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 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 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 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.

scholarly journals Wave Characteristics of Falling Film on Inclination Plate at Moderate Reynolds Number

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Chuan Lu ◽  
Sheng-Yao Jiang ◽  
Ri-Qiang Duan
Keyword(s):  
Reynolds Number ◽  
Solitary Wave ◽  
Film Flow ◽  
Three Dimensional ◽  
Wave Pattern ◽  
Two Dimensional ◽  
Irregular Wave ◽  
Moderate Reynolds Number ◽  
Pulse Spacing ◽  
Primary Pulse

Falling water film on an inclined plane is studied by shadowgraphy. The ranges of inclination angle and the film Reynolds number are, respectively, up to 21° and 60. Water is used as working fluid. The scenario of wave regime evolution is identified as three distinctive regimes, namely, initial quiescent smooth film flow, two-dimensional regular solitary wave pattern riding on film flow, and three-dimensional irregular wave pattern. Three characteristic parameters of two-dimensional solitary wave pattern, namely, inception length, primary pulse spacing, and propagation velocity, are examined, which are significant in engineering applications for estimation of heat and mass transfer on film flow. The present experimental data are well in agreement with the Koizumi correlations, the deviation from which is limited to 20% and 15%, respectively, for primary pulse spacing and propagation velocity. Through the scrutiny of the present experimental observation, it is concluded that wave evolution on film flow at the moderate Reynolds number is controlled by gravity and drag and the Rayleigh-Taylor instability that occurred on the steep front of primary pulse triggers the disintegration of continuous two-dimensional regular solitary wave pattern into three-dimensional irregular wave pattern.

Long-Wave and Integral Boundary Layer Analysis of Falling Film Flow on Walls With Three-Dimensional Periodic Structures

2009 ◽  
Author(s):  
Tatiana Gambaryan-Roisman ◽  
Hongyi Yu ◽  
Karsten Lo¨ffler ◽  
Peter Stephan
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Inclination Angle ◽  
Film Flow ◽  
Three Dimensional ◽  
Falling Film ◽  
Integral Boundary ◽  
Long Wave ◽  
Surface Patterns ◽  
Periodic Microstructures

Falling films exhibit very complex wavy patterns, which depend on the properties of the liquid, the Reynolds number, the wall inclination angle, and the distance from the film inlet. The film hydrodynamics and the surface patterns have a high impact on heat and mass transfer. Our aim is to control and enhance heat and mass transport by using walls with specific micro topographies that influence the falling film flow, stability and wavy pattern. In the present work long-wave theory and integral boundary layer (IBL) approximation are used for modelling the falling film flow on walls with three-dimensional periodic microstructures. The wall topography is periodic both in the main flow direction and in the transverse direction. Examples of such microstructures are longitudinal grooves with sinusoidal path (or meandering grooves) and herringbone structures. The effects of the Reynolds number, the wall inclination angle and the longitudinal and transverse periods of the structure on the shape of liquid-gas interface are investigated. It is shown that, as opposed to straight grooves in longitudinal direction, grooves with meandering path may lead to significant interface deformations.

scholarly journals Analysis of heat transfer in a heated tube with a different typed disc insertion

2012 ◽  
Vol 16 (1) ◽  
pp. 139-149
Author(s):  
Betül Turan ◽  
Hakan Öztop
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Finite Volume ◽  
Inclination Angle ◽  
Two Dimensional ◽  
Governing Equations ◽  
Heated Tube ◽  
Flat Side ◽  
Two Dimensional Flow

Heat transfer and fluid flow can be controlled in a tube by inserting different typed passive elements. The main objective of this study is to control heat transfer and fluid flow using cutting edged disc in pipe. Governing equations of laminar, two-dimensional flow is solved via finite volume technique. The disc is adiabatic and its thickness is 5mm. It is located into axial axis of the tube. Three cases were applied based on the type of the disc as inclination angle of the top side is 45? and 0?. Calculations were performed for different Reynolds number in the range of 335 < Re < 845. Three cases were tested based on types of discs. It is observed that each position exhibits different heat transfer ratio according to studied Reynolds number. The highest heat transfer is formed when inlet flow impinges to flat side of the cutting edged baffle.

scholarly journals Linear spatio-temporal instability analysis of ice growth under a falling water film

2010 ◽  
Vol 649 ◽  
pp. 453-466 ◽  
Author(s):  
JUN HU ◽  
BING-HONG ZHOU ◽  
YI-HONG HANG ◽  
QIU-SHENG LIU ◽  
SHU-DAO ZHANG
Keyword(s):  
Reynolds Number ◽  
Critical Reynolds Number ◽  
Temporal Stability ◽  
Water Film ◽  
Boundary Curve ◽  
Incline Angle ◽  
Ice Growth ◽  
Convective Instabilities ◽  
Spatio Temporal ◽  
Inclined Angle

A linear spatio-temporal stability analysis is conducted for the ice growth under a falling water film along an inclined ice plane. The full system of linear stability equations is solved by using the Chebyshev collocation method. By plotting the boundary curve between the linear absolute and convective instabilities (AI/CI) of the ice mode in the parameter plane of the Reynolds number and incline angle, it is found that the linear absolute instability exists and occurs above a minimum Reynolds number and below a maximum inclined angle. Furthermore, by plotting the critical Reynolds number curves with respect to the inclined angle for the downstream and upstream branches, the convectively unstable region is determined and divided into three parts, one of which has both downstream and upstream convectively unstable wavepackets and the other two have only downstream or upstream convectively unstable wavepacket. Finally, the effect of the Stefan number and the thickness of the ice layer on the AI/CI boundary curve is investigated.

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