scholarly journals Couette-Poiseuille flow experiment with zero mean advection velocity: Subcritical transition to turbulence

2017 ◽  
Vol 2 (4) ◽  
Author(s):  
L. Klotz ◽  
G. Lemoult ◽  
I. Frontczak ◽  
L. S. Tuckerman ◽  
J. E. Wesfreid
Keyword(s):  
Poiseuille Flow ◽  
Transition To Turbulence ◽  
Flow Experiment ◽  
Advection Velocity

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.

The Differentiation Method in Rheology: III. Couette Flow

1963 ◽  
Vol 3 (01) ◽  
pp. 14-18 ◽  
Author(s):  
J.G. Savins ◽  
G.C. Wallick ◽  
W.R. Foster
Keyword(s):  
Integral Equation ◽  
Difference Equation ◽  
Yield Stress ◽  
Couette Flow ◽  
Yield Point ◽  
Poiseuille Flow ◽  
Shearing Stress ◽  
Differentiation Method ◽  
Type Flow ◽  
Flow Experiment

Abstract The theory of the differentiation method for the Couette flow experiment is reviewed. Particular attention is given to the requirements on data analyses in the case of the class of non-Newtonian materials described as viscoplastics, i. e., materials characterized by a yield point or yield stress. Here, changes in boundary conditions arise when the shearing stress attains a critical value with the result that the form of the basic integral equation for Couette flow is determined by the flow conditions existing during the measurement. Introduction In the preceding papers in this series, the salient features of the differentiation method of rheological analysis in Poiseuille-type flow were discussed. It was shown that a dual differentiation- integration method analysis of the Poiseuille flow of idealized generalized Newtonian and visco-plastic models could be used to develop a spectrum of highly sensitive response patterns in terms of certain characteristic derivative functions. These functions were shown to optimize the selection of the most appropriate functional relationship between f(p) and p from the Poiseuille flow experiment. The present paper reviews the theory of the differentiation method as applied to the equally important Couette flow experiment. We will also discuss the range of variables over which the basic integral equation for Couette flow is applicable when the non-Newtonian material is of the viscoplastic type, i.e., characterized by a yield point or yield stress. THEORY Having described the application of the differentiation method to Poiseuille-type flow in the preceding papers, we now proceed to the case where the test liquid is confined to the annular space between coaxial cylinders of length L, one of which is in motion, i.e., Couette flow, formulating the basic integral equation after the method of Mooney. The observed kinematical and dynamical quantities are the angular velocityand the torque T. Here, the one nonvanishing component of the shear-rate tensor is ........................(1) and the corresponding component of the shearing-stress tensor at any point r is given by ..........................(2) The shearing stresses at the inner surface of radius R(1) and the outer surface of radius R(2) are related by .................(3) Combining Eqs. 1, 2 and 3, letting = 0 at p = p1 and = at p = p2 and integrating yield .........................(4) Note that the definite integral has a finite lower limit. Differentiating Eq. 4 with respect to p1, following the rule of Leibnitz (i.e., in Eq. 11 of Ref. 1), gives a difference equation in the desired function ..................(5) This result was initially obtained by Mooney who used it as a starting point for an approximate solution. Several other approximate solutions of the difference equation have been described, the principal results of which are described in the succeeding sections. The interested reader is referred to the original papers for the details. SPEJ P. 14^

scholarly journals Observation of laminar–turbulent transition of a yield stress fluid in Hagen–Poiseuille flow

2009 ◽  
Vol 627 ◽  
pp. 97-128 ◽  
Author(s):  
B. GÜZEL ◽  
T. BURGHELEA ◽  
I. A. FRIGAARD ◽  
D. M. MARTINEZ
Keyword(s):  
Yield Stress ◽  
Poiseuille Flow ◽  
High Speed ◽  
Shear Thinning ◽  
Transition To Turbulence ◽  
Reynolds Stresses ◽  
High Speed Imaging ◽  
Yield Stress Fluid ◽  
Turbulent Transition ◽  
Shear Thinning Fluid

We investigate experimentally the transition to turbulence of a yield stress shear-thinning fluid in Hagen–Poiseuille flow. By combining direct high-speed imaging of the flow structures with Laser Doppler Velocimetry (LDV), we provide a systematic description of the different flow regimes from laminar to fully turbulent. Each flow regime is characterized by measurements of the radial velocity, velocity fluctuations and turbulence intensity profiles. In addition we estimate the autocorrelation, the probability distribution and the structure functions in an attempt to further characterize transition. For all cases tested, our results indicate that transition occurs only when the Reynolds stresses of the flow equal or exceed the yield stress of the fluid, i.e. the plug is broken before transition commences. Once in transition and when turbulent, the behaviour of the yield stress fluid is somewhat similar to a (simpler) shear-thinning fluid. Finally, we have observed the shape of slugs during transition and found their leading edges to be highly elongated and located off the central axis of the pipe, for the non-Newtonian fluids examined.

scholarly journals Forced Linear Shear Flows with Rotation: Rotating Couette–Poiseuille Flow, Its Stability, and Astrophysical Implications

2021 ◽  
Vol 922 (2) ◽  
pp. 161
Author(s):  
Subham Ghosh ◽  
Banibrata Mukhopadhyay
Keyword(s):  
Shear Flow ◽  
Couette Flow ◽  
Accretion Disk ◽  
Poiseuille Flow ◽  
Small Region ◽  
Transition To Turbulence ◽  
Plane Couette Flow ◽  
Plane Poiseuille Flow ◽  
Plane Shear ◽  
Linear Shear

Abstract We explore the effect of forcing on the linear shear flow or plane Couette flow, which is also the background flow in the very small region of the Keplerian accretion disk. We show that depending on the strength of forcing and boundary conditions suitable for the systems under consideration, the background plane shear flow, and hence the accretion disk velocity profile, is modified into parabolic flow, which is a plane Poiseuille flow or Couette–Poiseuille flow, depending on the frame of reference. In the presence of rotation, the plane Poiseuille flow becomes unstable at a smaller Reynolds number under pure vertical as well as three-dimensional perturbations. Hence, while rotation stabilizes the plane Couette flow, the same destabilizes the plane Poiseuille flow faster and hence the forced local accretion disk. Depending on the various factors, when the local linear shear flow becomes a Poiseuille flow in the shearing box due to the presence of extra force, the flow becomes unstable even for Keplerian rotation, and hence turbulence will ensue. This helps to resolve the long-standing problem of subcritical transition to turbulence in hydrodynamic accretion disks and the laboratory plane Couette flow.

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