Onset of Soret convection in a nanoparticles-suspension heated from above

The onset of Soret-driven convection in a nanoparticles suspension heated from above is analyzed theoretically based on linear theory and relative instability concept. A new set of stability equations are derived and solved by using the dominant mode method. The dimensionless critical time τ _c to mark the onset of instability is presented here as a function of the Rayleigh number, the Lewis number and the separation ratio. Available experimental data indicate that for large Rayleigh number convective motion is detected starting from a certain time τ≈3 τ _c . This means that the growth period of initiated instabilities is needed for convective motion to be detected experimentally. It seems evident that during τ _c ≤ τ ≤ 3 τ _c convective motion is relatively very weak and the primary diffusive transfer is dominant. This article is dedicated to Professor Chang Kyun Choi for celebrating his retirement from the School of Chemical and Biological Engineering, Seoul National University.     

Onset of buoyancy-driven convection in the horizontal fluid layer heated from below with time-dependent manner

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with time-dependent manner is analyzed by using propagation theory. Here the dimensionless critical time Τ_c to mark the onset of convective instability is presented as a function of the Rayleigh number Ra_Ø and the Prandtl number Pr. The present stability analysis predicts that Τ_c decreases with increasing Pr for a given Ra_Ø. The present predictions compare reasonably well with existing experimental results. It is found that in deep-pool systems the deviation of temperature profiles from conduction state occurs starting from a certain time Τ?(2～4) Τ_c .     

Thermal instability of plane poiseuille flow in the thermal entrance region

The onset of thermal convection in plane Poiseuille flow is investigated theoretically. New stability equations are derived by using the propagation theory considering the variations of disturbance amplitudes in the main flow direction. In the thermal entrance region an analytical procedure to predict the critical conditions for extremely small Prandtl-number fluids is described, based on the local similarity. For x_c≤0.01 the critical Rayleigh numbers are well represented in the whole domain of the Prandtl number by Ra_c = 200(1 + 0.123Pr^-1)Ra _C =200(1+0.123Pr⁻¹)x _C ⁻¹ under the conventional boundary layer theory. It is of much interest that the time-independent, three dimensional disturbances become more stable with a decrease in the Prandil number.     

Onset of buoyancy-driven convection in the horizontal fluid layer subjected to ramp heating from below

The onset of buoyancy-driven convection in an initially isothermal, quiescent fluid layer heated from below with a constant heating rate is analyzed by the propagation theory. Here the dimensionless critical time τ_c to mark the onset of convective motion is presented as a function of the Rayleigh number Ra_φ and the Prandtl number Pr. The present stability analysis predicts that for a given large Ra_φ, τ_c decreases with increasing Pr and it is independent of the conditions of the upper boundary. For deep-pool systems, the deviation of the temperature profile from conduction state occurs starting from a certain time τ_o≅4τ_c. The present predictions are compared with other models and existing experimental results in the whole time domain.     

The onset of Taylor-Görtler vortices in impulsively decelerating swirl flow

The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using propagation theory. It is well-known that the primary transient swirl flow is laminar, but with initial high velocities secondary motion sets in at a certain time. The dimensionless critical time Τ_c to mark the onset of instability is presented here as a function of the Reynolds number Re. Available experimental data indicate that for large Re deviation of the velocity profiles from their momentum diffusion occurs starting from a certain time Τ≈4Τ_c. This means that secondary motion is detected at this characteristic time. It seems evident that during Τ_c⪯Τ⪯4Τ_c, secondary motion is relatively very weak and the primary diffusive momentum transfer is dominant.     

The onset of Taylor-Görtler vortices during impulsive spin-down to rest

The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using the propagation theory. The primary transient swirl flow is laminar but for an initially high rotating speed secondary motion sets in at a certain time. It is found here that the critical Reynolds number Re_c=320, below which the flow is unconditionally stable. For Re>Re_c the dimensionless critical time τ_c to mark the onset of a fastest growing instability is presented as a function of the Reynolds number Re. Available experimental data and also predictions show that deviation of the velocity profiles from their primary ones occurs starting from a certain time τ≈4τ_c. This means that secondary motion is detected experimentally at this characteristic time. It seems that during τ_c?τ?4τ_c secondary motion is relatively very weak.     

