Puffing in planar buoyant plumes: BiGlobal instability analysis and experiments

2019 ◽  
Vol 863 ◽  
pp. 817-849 ◽  
Author(s):  
Kuchimanchi K. Bharadwaj ◽  
Debopam Das
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Constant Density ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Buoyant Plumes ◽  
Number Range ◽  
Oscillation Frequencies

The present study investigates the puffing behaviour of planar buoyant plumes by employing linear BiGlobal stability analysis and experiments. The BiGlobal instability characteristics of two-dimensional plumes have been explored using stability analysis and compared with the puffing behaviour of both rectangular plumes and square plumes obtained from experiments. In the parameter space investigated, which spans a Richardson number range $0.03<Ri<960$, instability analysis reveals that planar plumes exhibit BiGlobal instability only for varicose perturbations, while they remain stable for sinuous perturbations. The BiGlobal frequency and growth rates of the unstable varicose mode are used to obtain Strouhal number correlation and stability curves. An investigation into the effect of the spanwise wavenumber on BiGlobal instability indicates that planar plumes are more unstable to two-dimensional perturbations than to three-dimensional perturbations. An increase in the spanwise wavenumber tends to stabilize planar plumes without affecting their oscillation frequencies. Experiments suggest that the puffing frequencies in rectangular plumes closely follow the power law obtained from two-dimensional instability analysis while exhibiting a weaker dependence on inlet aspect ratio. To further explore the effect of aspect ratio on puffing behaviour, experiments have been carried out in plumes of aspect ratio 1, i.e. square plumes. Square plumes are found to be more stable and to exhibit higher puffing frequencies than rectangular plumes. The reasons for these differences in puffing dynamics between rectangular and square plumes have been explored from the phase-locked streamwise and spanwise flow visualizations. In addition to puffing, spanwise visualizations in both rectangular and square plumes show the presence of secondary flows at their corners, similar to their constant-density jet counterparts. Finally, from experiments, we deduced a new universal puffing frequency correlation with the hydraulic diameter as the length scale which eliminates the aspect ratio dependence, and is valid for both square and low-aspect-ratio rectangular plumes.

Global instability analysis and experiments on buoyant plumes

2017 ◽  
Vol 832 ◽  
pp. 97-145 ◽  
Author(s):  
Kuchimanchi K. Bharadwaj ◽  
Debopam Das
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Settling Chamber ◽  
Global Instability ◽  
Instability Analysis ◽  
Buoyant Plumes ◽  
Number Range ◽  
Global Modes ◽  
Oscillation Frequencies

The present work investigates the puffing instability of circular buoyant plumes by performing global linear stability analysis and experiments. In the non-dimensional parameter space investigated, plumes exhibit global instability only for axisymmetric perturbations with two unstable modes, which are of oscillatory type. The frequencies of these two unstable global modes agree well with the experiments which suggest that puffing occurs in buoyant plumes as a result of linear global instability. A comprehensive investigation on the effect of various non-dimensional parameters and inlet velocity profiles on frequency and growth rates of the global modes is carried out. The results are used to delineate the stability boundaries for these global modes and to obtain scaling laws for the associated oscillation frequencies. The analysis demonstrates that the two buoyancy parameters, Froude number and source-to-ambient density ratio, play dominant roles in impacting plume transition and oscillation frequencies. Results from global linear stability analysis and earlier experiments have majorly differed in two aspects. The earlier experiments reported a switch in puffing frequency scaling in Richardson number range 100–500, while the instability analysis predicts this switch at around 6000. Also, the instability analysis predicts the occurrence of puffing at density ratios higher than the critical value 0.5–0.6 reported in earlier experiments. To address these differences and validate the results obtained from global linear stability analysis, experiments are performed in a set-up that has been carefully designed to minimize the settling chamber disturbances. The present experiments corroborate the findings of global linear stability analysis. The mechanisms responsible for global instability in plumes have been identified using perturbation vorticity transport equation.

