scholarly journals Enhanced effects from tiny flexible in-wall blips and shear flow

2015 ◽  
Vol 772 ◽  
pp. 16-41 ◽  
Author(s):  
Luisa Pruessner ◽  
Frank Smith
Keyword(s):  
Boundary Layer ◽  
Interactive Effect ◽  
Fluid Motion ◽  
Unsteady Motion ◽  
Local Motion ◽  
Second Stage ◽  
Order Of Magnitude ◽  
High Reynolds ◽  
Parameter Values ◽  
Nonlinear Solutions

Fluid motion at high Reynolds number over a flexible in-wall blip (a compliant bump or dip in an otherwise fixed wall) is considered theoretically for a very short blip buried low inside a boundary layer. Only the near-wall shear of the oncoming flow affects the local motion past the tiny blip. Slowly evolving features are examined first to allow for variations in the incident flow. Linear and nonlinear solutions show that at certain parameter values (eigenvalues) intensifications occur in which the interactive effect on flow and blip shape is larger by an order of magnitude than at most parameter values. Similar findings apply to the boundary layer with several tiny blips present or to channel flows with blips of almost any length. These intensifications lead on to fully nonlinear unsteady motion as a second stage, after some delay, thus combining with finite-time breakups to form a distinct path into transition of the flow.

Steady motion through a branching tube

1977 ◽  
Vol 355 (1681) ◽  
pp. 167-187 ◽  
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Cross Sections ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Steady Motion ◽  
Nonlinear Behaviour ◽  
Initial Development ◽  
Secondary Motion ◽  
High Reynolds

The fluid motion through a straight pipe that bifurcates symmetrically into two semi-circular pipes is considered at high Reynolds numbers, with the aim of deriving some of the effects of the three-dimensionality per se. In a corresponding planar problem the long-scale boundary layer approach yields the initial development of the induced pressure gradient fairly directly, the problem being linear. By contrast, in the three-dimensional situation the favourable pressure gradient is determined by a nonlinear eigenvalue relation, because the pressure gradient is much stronger here and interacts critically with the inviscid coreflow to produce nonlinear behaviour near the outer walls. The proposed structure of the initial part of the boundary layer is apparently self-consistent, with a two-tiered development near the outer walls where the secondary motion is of a relatively fast vortex type and the axial skin friction suffers a sharp increase. The secondary coreflow is a displacement-induced streaming combined with a vortex provoked by the pressure gradient. The analysis applies for any realistic oncoming flow in the single tube and can be extended to treat other tube cross-sections.

Receptivity of boundary layers to distributed wall vibrations

2005 ◽  
Vol 363 (1830) ◽  
pp. 1145-1155 ◽  
Author(s):  
Ruslan M Kerimbekov ◽  
Anatoly I Ruban
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Resonance Region ◽  
The Body ◽  
Large Reynolds Number ◽  
Order Of Magnitude ◽  
Tollmien Schlichting ◽  
Amplitude Growth

Linear three-dimensional receptivity of boundary layers to distributed wall vibrations in the large Reynolds number limit ( Re →∞) is studied in this paper. The fluid motion is analysed by means of the multiscale asymptotic technique combined with the method of matched asymptotic expansions. The body surface is assumed to be perturbed by small-amplitude oscillations being tuned in resonance with the neutral Tollmien–Schlichting wave at a certain point on the wall. The characteristic length of the resonance region is found to be O( Re −3/16 ), which follows from the condition that the boundary-layer non-parallelism and the wave amplitude growth have the same order of magnitude. The amplitude equation is derived as a solvability condition for the inhomogeneous boundary-value problem. Investigating detuning effects, we consider perturbations in the form of a wave packet with a narrow O( Re −3/16 ) discrete or continuous spectrum concentrated near the resonant wavenumber and frequency. The boundary-layer laminarization based on neutralizing the oncoming Tollmien–Schlichting waves (or wave packets) is also discussed.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

‘Inactive’ motion and pressure fluctuations in turbulent boundary layers

1967 ◽  
Vol 30 (2) ◽  
pp. 241-258 ◽  
Author(s):  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Outer Layer ◽  
Pressure Fluctuations ◽  
Turbulent Energy ◽  
Viscous Sublayer ◽  
Wave Number ◽  
Noticeable Effect ◽  
Frequency Spectra ◽  
Active Motion ◽  
Order Of Magnitude

Townsend's (1961) hypothesis that the turbulent motion in the inner region of a boundary layer consists of (i) an ‘active’ part which produces the shear stress τ and whose statistical properties are universal functions of τ and y, and (ii) an ‘inactive’ and effectively irrotational part determined by the turbulence in the outer layer, is supported in the present paper by measurements of frequency spectra in a strongly retarded boundary layer, in which the ‘inactive’ motion is particularly intense. The only noticeable effect of the inactive motion is an increased dissipation of kinetic energy into heat in the viscous sublayer, supplied by turbulent energy diffusion from the outer layer towards the surface. The required diffusion is of the right order of magnitude to explain the non-universal values of the triple products measured near the surface, which can therefore be reconciled with universality of the ‘active’ motion.Dimensional analysis shows that the contribution of the ‘active’ inner layer motion to the one-dimensional wave-number spectrum of the surface pressure fluctuations varies as τ2w/k1 up to a wave-number inversely proportional to the thickness of the viscous sublayer. This result is strongly supported by the recent measurements of Hodgson (1967), made with a much smaller ratio of microphone diameter to boundary-layer thickness than has been achieved previously. The disagreement of the result with most other measurements is attributed to inadequate transducer resolution in the other experiments.

