable for three-dimensional general flow situations. Two additional transport equations, one for the intermittency and one for the momentum thickness Reynolds number, which is a criterion for the transition onset, are added to the well known SST turbulence model by Menter. Instead of the proprietary model correlations by Menter et al. the authors used correlations by other research groups within the in-house code and tested these correlations for simple flat-plate test cases. The non-satisfying results indicate a strong code dependency of the model. Therefore also in-house correlations are presented and validated. A comprehensive study of the model performance on the well known ERCOFTAC flat plate test cases is performed. After this validation the model is applied to the steady flow in a T106A and a T106 turbine cascade.

Dynamics of three-dimensional coherent structures in a flat-plate boundary layer

1994 ◽  
Vol 275 ◽  
pp. 257-283 ◽  
Author(s):  
Dietmar Rempfer ◽  
Hermann F. Fasel
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Coherent Structures ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Plate Boundary ◽  
Galerkin Projection ◽  
Power Budget ◽  
Energy Flows ◽  
Flat Plate Boundary Layer

An investigation is presented that analyses the energy flows that are connected to the dynamical behaviour of coherent structures in a transitional flat-plate boundary layer. Based on a mathematical description of the three-dimensional coherent structures of this flow as provided by the Karhunen–Loève procedure, energy equations for the coherent structures are derived by Galerkin projection of the Navier–Stokes equations in vorticity transport formulation onto the corresponding basis of eigenfunctions. In a first step, the time-averaged energy balance – showing the energy flows that support the different coherent structures and thus maintain the fluctuations of the velocity field – is considered. In a second step, the instantaneous power budget is investigated for the particularly interesting case of a coherent structure providing a prime contribution to the characteristic spike events of the transitional boundary layer. As this structure shows a strong variation in energy, the question about which mechanisms cause these variations is addressed. Our results show that the occurrence of a spike must be attributed to an autonomous event and cannot be interpreted as just an epiphenomenon of the passage of a Λ-vortex.

Sign in / Sign up

Export Citation Format

Share Document