A model for subharmonic resonance within wavepackets in unstable boundary layers

2001 ◽  
Vol 432 ◽  
pp. 409-418 ◽  
Author(s):  
A. D. D. CRAIK
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Initial Phase ◽  
Nonlinear Effects ◽  
Subharmonic Resonance ◽  
Simple Explanation ◽  
Resonance Mechanism ◽  
Space And Time ◽  
Wave Resonance ◽  
Blasius Boundary Layer

In recent experiments on the growth of localized disturbances in a Blasius boundary layer, Medeiros & Gaster (1999a, b) observed that the development of nonlinear effects depends markedly on the initial phase of their imposed disturbance. Here, a simple explanation of this phenomenon is proposed. Because the disturbance is localized in space and time, it has a spread of wavenumbers and frequencies: among these are components which can initiate a pair of resonant subharmonic waves with well-determined phase, which are then amplified by the familiar three-wave resonance mechanism. The amplitude attained after some time is strongly phase-dependent, consistent with the experimental observations.

scholarly journals Influence of initial phase on subharmonic resonance in an incompressible boundary layer

2021 ◽  
Vol 33 (4) ◽  
pp. 044101
Author(s):  
Donghun Park ◽  
Jaeyoung Park ◽  
Minwoo Kim ◽  
Jiseop Lim ◽  
Seungtae Kim ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Initial Phase ◽  
Subharmonic Resonance ◽  
Incompressible Boundary Layer ◽  
Incompressible Boundary

Classical Boundary-Layer Theory

2018 ◽  
Author(s):  
Anatoly I. Ruban
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Boundary Layer Theory ◽  
Laminar Jet ◽  
Compressible Boundary Layers ◽  
Wedge Surface ◽  
Blasius Boundary Layer ◽  
Classical Boundary ◽  
Fast Rotating

Chapter 1 discusses the flows that can be described in the framework of Prandtl’s 1904 classical boundary-layer theory, including the Blasius boundary layer on a flat plate and the Falkner–Skan solutions for the boundary layer on a wedge surface. It presents Schlichting’s solution for the laminar jet and Tollmien’s solution for the viscous wake. These are followed by analysis of Chapman’s shear layer performed with the help of Prandtl’s transposition theorem. It also considers the boundary layer on the surface of a fast rotating cylinder with the purpose of linking the circulation around the cylinder with the speed of its rotation. It concludes discussion of the classical boundary-layer theory with analysis of compressible boundary layers, including the interactive boundary layers in hypersonic flows.

Simplified Analysis of Boundary-Layer Oscillations

1960 ◽  
Vol 4 (03) ◽  
pp. 37-54
Author(s):  
Robert Betchov
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Nonlinear Effects ◽  
Adverse Pressure Gradient ◽  
Neutral Curves ◽  
Elastic Wall ◽  
Unstable Boundary Layer ◽  
Incompressible Boundary ◽  
Negative Damping ◽  
The Stability

The stability of an incompressible boundary layer is analyzed in terms of three basic processes. These are (a) the oscillations of a boundary layer when friction is disregarded, (b) the effects of friction at the wall, and (c) the effects of friction at the critical layer. These processes are separately discussed and evaluated. Simple models are presented. A general equation leads to the eigenvalues. The neutral curves corresponding to five typical cases are determined—parabolic and Blasius boundary layers, boundary layers with suction and with adverse pressure gradient, two-dimensional Poiseuille flow. The unstable boundary layer is discussed briefly. The nonlinear effects of the oscillation on the velocity profile are evaluated. Finally, the case of a boundary layer along an elastic wall is considered, and it is found that the wall may have a significant effect on the layer. In particular, a wall with negative damping could completely stabilize the boundary layer.

