A Stability Investigation of Two-Dimensional Surface Waves on Evaporating, Isothermal or Condensing Liquid Films: Part II — A Universal Linear Stability Formulation

2004 ◽  
Author(s):  
Xuemin Ye ◽  
Weiping Yan ◽  
Chunxi Li
Keyword(s):  
Reynolds Number ◽  
Surface Waves ◽  
Isothermal Condition ◽  
Reynolds Numbers ◽  
Liquid Films ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Lower Reynolds Number ◽  
Liquid Property ◽  
Dimensional Surface

When liquid film is under evaporating or condensing conditions, the flow stability is clearly different to that under isothermal condition due to thermal non-equilibrium effect at interface, especially under lower Reynolds number. The universal linear temporal and spatial stability formulations of the two-dimensional surface waves on evaporating or isothermal or condensing liquid films are established in present paper with the collocation method based on the boundary layer theory and complete boundary conditions. The models include the effects of Reynolds number, thermocapillarity, inclination angle, liquid property, evaporation, isothermal or condensation. The effects of above factors are investigated with the neutral stability curves at different Reynolds numbers, and stabilities characteristics are fully indicated in theory for evaporating or condensing films.

Linear Stability of Two-Dimensional Stationary Waves on Evaporating or Condensing Liquid Films

2003 ◽  
Author(s):  
Xuemin Ye ◽  
Weiping Yan
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Liquid Films ◽  
Boundary Layer Theory ◽  
Stationary Waves ◽  
Two Dimensional ◽  
Stability Equation ◽  
Liquid Property

The linear spatial stability equation of the two-dimensional stationary waves of evaporating or isothermal or condensing liquid films falling down an inclined wall is established for the film thickness with the collocation method based on the boundary layer theory and complete boundary conditions. This model includes the effects of Reynolds number, thermocapillarity, inclination angle, liquid property, evaporation, isothermal or condensation. The stabilities characteristics of stationary waves are fully indicated in theory for evaporating or condensing films.

scholarly journals Three-dimensional Floquet stability analysis of the wake of a circular cylinder

1996 ◽  
Vol 322 ◽  
pp. 215-241 ◽  
Author(s):  
Dwight Barkley ◽  
Ronald D. Henderson
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Circular Cylinder ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Numerical Stability Analysis ◽  
Mode A

Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 188.5±1.0. The critical spanwise wavelength is 3.96 ± 0.02 diameters and the critical Floquet mode corresponds to a ‘Mode A’ instability. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0.822 diameters at onset. Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300.

Bifurcation Characteristics of Flows in Rectangular Sudden Expansion Channels

2005 ◽  
Author(s):  
Francine Battaglia ◽  
George Papadopoulos
Keyword(s):  
Reynolds Number ◽  
Laminar Flow ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Expansion Ratio ◽  
Sudden Expansion ◽  
Two Dimensional ◽  
Effective Expansion ◽  
Three Dimensional Simulations

The effect of three-dimensionality on low Reynolds number flows past a symmetric sudden expansion in a channel was investigated. The geometric expansion ratio of in the current study was 2:1 and the aspect ratio was 6:1. Both experimental velocity measurements and two- and three-dimensional simulations for the flow along the centerplane of the rectangular duct are presented for Reynolds numbers in the range of 150 to 600. Comparison of the two-dimensional simulations with the experiments revealed that the simulations fail to capture completely the total expansion effect on the flow, which couples both geometric and hydrodynamic effects. To properly do so requires the definition of an effective expansion ratio, which is the ratio of the downstream and upstream hydraulic diameters and is therefore a function of both the expansion and aspect ratios. When the two-dimensional geometry was consistent with the effective expansion ratio, the new results agreed well with the three-dimensional simulations and the experiments. Furthermore, in the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations was compared to other values reported in the literature. Overall, side-wall proximity was found to enhance flow stability, helping to sustain laminar flow symmetry to higher Reynolds numbers in comparison to nominally two-dimensional double-expansion geometries. Lastly, and most importantly, when the logarithm of the critical Reynolds number from all these studies was plotted against the reciprocal of the effective expansion ratio, a linear trend emerged that uniquely captured the bifurcation dynamics of all symmetric double-sided planar expansions.

