Temporal stability of two-dimensional waves on evaporating or condensing liquid films

2002 ◽  
Author(s):  
Weiping Yan ◽  
Xuemin Ye ◽  
Yue Zhang
Keyword(s):  
Temporal Stability ◽  
Liquid Films ◽  
Two Dimensional

A Stability Investigation of Two-Dimensional Surface Waves on Evaporating, Isothermal or Condensing Liquid Films: Part I — Thermal Non-Equilibrium Effects on Wave Velocity

2004 ◽  
Author(s):  
Chunxi Li ◽  
Xuemin Ye
Keyword(s):  
Wave Velocity ◽  
Temporal Stability ◽  
Reynolds Numbers ◽  
Liquid Films ◽  
Two Dimensional ◽  
Stability Equation ◽  
Equilibrium Conditions ◽  
Inclined Angle ◽  
Prandtl Boundary Layer ◽  
Non Equilibrium

When the liquid film is in the process of evaporation or condensation, the interfacial thermal non-equilibrium conditions are evidently different from that of isothermal film, and this difference will affect the flow stability and wave velocity of thin liquid films. The temporal stability equation of the two-dimensional traveling waves of evaporating or condensing liquid films falling down an inclined wall is established based on the Prandtl boundary layer theory and complete boundary conditions. The effects on wave velocity of evaporating, isothermal and condensing states, thermocapillarity, Reynolds number, fluid property and inclined angle are discussed, and are compared in different Reynolds numbers.

A Stability Investigation of Two-Dimensional Surface Waves on Evaporating, Isothermal or Condensing Liquid Films: Part III — Temporal Stability of Traveling Waves

2004 ◽  
Author(s):  
Xuemin Ye ◽  
Chunxi Li ◽  
Weiping Yan
Keyword(s):  
Reynolds Number ◽  
Inclination Angle ◽  
Traveling Waves ◽  
Film Flow ◽  
Temporal Stability ◽  
Liquid Films ◽  
Flow Stability ◽  
Condensation Process ◽  
Two Dimensional ◽  
Inclined Angle

The temporal stability equation of the two-dimensional traveling waves of evaporating or condensing liquid films falling down an inclined wall is established based on the Prandtl boundary layer theory and complete boundary conditions. By investigating the flow temporal characteristics curves, including the stability curves and stability curves of the fastest wave, the effects on flow stability of evaporating, isothermal and condensing states, thermocapillarity, Reynolds number, fluid property and inclined angle are discussed, and are compared in different Reynolds numbers. The theoretical study indicated that evaporation process destabilizes the film flow and condensation process stabilizes the film flow, the thermocapillarity take a destabilizing effect in evaporation condition and an adverse effect in condensation condition. Present study indicates that the temporal growth rate increases with increase of the Reynolds number and inclination angle, and decreases with increase of Ka numbers. And the effects on flow stability of liquid properties and inclination angle are always significant.

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.

A Two Dimensional Theory For Two Phase Detonation of Liquid Films

1971 ◽  
Vol 4 (1) ◽  
pp. 209-220 ◽  
Author(s):  
C. S. R. RAO ◽  
M. SICHEL ◽  
J. A. NICHOLLS
Keyword(s):  
Liquid Films ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Two Phase

Linear Spatial Evolution Formulation of Two-Dimensional Waves on Liquid Films Under Evaporating/Isothermal/Condensing Conditions

2002 ◽  
Author(s):  
Xuemin Ye ◽  
Chunxi Li ◽  
Weiping Yan
Keyword(s):  
Boundary Layer ◽  
Surface Tension ◽  
Reynolds Number ◽  
Evolution Equation ◽  
Film Thickness ◽  
Boundary Conditions ◽  
Liquid Films ◽  
Boundary Layer Theory ◽  
Spatial Evolution ◽  
Two Dimensional

The linear spatial evolution formulation of the two-dimensional waves of the 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. The evolution equation indicates that there are two different modes of waves in spatial evolution. And the flow stability is highly dependent on the evaporation or condensation, thermocapillarity, surface tension, inclination angle and Reynolds number.

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.

On perturbations of Jeffery-Hamel flow

1988 ◽  
Vol 186 ◽  
pp. 559-581 ◽  
Author(s):  
W. H. H. Banks ◽  
P. G. Drazin ◽  
M. B. Zaturska
Keyword(s):  
Stokes Equations ◽  
Temporal Stability ◽  
Pitchfork Bifurcation ◽  
Critical Value ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Nonlinear Perturbations ◽  
Navier Stokes Equations ◽  
Weakly Nonlinear ◽  
Rigid Plane

We examine various perturbations of Jeffery-Hamel flows, the exact solutions of the Navier-Stokes equations governing the steady two-dimensional motions of an incompressible viscous fluid from a line source at the intersection of two rigid plane walls. First a pitchfork bifurcation of the Jeffery-Hamel flows themselves is described by perturbation theory. This description is then used as a basis to investigate the spatial development of arbitrary small steady two-dimensional perturbations of a Jeffery-Hamel flow; both linear and weakly nonlinear perturbations are treated for plane and nearly plane walls. It is found that there is strong interaction of the disturbances up- and downstream if the angle between the planes exceeds a critical value 2α2, which depends on the value of the Reynolds number. Finally, the problem of linear temporal stability of Jeffery-Hamel flows is broached and again the importance of specifying conditions up- and downstream is revealed. All these results are used to interpret the development of flow along a channel with walls of small curvature. Fraenkel's (1962) approximation of channel flow locally by Jeffery-Hamel flows is supported with the added proviso that the angle between the two walls at each station is less than 2α2.

