Effect of heat transfer augmentation on two-phase flow instabilities in a vertical boiling channel

The effect of different heater surface configurations on two-phase flow instabilities has been investigated in a single channel, forced convection, open loop, up-flow system. Freon-11 is used as the test fluid, and six different heater tubes with various inside surface configurations have been tested at five different heat inputs. In addition to temperature and pressure recordings, high speed motion pictures of the two-phase flow were taken for some of the experiments to study the two-phase flow behavior at different operating points. Experimental results are shown on system pressure drop versus mass flow rate curves, and stability boundaries are also indicated on these curves. Comparison of different heater tubes is made by the use of the stability boundary maps and the plots of inlet throttling necessary to stabilize the system versus mass flow rate. Tubes with internal springs were found to be more stable than the other tubes.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.     

Dielectric liquid drop in a harmonic electric field

The problem of the shape of a liquid drop and flows inside and outside the drop in a harmonic electric field is theoretically considered using the small-parameter expansion method. Taking the second-order terms into account makes it possible to consider charge transport over the drop surface.     

Impact of a drop on a solid surface

A numerical solution is obtained to the unsteady-state problem of a direct collision between a liquid drop of cylindrical form and a rigid surface. It is shown that unsteady-state interaction between shock waves inside the drop leads to the development of broad zones of cavitation, promoting the dispersion of the drop.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 151–155, September–October, 1977.The authors thank L. F. Shaikhatarova for making the calculations.     

Thermocapillary migration of a fluid droplet inside a drop in a space laboratory

The thermocapillary migration of a fluid droplet located inside a liquid drop in a space laboratory is analyzed. The quasi-static momentum and energy equations are solved at the instant when the droplet passes the center of the drop. Results are presented for prescribed axisymmetric distributions of temperature on the drop surface.     

Shear cell rupture of nematic liquid crystal droplets in viscous fluids

We model the hydrodynamics of a shear cell experiment with an immiscible nematic liquid crystal droplet in a viscous fluid using an energetic variational approach and phase-field methods [86]. The model includes the coupled system for the flow field for each phase, a phase-field function for the diffuse interface and the orientational director field of the liquid crystal phase. An efficient numerical scheme is implemented for the two-dimensional evolution of the shear cell experiment for this initial data. The same model reduces to an immiscible viscous droplet in a viscous fluid, which we simulate first to compare with other numerical and experimental behavior. Then we simulate drop deformation by varying capillary number (independent of liquid crystal physics), liquid crystal interfacial anchoring energy and Oseen–Frank distortional elastic energy. We show the number of eventual droplets (one to several) and “beads on a string” behavior are tunable with these three physical parameters. All stable droplets possess signature quadrupolar shear and normal stress distributions. The liquid crystal droplets always possess a global surface defect structure, called a boojum, when tangential surface anchoring is imposed. Boojums [79], [32] consist of degree +1/2 and ?1/2 surface defects within a bipolar global orientational structure.     

Effect of surface electric current on the electrohydrodynamic flow inside and outside a spherical drop

The problem of electrohydrodynamic flow of a viscous, low-conducting, polarizable liquid inside and outside a spherical drop in an applied homogeneous constant electric field is analytically solved with account for the effect of both surface conduction current and surface convection current. The influence of the drop deformation on the field and the flow is neglected. The solution is obtained in the form of asymptotic expansions in a small parameter corresponding to weak surface convection electric currents.     

Isothermal extrusion of non-dilute fiber suspensions

The extrusion of a rod-like fiber suspension is a Newtonian solvent, as a first step to the fast and inexpensive production of composite materials, is investigated. The analysis is carried out by means of an integral constitutive equation for a non-dilute suspension, streamlined finite element for liquid with memory, and Newton iteration of nonlinear integro-differential equations. The predictions show substantial differences between dilute and nondilute fiber suspension regarding the processing conditions (pressure drop, velocity distribution, die-swell) and the resulting fiber orientation. Nondilute fiber suspensions exhibit substantial shear-thinning and negligible elasticity as evidenced by the small die-swell, and fiber concentration viscosity-thickening as evidenced by the large pressure drop. The fiber orientation is computed by solving the orientation distribution function along selected streamlines of the complex velocity field. It is shown that the fiber orientation far downstream can be made independent of the random fiber orientation at the inlet.     