The stability of a fluid layer heated uniformly from below

The onset of convective motion in a horizontal fluid layer under constant flux heating is analyzed by the modified frozen-time analysis confining temperature disturbances within a thermal penetration distance. For this purpose a new mathematical method is introduced in detail. It is found that the present stability analysis predicts the most reliable critical conditions based on the comparisons with the published experiments and theoretical models. At τ_c <0.01, the stability conditions lead to Ra_c = 14.1 τ _c ^-2 and a_c = 0.248 Ra _c ^1/4 and the period required for the growth of disturbances to a detectable size is inversely proportional to Ra _c ^1/2 .     

含相变颗粒流体的Rayleigh-Benard对流热启动

引　言含固液相变颗粒的乳胶液流体是一种混合物质的复杂流体,这种流体在化工、空调等工业领域有较好的应用潜力,近年来对它的研究比较活跃[1～3] .人们把在一定温度范围内的潜热变化归结为表观比热容或有效比热容.在相变温度范围内,由于热物性的剧烈变化,对流换热的机理研究也就显得十分必要.而Rayleigh Bnard对流问题是一个经典的复杂物理现象,它是指上下分别有固体冷却和加热面的自然对流问题.在重力场内,对水平放置的流体层,这种传热方式没有自然对流存在的充分条件,只有超过一定的临界状态时自然对流才会发生.由于这一问题也涉及到…     

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

The onset of Marangoni convection in an initially quiescent spherical droplet subjected to the impulsive change in boundary temperature is analyzed under the linear theory. For this system in which instabilities are driven by interface-tension gradients, a stability analysis on regular cell modes is conducted on the basis of the propagation theory we have developed. The present stability analysis predicts that τ _c decreases with increasing Ma. For the limiting case of τ→0, the present study approaches the planar limit as expected.     

The onset of Taylor-Görtler vortices in the time-dependent Couette flow induced by an impulsively imposed shear stress

The onset of Taylor-Görtler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τ _c to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as V _i ∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (V _i =constant). Based on the present τ _c and the Foster’s [1969] comment, the manifest stability guideline is suggested.     

On the onset of incipient fluidization

The onset of incipient fluidization is investigated theoretically and simulated by a computational fluid dynamics (CFD) procedure. The onset of incipient instability in a particle bed is preceded by stable gas diffusion in the interstices and is caused by a critical momentum force that may overcome the inertia of the particles. The critical momentum force is provided by the critical superficial gas velocity U_c in the form of critical mass flux of diffusion. It is found that the first movement of particles may be predicted by a critical transient Rayleigh number determined by a critical superficial velocity equals to the minimum fluidization velocity, U_mf. The onset of incipient fluidization was found to occur at a critical transient Rayleigh number of 3.1, which is close to the lowest theoretical value for buoyancy convection in a porous medium bounded by free surfaces. Consequently the onset times of incipient fluidization may be predicted accurately. The finding has been found to be supported by the present CFD study, past experiments and simulations in the literature.     

Nonlinear numerical simulation on the onset of Soret-driven motion in a silica nanoparticles suspension

The onset of buoyancy-driven convection in an initially quiescent, horizontal silica nanoparticle suspension layer heated from above is analyzed theoretically. In this thermally-stably stratified fluid layer the Soret diffusion can induce buoyancy-driven motion for the case of the negative separation ratio. For the high Rayleigh number the convective motion sets in during the transient diffusion stage and the onset time of this motion is analyzed by employing the nonlinear numerical simulation. It is interesting that the convective motion is very weak and the diffusional process is dominant even after the onset time of convection, τ _c , and the nonlinear effects are manifested from the time τ _m (>τ _c ). The present τ _m explains the existing experimental results quite well.     

The onset of instability in the flow induced by an impulsively started rotating cylinder

The onset of initial instability in a developing Couette flow following the impulsive starting of an inner rotating cylinder is analyzed using linear theory. It is well known that there is a critical Taylor number Ta_c at which Taylor vortices first appear between two concentric cylinders. For Ta>Ta_c Taylor-like vortices occur at a certain elapsed time. In the present study, the critical time t_c to represent the onset of this initiating instability, which then grows as toroidal vortices, is analyzed using propagation theory. For this purpose a self-similar transformation is forced through scaling analysis. The resulting stability criteria compare well with the available experimental data for vortices in water. The new measures represent the onset of the fastest growing instability and also suggest the detection time for the manifestation of secondary flow in the primary time-dependent Couette flow.     

