Near-Critical Swirling Flow of Viscoelastic Fluids in a Pipe

2002 ◽  
Author(s):  
Zvi Rusak ◽  
John A. Tichy
Keyword(s):  
Relaxation Time ◽  
Viscoelastic Fluid ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Equations Of Motion ◽  
Fluid Viscosity ◽  
Retardation Time ◽  
Flow Perturbation ◽  
Boger Fluids ◽  
Flow Inertia

The interaction between flow inertia and elasticity in high Reynolds number, axisymmetric, and near-critical swirling flows of an incompressible and viscoelastic fluid in a straight circular pipe is studied. The stresses of the viscoelastic fluid are described by the Oldroyd-B constitutive model (representing the low constant-viscosity Boger fluids). A nonlinear small-disturbance analysis is developed from the governing equations of motion in order to understand the complicated interactions between flow inertia and fluid viscosity and elasticity. The effects of the fluid viscosity, relaxation time, and retardation time on the flow development in the pipe and on the critical swirl for vortex breakdown are explored. It is found that increasing the relaxation time with other parameters being fixed increases the critical swirl for vortex breakdown whereas increasing the retardation time with other parameters being fixed decreases the critical swirl for breakdown. Also, when the relaxation and retardation times are the same the critical swirl is the same as that of a Newtonian fluid. The viscoelastic characteristic times also effect the size of the flow perturbation. These results may explain the changes in the appearance of breakdown zones as function of Reynolds numbers (swirl level) that have been recently observed in the experiments by Stokes et al. (2001) where Boger fluids were used. This work extends for the first time the theory of vortex stability and breakdown to include effects of non-Newtonian fluids.

Some developments in the theory of vortex breakdown

1967 ◽  
Vol 28 (1) ◽  
pp. 65-84 ◽  
Author(s):  
T. Brooke Benjamin
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Theoretical Treatment ◽  
Stationary Waves ◽  
Flow Models ◽  
Essential Properties ◽  
Small Flow ◽  
Basic Equations

The primary aim of the analysis presented herein is to consolidate the ideas of the ‘conjugate-flow’ theory, which proposes that vortex breakdown is fundamentally a transition from a uniform state of swirling flow to one featuring stationary waves of finite amplitude. The original flow is assumed to be supercritical (i.e. incapable of bearing infinitesimal stationary waves), and the mechanism of the transition is explained on the basis of physical principles that are well established in relation to the analogous supercritical-flow phenomenon of the hydraulic jump or bore. In previous presentations of the theory the existence of appropriately descriptive solutions to the full equations of motion has only been inferred from these general principles, but here the solutions are demonstrated explicitly by means of a perturbation analysis. This has basically much in common with the classical theory of solitary and cnoidal waves, which is known to explain well the essential properties of weak bores.In § 2 the basic equations of the problem are set out and the leading results of the original theoretical treatment are recalled. The new developments are mainly presented in § 3, where an analysis of finite-amplitude waves is completed by two different methods, each serving to illustrate points of interest. The effects of small energy losses and of small flow-force reductions (i.e. wave-resistance effects) are considered, and the analysis leads to a general classification of possible phenomena accompanying such changes of integral properties in either slightly supercritical or slightly subcritical vortex flows. The application to vortex breakdown remains the focus of attention, however, and § 3 includes a careful appraisal of some experimental observations on the phenomenon. In § 4 a summary is given of a variant on the previous methods which is required when the radial boundary of the flow is taken to infinity. The main analysis is developed without restriction to particular flow models, but in § 5 the results are applied to a specific example.

Swirling flow of viscoelastic fluids. Part 1. Interaction between inertia and elasticity

2001 ◽  
Vol 429 ◽  
pp. 67-115 ◽  
Author(s):  
JASON R. STOKES ◽  
LACHLAN J. W. GRAHAM ◽  
NICK J. LAWSON ◽  
DAVID V. BOGER
Keyword(s):  
Flow Field ◽  
Axial Velocity ◽  
Xanthan Gum ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Central Axis ◽  
Driven Cavity ◽  
Low Viscosity ◽  
Existence Domain ◽  
Boger Fluids

