Linear Stability Analysis of Convection in Two-Layer System with an Evaporating Vapor-Liquid Interface

Classical theories have successfully provided an explanation for convection in a liquid layer heated from below without evaporation. However, these theories are inadequate to account for the convective instabilities in an evaporating liquid layer, especially in the case when it is cooled from below. In the present paper, we study the onset of Marangoni convection in a liquid layer being overlain by a vapor layer.A new two-sided model is put forward instead of the one-sided model in previous studies. Marangoni-Bénard instabilities in evaporating liquid thin layers are investigated with a linear instability analysis. We define a new evaporation Biot number, which is different from that in previous studies and discuss the influences of reference evaporating velocity and evaporation Biot number on the vapor-liquid system. At the end, we explain why the instability occurs even when an evaporating liquid layer is cooled from below.

A Linear Stability Analysis Of Large-Prandtl-Number Thermocapillary Liquid Bridges

A linear stability analysis is applied to determine the onset of oscillatory thermocapillary convection in cylindrical liquid bridges of large Prandtl numbers (4 <= Pr <= 50). We focus on the relationships between the critical Reynolds number Re-c, the azimuthal wave number m, the aspect ratio F and the Prandtl number Pr. A detailed Re-c-Pr stability diagram is given for liquid bridges with various Gamma. In the region of Pr > 1, which has been less studied previously and where Re, has been usually believed to decrease with the increase of Pr, we found Re-c exhibits an early increase for liquid bridges with Gamma around one. From the computed surface temperature gradient, it is concluded that the boundary layers developed at both solid ends of liquid bridges strengthen the stability of basic axisymmetric thermocapillary convection at large Prandtl number, and that the stability property of the basic flow is determined by the "effective" part of liquid bridge. (c) 2008 Published by Elsevier Ltd on behalf of COSPAR.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Stability Analysis Of The Moving Interface In Piston- And Non-Piston-Like Displacements

From the macroscopic point of view, expressions involving reservoir and operational parameters are established for investigating the stability of moving interface in piston- and non-piston-like displacements. In the case of axi-symmetrical piston-like displacement, the stability is related to the moving interface position and water to oil mobility ratio. The capillary effect on the stability of moving interface depends on whether or not the moving interface is already stable and correlates with the wettability of the reservoir rock. In the case of non-piston-like displacement, the stability of the front is governed by both the relative permeability and the mobility ratio.

Effects of wall temperature on boundary layer stability over a blunt cone at Mach 7.99

Effects of wall temperature on stabilities of hypersonic boundary layer over a 7-degree half-cone-angle blunt cone are studied by using both direct numerical simulation (DNS) and linear stability theory (LST) analysis. Four isothermal wall cases with Tw/T0= 0.5, 0.7, 0.8 and 0.9, as well as an adiabatic wall case are considered. Results of both DNS and LST indicate that wall temperature has significant effects on the growth of disturbance waves. Cooling the surface accelerates unstable Mack II mode waves and decelerates the first mode (Tollmien–Schlichting mode) waves. LST results show that growth rate of the most unstable Mack II mode waves for the cases of cold wall Tw/T0=0.5 and 0.7 are about 45% and 25% larger than that for the adiabatic wall, respectively. Numerical results show that surface cooling modifies the profiles of rdut/dyn and temperature in the boundary layers, and thus changes the stability haracteristic of the boundary layers, and then effects on the growth of unstable waves. The results of DNS indicate that the disturbances with the frequency range from about 119.4 to 179.1 kHz, including the most unstable Mack modes, produce strong mode competition in the downstream region from about 11 to 100 nose radii. And adiabatic wall enhances the amplitudes of disturbance according to the results of DNS, although the LST indicates that the growth rate of the disturbance of cold wall is larger. That because the growth of the disturbance does not only depend on the development of the second unstable mode.

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

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.

Novel Investigation on Principle of Similarity for Microgravity Two-Phase Flow

根据两流体同心环状流线性稳定性分析的结果 ,对微重力气 /液两相流地面模拟实验所应遵循的相似准则进行了探讨 ,得到了一个新的重力无关性准则 ,即Bond数和环形区流体相的毛细数之比的绝对值不大于 1 .此外 ,微重力气 /液两相流模拟实验还必须满足两个条件 ,即流量比和气相表观Weber数应与所模拟的流动中对应数值相等 . In the present paper, the principle of similarity for two phase flows at microgravity is studied based on the results of the linear stability analysis of the two fluid concentric annular flow configuration. A new criterion of gravity independence, namely the absolute value of the ratio between the Bond number and the capillary number of the phase flowing in the annulus is no more than one, is achieved. It is also pointed out that the flowrate ratio and the gas superficial Weber number must have the same ...

Oscillatory Instabilities of Two-Layer Rayleigh-Marangoni-Benard Convection

The Rayleigh–Marangoni–Bénard convective instability (R–M–B instability) in the two-layer systems such as Silicone oil (10cSt)/Fluorinert (FC70) and Silicone oil (2cSt)/water liquids are studied. Both linear instability analysis and nonlinear instability analysis (2D numerical simulation) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. The results show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. The secondary instability phenomenon found in the real two-layer system of Silicone oil over water could explain the difference in the comparison of the Degen’s experimental observation with the previous linear stability analysis results of Renardy et al.