A level set method for simulating wrinkling of extruded viscoelastic sheets

When a polymer is extruded freely from a rectangular die of large cross-sectional aspect ratio, wrinkles are observed. While not present in extruded Newtonian materials, such wrinkles develop in extruded viscoelastic sheets and are understood as an elastic stress-driven instability. The present study is devoted in developing a transient finite element method, which combines the matrix-logarithm-based formulation of the conformation tensor and the single-phase level set method, for simulating wrinkles that form during sheet extrusion of viscoelastic fluids. Numerical analyses of sheet extrusion were conducted over a wide range of flow rate and width-to-thickness ratio of the die exit cross section, χ, to determine critical conditions for the onset of wrinkling of extruded sheets. For large aspect ratios, that is, χ >> 1 , wrinkles develop at moderate extrusion flow rate, corresponding to a Weissenberg number of about 29. Calculations based on Rayleigh's energy method show that the critical compressive stress, σ_c, for the onset of wrinkling of an elastic sheet scales like σ_c~1/χ² , with a significant drop for χ >> 1 . As next to the die exit lip, compressive normal stresses are induced in the extruded sheet, wrinkling will take place for large χ (σ_c being small), in accordance with numerical predictions.     

Modeling of Rayleigh convection in gas–liquid interfacial mass transfer using lattice Boltzmann method

Interfacial Rayleigh convection can be generated by concentration gradient near the interface in mass transfer processes. In the present study, a 2D time-dependent lattice Boltzmann method (LBM) with a double distribution model was established for simulating the liquid-phase Rayleigh convection in the mass transfer process of CO₂ absorption into various solvents. Two random parameters P and C_D denoting respectively the possibility and the magnitude of concentration perturbation at interface were introduced to model the interfacial disturbance, which is known as one of the necessary conditions of onset of Rayleigh convection. The values of the parameters were identified (0.05 ≤ P < 0.3 and 0 < C_D ≤ 10⁻⁹ kg m⁻³) by comparing simulated critical onset times of the Rayleigh convection with the experimental result from Blair and Quinn (1969) and theoretical predictions proposed by Kim et al. (2006) and 0245 and 0250. The maximum penetration depths, maximum transient Rayleigh numbers, and critical times for the onset of Rayleigh convection were obtained by the proposed model. The simulations captured the detailed information of the onset and the temporal–spatial evolution of Rayleigh convection, and gave the concentration contours of typical plume convection patterns which were well consistent with literatures. Enhancement of mass transfer by the Rayleigh convection was also demonstrated by comparing the simulated instantaneous mass flux across the interface with that predicted by penetration theory.     

Phase and Rheological Behavior of Cetyldimethylbenzylammonium Salicylate (CDBAS) and Water

The temperature–composition phase diagram in the diluted region of the cationic surfactant cetyldimethylbenzylammonium salicylate/water system was studied with a battery of techniques. The Krafft temperature (T _k = 33 ± 1 °C) was measured by differential scanning calorimetry, polarizing microscopy, conductimetry, viscosimetry, and rheometry. The critical vesicle concentration (cvc, ~0.002 wt%) and a vesicle–micellar transition (cvm, ~0.005 wt%) was detected at a temperature of 35 °C. Below T _k and concentrations ≤2 wt%, a transparent solution is formed (I). Above 2–8.5 wt%, a lamellar (L₁) phase forms. At higher concentrations and up to 12 wt%, a second lamellar phase (L₂) is detected. From 12.4 to 15.5 wt%, an emulsion phase (E) is formed. Rheological dynamic measurements for the I phase indicate that the system exhibits a predominantly viscous behavior (G′ < G″) for concentrations lower than the overlap or entanglement concentration (C _e, ~0.75 wt%). At higher concentrations, wormlike micelles form and the elastic behavior predominates (G′ > G″). The elastic (G′) modulus collapses in a concentration–time master curve in the whole reduced frequencies range ωτ _c examined, whereas the viscous modulus (G″) collapses only at reduced frequencies lower than 0.1. Reduced stress plotted as a function of the reduced shear rate yields a good superposition of the curves at the different concentrations up to the onset of the non-linear behavior.     

