Influence of Coflow On Buoyant Plume Puffing

2021 ◽  
Author(s):  
Kuchimanchi K Bharadwaj ◽  
Debopam Das
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Density Ratio ◽  
Buoyant Plume ◽  
Frequency Increase ◽  
Buoyant Plumes ◽  
Air Stream ◽  
Wide Range ◽  
Dimensional Parameters ◽  
The Stability

Abstract The present study investigates the influence of an annular coflowing air stream on the puffing behaviour of a buoyant plume by employing the BiGlobal Linear Stability Analysis. An increase in the coflow is found to mitigate the puffing intensity and eventually stabilize the plumes. From the stability analysis, the critical coflow ratios, which represent the amount of coflow required to completely suppress the puffing, have been estimated for plumes spanning a wide range of non-dimensional parameters. The analysis shows that the critical coflow ratio largely depends on the two buoyancy parameters, the Froude number, and the density ratio whereas it remains marginally affected by the plume Reynolds number. Plumes with higher buoyancy require larger coflow for suppressing puffing. From the instability analysis, we have obtained a correlation law for critical coflow ratios in buoyant plumes. Also, it is found that the plume puffing frequency increases with an increase in the coflow. We attempt to ascertain the reasons for instability mitigation and frequency increase in the puffing plumes because of coflow.

scholarly journals The linear instability of the stratified plane Couette flow

2018 ◽  
Vol 853 ◽  
pp. 205-234 ◽  
Author(s):  
Giulio Facchini ◽  
Benjamin Favier ◽  
Patrice Le Gal ◽  
Meng Wang ◽  
Michael Le Bars
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Couette Flow ◽  
Vertical Direction ◽  
Stability Diagram ◽  
Linear Instability ◽  
Plane Couette Flow ◽  
Horizontal Shear ◽  
The Stability

We present the stability analysis of a plane Couette flow which is stably stratified in the vertical direction orthogonal to the horizontal shear. Interest in such a flow comes from geophysical and astrophysical applications where background shear and vertical stable stratification commonly coexist. We perform the linear stability analysis of the flow in a domain which is periodic in the streamwise and vertical directions and confined in the cross-stream direction. The stability diagram is constructed as a function of the Reynolds number $Re$ and the Froude number $Fr$, which compares the importance of shear and stratification. We find that the flow becomes unstable when shear and stratification are of the same order (i.e. $Fr\sim 1$) and above a moderate value of the Reynolds number $Re\gtrsim 700$. The instability results from a wave resonance mechanism already known in the context of channel flows – for instance, unstratified plane Couette flow in the shallow-water approximation. The result is confirmed by fully nonlinear direct numerical simulations and, to the best of our knowledge, constitutes the first evidence of linear instability in a vertically stratified plane Couette flow. We also report the study of a laboratory flow generated by a transparent belt entrained by two vertical cylinders and immersed in a tank filled with salty water, linearly stratified in density. We observe the emergence of a robust spatio-temporal pattern close to the threshold values of $Fr$ and $Re$ indicated by linear analysis, and explore the accessible part of the stability diagram. With the support of numerical simulations we conclude that the observed pattern is a signature of the same instability predicted by the linear theory, although slightly modified due to streamwise confinement.

Stability of jets in a shallow water layer

2015 ◽  
Vol 25 (2) ◽  
pp. 358-374 ◽  
Author(s):  
Zhanhong Wan ◽  
Saihua Huang ◽  
Zhilin Sun ◽  
Zhenjiang You
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Shallow Water ◽  
Large Scale ◽  
Bottom Topography ◽  
Bottom Friction ◽  
Rossby Number ◽  
Content Type ◽  
The Stability ◽  
Topographic Parameters