The Influence of Blade Wakes on the Performance of Interturbine Diffusers

1996 ◽  
Vol 118 (2) ◽  
pp. 347-352 ◽  
Author(s):  
R. G. Dominy ◽  
D. A. Kirkham
Keyword(s):  
Performance Modeling ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Correct Performance ◽  
Analysis Methods ◽  
Flow Factor ◽  
The Mean ◽  
Lp Turbine

Interturbine diffusers provide continuity between HP and LP turbines while diffusing the flow upstream of the LP turbine. Increasing the mean turbine diameter offers the potential advantage of reducing the flow factor in the following stages, leading to increased efficiency. The flows associated with these interturbine diffusers differ from those in simple annular diffusers both as a consequence of their high-curvature S-shaped geometry and of the presence of wakes created by the upstream turbine. It is shown that even the simplest two-dimensional wakes result in significantly modified flows through such ducts. These introduce strong secondary flows demonstrating that fully three-dimensional, viscous analysis methods are essential for correct performance modeling.

The Effect of a Wall Boundary Layer on Local Mass Transfer From a Cylinder in Crossflow

1984 ◽  
Vol 106 (2) ◽  
pp. 260-267 ◽  
Author(s):  
R. J. Goldstein ◽  
J. Karni
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Two Dimensional ◽  
Tunnel Wall ◽  
Wall Boundary Layer ◽  
Naphthalene Sublimation Technique ◽  
Displacement Thickness ◽  
Two Dimensional Flow

A naphthalene sublimation technique is used to determine the circumferential and longitudinal variations of mass transfer from a smooth circular cylinder in a crossflow of air. The effect of the three-dimensional secondary flows near the wall-attached ends of a cylinder is discussed. For a cylinder Reynolds number of 19000, local enhancement of the mass transfer over values in the center of the tunnel are observed up to a distance of 3.5 cylinder diameters from the tunnel wall. In a narrow span extending from the tunnel wall to about 0.066 cylinder diameters above it (about 0.75 of the mainstream boundary layer displacement thickness), increases of 90 to 700 percent over the two-dimensional flow mass transfer are measured on the front portion of the cylinder. Farther from the wall, local increases of up to 38 percent over the two-dimensional values are measured. In this region, increases of mass transfer in the rear portion of the cylinder, downstream of separation, are, in general, larger and cover a greater span than the increases in the front portion of the cylinder.

Improving the Performance of a Turbine With Low Aspect Ratio Stators by Aft-Loading

2004 ◽  
Vol 128 (3) ◽  
pp. 492-499 ◽  
Author(s):  
Graham Pullan ◽  
John Denton ◽  
Eric Curtis
Keyword(s):  
Aspect Ratio ◽  
Three Dimensional ◽  
Secondary Flows ◽  
Loss Reduction ◽  
Low Aspect Ratio ◽  
Surface Pressure Distribution ◽  
Loaded Surface ◽  
Nozzle Guide ◽  
Nozzle Guide Vanes ◽  
Stage Efficiency

Experimental data and numerical simulations are presented from a research turbine with low aspect ratio nozzle guide vanes (NGVs). The combined effects of mechanical and aerodynamic constraints on the NGV create very strong secondary flows. This paper describes three designs of NGV that have been tested in the turbine, using the same rotor row in each case. NGV 2 used three-dimensional design techniques in an attempt to improve the performance of the datum NGV 1 blade, but succeeded only in creating an intense vortex shed from the trailing edge (as previously reported) and lowering the measured stage efficiency by 1.1% points. NGV 3 was produced to avoid the “shed vortex” while adopting a highly aft-loaded surface pressure distribution to reduce the influence of the secondary flows. The stage with NGV 3 had an efficiency 0.5% points greater than that with NGV 1. Detailed comparisons between experiment and computations, including predicted entropy generation rates, are used to highlight the areas where the loss reduction has occurred and hence to quantify the effects of employing highly aft-loaded NGVs.