Drop size measurements for annular two-phase flow in a 20 mm diameter vertical tube

As part of a study on the effect of tube diameter on the mean drop size and liquid film flow rate in annular two-phase flow, data was obtained for the vertical upflow of an air-water system in a 20 mm internal diameter tube, held at a pressure of 1.5 bar and ambient temperature. This complements data taken in earlier experiments on 10 and 32 mm tubes. Increases in the superficial gas velocity caused reductions in the mean drop size whilst increasing the liquid mass flux in all but the lowest gas velocity case, caused the drop size to rise. Comparisons were made between the current drop size data and that from a 10 mm and 32 mm internal diameter tube, for similar conditions of temperature and pressure. The current drop size measurements, which fall between those from earlier work, confirm the dependence of drop size on tube diameter. The performance of several drop size correlations have been tested. Because the correlations do not account for the influence of tube diameter, they fail to predict the drop size data accurately. The influence of gas and liquid flow rate on the measured film flow rate show trends similar to those seen in data from the 10 mm and 32 mm diameter tubes. Models, to calculate the entrained liquid mass flux were tested; good predictions were given.     

Experimental comparison of measurement techniques for drop size distributions in liquid/liquid dispersions

An online measurement technique for drop size distribution in stirred tank reactors is needed but has not yet been developed. Different approaches and different techniques have been published as the new standard during the last decade. Three of them (focus beam reflectance measurement, two-dimensional optical reflectance measurement techniques and a fiber optical FBR sensor) are tested, and their results are compared with trustful image analysis results from an in situ microscope. The measurement of drop sizes in liquid/liquid distribution is a major challenge for all tested measurement probes, and none provides exact results for the tested system of pure toluene/water compared to an endoscope. Not only the size analysis but also the change of the size over time gives unreasonable results. The influence of the power input on the drop size distribution was the only reasonable observation in this study. The FBR sensor was not applicable at all to the used system. While all three probes are based on laser back scattering, the general question of the usability of this principle for measuring evolving drop size distributions in liquid/liquid system is asked. The exterior smooth surface of droplets in such systems is leading to strong errors in the measurement of the size of the drops. That leads to widely divergent results. A different measurement principle should be used for online measurements of drop size distributions than laser back scattering.     

Configurations of gas-liquid two-phase bubbles in immiscible liquid media

The configuration of a “two-phase bubble” constituted of a gas phase and a liquid phase in an immiscible liquid medium is classified into three types: complete engulfing of a gas bubble inside a liquid shell, partial coalescence of a gas bubble and a liquid drop forming a three-phase contact line, and non-coalescence whereby a gas bubble and a liquid drop remain separated. Simple criteria have been presented by which the favorable type of configuration in a given system is predicted from the values of the spreading coefficients characterizing the system. Experiments using some combinations of liquids as well as air suggest the general validity of the criteria.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of the phase transition on intra-tow flow behavior and void formation in liquid composite molding

A model describing the microscopic isothermal flow inside a fiber bundle completely surrounded by a resin during a liquid molding process is developed. A distinguishing feature of this model is that it takes into account the liquid/vapor phase transition occurring in the gas entrapped inside the tow. In contrast to the existing void formation models which assume that the entrapped gas behaves as an ideal gas, in the present analysis, the condensation and vaporization processes inherent in the liquid/vapor system under high external pressures are simulated by using the Peng–Robinson equation of state. The numerical results show that the phase transition inside the fiber tow has strong effect on both the void dynamics and its size, thus indicating the need to account for this phenomenon in simulation of liquid composite molding processes.     

Numerical study of macroscopical drainage process in fabricating foamed aluminum using microscopical method

The velocity field in a single Plateau border（PB） of the aluminum foam in the drainage process is studied using a mathematical model for the flow inside a microchannel.We show that the liquid/gas interface mobility characterized by the Newtonian surface viscosity has a substantial effect on the velocity inside the single PB.With the same liquid/gas interfacial mobility and the same radius of the curvature,the maximum velocity inside an exterior PB is about 6～8 times as large as that inside an interior PB.We also find a critical value of the interfacial mobility in the interior PB.For the values greater and less than this critical value,the effects of the film thickness on the velocity in the PB show opposite tendencies.Based on the multiscale methodology,with the coupling between the microscale and the macroscale and the results obtained from the microscopical model,a simplified macroscopical drainage model is presented for the aluminum foams.The comparisons among the computational results obtained from the present model,the experimental data quoted in the literature,and the results of the classical drainage equation show a reasonable agreement.The computational results reveal that the liquid holdup of the foams is strongly dependent on the value of the mobility and the bubble radius.     