Purpose – The present work is devoted to the numerical study of the stability of shallow jet. The effects of important parameters on the stability behavior for large scale shallow jets are considered and investigated. Connections between the stability theory and observed features reported in the literature are emphasized. The paper aims to discuss these issues. Design/methodology/approach – A linear stability analysis of shallow jet incorporating the effects of bottom topography, bed friction and viscosity has been carried out by using the shallow water stability equation derived from the depth averaged shallow water equations in conjunction with both Chézy and Manning resistance formulae. Effects of the following main factors on the stability of shallow water jets are examined: Rossby number, bottom friction number, Reynolds number, topographic parameters, base velocity profile and resistance model. Special attention has been paid to the Coriolis effects on the jet stability by limiting the rotation number in the range of Ro∈[0, 1.0]. Findings – It is found that the Rossby number may either amplify or attenuate the growth of the flow instability depending on the values of the topographic parameters. There is a regime where the near cancellation of Coriolis effects due to other relevant parameters influences is responsible for enhancement of stability. The instability can be suppressed by the bottom friction when the bottom friction number is large enough. The amplification rate may become sensitive to the relatively small Reynolds number. The stability region using the Manning formula is larger than that using the Chézy formula. The combination of these effects may stabilize or destabilize the shallow jet flow. These results of the stability analysis are compared with those from the literature. Originality/value – Results of linear stability analysis on shallow jets along roughness bottom bed are presented. Different from the previous studies, this paper includes the effects of bottom topography, Rossby number, Reynolds number, resistance formula and bed friction. It is found that the influence of Reynolds number on the stability of the jet is notable for relative small value. Therefore, it is important to experimental investigators that the viscosity should be considered with comparison to the results from inviscid assumption. In contrast with the classical analysis, the use of multi-parameters of the base velocity and topographic profile gives an extension to the jet stability analysis. To characterize the large scale motion, besides the bottom friction as proposed in the related literature, the Reynolds number Re, Rossby number Ro, the topographic parameters and parameters controlling base velocity profile may also be important to the stability analysis of shallow jet flows.

scholarly journals Local stability analysis and eigenvalue sensitivity of reacting bluff-body wakes

2016 ◽  
Vol 788 ◽  
pp. 549-575 ◽  
Author(s):  
Benjamin Emerson ◽  
Tim Lieuwen ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Acoustic Waves ◽  
Local Stability ◽  
Bluff Body ◽  
Density Ratio ◽  
Global Mode ◽  
Eigenvalue Sensitivity ◽  
Local Stability Analysis ◽  
Measured Time ◽  
The Stability

This paper presents an experimental and theoretical investigation of high-Reynolds-number low-density reacting wakes near a hydrodynamic Hopf bifurcation. This configuration is applicable to the wake flows that are commonly used to stabilize flames in high-velocity flows. First, an experimental study is conducted to measure the limit-cycle oscillation of this reacting bluff-body wake. The experiment is repeated while independently varying the bluff-body lip velocity and the density ratio across the flame. In all cases, the wake exhibits a sinuous oscillation. Linear stability analysis is performed on the measured time-averaged velocity and density fields. In the first stage of this analysis, a local spatiotemporal stability analysis is performed on the measured time-averaged velocity and density fields. The stability analysis results are compared to the experimental measurement and demonstrate that the local stability analysis correctly captures the influence of the lip-velocity and density-ratio parameters on the sinuous mode. In the second stage of the analysis, the linear direct and adjoint global modes are estimated by combining the local results. The sensitivity of the eigenvalue to changes in intrinsic feedback mechanisms is found by combining the direct and adjoint global modes. This is referred to as the eigenvalue sensitivity throughout the paper for reasons of brevity. The predicted global mode frequency is consistently within 10 % of the measured value, and the linear global mode shape closely resembles the measured nonlinear oscillations. The adjoint global mode reveals that the oscillation is strongly sensitive to open-loop forcing in the shear layers. The eigenvalue sensitivity identifies a wavemaker in the recirculation zone of the wake. A parametric study shows that these regions change little when the density ratio and lip velocity change. In the third stage of the analysis, the stability analysis is repeated for the varicose hydrodynamic mode. Although not physically observed in this unforced flow, the varicose mode can lock into longitudinal acoustic waves and cause thermoacoustic oscillations to occur. The paper shows that the local stability analysis successfully predicts the global hydrodynamic stability characteristics of this flow and shows that experimental data can be post-processed with this method in order to identify the wavemaker regions and the regions that are most sensitive to external forcing, for example from acoustic waves.

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.

The effect of surfactant on the stability of a fluid filament embedded in a viscous fluid

1999 ◽  
Vol 382 ◽  
pp. 331-349 ◽  
Author(s):  
S. HANSEN ◽  
G. W. M. PETERS ◽  
H. E. H. MEIJER
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Viscous Fluid ◽  
High Elasticity ◽  
Fluid Filament ◽  
The Stability ◽  
Elasticity Number

The effect of surfactant on the breakup of a viscous filament, initially at rest, surrounded by another viscous fluid is studied using linear stability analysis. The role of the surfactant is characterized by the elasticity number – a high elasticity number implies that surfactant is important. As expected, the surfactant slows the growth rate of disturbances. The influence of surfactant on the dominant wavenumber is less trivial. In the Stokes regime, the dominant wavenumber for most viscosity ratios increases with the elasticity number; for filament to matrix viscosity ratios ranging from about 0.03 to 0.4, the dominant wavenumber decreases when the elasticity number increases. Interestingly, a surfactant does not affect the stability of a filament when the surface tension (or Reynolds) number is very large.