Effect of the chain initiation reaction rate on direct initiation of detonation

The effect of the initiation step of a reaction mechanism on direct initiation of a self-sustained detonation has been studied numerically. For this purpose, the reaction mechanism has been simulated with a three-step chemical kinetics model that consists sequentially of the chain-initiation and chain-branching steps, followed by chain termination. A characteristic time τ _I is defined for each step of the mechanism, which includes effects of different kinetics parameters. It is shown that τ _I is a determining factor of the minimum allowable shock pressure. It is observed that the minimum shock pressure in the decaying period of critical initiation tends to the von Neumann pressure when τ _I becomes large. As a result, at large τ _I , the critical initiation becomes similar to the supercritical initiation. On the other hand, the amplification mechanism of the leading shock in the decaying period depends on τ _I .     

Electrolysis in an annular flow cell with gas generation

A cylindrical electrochemical cell with axial flow in the annulus, formed by the inner indifferent anode tube and the outer cathode tube, is analysed in terms of various reactor models. One alternative characterization, the radial dispersion model, allows the estimation of an apparent radial dispersion on the basis of experimental conversion data.Nomenclature a ratio of the inner electrode radius to the outer electrode radius - c active ion concentration;c _o same in bulk - d _e equivalent (or hydraulic) diameter - D _i ionic diffusion coefficient - D _r radial dispersion coefficient - F Faraday's constant - i _z current density distribution along the cathode - J _n Bessel function of the first kind, ordern - I current flow between the electrodes;I _m its mean value - L length of the cathode - n number of electrons transferred in the cathode reaction - p eigenvalue set in the Annular Hankel Transform - Q volumetric flow rate of electrolyte - r radius - R _i radius of the inner electrode (anode) - R _o radius of the outer electrode (cathode) - (Re) Reynolds number (characteristic length: hydraulic diameter) - S dimensionless radius,r/R _o - S _i stoichiometric number - (Sc) Schmidt number - u _m mean value of electrolyte linear velocity - x conversion, defined as (c _o-c)/c ₀;x _E average exit conversion;x_E:x _E computed from a regression line;x_w conversion at the cathode tube - y dimensionless axial variable,z/L - Y _n Bessel function of the second kind, ordern - z axial coordinate - degree of dissociation - lumped parameter in radial dispersion model - geometric-aspect parameter in annulus flow theory - electrolyte residence time in cell     

Effect of power-law index on critical parameters for power-law flow across an unconfined circular cylinder

The conditions for the formation of a wake and for the onset of wake instability for the flow of power-law fluids over an unconfined circular cylinder are investigated numerically by solving the continuity and momentum equations using FLUENT (version 6.2). The effect of power-law index on the critical Reynolds numbers, Strouhal number and drag coefficient has been presented over a wide range of power-law index (0.3?n?1.8) thereby establishing the limits of the flow without separation and the steady symmetric flow regimes, respectively. While both the shear-thinning (n<1) and the shear-thickening (n>1) seem to lower the value of the critical Reynolds number denoting the onset of wake instability as compared to that for Newtonian fluids, the effect is seen to be more prominent for shear-thickening fluids than that for shear-thinning fluids. The corresponding values of the critical Strouhal number (St_c) and drag coefficient have also been presented for the critical values of the Reynolds number. Included here are also a series of streamline plots showing the onset of asymmetry and of the time-dependent flow regime.     

Natural Convection in Heat Generating Oval Porous Enclosures: A Non‐Darcian Model

This paper presents a series of numerical simulations dealing with the problem of natural convection flows and associated heat transfer in an enclosure filled with a fluid‐saturated porous medium. The analysis is based on the finite element technique and incorporates the Brinkman‐extended Darcy model for an oval enclosure. The numerical results obtained for a modified Rayleigh number, Ra, Darcy number, Da, offset, E, and eccentricity, e, are presented and discussed. The numerical predictions for a square enclosure compared well with published data. It is found that any increase in Da or Ra results in a higher fluid velocity that is responsible for shifting the core of the flow. Moreover, at higher ovality (E = 0.5), asymmetric flow is observed even at the lower range of Rayleigh number (Ra ? 20), which may be attributed to the effect of curved isothermal wall.