Linear and nonlinear stability of the Blasius boundary layer

1992 ◽  
Vol 242 ◽  
pp. 441-474 ◽  
Author(s):  
F. P. Bertolotti ◽  
Th. Herbert ◽  
P. R. Spalart
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Parabolic Type ◽  
Nonlinear Effects ◽  
Neutral Curve ◽  
Mean Flow ◽  
Buffer Zones ◽  
Navier Stokes Equation ◽  
Blasius Boundary Layer ◽  
Linear And Nonlinear

Two new techniques for the study of the linear and nonlinear instability in growing boundary layers are presented. The first technique employs partial differential equations of parabolic type exploiting the slow change of the mean flow, disturbance velocity profiles, wavelengths, and growth rates in the streamwise direction. The second technique solves the Navier–Stokes equation for spatially evolving disturbances using buffer zones adjacent to the inflow and outflow boundaries. Results of both techniques are in excellent agreement. The linear and nonlinear development of Tollmien–Schlichting (TS) waves in the Blasius boundary layer is investigated with both techniques and with a local procedure based on a system of ordinary differential equations. The results are compared with previous work and the effects of non-parallelism and nonlinearly are clarified. The effect of nonparallelism is confirmed to be weak and, consequently, not responsible for the discrepancies between measurements and theoretical results for parallel flow. Experimental uncertainties, the adopted definition of the growth rate, and the transient initial evolution of the TS wave in vibrating-ribbon experiments probably cause the discrepancies. The effect of nonlinearity is consistent with previous weakly nonlinear theories. White nonlinear effects are small near branch I of the neutral curve, they are significant near branch II and delay or event prevent the decay of the wave.

scholarly journals Effects of phase difference between instability modes on boundary-layer transition

2021 ◽  
Vol 927 ◽  
Author(s):  
Minwoo Kim ◽  
Seungtae Kim ◽  
Jiseop Lim ◽  
Ray-Sing Lin ◽  
Solkeun Jee ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Phase Difference ◽  
Fundamental Mode ◽  
Initial Phase ◽  
Subharmonic Resonance ◽  
Boundary Layer Transition ◽  
Modal Interaction ◽  
Initial Phase Difference ◽  
Nonlinear Stage ◽  
Instability Modes

Phase effect on the modal interaction of flow instabilities is investigated for laminar-to-turbulent transition in a flat-plate boundary-layer flow. Primary and secondary three-dimensional (3-D) oblique waves at various initial phase differences between these two instability modes. Three numerical methods are used for a systematic approach for the entire transition process, i.e. before the onset of transition well into fully turbulent flow. Floquet analysis predicts the subharmonic resonance where a subharmonic mode locally resonates for a given basic flow composed of the steady laminar flow and the fundamental mode. Because Floquet analysis is limited to the resonating subharmonic mode, nonlinear parabolised stability equation analysis (PSE) is conducted with various phase shifts of the subharmonic mode with respect to the given fundamental mode. The application of PSE offers insights on the modal interaction affected by the phase difference up to the weakly nonlinear stage of transition. Large-eddy simulation (LES) is conducted for a complete transition to turbulent boundary layer because PSE becomes prohibitively expensive in the late nonlinear stage of transition. The modulation of the subharmonic resonance with the initial phase difference leads to a significant delay in the transition location up to $\Delta Re_{x, tr} \simeq 4\times 10^5$ as predicted by the current LES. Effects of the initial phase difference on the spatial evolution of the modal shape of the subharmonic mode are further investigated. The mechanism of the phase evolution is discussed, based on current numerical results and relevant literature data.

The Departure from Equilibrium of Turbulent Boundary Layers

1968 ◽  
Vol 19 (1) ◽  
pp. 1-19 ◽  
Author(s):  
H. McDonald
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Kinetic Energy ◽  
Stress Distribution ◽  
Boundary Layers ◽  
Turbulent Boundary Layers ◽  
Two Dimensional ◽  
Pressure Distributions ◽  
Momentum Integral ◽  
State Examination

SummaryRecently two authors, Nash and Goldberg, have suggested, intuitively, that the rate at which the shear stress distribution in an incompressible, two-dimensional, turbulent boundary layer would return to its equilibrium value is directly proportional to the extent of the departure from the equilibrium state. Examination of the behaviour of the integral properties of the boundary layer supports this hypothesis. In the present paper a relationship similar to the suggestion of Nash and Goldberg is derived from the local balance of the kinetic energy of the turbulence. Coupling this simple derived relationship to the boundary layer momentum and moment-of-momentum integral equations results in quite accurate predictions of the behaviour of non-equilibrium turbulent boundary layers in arbitrary adverse (given) pressure distributions.

