Mixed Convection in an Annulus of Large Aspect Ratio

1989 ◽  
Vol 111 (3) ◽  
pp. 683-689 ◽  
Author(s):  
L. S. Yao ◽  
B. B. Rogers
Keyword(s):  
Aspect Ratio ◽  
Mixed Convection ◽  
Channel Flow ◽  
Practical Interest ◽  
Base Flow ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Fully Developed Flow ◽  
The Stability ◽  
Stability Results

Mixed convection in an annulus of large aspect ratio is studied. At an aspect ratio of 100, the effect of wall curvature is minimal, and both the base flow and the stability characteristics approach those of a two-dimensional channel flow. The linear-stability results demonstrate that the fully developed flow is unstable in regions of practical interest in an appropriate parameter space. Consequently, commonly assumed steady parallel countercurrent flows in many idealized numerical and analytical studies are unlikely to be observed experimentally.

Effect of Elliptical Burner Geometry on Stability and Global Emission Characteristics of Pre-Mixed Flames

2002 ◽  
Author(s):  
Benjamin D. Baird ◽  
S. R. Gollahalli
Keyword(s):  
Aspect Ratio ◽  
Emission Reduction ◽  
Pollutant Emission ◽  
Emission Characteristics ◽  
Global Emission ◽  
Harmful Emissions ◽  
Reduction Of Emissions ◽  
Fuel Mixtures ◽  
The Stability ◽  
Stability Results

An important topic in combustion research today is pollutant emission reduction. With the current demand for large amounts of economical, clean power, there is a need for research in both the increase of combustion performance and the reduction of emissions. Two methods of the so-called ‘passive’ flame controls are the use of premixing the air and fuel and the variation of the geometry of the flame. Both mechanisms offer the promise of increasing efficiency as well as reducing harmful emissions. However, the effect of these controls on the stability of the flame has not been fully studied. This paper will attempt to fill in some of this gap and will study the effects of elliptical burner geometry on premixed flames. The study will present stability results for circular and 4:1 aspect ratio elliptical burner geometry for a range of fuel mixtures of propane and hydrogen. The paper will also report the emission indices of CO and NO of the 40% by mass hydrogen in propane mixture. It was found that the 4:1 aspect ratio burner had reduced blow-out stability, produced a much shorter flame, and, in general, produced more carbon monoxide and less nitric oxide than a circular burner.

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.

scholarly journals On the stability of plane Couette–Poiseuille flow with uniform crossflow

2010 ◽  
Vol 656 ◽  
pp. 417-447 ◽  
Author(s):  
ANIRBAN GUHA ◽  
IAN A. FRIGAARD
Keyword(s):  
Linear Stability ◽  
Poiseuille Flow ◽  
Energy Production ◽  
Base Flow ◽  
Two Dimensional ◽  
Wall Velocity ◽  
Resonant Interactions ◽  
Flow Stabilization ◽  
Tollmien Schlichting ◽  
The Stability

We present a detailed study of the linear stability of the plane Couette–Poiseuille flow in the presence of a crossflow. The base flow is characterized by the crossflow Reynolds number Rinj and the dimensionless wall velocity k. Squire's transformation may be applied to the linear stability equations and we therefore consider two-dimensional (spanwise-independent) perturbations. Corresponding to each dimensionless wall velocity, k ∈ [0, 1], two ranges of Rinj exist where unconditional stability is observed. In the lower range of Rinj, for modest k we have a stabilization of long wavelengths leading to a cutoff Rinj. This lower cutoff results from skewing of the velocity profile away from a Poiseuille profile, shifting of the critical layers and the gradual decrease of energy production. Crossflow stabilization and Couette stabilization appear to act via very similar mechanisms in this range, leading to the potential for a robust compensatory design of flow stabilization using either mechanism. As Rinj is increased, we see first destabilization and then stabilization at very large Rinj. The instability is again a long-wavelength mechanism. An analysis of the eigenspectrum suggests the cause of instability is due to resonant interactions of Tollmien–Schlichting waves. A linear energy analysis reveals that in this range the Reynolds stress becomes amplified, the critical layer is irrelevant and viscous dissipation is completely dominated by the energy production/negation, which approximately balances at criticality. The stabilization at very large Rinj appears to be due to decay in energy production, which diminishes like Rinj−1. Our study is limited to two-dimensional, spanwise-independent perturbations.