scholarly journals Numerical Method for the Stability Analysis of Ideal MHD Modes with a Wide Range of Toroidal Mode Numbers in Tokamaks

2007 ◽  
Vol 2 (0) ◽  
pp. 010-010 ◽  
Author(s):  
Nobuyuki AIBA ◽  
Shinji TOKUDA ◽  
Takaaki FUJITA ◽  
Takahisa OZEKI ◽  
Ming S. CHU ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Toroidal Mode ◽  
Wide Range ◽  
Ideal Mhd ◽  
The Stability

Flow and Heat Transfer in an Internally Ribbed Duct With Rotation: An Assessment of LES and URANS

2003 ◽  
Author(s):  
A. K. Saha ◽  
Sumanta Acharya
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Density Ratio ◽  
Navier Stokes ◽  
Flow And Heat Transfer ◽  
Number Ratio ◽  
Wide Range ◽  
Side Walls ◽  
Subgrid Stresses

Large Eddy Simulations (LES) and Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations have been performed for flow and heat transfer in a rotating ribbed duct. The ribs are oriented normal to the flow and arranged in a staggered configuration on the leading and trailing surfaces. The LES results are based on a higher-order accurate finite difference scheme with a dynamic Smagorinsky model for the subgrid stresses. The URANS procedure utilizes a two equation k-ε model for the turbulent stresses. Both Coriolis and centrifugal buoyancy effects are included in the simulations. The URANS computations have been carried out for a wide range of Reynolds number (Re = 12,500–100,000), rotation number (Ro = 0–0.5) and density ratio (Δρ/ρ = 0–0.5), while LES results are reported for a single Reynolds number of 12,500 without and with rotation (Ro = 0.12, Δρ/ρ = 0.13). Comparison is made between the LES and URANS results, and the effects of various parameters on the flow field and surface heat transfer are explored. The LES results clearly reflect the importance of coherent structures in the flow, and the unsteady dynamics associated with these structures. The heat transfer results from both LES and URANS are found to be in reasonable agreement with measurements. LES is found to give higher heat transfer predictions (5–10% higher) than URANS. The Nusselt number ratio (Nu/Nu0) is found to decrease with increasing Reynolds number on all walls, while they increase with the density ratio along the leading and trailing walls. The Nusselt number ratio on the trailing and side walls also increases with rotation. However, the leading wall Nusselt number ratio shows an initial decrease with rotation (till Ro = 0.12) due to the stabilizing effect of rotation on the leading wall. However, beyond Ro = 0.12, the Nusselt number ratio increases with rotation due to the importance of centrifugal-buoyancy at high rotation.

scholarly journals Laminar–turbulent transition in pipe flow for Newtonian and non-Newtonian fluids

1998 ◽  
Vol 377 ◽  
pp. 267-312 ◽  
Author(s):  
A. A. DRAAD ◽  
G. D. C. KUIKEN ◽  
F. T. M. NIEUWSTADT
Keyword(s):  
Reynolds Number ◽  
Pipe Flow ◽  
Polymer Solutions ◽  
Reynolds Numbers ◽  
Cylindrical Pipe ◽  
Turbulent Transition ◽  
Wide Range ◽  
Flow Changes ◽  
Transition Points ◽  
The Stability