Laminar boundary layers behind detonation waves

1983 ◽  
Vol 387 (1793) ◽  
pp. 331-349 ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Flow Analysis ◽  
Time Dependent ◽  
Detonation Waves ◽  
Planar Geometry ◽  
Laminar Boundary Layers ◽  
Spherical Detonation ◽  
Layer Flow

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

scholarly journals Computational Modeling of Boundary Layer Flashback in a Swirling Stratified Flame Using a LES-Based Non-Adiabatic Tabulated Chemistry Approach

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 567
Author(s):  
Xudong Jiang ◽  
Yihao Tang ◽  
Zhaohui Liu ◽  
Venkat Raman
Keyword(s):  
Boundary Layer ◽  
Heat Loss ◽  
Boundary Layers ◽  
Gas Turbines ◽  
Predictive Accuracy ◽  
Safety Issue ◽  
Combustion Model ◽  
Tabulated Chemistry ◽  
Lean Fuel ◽  
Flame Flashback

When operating under lean fuel–air conditions, flame flashback is an operational safety issue in stationary gas turbines. In particular, with the increased use of hydrogen, the propagation of the flame through the boundary layers into the mixing section becomes feasible. Typically, these mixing regions are not designed to hold a high-temperature flame and can lead to catastrophic failure of the gas turbine. Flame flashback along the boundary layers is a competition between chemical reactions in a turbulent flow, where fuel and air are incompletely mixed, and heat loss to the wall that promotes flame quenching. The focus of this work is to develop a comprehensive simulation approach to model boundary layer flashback, accounting for fuel–air stratification and wall heat loss. A large eddy simulation (LES) based framework is used, along with a tabulation-based combustion model. Different approaches to tabulation and the effect of wall heat loss are studied. An experimental flashback configuration is used to understand the predictive accuracy of the models. It is shown that diffusion-flame-based tabulation methods are better suited due to the flashback occurring in relatively low-strain and lean fuel–air mixtures. Further, the flashback is promoted by the formation of features such as flame tongues, which induce negative velocity separated boundary layer flow that promotes upstream flame motion. The wall heat loss alters the strength of these separated flows, which in turn affects the flashback propensity. Comparisons with experimental data for both non-reacting cases that quantify fuel–air mixing and reacting flashback cases are used to demonstrate predictive accuracy.

scholarly journals Development of Depth-Limited Wave Boundary Layers over a Smooth Bottom

2020 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Hitoshi Tanaka ◽  
Nguyen Xuan Tinh ◽  
Xiping Yu ◽  
Guangwei Liu
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Boundary Layers ◽  
Wave Motion ◽  
Numerical Study ◽  
Experiment Data ◽  
Tidal Motion ◽  
Long Period ◽  
Simulation Results ◽  
Wave Boundary

A theoretical and numerical study is carried out to investigate the transformation of the wave boundary layer from non-depth-limited (wave-like boundary layer) to depth-limited one (current-like boundary layer) over a smooth bottom. A long period of wave motion is not sufficient to induce depth-limited properties, although it has simply been assumed in various situations under long waves, such as tsunami and tidal currents. Four criteria are obtained theoretically for recognizing the inception of the depth-limited condition under waves. To validate the theoretical criteria, numerical simulation results using a turbulence model as well as laboratory experiment data are employed. In addition, typical field situations induced by tidal motion and tsunami are discussed to show the usefulness of the proposed criteria.

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.

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