Disturbance energy growth in core–annular flow

2014 ◽  
Vol 747 ◽  
pp. 44-72 ◽  
Author(s):  
A. Orazzo ◽  
G. Coppola ◽  
L. de Luca
Keyword(s):  
Pipe Flow ◽  
Annular Flow ◽  
Three Dimensional ◽  
Point Of View ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Water Mixture ◽  
Horizontal Pipe ◽  
Transient Phenomena ◽  
Modal Theory

AbstractThe linear stability of the horizontal pipe flow of an equal density oil–water mixture, arranged as acore–annular flow(CAF), is here reconsidered from the point of view of non-modal analysis in order to assess the effects of non-normality of the linearized Navier–Stokes operator on the transient evolution of small disturbances. The aim of this investigation is to give insight into physical situations in which poor agreement occurs between the predictions of linear modal theory and classical experiments. The results exhibit high transient amplifications of the energy of three-dimensional perturbations and, in analogy with single-fluid pipe flow, the largest amplifications arise for non-axisymmetric disturbances of vanishing axial wavenumber. Energy analysis shows that the mechanisms leading to these transient phenomena mostly occur in the annulus, occupied by the less viscous fluid. Consequently, higher values of energy amplifications are obtained by increasing the gap between the core and the pipe wall and the annular Reynolds number. It is argued that these linear transient mechanisms of disturbance amplification play a key role in explaining the transition to turbulence of CAF.

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.

Non-Modal Instability of Core-Annular Flow

2012 ◽  
Vol 13 (6) ◽  
Author(s):  
Gennaro Coppola ◽  
Annagrazia Orazzo ◽  
Luigi de Luca
Keyword(s):  
Annular Flow ◽  
Three Dimensional ◽  
Classical Problem ◽  
Maximum Energy ◽  
Point Of View ◽  
Polar Coordinates ◽  
Tension Parameter ◽  
Two Phases ◽  
The Stability ◽  
Energy Amplification

AbstractThe classical problem of the stability of Core-Annular Flow (CAF) in pipes is reconsidered from the point of view of the linear non-modal analysis. An accurate Chebyshev pseudospectral code in polar coordinates has been developed in order to separately discretize the two phases of the flow. Transient amplifications of the energy of three-dimensional perturbations are computed by taking into account the effects of viscosity and volume ratios between the two liquids, as well as of Reynolds number and a surface tension parameter.A detailed investigation is conducted in wide regions of the parameters space and the occurrence of remarkable transient growths is found for asymptotically both stable and unstable configurations. Optimal perturbations (i.e. giving the maximum energy amplification) are determined and their structure is analyzed. It is shown that in conditions in which axisymmetric modes are expected to constitute the most dangerous exponential disturbances, spiral perturbations can provide higher levels of transient energy amplification. Growth rates and amplification levels relative to modal and non-modal mechanisms are compared in order to analyze more in depth previous disagreements between experiments and modal theory.

Oscillating Pipe Flow: High-Resolution Simulation of Nonlinear Mechanisms

2006 ◽  
Author(s):  
Arash Ghasemi
Keyword(s):  
Pipe Flow ◽  
Stokes Equations ◽  
Stationary Flow ◽  
Current Approach ◽  
Laminar Flows ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Frequency Change ◽  
Starting Point ◽  
Corner Points

A new perspective suitable for understanding the details of nonlinear pumping (formation of traveling shocks) inside a pressurized cavity is constructed in this paper. Full compressible axisymmetric three-dimensional Navier-Stokes equations are used as the starting point to cover all complexities of the problem that exceedingly increase for particular ranges of Mach, Reynolds and Prandtl numbers. Then a very high-order numerical method is introduced to preserve the user-defined order of accuracy for practical simulations. For removal of spurious waves, higher-order compact filters are derived. All equations are marched in time using the classical Runge-Kutta algorithm which is appropriate for problems involving fine-scale temporal fluctuations. As the most important part of simulation, Navier-Stokes Characteristic Boundary Conditions are used for accurate calculation of wave reflection specially at singular points, i.e., corner points and points across the axis of symmetry. A simultaneous characteristic-decomposition is devised in this paper which completely resolves stability problems arising from problem-dependent treatment of corner points. Numerical experiments are performed for high-Reynolds laminar flows inside the shock region to determine the effect of frequency change on both shock formation (stationary flow) and transient solution. The current approach which favorably compares to the previous experimental data, may be used as a robust tool for understanding the less-understood problem of shock/Stokes-Layer interaction and its consequences on transition to turbulence in Oscillating Pipe Flow.

scholarly journals Doubly localized states in plane Couette flow

2014 ◽  
Vol 758 ◽  
pp. 1-4 ◽  
Author(s):  
Bruno Eckhardt
Keyword(s):  
Couette Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Linear Instability ◽  
Localized States ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Plane Couette Flow ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

AbstractMuch of our understanding of the transition to turbulence in flows without a linear instability came with the discovery and characterization of fully three-dimensional solutions to the Navier–Stokes equation. The first examples in plane Couette flow were periodic in both spanwise and streamwise directions, and could explain the transitions in small domains only. The presence of localized turbulent spots in larger domains, the spatiotemporal decoherence on larger scales and the ability to trigger turbulence with pointwise perturbations require solutions that are localized in both directions, like the one presented by Brand & Gibson (J. Fluid Mech., vol. 750, 2014, R3). They describe a steady solution of the Navier–Stokes equations and characterize in unprecedented detail, including an analytic computation of its localization properties. The study opens up new ways to describe localized turbulent patches.