Vortex Shedding From a Bluff Body Adjacent to a Plane Sliding Wall

1991 ◽  
Vol 113 (3) ◽  
pp. 384-398 ◽  
Author(s):  
M. P. Arnal ◽  
D. J. Goering ◽  
J. A. C. Humphrey
Keyword(s):  
Reynolds Number ◽  
Vortex Shedding ◽  
Bluff Body ◽  
Solid Wall ◽  
Reynolds Numbers ◽  
Careful Examination ◽  
Recirculation Region ◽  
Stream Velocity ◽  
Flow Past ◽  
Lower Reynolds Number

The characteristics of the flow around a bluff body of square cross-section in contact with a solid-wall boundary are investigated numerically using a finite difference procedure. Previous studies (Taneda, 1965; Kamemoto et al., 1984) have shown qualitatively the strong influence of solid-wall boundaries on the vortex-shedding process and the formation of the vortex street downstream. In the present study three cases are investigated which correspond to flow past a square rib in a freestream, flow past a rib on a fixed wall and flow past a rib on a sliding wall. Values of the Reynolds number studied ranged from 100 to 2000, where the Reynolds number is based on the rib height, H, and bulk stream velocity, Ub. Comparisons between the sliding-wall and fixed-wall cases show that the sliding wall has a significant destabilizing effect on the recirculation region behind the rib. Results show the onset of unsteadiness at a lower Reynolds number for the sliding-wall case (50 ≤ Recrit ≤100) than for the fixed-wall case (Recrit≥100). A careful examination of the vortex-shedding process reveals similarities between the sliding-wall case and both the freestream and fixed-wall cases. At moderate Reynolds numbers (Re≥250) the sliding-wall results show that the rib periodically sheds vortices of alternating circulation in much the same manner as the rib in a freestream; as in, for example, Davis and Moore [1982]. The vortices are distributed asymmetrically downstream of the rib and are not of equal strength as in the freestream case. However, the sliding-wall case shows no tendency to develop cycle-to-cycle variations at higher Reynolds numbers, as observed in the freestream and fixed-wall cases. Thus, while the moving wall causes the flow past the rib to become unsteady at a lower Reynolds number than in the fixed-wall case, it also acts to stabilize or “lock-in” the vortex-shedding frequency. This is attributed to the additional source of positive vorticity immediately downstream of the rib on the sliding wall.

A two-dimensional-three-component model for spanwise rotating plane Poiseuille flow

2019 ◽  
Vol 880 ◽  
pp. 478-496 ◽  
Author(s):  
Shengqi Zhang ◽  
Zhenhua Xia ◽  
Yipeng Shi ◽  
Shiyi Chen
Keyword(s):  
Reynolds Number ◽  
Poiseuille Flow ◽  
Reynolds Shear Stress ◽  
Streamwise Velocity ◽  
Channel Height ◽  
Neutral Stability ◽  
Two Dimensional ◽  
Plane Poiseuille Flow ◽  
Rotation Numbers ◽  
3C Model

Spanwise rotating plane Poiseuille flow (RPPF) is one of the canonical flow problems to study the effect of system rotation on wall-bounded shear flows and has been studied a lot in the past. In the present work, a two-dimensional-three-component (2D/3C) model for RPPF is introduced and it is shown that the present model is equivalent to a thermal convection problem with unit Prandtl number. For low Reynolds number cases, the model can be used to study the stability behaviour of the roll cells. It is found that the neutral stability curves, critical eigensolutions and critical streamfunctions of RPPF at different rotation numbers ($Ro$) almost collapse with the help of a rescaling with a newly defined Rayleigh number $Ra$ and channel height $H$. Analytic expressions for the critical Reynolds number and critical wavenumber at different $Ro$ can be obtained. For a turbulent state with high Reynolds number, the 2D/3C model for RPPF is self-sustained even without extra excitations. Simulation results also show that the profiles of mean streamwise velocity and Reynolds shear stress from the 2D/3C model share the same linear laws as the fully three-dimensional cases, although differences on the intercepts can be observed. The contours of streamwise velocity fluctuations behave like plumes in the linear law region. We also provide an explanation to the linear mean velocity profiles observed at high rotation numbers.

