scholarly journals Transition of unsteady velocity profiles with reverse flow

1998 ◽  
Vol 374 ◽  
pp. 251-283 ◽  
Author(s):  
DEBOPAM DAS ◽  
JAYWANT H. ARAKERI
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Pipe Flow ◽  
Boundary Layer Thickness ◽  
Reverse Flow ◽  
Boundary Layer Separation ◽  
Velocity Profiles ◽  
Transition To Turbulence ◽  
Unsteady Boundary Layer ◽  
The Stability

This paper deals with the stability and transition to turbulence of wall-bounded unsteady velocity profiles with reverse flow. Such flows occur, for example, during unsteady boundary layer separation and in oscillating pipe flow. The main focus is on results from experiments in time-developing flow in a long pipe, which is decelerated rapidly. The flow is generated by the controlled motion of a piston. We obtain analytical solutions for laminar flow in the pipe and in a two-dimensional channel for arbitrary piston motions. By changing the piston speed and the length of piston travel we cover a range of values of Reynolds number and boundary layer thickness. The velocity profiles during the decay of the flow are unsteady with reverse flow near the wall, and are highly unstable due to their inflectional nature. In the pipe, we observe from flow visualization that the flow becomes unstable with the formation of what appears to be a helical vortex. The wavelength of the instability ≃3δ where δ is the average boundary layer thickness, the average being taken over the time the flow is unstable. The time of formation of the vortices scales with the average convective time scale and is ≃39/(Δū/δ), where Δu=(umax−umin) and umax, umin and δ are the maximum velocity, minimum velocity and boundary layer thickness respectively at each instant of time. The time to transition to turbulence is ≃33/(Δū/δ). Quasi-steady linear stability analysis of the velocity profiles brings out two important results. First that the stability characteristics of velocity profiles with reverse flow near the wall collapse when scaled with the above variables. Second that the wavenumber corresponding to maximum growth does not change much during the instability even though the velocity profile does change substantially. Using the results from the experiments and the stability analysis, we are able to explain many aspects of transition in oscillating pipe flow. We postulate that unsteady boundary layer separation at high Reynolds numbers is probably related to instability of the reverse flow region.

scholarly journals Suction/Injection Effects on the Swirling Flow of a Reiner-Rivlin Fluid near a Rough Surface

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Bikash Sahoo ◽  
Sébastien Poncet ◽  
Fotini Labropulu
Keyword(s):  
Boundary Layer ◽  
Boundary Conditions ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Swirling Flow ◽  
Velocity Profiles ◽  
Partial Slip ◽  
Injection Velocity ◽  
Slip Boundary Conditions ◽  
Slip Boundary

The similarity equations for the Bödewadt flow of a non-Newtonian Reiner-Rivlin fluid, subject to uniform suction/injection, are solved numerically. The conventional no-slip boundary conditions are replaced by corresponding partial slip boundary conditions, owing to the roughness of the infinite stationary disk. The combined effects of surface slip (λ), suction/injection velocity (W), and cross-viscous parameter (L) on the momentum boundary layer are studied in detail. It is interesting to find that suction dominates the oscillations in the velocity profiles and decreases the boundary layer thickness significantly. On the other hand, injection has opposite effects on the velocity profiles and the boundary layer thickness.

Spatio–temporal instability in mixed convection boundary layers

2000 ◽  
Vol 402 ◽  
pp. 89-107 ◽  
Author(s):  
P. MORESCO ◽  
J. J. HEALEY
Keyword(s):  
Boundary Layer ◽  
Reverse Flow ◽  
Temporal Stability ◽  
Leading Edge ◽  
Boundary Layer Separation ◽  
Absolute Instability ◽  
Limiting Similarity ◽  
Buoyancy Forces ◽  
Spatio Temporal ◽  
The Stability