Thermal effect on large-aspect-ratio Couette–Taylor system: numerical simulations

2015 ◽  
Vol 771 ◽  
pp. 57-78 ◽  
Author(s):  
Changwoo Kang ◽  
Kyung-Soo Yang ◽  
Innocent Mutabazi
Keyword(s):  
Heat Transfer ◽  
Temperature Gradient ◽  
Aspect Ratio ◽  
Numerical Simulations ◽  
Convective Cell ◽  
Base Flow ◽  
Large Aspect Ratio ◽  
Radial Temperature ◽  
Instability Modes ◽  
Momentum And Heat Transfer

We have performed numerical simulations of the flow in a large-aspect-ratio Couette–Taylor system with rotating inner cylinder and with a radial temperature gradient. The aspect ratio was chosen in such a way that the base state is in the conduction regime. Away from the endplates, the base flow is a superposition of an azimuthal flow induced by rotation and an axial flow (large convective cell) induced by the temperature gradient. For a fixed rotation rate of the inner cylinder in the subcritical laminar regime, the increase of the temperature difference imposed on the annulus destabilizes the convective cell to give rise to co-rotating vortices as primary instability modes and to counter-rotating vortices as secondary instability modes. The space–time properties of these vortices have been computed, together with the momentum and heat transfer coefficients. The temperature gradient enhances the momentum and heat transfer in the flow independently of its sign.

On the stability of extending films: a model for the film casting process

1974 ◽  
Vol 66 (3) ◽  
pp. 613-622 ◽  
Author(s):  
Y. L. Yeow
Keyword(s):  
Simple Model ◽  
Eigenvalue Problems ◽  
Film Flow ◽  
Casting Process ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Film Casting ◽  
Hydrodynamic Stability Theory ◽  
The Stability ◽  
Stability Results

Isothermal Newtonian film flow is put forward as a simple model of the film casting process. Methods of linear hydrodynamic stability theory are applied to study the stability of the film flow. The relevant eigenvalue problems are formulated and solved numerically. Results are presented in the form of neutral-stability curves in the appropriate parameter space. For the case of two-dimensional disturbances stability results obtained here are compared with those of Pearson & Matovich (1969) and Gelder (1971) for the stability of isothermal Newtonian threadline flow.

Weakly nonlinear oscillatory convection in a rotating fluid

1992 ◽  
Vol 436 (1896) ◽  
pp. 33-54 ◽  
Keyword(s):  
Standing Wave ◽  
Perturbation Technique ◽  
Vertical Axis ◽  
Travelling Wave ◽  
Base Flow ◽  
Two Dimensional ◽  
Oscillatory Convection ◽  
Weakly Nonlinear ◽  
Wave Disturbances ◽  
The Stability

The problem of weakly nonlinear two- and three-dimensional oscillatory convection in the form of standing waves is studied for a horizontal layer of fluid heated from below and rotating about a vertical axis. The solutions to the nonlinear problem are determined by a perturbation technique and the stability of all the base flow solutions is investigated with respect to both standing wave and travelling wave disturbances. The results of the stability and the nonlinear analyses for various values of the rotation parameter τ and the Prandtl number P (0 ≼ P < 0.677) indicate that there is no subcritical instability and that all the base flow solutions are unstable. Disturbances with highest growth rates are found to be some particular disturbances superimposed on two-dimensional base flow. Particular standing wave disturbances parallel to two-dimensional base flow are the most unstable ones either for sufficiently small P or for intermediate values of P with τ below some critical value τ *. Travelling wave disturbances inclined at an angle of about 45° to the wave vector of two-dimensional base flow are the most unstable disturbances either for P sufficiently close to its upper limit or for intermediate values of P with τ ≽ τ *. The dependence on P and τ of the nonlinear effect on the frequency and of the heat flux are also discussed.

Sign in / Sign up

Export Citation Format

Share Document