Influence Of Rayleigh Effect Combined With Marangoni Effect On The Onset Of Convection In A Liquid Layer Overlying A Porous Layer

The coupling mechanism of Rayleigh effect and Marangoni effect in a liquid-porous system is investigated using a linear stability analysis. The eigenvalue problem is solved by means of a Chebyshev tau method. Results indicate that there are three coupling modes between the Rayleigh effect and the Marangoni effect for different depth ratios. (C) 2008 Elsevier Ltd. All rights reserved.

Direct Numerical Simulation Of Hypersonic Boundary-Layer Transition Over A Blunt Cone

Direct numerical simulation of transition How over a blunt cone with a freestream Mach number of 6, Reynolds number of 10,000 based on the nose radius, and a 1-deg angle of attack is performed by using a seventh-order weighted essentially nonoscillatory scheme for the convection terms of the Navier-Stokes equations, together with an eighth-order central finite difference scheme for the viscous terms. The wall blow-and-suction perturbations, including random perturbation and multifrequency perturbation, are used to trigger the transition. The maximum amplitude of the wall-normal velocity disturbance is set to 1% of the freestream velocity. The obtained transition locations on the cone surface agree well with each other far both cases. Transition onset is located at about 500 times the nose radius in the leeward section and 750 times the nose radius in the windward section. The frequency spectrum of velocity and pressure fluctuations at different streamwise locations are analyzed and compared with the linear stability theory. The second-mode disturbance wave is deemed to be the dominating disturbance because the growth rate of the second mode is much higher than the first mode. The reason why transition in the leeward section occurs earlier than that in the windward section is analyzed. It is not because of higher local growth rate of disturbance waves in the leeward section, but because the growth start location of the dominating second-mode wave in the leeward section is much earlier than that in the windward section.

Thermocapillary Flows In Liquid Bridges Of Molten Tin With Small Aspect Ratios

Numerical simulations were conducted to study thermocapillary flows in short half-zone liquid bridges of molten tin with Prandtl number Pr = 0.009, under ramped temperature difference. The spatio-temporal structures in the thermocapillary flows in short half-zone liquid bridges with aspect ratios As = 0.6, 0.8, and 1.0 were investigated. The first critical Marangoni numbers were compared with those predicted by linear stability analyses (LSA). The second critical Marangoni numbers for As = 0.6 and 0.8 were found to be larger than that for As = 1.0. The time evolutions of the thermocapillary flows exhibited unusual features such as a change in the azimuthal wave number during the three-dimensional stationary (non-oscillating) flow regime, a change in the oscillation mode during the three-dimensional oscillatory flow regime, and the decreasing and then increasing of amplitudes in a single oscillation mode. The effects of the ramping rate of the temperature difference on the flow modes and critical conditions were studied as well. In this paper, the experimental observability of the critical conditions was also discussed. (C) 2008 Elsevier Inc. All rights reserved.

Hydrothermal Instability Of Thermocapillary Convection In Large-Prandtl-Number Liquid Bridges Under Microgravity

Linear stability analysis was performed to study the mechanism of transition of thermocapillary convection in liquid bridges with liquid volume ratios ranging from 0.4 to 1.2, aspect ratio of 0.75 and Prandtl number of 100. 2-D governing equations were solved to obtain the steady axi-symmetric basic flow and temperature distributions. 3-D perturbation equations were discretized at the collocation grid points using the Chebyshev-collocation method. Eigenvalues and eigenfunctions were obtained by using the Q-R. method. The predicted critical Marangoni numbers and critical frequencies were compared with data from space experiments. The disturbance of the temperature distribution on the free surface causes the onset of oscillatory convection. It is shown that the origin of instability is related to the hydrothermal origin for convections in large-Prandtl-number liquid bridges. (C) 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

A new dynamic model for study of dislocation pattern formation

Based on the principle given in nonlinear diffusion-reaction dynamics, a new dynamic model for dislocation patterning is proposed by introducing a relaxation time to the relation between dislocation density and dislocation flux. The so-called chemical potential like quantities, which appear in the model can be derived from variation principle for free energy functional of dislocated media, where the free energy density function is expressed in terms of not only the dislocation density itself but also their spatial gradients. The Linear stability analysis on the governing equations of a simple dislocation density shows that there exists an intrinsic wave number leading to bifurcation of space structure of dislocation density. At the same time, the numerical results also demonstrate the coexistence and transition between different dislocation patterns.

线性稳定性理论在圆管充分发展两相流型研究中的应用

圆截面光滑直管内充分发展的两流体同心环状流的线性稳定性研究不仅具有重要的学术意义，而且在预测两相流型转换方面有着重要应用。本文评述了该流动构型的线性稳定性研究进展，着重分析了该流动构型的失稳机制及其与两相流型转换间的关系，并针对微重力气－液两相流地面模拟实验问题，探讨了今后需要着重研究的若干方面。

Oscillatory Instabilities of Two-Layer Rayleigh-Marangoni-Benard Convection

The Rayleigh-Marangoni-Benard convective instability (R-M-B instability) in the two-layer systems such as Silicone oil (10cSt)/Fluorinert (FC70) and Silicone oil (2cSt)/water liquids are studied. Both linear instability analysis and nonlinear instability analysis (2D numerical simulation) were performed to study the influence of thermocapillary force on the convective instability of the two-layer system. The results show the strong effects of thermocapillary force at the interface on the time-dependent oscillations at the onset of instability convection. The secondary instability phenomenon found in the real two-layer system of Silicone oil over water could explain the difference in the comparison of the Degen's experimental observation with the previous linear stability analysis results of Renardy et al.