In this work we analyse the stability properties of the flow over an isothermal, semi-infinite vertical plate, placed at zero incidence to an otherwise uniform stream at a different temperature. Near the leading edge the boundary layer resembles Blasius flow, but further downstream it approaches that of pure buoyancy-driven flow. A coordinate transformation that describes in a smooth way the evolution between these two limiting similarity states, where the viscous and buoyancy forces are respectively dominant, is used to calculate the basic flow. The stability of this flow has been investigated by making the parallel flow approximation, and using an accurate spectral method on the resulting stability equations. We show how the stability modes discussed by other authors can be followed continuously between the forced and free convection limits; in addition, new instability modes not previously reported in the literature have been found. A spatio–temporal stability analysis of these modes has been carried out to distinguish between absolute and convective instabilities. It seems that absolute instability can only occur when buoyancy forces are opposed to the free stream and when there is a region of reverse flow. Model profiles have been used in this latter case beyond the point of boundary layer separation to estimate the range of reverse flows that support absolute instability. Analysis of the Rayleigh equations for this problem suggests that the absolute instability has an inviscid origin.

Onset of natural convection in layered aquifers

2015 ◽  
Vol 767 ◽  
pp. 763-781 ◽  
Author(s):  
Don Daniel ◽  
Amir Riaz ◽  
Hamdi A. Tchelepi
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Onset Of Convection ◽  
Transient Nature ◽  
Gradient Of Permeability ◽  
Permeability Variation ◽  
Vorticity Production ◽  
The Stability

AbstractThe stability of gravitationally unstable, transient boundary layers in heterogeneous saline aquifers is examined with respect to the onset of natural convection. Permeability is assumed to vary periodically across the thickness of the aquifer. We study the interaction between permeability variation and concentration perturbations within the boundary layer. We observe that the instability decreases with an increase in the permeability variance if the boundary layer thickness is large compared with the permeability wavelength. On the other hand, when the boundary layer thickness is smaller than the permeability wavelength, the behaviour of instability as a function of variance depends on the phase of permeability variation. Such behaviours are shown to result from the interaction of two modes of vorticity production related to the coupling of concentration and velocity perturbations with the magnitude and gradient of permeability variation, respectively. We show that these two modes of vorticity production, when coupled with the transient nature of the boundary layer, determine the evolutionary paths followed by the most amplified perturbations that trigger the onset of convection. When the permeability variance is large, we find that small changes in the permeability field can lead to large changes in the onset times for convection.

Rapid Transition to Turbulence in Pipe Flows Accelerated From Rest

2003 ◽  
Vol 125 (6) ◽  
pp. 1072-1075 ◽  
Author(s):  
David Greenblatt ◽  
Edward A. Moss
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Laminar Boundary Layer ◽  
Pipe Flow ◽  
Velocity Profiles ◽  
Transition To Turbulence ◽  
Acceleration Phase ◽  
Pipe Flows ◽  
Rapid Transition ◽  
Rapid Deceleration

Rapid transition to turbulence in a pipe flow, initially at rest, was achieved by temporally accelerating the flow and then sharply decelerating it to its final Reynolds number. The acceleration phase was characterized by the growth of a laminar boundary layer close to the wall. The subsequent rapid deceleration resulted in inflectional velocity profiles near the wall, followed immediately by transition to turbulence. The time taken to transition was significantly less than the time to transition in a pipe flow monotonically accelerated to the same Reynolds number. Transition is intrinsically different to that observed in oscillatory pipe flows, but is qualitatively similar to pipe flows decelerated to rest.

Influence of boundary-layer disturbances on the instability of a roughness wake in a high-speed boundary layer

2014 ◽  
Vol 763 ◽  
pp. 136-165 ◽  
Author(s):  
Nicola De Tullio ◽  
Neil D. Sandham
Keyword(s):  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layers ◽  
Boundary Layer Thickness ◽  
High Speed ◽  
Stokes Equations ◽  
Roughness Element ◽  
Transition To Turbulence ◽  
Local Boundary ◽  
Wake Modes