Nonlinear dynamical wave structures to the Date–Jimbo–Kashiwara–Miwa equation and its modulation instability analysis

2021 ◽  
pp. 2150300
Author(s):  
M. Younis ◽  
A. R. Seadawy ◽  
M. Bilal ◽  
S. T. R. Rizvi ◽  
Saad Althobaiti ◽  
...  
Keyword(s):  
Function Method ◽  
Modulation Instability ◽  
Existence Of Solutions ◽  
Three Dimensional ◽  
Algebraic Method ◽  
Two Dimensional ◽  
Instability Analysis ◽  
Nonlinear Dynamical ◽  
Wave Solutions ◽  
Different Shapes

A particular attention is paid to the nonlinear dynamical exact wave solutions to the (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa equation (DJKME). A variety of solutions are extracted in different shapes like dark, singular, dark-singular by implementing [Formula: see text]-expansion function method and modified direct algebraic method. In addition, we also secure singular periodic and plane wave solutions with arbitrary parameters. We also discussed the modulation instability analysis of the governing model. The constraint conditions for the validity of existence of solutions are also reported. Moreover, three-dimensional and two-dimensional, and their corresponding contour graphs are sketched for a better understanding of the derived solutions with the values of arbitrary parameters.

scholarly journals Surface, size and topological effects for some nematic equilibria on rectangular domains

2020 ◽  
Vol 25 (5) ◽  
pp. 1101-1123 ◽  
Author(s):  
Lidong Fang ◽  
Apala Majumdar ◽  
Lei Zhang
Keyword(s):  
Aspect Ratio ◽  
Point Defects ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
Variable Formula ◽  
Limiting Profile ◽  
Switching Dynamics ◽  
Line Defects ◽  
Carry Over

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, [Formula: see text], which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the [Formula: see text] 0 limit relevant for macroscopic domains and the [Formula: see text] limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the [Formula: see text] limit, whereas we observe fractional point defects in the [Formula: see text] 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of [Formula: see text] and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.

Three-dimensional stability analysis for a salt-finger convecting layer

2018 ◽  
Vol 841 ◽  
pp. 636-653
Author(s):  
Ting-Yueh Chang ◽  
Falin Chen ◽  
Min-Hsing Chang
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Longitudinal Mode ◽  
Transverse Mode ◽  
Solute Diffusion ◽  
Two Dimensional ◽  
Grashof Number ◽  
Significant Difference ◽  
The Stability ◽  
Mode A

A three-dimensional linear stability analysis is carried out for a convecting layer in which both the temperature and solute distributions are linear in the horizontal direction. The three-dimensional results show that, for $Le=3$ and 100, the most unstable mode occurs invariably as the longitudinal mode, a vortex roll with its axis perpendicular to the longitudinal plane, suggesting that the two-dimensional results are sufficient to illustrate the stability characteristics of the convecting layer. Two-dimensional results show that the stability boundaries of the transverse mode (a vortex roll with its axis perpendicular to the transverse plane) and the longitudinal modes are virtually overlapped in the regime dominated by thermal diffusion and the regime dominated by solute diffusion, while these two modes hold a significant difference in the regime the salt-finger instability prevails. More precisely, the instability area in terms of thermal Grashof number $Gr$ and solute Grashof number $Gs$ is larger for the longitudinal mode than the transverse mode, implying that, under any circumstance, the longitudinal mode is always more unstable than the transverse mode.

scholarly journals Stability analysis of the elliptic cylinder wake

2014 ◽  
Vol 763 ◽  
pp. 302-321 ◽  
Author(s):  
Justin S. Leontini ◽  
David Lo Jacono ◽  
Mark C. Thompson
Keyword(s):  
Stability Analysis ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Elliptic Cylinder ◽  
Cylinder Wake ◽  
Long Wavelength ◽  
Aspect Ratios ◽  
Numerical Stability Analysis ◽  
Spatiotemporal Symmetries ◽  
Three Dimensional Simulations

AbstractThis paper presents the results of numerical stability analysis of the wake of an elliptical cylinder. Aspect ratios where the ellipse is longer in the streamwise direction than in the transverse direction are considered. The focus is on the dependence on the aspect ratio of the ellipse of the various bifurcations to three-dimensional flow from the two-dimensional Kármán vortex street. It is shown that the three modes present in the wake of a circular cylinder (modes A, B and QP) are present in the ellipse wake, and that in general they are all stabilized by increasing the aspect ratio of the ellipse. Two new pertinent modes are found: one long-wavelength mode with similarities to mode A, and a second that is only unstable for aspect ratios greater than approximately 1.75, which has similar spatiotemporal symmetries to mode B but has a distinct spatial structure. Results from fully three-dimensional simulations are also presented confirming the existence and growth of these two new modes in the saturated wakes.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

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