Detailed Flow Analysis Around Blade Tip With a Mie Vane in Case of Different Blade Aspect Ratios and Different Reynolds Numbers

2003 ◽  
Author(s):  
Yukimaru Shimizu ◽  
Edmond Ismaili ◽  
Yasunari Kamada ◽  
Takao Maeda
Keyword(s):  
Reynolds Number ◽  
Research Work ◽  
Flow Analysis ◽  
Reynolds Numbers ◽  
Power Coefficient ◽  
Work Related ◽  
Aspect Ratios ◽  
Power Increase ◽  
Lower Reynolds Number ◽  
Blade Tip

The results of an extensive experimental research work related to the performance of a HAWT with a tip-mounted Mie type vane are presented in this paper. From performance experiments carried out on four sets of blades with varying aspect ratios and for different Reynolds number, it was found that the application of a tip-mounted Mie vane resulted in a larger increase in maximum power coefficient for rotors with smaller aspect ratio and for lower Reynolds number. To investigate further the phenomenon and to explain the relationships found between power increase due to a Mie vane and blade aspect ratios and Reynolds number, detailed flow visualization around blade tip and the Mie vane were performed. It was found that the tendency of the power increase due to a Mie vane was dependent on the size of a corner vortex between blade tip and the downstream extension of the Mie vane.

Three-dimensional instabilities in the boundary-layer flow over a long rectangular plate

2011 ◽  
Vol 681 ◽  
pp. 411-433 ◽  
Author(s):  
HEMANT K. CHAURASIA ◽  
MARK C. THOMPSON
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Vortical Flow ◽  
Forced Flow ◽  
Recirculation Region ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Dimensional Instability

A detailed numerical study of the separating and reattaching flow over a square leading-edge plate is presented, examining the instability modes governing transition from two- to three-dimensional flow. Under the influence of background noise, experiments show that the transition scenario typically is incompletely described by either global stability analysis or the transient growth of dominant optimal perturbation modes. Instead two-dimensional transition effectively can be triggered by the convective Kelvin–Helmholtz (KH) shear-layer instability; although it may be possible that this could be described alternatively in terms of higher-order optimal perturbation modes. At least in some experiments, observed transition occurs by either: (i) KH vortices shedding downstream directly and then almost immediately undergoing three-dimensional transition or (ii) at higher Reynolds numbers, larger vortical structures are shed that are also three-dimensionally unstable. These two paths lead to distinctly different three-dimensional arrangements of vortical flow structures. This paper focuses on the mechanisms underlying these three-dimensional transitions. Floquet analysis of weakly periodically forced flow, mimicking the observed two-dimensional quasi-periodic base flow, indicates that the two-dimensional vortex rollers shed from the recirculation region become globally three-dimensionally unstable at a Reynolds number of approximately 380. This transition Reynolds number and the predicted wavelength and flow symmetries match well with those of the experiments. The instability appears to be elliptical in nature with the perturbation field mainly restricted to the cores of the shed rollers and showing the spatial vorticity distribution expected for that instability type. Indeed an estimate of the theoretical predicted wavelength is also a good match to the prediction from Floquet analysis and theoretical estimates indicate the growth rate is positive. Fully three-dimensional simulations are also undertaken to explore the nonlinear development of the three-dimensional instability. These show the development of the characteristic upright hairpins observed in the experimental dye visualisations. The three-dimensional instability that manifests at lower Reynolds numbers is shown to be consistent with an elliptic instability of the KH shear-layer vortices in both symmetry and spanwise wavelength.

Effects of the Divergence Angle on the Onset of Asymmetric Flow Through a Planar Diffuser

2009 ◽  
Author(s):  
Majid Nabavi ◽  
Luc Mongeau
Keyword(s):  
Reynolds Number ◽  
Flow Regime ◽  
Critical Reynolds Number ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Asymmetric Flow ◽  
Symmetric Flow ◽  
Turbulent Flow Regime ◽  
Flow Through ◽  
Gradual Expansion

In this study, two-dimensional laminar incompressible and turbulent compressible flow through the planar diffuser (gradual expansion) for different divergence half angles of the diffuser (θ), and different Reynolds numbers (Re) was numerically studied. The effects of θ on the critical Reynolds number at which the onset of asymmetric flow is observed, were investigated. In the laminar flow regime, it was observed that for every values of θ, there is a critical Re beyond which the flow is asymmetric. However, in the turbulent flow regime, for θ ≥ 20°, even at low Reynolds number the flow is asymmetric. Only for θ ≤ 10°, symmetric flow was observed below a critical Re.

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