Effects of Reynolds Number and Free-Stream Turbulence on Boundary Layer Transition in a Compressor Cascade

2000 ◽  
Author(s):  
Heinz-Adolf Schreiber ◽  
Wolfgang Steinert ◽  
Bernhard Küsters
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Bypass Transition ◽  
Layer Transition ◽  
Free Stream Turbulence ◽  
High Reynolds Numbers ◽  
High Turbulence ◽  
High Reynolds

An experimental and analytical study has been performed on the effect of Reynolds number and free-stream turbulence on boundary layer transition location on the suction surface of a controlled diffusion airfoil (CDA). The experiments were conducted in a rectilinear cascade facility at Reynolds numbers between 0.7 and 3.0×106 and turbulence intensities from about 0.7 to 4%. An oil streak technique and liquid crystal coatings were used to visualize the boundary layer state. For small turbulence levels and all Reynolds numbers tested the accelerated front portion of the blade is laminar and transition occurs within a laminar separation bubble shortly after the maximum velocity near 35–40% of chord. For high turbulence levels (Tu > 3%) and high Reynolds numbers transition propagates upstream into the accelerated front portion of the CDA blade. For those conditions, the sensitivity to surface roughness increases considerably and at Tu = 4% bypass transition is observed near 7–10% of chord. Experimental results are compared to theoretical predictions using the transition model which is implemented in the MISES code of Youngren and Drela. Overall the results indicate that early bypass transition at high turbulence levels must alter the profile velocity distribution for compressor blades that are designed and optimized for high Reynolds numbers.

scholarly journals Time scale of the largest imaginable magnetic storm

2013 ◽  
Vol 20 (1) ◽  
pp. 19-23 ◽  
Author(s):  
V. M. Vasyliūnas
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Magnetic Storm ◽  
Energy Content ◽  
Horizontal Magnetic Field ◽  
Order Of Magnitude ◽  
Magnetosphere Plasma ◽  
Time Required ◽  
Parameter Values ◽  
Magnetic Field Perturbation

Abstract. The depression of the horizontal magnetic field at Earth's equator for the largest imaginable magnetic storm has been estimated (Vasyliūnas, 2011a) as −Dst ~ 2500 nT, from the assumption that the total pressure in the magnetosphere (plasma plus magnetic field perturbation) is limited, in order of magnitude, by the minimum pressure of Earth's dipole field at the location of each flux tube. The obvious related question is how long it would take the solar wind to supply the energy content of this largest storm. The maximum rate of energy input from the solar wind to the magnetosphere can be evaluated on the basis either of magnetotail stress balance or of polar cap potential saturation, giving an estimate of the time required to build up the largest storm, which (for solar-wind and magnetospheric parameter values typical of observed superstorms) is roughly between ~2 and ~6 h.

Trailing-edge stall

1970 ◽  
Vol 42 (3) ◽  
pp. 561-584 ◽  
Author(s):  
S. N. Brown ◽  
K. Stewartson
Keyword(s):  
Boundary Layer ◽  
Complete Solution ◽  
Leading Edge ◽  
Asymptotic Solutions ◽  
Angle Of Incidence ◽  
Trailing Edge ◽  
Boundary Layer Equations ◽  
Order Of Magnitude ◽  
Stall Angle ◽  
Fundamental Equations

A study is made of the laminar flow in the neighbourhood of the trailing edge of an aerofoil at incidence. The aerofoil is replaced by a flat plate on the assumption that leading-edge stall has not taken place. It is shown that the critical order of magnitude of the angle of incidence α* for the occurrence of separation on one side of the plate is$\alpha^{*} = O(R^{\frac{1}{16}})$, whereRis a representative Reynolds number, for incompressible flow, and α* =O(R−¼) for supersonic flow. The structure of the flow is determined by the incompressible boundary-layer equations but with unconventional boundary conditions. The complete solution of these fundamental equations requires a numerical investigation of considerable complexity which has not been undertaken. The only solutions available are asymptotic solutions valid at distances from the trailing edge that are large in terms of the scaled variable of orderR−⅜, and a linearized solution for the boundary layer over the plate which gives the antisymmetric properties of the aerofoil at incidence. The value of α* for which separation occurs is the trailing-edge stall angle and an estimate is obtained from the asymptotic solutions. The linearized solution yields an estimate for the viscous correction to the circulation determined by the Kutta condition.

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