Instability and Frontal Breakup in Super-Meniscus Films

1996 ◽  
Vol 464 ◽  
Author(s):  
Dawn E. Kataoka ◽  
Sandra M. Troian
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Temperature Distribution ◽  
Liquid Film ◽  
Linear Stability Analysis ◽  
Surface Coverage ◽  
Flow Behavior ◽  
Leading Edge ◽  
Nonuniform Temperature ◽  
Unstable Flow

ABSTRACTSurface tension gradients created by a nonuniform temperature distribution in athin liquid film can force vertical spreading beyond the equilibrium meniscus [1]. Experiments designed to probe the flow behavior of super-meniscus films have shown that the leading edge can either spread uniformly with complete surface coverage or become corrugated and breakupinto long slender rivulets. We show that within linear stability analysis, both the conditions for unstable flow and the most unstable wavelength compare favorably with recent experiments reported in the literature.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

Stability Analysis of Thermocapillary Convection of B2O3/Sapphire Melt in an Annular Pool

2021 ◽  
Vol 1036 ◽  
pp. 175-184
Author(s):  
Dong Ming Mo
Keyword(s):  
Stability Analysis ◽  
Temperature Distribution ◽  
Thermocapillary Convection ◽  
Silicone Oil ◽  
Liquid Interface ◽  
Sapphire Crystal ◽  
Neutral Stability ◽  
Unstable Flow ◽  
Fluid Layers ◽  
Lower Fluid

Aiming at the thermocapillary convection stability of sapphire crystal grown by liquid-encapsulated Czochralski method, by non-linear numerical simulation, obtained the flow function and temperature distribution of R-Z cross section, as well as the velocity and temperature distribution at liquid-liquid interface and monitoring point of B2O3/sapphire melt in annular two liquid system, covered with solid upper wall and in microgravity. By means of linear stability analysis, obtained the neutral stability curve and critical stability parameters of the system, and revealed the temperature fluctuation of the liquid-liquid interface. The calculated results of B2O3/sapphire melt were compared with 5cSt silicone oil/HT-70. The results show that under the same geometrical conditions, the flow of B2O3/sapphire melt system is more unstable than 5cSt silicone oil/HT-70, there are two unstable flow patterns, radial three-dimensional steady flow cell and hydrothermal waves near the hot wall. The larger the ratio of Pr number of upper and lower fluid layers is, the better the effect of restraining the flow of lower fluid layers is.

Flow Behavior of a Centrifugal Compressor With Vaneless Diffuser at Design and Off Design Conditions

2012 ◽  
Author(s):  
Chuang Gao ◽  
Weiguang Huang ◽  
Haiqing Liu ◽  
Hongwu Zhang ◽  
Jundang Shi
Keyword(s):  
Centrifugal Compressor ◽  
Flow Behavior ◽  
Travelling Waves ◽  
Leading Edge ◽  
Pressure Oscillation ◽  
Rotating Stall ◽  
Vaneless Diffuser ◽  
Unstable Flow ◽  
Flow Recirculation ◽  
Static Performance

This paper concerns with the numerical and experimental aspects of both steady and unsteady flow behavior in a centrifugal compressor with vaneless diffuser and downstream collector. Specifically, the appearance of flow instabilities i.e., rotating stall and surge is investigated in great detail. As the first step, the static performance of both stage and component was analyzed and possible root cause of system surge was put forward based on the classic stability theory. Then the unsteady pressure data was utilized to find rotating stall and surge in frequency domain which could be classified as mild surge and deep surge. With the circumferentially installed transducers at impeller inlet, backward travelling waves during stall ramp could be observed. The modes of stall waves could be clearly identified which is caused by impeller leading edge flow recirculation at Mu = 0.96. However, for the unstable flow at Mu = 1.08, the system instability seems to be caused by reversal flow in vaneless diffuser where the pressure oscillation was strongest. Thus steady numerical simulation were performed and validated with the experimental performance data. With the help of numerical analysis, the conjectures are proved.

scholarly journals Towards the Understanding of Humpback Whale Tubercles: Linear Stability Analysis of a Wavy Flat Plate

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 212
Author(s):  
Miles Owen ◽  
Abdelkader Frendi
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Flat Plate ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Global Analysis ◽  
Leading Edge ◽  
Local Analysis ◽  
Mean Flow