Development of Accelerating Pipe Flow Starting From Rest

2013 ◽  
Vol 135 (11) ◽  
Author(s):  
Ivar Annus ◽  
Tiit Koppel ◽  
Laur Sarv ◽  
Leo Ainola
Keyword(s):  
Pipe Flow ◽  
Large Scale ◽  
Transformation Method ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Axial Velocity Component ◽  
Flow Equations ◽  
Continuity Equations ◽  
Start Up ◽  
Experimental Findings

A uniformly accelerated laminar flow in a pipe, initially at rest, is analyzed. One-dimensional unsteady flow equations for start-up flow were derived from the Navier–Stokes and continuity equations. The dynamical boundary layer in a pipe is described theoretically with the Laplace transformation method for small values of time. A mathematical model describing the development of the velocity profile for accelerating flow starting from rest up to the point of transition to turbulence is given. The theoretical results are compared with experimental findings gained in a large-scale pipeline. Particle image velocimetry (PIV) technique is used to deduce the development of accelerating pipe flow starting from rest. The measured values of the axial velocity component are found to be in a good agreement with the analytical values.

scholarly journals Localised turbulence in a circular pipe flow with gradual expansion

2015 ◽  
Vol 771 ◽  
Author(s):  
Kamal Selvam ◽  
Jorge Peixinho ◽  
Ashley P. Willis
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Transition To Turbulence ◽  
Circular Pipe ◽  
Recirculation Region ◽  
Circular Pipe Flow ◽  
Gradual Expansion

We report the results of three-dimensional direct numerical simulations for incompressible viscous fluid in a circular pipe flow with a gradual expansion. At the inlet, a parabolic velocity profile is applied together with a constant finite-amplitude perturbation to represent experimental imperfections. Initially, at low Reynolds number, the solution is steady. As the Reynolds number is increased, the length of the recirculation region near the wall grows linearly. Then, at a critical Reynolds number, a symmetry-breaking bifurcation occurs, where linear growth of asymmetry is observed. Near the point of transition to turbulence, the flow experiences oscillations due to a shear layer instability for a narrow range of Reynolds numbers. At higher Reynolds numbers, the recirculation region breaks into a turbulent state which remains spatially localised and unchanged when the perturbation is removed from the flow. Spatial correlation analysis suggests that the localised turbulence in the gradual expansion possesses a different flow structure from the turbulent puff of uniform pipe flow.

scholarly journals NUMERICAL SIMULATIONS OF BREAKING SOLITARY WAVES

2012 ◽  
Vol 1 (33) ◽  
pp. 59 ◽  
Author(s):  
Pierre Lubin ◽  
Stéphane Glockner
Keyword(s):  
Experimental Data ◽  
Solitary Waves ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Point Of View ◽  
Numerical Code ◽  
Scale Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Surface Description

This paper presents the application of a parallel numerical code to breaking solitary waves impacting a seawall structure. The three-dimensional Navier-Stokes equations are solved in air and water, coupled with a subgrid-scale model to take turbulence into account. We compared three numerical methods for the free-surface description, using the classical VOF-PLIC and VOF-TVD methods, and an original VOF-SM method recently developed in our numerical tool (Vincent et al., 2010). Some experimental data for solitary waves impinging and overtopping coastal structures are available in literature (Hsiao et al., 2010). Solitary waves are often used to model tsunami behaviors because of their hydrodynamic similarities. From a numerical point of view, it allows shorter CPU time simulations, as only one wave breaks. Here we apply the model to simulate three-dimensional solitary waves and compare qualitatively our results with the experimental data. We investigate three configurations of solitary waves impinging and overtopping an impermeable seawall on a 1:20 sloping beach.

Validation of Equilibrium-Based, One-Dimensional, Two-Phase Pipe Flow Models With Transient, Three-Dimensional, CFD Simulations for Horizontal Flows

2015 ◽  
Author(s):  
Florentina Popa ◽  
Andrey Filippov ◽  
Brent C. Houchens
Keyword(s):  
Pipe Flow ◽  
Mechanistic Model ◽  
Three Dimensional ◽  
Cfd Simulations ◽  
Two Phase ◽  
Horizontal Pipe ◽  
One Dimensional ◽  
Flow Models ◽  
Horizontal Flows ◽  
Closure Relations

One-dimensional (1D), equilibrium-based mechanistic model predictions are compared to three-dimensional (3D) transient computational fluid dynamics results for horizontal two-phase, gas-liquid pipe flow. The 3D regions of interest include both those expected to be in equilibrium conditions and those where transitions between flow regimes occur. Equilibrium simulations, such as those for stratified flow in a horizontal pipe, allow crucial validation of the equilibrium-based closure relations by means of numerical experiments. In the transitional regions, fully 3D, time-dependent numerical simulations provide a means to estimate the error in the equilibrium-based models and suggest how reasonable approximations can be made in these regions.

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