AbstractThe excitation of instability modes in the wake generated behind a discrete roughness element in a boundary layer at Mach 6 is analysed through numerical simulations of the compressible Navier–Stokes equations. Recent experimental observations show that transition to turbulence in high-speed boundary layers during re-entry flight is dominated by wall roughness effects. Therefore, understanding the roughness-induced transition to turbulence in this flow regime is of primary importance. Our results show that a discrete roughness element with a height of about half the local boundary-layer thickness generates an unstable wake able to sustain the growth of a number of modes. The most unstable of these modes are a sinuous mode (mode SL) and two varicose modes (modes VL and VC). The varicose modes grow approximately 17 % faster than the most unstable Mack mode and their growth persists over a longer streamwise distance, thereby leading to a notable acceleration of the laminar–turbulent transition process. Two main mechanisms are identified for the excitation of wake modes: the first is based on the interaction between the external disturbances and the reverse flow regions induced by the roughness element and the second is due to the interaction between the boundary-layer modes (first modes and Mack modes) and the non-parallel roughness wake. An important finding of the present study is that, while being less unstable, mode SL is the preferred instability for the first of the above excitation mechanisms, which drives the wake modes excitation in the absence of boundary-layer modes. Modes VL and VC are excited through the second mechanism and, hence, become important when first modes and Mack modes come into interaction with the roughness wake. The new mode VC presents similarities with the Mack mode instability, including the tuning between its most unstable wavelength and the local boundary-layer thickness, and it is believed to play a fundamental role in the roughness-induced transition of high-speed boundary layers. In contrast to the smooth-wall case, wall cooling is stabilising for all the roughness-wake modes.

scholarly journals Turbulent theory of velocity-profile-induced jet breakup

2019 ◽  
Author(s):  
Ben Trettel
Keyword(s):  
Boundary Layer ◽  
Velocity Profile ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Turbulent Jets ◽  
Velocity Profiles ◽  
Common Belief ◽  
Integral Scale ◽  
Nozzle Length ◽  
Jet Breakup

Velocity profile relaxation is commonly believed to be a cause of jet breakup. This claim is critically reevaluated in this work. Contrary to common belief, laminar liquid jets with parabolic velocity profiles are actually more stable than laminar jets with flatter velocity profiles. This is shown using prior theory and experiments. For turbulent jets, the influence of the velocity profile is more difficult to determine. Previous experimentalists claimed to show that the velocity profile has an effect by varying the nozzle length. The claim is that the boundary layer thickness grows with nozzle length, and that the larger the boundary layer, the less stable the jet. In this work, nozzle length is shown to be a poor proxy for velocity profile effects because the turbulence intensity also increases as the nozzle length increases. Studies with this confounding were ignored in this work. Thinner boundary layers have greater shear, yet experiments have shown that if the boundary layer were made thinner (all else constant), the jet often is more stable. This is termed the "shear paradox". A potential resolution to the shear paradox is developed by considering that the area with shear also decreases as the boundary layer thickness is decreased, and by non-dimensionalizing the turbulent production rate by the dissipation. This theory shows an interaction between the integral scale and velocity profile relaxation which has not been previously discussed. The theoretical prediction that a smaller integral scale leads to more stable jets (due to increased turbulent dissipation) is shown to be somewhat consistent with the limited experimental and DNS data available.

scholarly journals Experimental and theoretical progress in pipe flow transition

2008 ◽  
Vol 366 (1876) ◽  
pp. 2671-2684 ◽  
Author(s):  
A.P Willis ◽  
J Peixinho ◽  
R.R Kerswell ◽  
T Mullin
Keyword(s):  
Pipe Flow ◽  
Quantitative Agreement ◽  
Travelling Wave ◽  
Turbulent Pipe Flow ◽  
Transition To Turbulence ◽  
Reynolds Number Flow ◽  
Threshold Amplitude ◽  
Number Flow ◽  
The Stability ◽  
Laminar State

There have been many investigations of the stability of Hagen–Poiseuille flow in the 125 years since Osborne Reynolds' famous experiments on the transition to turbulence in a pipe, and yet the pipe problem remains the focus of attention of much research. Here, we discuss recent results from experimental and numerical investigations obtained in this new century. Progress has been made on three fundamental issues: the threshold amplitude of disturbances required to trigger a transition to turbulence from the laminar state; the threshold Reynolds number flow below which a disturbance decays from turbulence to the laminar state, with quantitative agreement between experimental and numerical results; and understanding the relevance of recently discovered families of unstable travelling wave solutions to transitional and turbulent pipe flow.

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