A torsionally driven cavity, consisting of a fully enclosed cylinder with rotating bottom lid, is used to examine the confined swirling flow of low-viscosity Boger fluids for situations where inertia dominates the flow field. Flow visualization and the optical technique of particle image velocimetry (PIV) are used to examine the effect of small amounts of fluid elasticity on the phenomenon of vortex breakdown. Low-viscosity Boger fluids are used which consist of dilute concentrations of high molecular weight polyacrylamide or semi-dilute concentrations of xanthan gum in a Newtonian solvent. The introduction of elasticity results in a 20% and 40% increase in the minimum critical aspect ratio required for vortex breakdown to occur using polyacrylamide and xanthan gum, respectively, at concentrations of 45 p.p.m. When the concentrations of either polyacrylamide or xanthan gum are raised to 75 p.p.m., vortex breakdown is entirely suppressed for the cylinder aspect ratios examined. Radial and axial velocity measurements along the axial centreline show that the alteration in existence domain is linked to a decrease in the magnitude of the peak in axial velocity along the central axis. The minimum peak axial velocities along the central axis for the 75 p.p.m. polyacrylamide and 75 p.p.m. xanthan gum Boger fluids are 67% and 86% lower in magnitude, respectively, than for the Newtonian fluid at Reynolds number of Re ≈ 1500–1600. This decrease in axial velocity is associated with the interaction of elasticity in the governing boundary on the rotating base lid and/or the interaction of extensional viscosity in areas with high velocity gradients. The low-viscosity Boger fluids used in this study are rheologically characterized and the steady complex flow field has well-defined boundary conditions. Therefore, the results will allow validation of non-Newtonian constitutive models in a numerical model of a torsionally driven cavity flow.

Near-critical swirling flow of a viscoelastic fluid in a circular pipe

2017 ◽  
Vol 814 ◽  
pp. 325-360
Author(s):  
Zvi Rusak ◽  
Nguyen Ly ◽  
John A. Tichy ◽  
Shixiao Wang
Keyword(s):  
Reynolds Number ◽  
Viscoelastic Fluid ◽  
Vortex Breakdown ◽  
Shear Thinning ◽  
Weissenberg Number ◽  
Swirling Flows ◽  
Circular Pipe ◽  
Viscoelastic Characteristic ◽  
Mobility Parameter ◽  
Flow Inertia

The interaction between flow inertia and elasticity in high-Reynolds-number, axisymmetric and near-critical swirling flows of an incompressible and viscoelastic fluid in an open finite-length straight circular pipe is studied at the limit of low elasticity. The stresses of the viscoelastic fluid are described by the generalized Giesekus constitutive model. This model helps to focus the analysis on low fluid elastic effects with shear thinning of the viscosity. The application of the Giesekus model to columnar streamwise vortices is first investigated. Then, a nonlinear small-disturbance analysis is developed from the governing equations of motion. It reveals the complicated interactions between flow inertia, swirl and fluid rheology. An effective Reynolds number that links between steady states of swirling flows of a viscoelastic fluid and those of a Newtonian fluid is revealed. The effects of the fluid viscosity, relaxation time, retardation time and mobility parameter on the flow development in the pipe and on the critical swirl for the appearance of vortex breakdown are explored. It is found that in vortex flows with either an axial jet or an axial wake profile, increasing the shear thinning by decreasing the ratio of the viscoelastic characteristic times from one (with fixed values of the Weissenberg number and the mobility parameter) increases the critical swirl ratio for breakdown. Increasing the fluid elasticity by increasing the Weissenberg number from zero (with a fixed ratio of the viscoelastic characteristic times and a fixed value of the mobility parameter) or increasing the fluid mobility parameter from zero (with fixed values of the Weissenberg number and the ratio of viscoelastic times) causes a similar effect. The results may explain the trend of changes in the appearance of breakdown zones as a function of swirl level that were observed in the experiments by Stokes et al. (J. Fluid Mech., vol. 429, 2001, pp. 67–115), where Boger fluids were used. This work extends for the first time the theory of vortex breakdown to include effects of non-Newtonian fluids.

scholarly journals Vortex breakdown of the swirling flow in a Lean Direct Injection burner

2020 ◽  
Vol 32 (12) ◽  
pp. 125118
Author(s):  
Yazhou Shen ◽  
Mohamad Ghulam ◽  
Kai Zhang ◽  
Ephraim Gutmark ◽  
Christophe Duwig
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Direct Injection ◽  
Lean Direct Injection ◽  
Injection Burner

Forced and Periodic Vortex Breakdown

1967 ◽  
Vol 89 (3) ◽  
pp. 609-615
Author(s):  
Turgut Sarpkaya
Keyword(s):  
Experimental Study ◽  
Opposite Direction ◽  
Vortex Tube ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Typical Data ◽  
Circular Orifice ◽  
Pros And Cons

The results of an experimental study of the forced and periodic breakdown of a confined vortex rotating in the opposite direction are presented. The vortex tube consists of two chambers connected by a short conduit through streamlined transitions. The upstream end is closed by a plain wall, and a circular orifice is provided at the downstream end. The swirling flow and the breaker-vortex are generated by introducing varying proportions of air or water through tangential ports located near the upstream and downstream walls of the unit. The cases of single breakdown and periodic breakdown are explored and typical data are presented for each case. Finally, the pros and cons of the two existing transition theories are discussed.