On the spatio-temporal stability of primary and secondary crossflow vortices in a three-dimensional boundary layer

2002 ◽  
Vol 456 ◽  
pp. 85-111 ◽  
Author(s):  
WERNER KOCH
Keyword(s):  
Saddle Point ◽  
High Frequency ◽  
Wave Packets ◽  
Temporal Stability ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Boundary ◽  
Spatio Temporal ◽  
Secondary Instabilities ◽  
Dimensional Wave

To examine possible links between a global instability and laminar–turbulent breakdown in a three-dimensional boundary layer, the spatio-temporal stability of primary and secondary crossflow vortices has been investigated for the DLR swept-plate experiment. In the absence of any available procedure for the direct verification of pinching for three-dimensional wave packets the alternative saddle-point continuation method has been applied. This procedure is known to give reliable results only in a certain vicinity of the most unstable ray. Therefore, finding no absolute instability by this method does not prove that the flow is absolutely stable. Accordingly, our results obtained this way need to be confirmed experimentally or by numerical simulations. A geometric interpretation of the time-asymptotic saddle-point result explains certain convergence and continuation problems encountered in the numerical wave packet analysis. Similar to previous results, all our three-dimensional wave packets for primary crossflow vortices were found to be convectively unstable.Due to prohibitive CPU time requirements the existing procedure for the verification of pinching for two-dimensional wave packets of secondary high-frequency instabilities could not be implemented. Again saddle-point continuation was used. Surprisingly, all two-dimensional wave packets of high-frequency secondary instabilities investigated were also found to be convectively unstable. This finding was corroborated by recent spatial direct numerical simulations of Wassermann & Kloker (2001) for a similar problem. This suggests that laminar–turbulent breakdown occurs after the high-frequency secondary instabilities enter the nonlinear stage, and spatial marching techniques, such as the parabolized stability equation method, should be applicable for the computation of these nonlinear states.

Highly Thermal Stable Lambda-Shaped Main-Chain Nonlinear Optical Polyimide

2005 ◽  
Vol 889 ◽  
Author(s):  
Hsieh-Chih Tsai ◽  
Wen-Jang Kuo ◽  
Ging-Ho Hsiue
Keyword(s):  
Glass Transition ◽  
Elevated Temperatures ◽  
Main Chain ◽  
Molecular Design ◽  
Polymer Networks ◽  
Temporal Stability ◽  
Two Dimensional ◽  
Transient Time ◽  
Polymer Backbone ◽  
Rigid Rod

ABSTRACTIn poled electro-optical (E-O) polymer systems, the relaxation of oriented chromophores is maintained by either introducing the guest chromophores into host polymers with high glass transition temperatures, or by confining the chromophores in polymer networks. Various highly stable NLO polymers have been prepared by grafting NLO-active chromophores onto aromatic polyimide backbones. The pendent chromophores of side chain polyimides can be stabilized at low temperature because they have rigid rod-like structures. However, the orientation decays quickly at elevated temperatures because the local free volumes that surround the chromophores increase. Taking advantage of the multifunctional characteristics of carbazole along with rational molecular design, a new NLO-active lambda-shape main-chain polyimide that comprises the two-dimensional carbazole chromophore was synthesized. This polyimide exhibits high thermal and temporal stability. it can endure as high as 240 °C in a transient time and maintain large SH signal at 100 °C for a long time. The high-glass transition polyimide as a matrix and embedding the two-dimensional chromophore into the polymer backbone are the major reasons that effectively restrict randomization of the oriented dipole.

Experimental and numerical study of vortex couples in two-dimensional flows

1986 ◽  
Vol 173 ◽  
pp. 225-251 ◽  
Author(s):  
Y. Couder ◽  
C. Basdevant
Keyword(s):  
Numerical Simulation ◽  
Turbulent Flows ◽  
Opposite Sign ◽  
Numerical Study ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Two Dimensional ◽  
Spontaneous Formation ◽  
Laboratory Results ◽  
Two Dimensional Flows

Two-dimensional turbulence is investigated experimentally in thin liquid films. This study shows the spontaneous formation of couples of opposite-sign vortices in von Kármán wakes. The structure of these couples, their behaviour and their role in turbulent flows is then studied using both a numerical simulation and laboratory results.

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