Finite amplitude steady waves in the Blasius boundary layer

1993 ◽  
Vol 5 (7) ◽  
pp. 1840-1842 ◽  
Author(s):  
James M. Rotenberry
Keyword(s):  
Boundary Layer ◽  
Finite Amplitude ◽  
Blasius Boundary Layer

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 Initial Value Method for the Solution of a Class of Nonlinear Equations in Fluid Mechanics

1970 ◽  
Vol 92 (3) ◽  
pp. 503-508 ◽  
Author(s):  
T. Y. Na
Keyword(s):  
Differential Equation ◽  
Boundary Layer ◽  
Porous Medium ◽  
Fluid Mechanics ◽  
Boundary Layer Equation ◽  
Physical Parameters ◽  
Point Boundary ◽  
Trial And Error ◽  
Initial Value ◽  
Blasius Boundary Layer

An initial value method is introduced in this paper for the solution of a class of nonlinear two-point boundary value problems. The method can be applied to the class of equations where certain physical parameters appear either in the differential equation or in the boundary conditions or both. Application of this method to two problems in Fluid Mechanics, namely, Blasius’ boundary layer equation with suction (or blowing) and/or slip and the unsteady flow of a gas through a porous medium, are presented as illustrations of this method. The trial-and-error process usually required for the solution of such equations is eliminated.

scholarly journals Finite-amplitude steady waves in plane viscous shear flows

1985 ◽  
Vol 160 ◽  
pp. 281-295 ◽  
Author(s):  
F. A. Milinazzo ◽  
P. G. Saffman
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Linear Instability ◽  
Navier Stokes ◽  
Unidirectional Flow ◽  
Viscous Shear ◽  
Finite Amplitude Waves

Computations of two-dimensional solutions of the Navier–Stokes equations are carried out for finite-amplitude waves on steady unidirectional flow. Several cases are considered. The numerical method employs pseudospectral techniques in the streamwise direction and finite differences on a stretched grid in the transverse direction, with matching to asymptotic solutions when unbounded. Earlier results for Poiseuille flow in a channel are re-obtained, except that attention is drawn to the dependence of the minimum Reynolds number on the physical constraint of constant flux or constant pressure gradient. Attempts to calculate waves in Couette flow by continuation in the velocity of a channel wall fail. The asymptotic suction boundary layer is shown to possess finite-amplitude waves at Reynolds numbers orders of magnitude less than the critical Reynolds number for linear instability. Waves in the Blasius boundary layer and unsteady Rayleigh profile are calculated by employing the artifice of adding a body force to cancel the spatial or temporal growth. The results are verified by comparison with perturbation analysis in the vicinity of the linear-instability critical Reynolds numbers.

Stability of Flat Plate Boundary Layer Over Compliant Coating with Increased Rigidity

2011 ◽  
Vol 6 (4) ◽  
pp. 25-41
Author(s):  
Andrey Boiko ◽  
Viktor Kulik ◽  
V. Filimonov
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Viscoelastic Properties ◽  
Loss Factor ◽  
Plate Boundary ◽  
Single Layer ◽  
Interface Conditions ◽  
Compliant Coating ◽  
Blasius Boundary Layer ◽  
Flat Plate Boundary Layer

In the paper the results of hydrodynamic stability computations for Blasius boundary layer over single-layer compliant coatings in the framework of complete (in respect to interface conditions) linear quasi-parallel approach are presented. Data on viscoelastic properties (elastic modulus and loss factor) of the coatings as functions of frequency obtained in a series of special experiments were used. A range of the coating parameters, which provide a compromise between their rigidity and intensity of interaction with the flow, was determined. Based on en -method, estimations of the transition Reynolds number were done

Stabilization of the hypersonic boundary layer by finite-amplitude streaks

2016 ◽  
Vol 28 (2) ◽  
pp. 024110 ◽  
Author(s):  
Jie Ren ◽  
Song Fu ◽  
Ardeshir Hanifi
Keyword(s):  
Boundary Layer ◽  
Finite Amplitude ◽  
Hypersonic Boundary Layer

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.

scholarly journals Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary Layer

2021 ◽  
Vol 9 (2) ◽  
pp. 35-41
Author(s):  
Manisha Patel ◽  
Hema Surati ◽  
M G Timol
Keyword(s):  
Boundary Layer ◽  
Similarity Solutions ◽  
Power Law Model ◽  
Prandtl Model ◽  
Blasius Boundary Layer ◽  
Blasius Equation ◽  
Boundary Layer Problems ◽  
The One ◽  
Graphical Presentation ◽  
Theory Technique

Blasius equation is very well known and it aries in many boundary layer problems of fluid dynamics. In this present article, the Blasius boundary layer is extended by transforming the stress strain term from Newtonian to non-Newtonian. The extension of Blasius boundary layer is discussed using some non-newtonian fluid models like, Power-law model, Sisko model and Prandtl model. The Generalised governing partial differential equations for Blasius boundary layer for all above three models are transformed into the non-linear ordinary differewntial equations using the one parameter deductive group theory technique. The obtained similarity solutions are then solved numerically. The graphical presentation is also explained for the same. It concludes that velocity increases more rapidly when fluid index is moving from shear thickninhg to shear thininhg fluid.MSC 2020 No.: 76A05, 76D10, 76M99

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