scholarly journals Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Justine Yasappan ◽  
Ángela Jiménez-Casas ◽  
Mario Castro
Keyword(s):  
Asymptotic Behavior ◽  
Viscoelastic Fluid ◽  
Closed Loop ◽  
Theoretical Study ◽  
Equations Of Motion ◽  
Asymptotic Properties ◽  
Inertial Manifold ◽  
Thermal Gradients ◽  
External Temperature ◽  
First Time

Fluids subject to thermal gradients produce complex behaviors that arise from the competition with gravitational effects. Although such sort of systems have been widely studied in the literature for simple (Newtonian) fluids, the behavior of viscoelastic fluids has not been explored thus far. We present a theoretical study of the dynamics of a Maxwell viscoelastic fluid in a closed-loop thermosyphon. This sort of fluid presents elastic-like behavior and memory effects. We study the asymptotic properties of the fluid inside the thermosyphon and the exact equations of motion in the inertial manifold that characterizes the asymptotic behavior. We derive, for the first time, the mathematical derivations of the motion of a viscoelastic fluid in the interior of a closed-loop thermosyphon under the effects of natural convection and a given external temperature gradient.

Topological Flow Structures of Annular Swirling Jets

2001 ◽  
Vol 17 (3) ◽  
pp. 131-138
Author(s):  
Feng Chin Tsai ◽  
Rong Fung Huang
Keyword(s):  
Vortex Breakdown ◽  
Swirling Flow ◽  
Single Bubble ◽  
Flow Structures ◽  
Complex Flow ◽  
Swirl Number ◽  
Recirculation Bubble ◽  
Annular Jet ◽  
Ring Mode ◽  
Dual Ring

AbstractThe effects of blockage and swirl on the macro flow structures of the annular jet past a circular disc are experimentally studied through the time-averaged streamline patterns. In the blockage-effect regime, the flows present multiple modes, single bubble, dual rings, vortex breakdown, and triple rings, in different regimes of blockage ratio and swirl number. The topological models of the flow structures are proposed and discussed according to the measured flow fields to manifest the complex flow structures. The single bubble is a closed recirculation bubble with a stagnation point on the central axis. The dual-ring flow is an open-top recirculsation zone, in which a pair of counter-rotating vortex rings exists in the near wake. The fluids in the dual rings are expelled downstream through a central jet-like swirling flow. A vortex breakdown may occur in the central jet-like swirling flow if the exit swirl number exceeds critical values. When the vortex breakdown interacts with the dual rings, a complex triple-ring flow structure forms. Axial distributions of the local swirl number are presented and discussed. The local swirl number increases with the increase of the exit swirl number and attains the maximum in the dual-ring mode. At large exit swirl numbers where the vortex breakdown occurs, the local swirl number decreases drastically to a low value.

Investigation of the Dynamics of an Ultra Low NOx Injection System by POD Data Post-Processing

2015 ◽  
Author(s):  
M. Berrino ◽  
D. Lengani ◽  
F. Satta ◽  
M. Ubaldi ◽  
P. Zunino ◽  
...  
Keyword(s):  
Flow Field ◽  
Spatial Information ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Measurement Techniques ◽  
Injection System ◽  
Post Processing ◽  
Particle Image Velocimetry Technique ◽  
Annular Sector ◽  
Random Fluctuations

The present paper is focused on the investigation of the dynamics of the flow downstream of an Ultra Low NOx (ULN) injection system, designed to reduce NOx emissions and combustor axial length. Two rectangular flame tubes have been experimentally investigated: one aimed at simulating an unconfined exit flow, and another with the same transverse dimensions of the combustor annular sector, to simulate the confined flow field. The effects induced by the realistic flame tube presence are investigated comparing the flow field with that generated in the unconfined case. Particular attention is paid to the vortex breakdown phenomena associated with the flow generated by the two co-rotating swirlers constituting the injection system. Two different and complementary measurement techniques have been adopted to characterize the aerodynamics of the vortex breakdown. The hot-wire investigation results reveal the frequencies associated with the precession motion due to the vortex breakdown. The Particle Image Velocimetry technique has been coupled with Proper Orthogonal Decomposition (POD) for data post-processing in order to reconstruct the swirling motion generated by the injection system. The property of POD, which consists of splitting temporal from spatial information of the flow field in analysis, allows the distinction between deterministic and random fluctuations without the need of an external trigger signal. This feature is fundamental for the better understanding of an highly-swirling flow.

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