scholarly journals Localised streak solutions for a Blasius boundary layer

2018 ◽  
Vol 849 ◽  
pp. 885-901 ◽  
Author(s):  
Richard E. Hewitt ◽  
Peter W. Duck
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Theoretical Work ◽  
Spanwise Direction ◽  
Growth Mechanisms ◽  
Boundary Layer Flows ◽  
Periodic Disturbances ◽  
Blasius Boundary Layer ◽  
Global Nature ◽  
Field Decay

Streaks are a common feature of disturbed boundary-layer flows. They play a central role in transient growth mechanisms and are a building block of self-sustained structures. Most theoretical work has focused on streaks that are periodic in the spanwise direction, but in this work we consider a single spatially localised streak embedded into a Blasius boundary layer. For small streak amplitudes, we show the perturbation can be described in terms of a set of eigenmodes that correspond to an isolated streak/roll structure. These modes are new, and arise from a bi-global eigenvalue calculation; they decay algebraically downstream and may be viewed as the natural three-dimensional extension of the classical two-dimensional Libby & Fox (J. Fluid Mech., vol. 17 (3), 1963, pp. 433–449) solutions. Despite their bi-global nature, we show that a subset of these eigenmodes (including the slowest decaying) is fundamentally related to the solutions first presented by Luchini (J. Fluid Mech., vol. 327, 1996, pp. 101–116), as derived for spanwise-periodic disturbances (at small spanwise wavenumber). This surprising connection is made by an analysis of the far-field decay of the bi-global state. We also address the fully non-parallel downstream development of nonlinear streaks, confirming that the aforementioned eigenmodes are recovered as the streak/roll decays downstream. Encouraging comparisons are made with available experimental data.

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

An Assessment of Three-Dimensional Turbulent Boundary Layer Prediction Methods

1973 ◽  
Vol 95 (3) ◽  
pp. 415-421 ◽  
Author(s):  
A. J. Wheeler ◽  
J. P. Johnston
Keyword(s):  
Boundary Layer ◽  
Eddy Viscosity ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Boundary Layer Flows ◽  
Mean Velocity ◽  
Eddy Viscosity Model ◽  
Separating Flow ◽  
Dimensional Boundary ◽  
Stress Models

Predictions have been made for a variety of experimental three-dimensional boundary layer flows with a single finite difference method which was used with three different turbulent stress models: (i) an eddy viscosity model, (ii) the “Nash” model, and (iii) the “Bradshaw” model. For many purposes, even the simplest stress model (eddy viscosity) was adequate to predict the mean velocity field. On the other hand, the profile of shear stress direction was not correctly predicted in one case by any model tested. The high sensitivity of the predicted results to free stream pressure gradient in separating flow cases is demonstrated.

Rotating Flow Over a Disk Sector

1982 ◽  
Vol 49 (1) ◽  
pp. 13-18
Author(s):  
M. Toren ◽  
A. Solan ◽  
M. Ungarish
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Rotating Flow ◽  
Radial Coordinate ◽  
Large Radius ◽  
Full Circle ◽  
Blasius Boundary Layer ◽  
Layer Flow ◽  
Rotating Boundary ◽  
Limiting Values

The rotating boundary layer flow over a plane sector of angle θs and infinite radius is solved. For sufficiently large radius the radial coordinate is eliminated by a Von Karman transformation, leaving a nonaxisymmetric flow in (θ,z), which cyclically changes over the full circle, from a Blasius boundary layer, to a Bodewadt flow, and to a rotating wake. Leading terms of the three-dimensional perturbation of the Blasius flow, and of the rotating wake are given, and the matching over the full circle is outlined for limiting values of θs.

Three-Dimensional Calculation of Wall Boundary Layer Flows in Turbomachines

1987 ◽  
Author(s):  
W. L. Lindsay ◽  
H. B. Carrick ◽  
J. H. Horlock
Keyword(s):  
Boundary Layer ◽  
Flow Analysis ◽  
Three Dimensional ◽  
Cross Flow ◽  
Flow Profile ◽  
Boundary Layer Flows ◽  
Wall Boundary Layer ◽  
Boundary Layer Development ◽  
Flow Through ◽  
The Cross

An integral method of calculating the three-dimensional turbulent boundary layer development through the blade rows of turbomachines is described. It is based on the solution of simultaneous equations for (i) & (ii) the growth of streamwise and cross-flow momentum thicknesses; (iii) entrainment; (iv) the wall shear stress; (v) the position of maximum cross-flow. The velocity profile of the streamwise boundary layer is assumed to be that described by Coles. The cross-flow profile is assumed to be the simple form suggested by Johnston, but modified by the effect of bounding blade surfaces, which restrict the cross-flow. The momentum equations include expressions for “force-defect” terms which are also based on secondary flow analysis. Calculations of the flow through a set of guide vanes of low deflection show good agreement with experimental results; however, attempts to calculate flows of higher deflection are found to be less successful.

Algebraic disturbance growth by interaction of Orr and lift-up mechanisms

2017 ◽  
Vol 829 ◽  
pp. 112-126 ◽  
Author(s):  
M. J. Philipp Hack ◽  
Parviz Moin
Keyword(s):  
Boundary Layer ◽  
Linear Trend ◽  
Optimization Approach ◽  
Finite Frequency ◽  
Boundary Layer Flows ◽  
Limited Region ◽  
Blasius Boundary Layer ◽  
Streamwise Pressure Gradient ◽  
Simultaneous Activity ◽  
Disturbance Growth

Algebraic disturbance growth in spatially developing boundary-layer flows is investigated using an optimization approach. The methodology builds on the framework of the parabolized stability equations and avoids some of the limitations associated with adjoint-based schemes. In the Blasius boundary layer, non-parallel effects are shown to significantly enhance the energy gain due to algebraic growth mechanisms. In contrast to parallel flow, the most energetic perturbations have finite frequency and are generated by the simultaneous activity of the Orr and lift-up mechanisms. The highest amplification occurs in a limited region of the parameter space that is characterized by a linear relation between the wavenumber and frequency of the disturbances. The frequency of the most highly amplified perturbations decreases with Reynolds number. Adverse streamwise pressure gradient further enhances the amplification of disturbances while preserving the linear trend between the wavenumber and frequency of the most energetic perturbations.

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