The results from a temporal linear stability analysis of a subsonic boundary layer over a flat plate with a straight and wavy leading edge are presented in this paper for a swept and un-swept plate. For the wavy leading-edge case, an extensive study on the effects of the amplitude and wavelength of the waviness was performed. Our results show that the wavy leading edge increases the critical Reynolds number for both swept and un-swept plates. For the un-swept plate, increasing the leading-edge amplitude increased the critical Reynolds number, while changing the leading-edge wavelength had no effect on the mean flow and hence the flow stability. For the swept plate, a local analysis at the leading-edge peak showed that increasing the leading-edge amplitude increased the critical Reynolds number asymptotically, while the leading-edge wavelength required optimization. A global analysis was subsequently performed across the span of the swept plate, where smaller leading-edge wavelengths produced relatively constant critical Reynolds number profiles that were larger than those of the straight leading edge, while larger leading-edge wavelengths produced oscillating critical Reynolds number profiles. It was also found that the most amplified wavenumber was not affected by the wavy leading-edge geometry and hence independent of the waviness.

scholarly journals Shear instability of an axisymmetric air–water coaxial jet

2018 ◽  
Vol 843 ◽  
pp. 575-600 ◽  
Author(s):  
Jean-Philippe Matas ◽  
Antoine Delon ◽  
Alain Cartellier
Keyword(s):  
Surface Tension ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Convective Instability ◽  
Scaling Laws ◽  
Shear Instability ◽  
Liquid Jet ◽  
Absolute Instability ◽  
Instability Waves

We study the destabilization of a round liquid jet by a fast annular gas stream. We measure the frequency of the shear instability waves for several geometries and air/water velocities. We then carry out a linear stability analysis, and show that there are three competing mechanisms for the destabilization: a convective instability, an absolute instability driven by surface tension and an absolute instability driven by confinement. We compare the predictions of this analysis with experimental results, and propose scaling laws for wave frequency in each regime. We finally introduce criteria to predict the boundaries between these three regimes.

THE INFLUENCE OF INDIVIDUAL DRIVER CHARACTERISTICS ON CONGESTION FORMATION

2011 ◽  
Vol 22 (03) ◽  
pp. 305-318 ◽  
Author(s):  
LANJUN WANG ◽  
HAO ZHANG ◽  
HUADONG MENG ◽  
XIQIN WANG
Keyword(s):  
Stability Analysis ◽  
Traffic Flow ◽  
Linear Stability Analysis ◽  
Traffic Congestion ◽  
Velocity Model ◽  
Model Parameters ◽  
Unstable Flow ◽  
Optimal Velocity ◽  
Optimal Velocity Model ◽  
Langevin Approach

Previous works have pointed out that one of the reasons for the formation of traffic congestion is instability in traffic flow. In this study, we investigate theoretically how the characteristics of individual drivers influence the instability of traffic flow. The discussions are based on the optimal velocity model, which has three parameters related to individual driver characteristics. We specify the mappings between the model parameters and driver characteristics in this study. With linear stability analysis, we obtain a condition for when instability occurs and a constraint about how the model parameters influence the unstable traffic flow. Meanwhile, we also determine how the region of unstable flow densities depends on these parameters. Additionally, the Langevin approach theoretically validates that under the constraint, the macroscopic characteristics of the unstable traffic flow becomes a mixture of free flows and congestions. All of these results imply that both overly aggressive and overly conservative drivers are capable of triggering traffic congestion.

Imaging of Surface-Tension-Driven Convection Using Liquid Crystal Thermography

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
T. W. Dutton ◽  
L. R. Pate ◽  
D. K. Hollingsworth
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Liquid Crystal ◽  
Temperature Distribution ◽  
Liquid Film ◽  
Lower Boundary ◽  
Processing System ◽  
Metal Foil ◽  
Lower Boundary Condition ◽  
Liquid Crystal Thermography

Surface-tension forces can drive fluid motion within thin liquid layers with a free surface. Spatial variations in the temperature of the free surface create surface tractions that drive cellular motions. The cells are most commonly hexagonal in shape and they scale on the thickness of the fluid layer. This investigation documents the formation of cells in the liquid film in the presence of a uniform-heat-flux lower boundary condition. Liquid crystal thermography was used to image the cells and measure the temperature distribution on the lower surface of the liquid layer. A 1.1 mm deep pool of silicone oil was supported on a 50 μm thick electrically heated metal foil. The oil was retained inside an independently heated acrylic ring mounted on the top surface of the foil and a dry-ice cooling plate served as the low-temperature sink above the free surface of the oil. Color images of hexagonal convection cells were captured using liquid crystal thermography and a digital image acquisition and processing system. The temperature distribution inside a typical cell was measured using thermographic image analysis. Experimental issues, such as the use of an independently heated retaining ring to control the height of the liquid film and the utility of a flux-based Marangoni number are discussed.

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