A cylindrical pipe facility with a length of 32 m and a diameter of 40 mm has been designed. The natural transition Reynolds number, i.e. the Reynolds number at which transition occurs as a result of non-forced, natural disturbances, is approximately 60 000. In this facility we have studied the stability of cylindrical pipe flow to imposed disturbances. The disturbance consists of periodic suction and injection of fluid from a slit over the whole circumference in the pipe wall. The injection and suction are equal in magnitude and each distributed over half the circumference so that the disturbance is divergence free. The amplitude and frequency can be varied over a wide range.First, we consider a Newtonian fluid, water in our case. From the observations we compute the critical disturbance velocity, which is the smallest disturbance at a given Reynolds number for which transition occurs. For large wavenumbers, i.e. large frequencies, the dimensionless critical disturbance velocity scales according to Re−1, while for small wavenumbers, i.e. small frequencies, it scales as Re−2/3. The latter is in agreement with weak nonlinear stability theory. For Reynolds numbers above 30 000 multiple transition points are found which means that increasing the disturbance velocity at constant dimensionless wavenumber leads to the following course of events. First, the flow changes from laminar to turbulent at the critical disturbance velocity; subsequently at a higher value of the disturbance it returns back to laminar and at still larger disturbance velocities the flow again becomes turbulent.Secondly, we have carried out stability measurements for (non-Newtonian) dilute polymer solutions. The results show that the polymers reduce in general the natural transition Reynolds number. The cause of this reduction remains unclear, but a possible explanation may be related to a destabilizing effect of the elasticity on the developing boundary layers in the entry region of the flow. At the same time the polymers have a stabilizing effect with respect to the forced disturbances, namely the critical disturbance velocity for the polymer solutions is larger than for water. The stabilization is stronger for fresh polymer solutions and it is also larger when the polymers adopt a more extended conformation. A delay in transition has been only found for extended fresh polymers where delay means an increase of the critical Reynolds number, i.e. the number below which the flow remains laminar at any imposed disturbance.

A Method for Correlating the Influence of External Crossflow on the Discharge Coefficients of Film Cooling Holes

2000 ◽  
Author(s):  
D. A. Rowbury ◽  
M. L. G. Oldfield ◽  
G. D. Lock
Keyword(s):  
Reynolds Number ◽  
Mach Number ◽  
Film Cooling ◽  
Guide Vane ◽  
Density Ratio ◽  
External Flow ◽  
Published Data ◽  
Discharge Coefficients ◽  
Wide Range ◽  
Film Cooling Holes

An empirical means of predicting the discharge coefficients of film cooling holes in an operating engine has been developed. The method quantifies the influence of the major dimensionless parameters, namely hole geometry, pressure ratio across the hole, coolant Reynolds number, and the freestream Mach number. The method utilises discharge coefficient data measured on both a first-stage high-pressure nozzle guide vane from a modern aero-engine and a scale (1.4 times) replica of the vane. The vane has over 300 film cooling holes, arranged in 14 rows. Data was collected for both vanes in the absence of external flow. These non-crossflow experiments were conducted in a pressurised vessel in order to cover the wide range of pressure ratios and coolant Reynolds numbers found in the engine. Regrettably, the proprietary nature of the data collected on the engine vane prevents its publication, although its input to the derived correlation is discussed. Experiments were also conducted using the replica vanes in an annular blowdown cascade which models the external flow patterns found in the engine. The coolant system used a heavy foreign gas (SF6/Ar mixture) at ambient temperatures which allowed the coolant-to-mainstream density ratio and blowing parameters to be matched to engine values. These experiments matched the mainstream Reynolds and Mach numbers and the coolant Mach number to engine values, but the coolant Reynolds number was not engine representative (Rowbury et al., 1997 and 1998). A correlation for discharge coefficients in the absence of external crossflow has been derived from this data and other published data. An additive loss coefficient method is subsequently applied to the cascade data in order to assess the effect of the external crossflow. The correlation is used successfully to reconstruct the experimental data. It is further validated by successfully predicting data published by other researchers. The work presented is of considerable value to gas turbine design engineers as it provides an improved means of predicting the discharge coefficients of engine film cooling holes.

Stability Analysis of QFT Controllers Designed for Hydraulic Actuators Using Takagi-Sugeno Fuzzy Modeling Approach

2013 ◽  
Author(s):  
Masoumeh Esfandiari ◽  
Nariman Sepehri
Keyword(s):  
Stability Analysis ◽  
Linear Models ◽  
Fuzzy Model ◽  
Hydraulic Actuators ◽  
Local Linear ◽  
Guaranteed Stability ◽  
Wide Range ◽  
Position Controller ◽  
The Stability ◽  
Takagi Sugeno

Although, robust controllers that have been designed for hydraulic actuators based on quantitative feedback theory (QFT) have shown satisfactory performance, their stability is limited to certain set of inputs-outputs. This paper explores, for the first time, the stability of a QFT controller using stability theorem of Takagi-Sugeno (T-S) fuzzy systems. To do this, first the hydraulic closed-loop system is represented by a T-S fuzzy model that is formed through a nonlinear combination of some local linear models. Next, the stability of the resulting T-S fuzzy system is analyzed simply by stability analysis of its local linear models. This approach is used to study the stability of a QFT position controller previously developed for hydraulic actuators. Results show guaranteed stability of the QFT controller over a wide range of operation and in the presence of parametric uncertainties.

Sign in / Sign up

Export Citation Format

Share Document