Optical fiber instability during coating process

In the present work, we study the stability of a system designed for the coating of optical fiber. This is achieved by studying the stability of the flowing resin in the die while coupled with a viscoelastic optical fiber. We develop a numerical code based on a sixth-order compact finite-difference method in order to solve the two-dimensional Navier–Stokes equations. We show that there is a bifurcation flow for a given value of the Reynolds number, wherever the vibration of the optical fiber has been experimentally observed. The stability of the resulting flow, coupled with a nonrigid optical fiber, is considered. Two-dimensional and three-dimensional stability analyses were made. The system was found to be subjected to two kinds of instability induced by two distinguishable groups of modes. For an optical fiber with a small radius, we assume that the preceding vibration may not be the only cause of the irregularity in the coating thickness. Therefore, a model taking into account the deformation of the liquid resin surface, under the action of the surface-tension forces, before resin solidification, and after leaving the die, is proposed. This model assumes that the liquid layer is subjected to surface-tension and gravity forces. It was found that the dynamic equation depends on two dimensionless parameters. It is found that the surface of the fiber has a wavy form. The length of the wave depends on the two dimensionless parameters. Our work shows qualitative agreement with the experimental results without adjusting arbitrary constants.     

Air flow and pressure inside a pressure-swirl spray and their effects on spray development

Air flow and pressure inside a pressure-swirl spray for direct injection (DI) gasoline engines and their effects on spray development have been analyzed at different injector operating conditions. A simulation tool was utilized and the static air pressure at the centerline of the spray was measured to investigate the static pressure and flow structure inside the swirl spray. To investigate the effect of static air pressure on swirl spray development, a liquid film model was applied and the Mie-scattered images were captured. The simulation and experiment showed that recirculation vortex and air pressure drop inside the swirl spray were observable and the air pressure drop was greater at high injection pressure. At high fuel temperature, the air pressure at the nozzle exit showed higher value compared to the atmospheric pressure and then continuously decreased up to few millimeters distance from the nozzle exit. The pressure drop at high fuel temperatures was more than that of atmospheric temperature. This reduced air pressure was recovered to the atmospheric pressure at further downstream. The results from the liquid film model and macroscopic spray images showed that the air pressure started to affect the liquid film trajectory about 3 mm from the nozzle exit and this effect was sustained until the air pressure recovered to the atmospheric pressure. However, the entrained air motion and droplet size have more significant influence on the spray development after the most of the liquid sheet is broken-up and the spray loses its initial momentum.     

Augmented heat transfer and pressure drop of strip-type inserts in the small tubes

An experiment is carried out to investigate the characteristics of the augmentation of heat transfer and pressure drop by different strip-type inserts in small tube having an inside diameter of 2.0 mm. The effects of the imposed wall heat flux, mass flux, strip inserts with various configurations (heights, widths, pitches) on the measured augmentative heat transfer and pressure drop are examined in detail. In order to obtain insight into the fluid flow phenomena, flow visualization was also made to observe the detailed fluid flow characteristics of the present tubes inserted with strip-type inserts. In addition, comparisons are made with a plain tube having the same length, heat transfer area and experimental conditions. The measured heat transfer coefficients and pressure drops for this small pipe are also emphasized to compare with those for larger pipes. Furthermore, in order to compare results from the different configurations of strip-type inserts, several enhancement factors and performance ratios are defined to account for the effects of augmentation. Moreover, correlation equations for the heat transfer coefficient and pressure drop of the present study are proposed.The financial support extended by the National Science Council of the Republic of China through grant No. NSC-89-2212-E-230-004.     

Measurement of permeability of microfluidic porous media with finite-sized colloidal tracers

We present two methods how the permeability in porous microstructures can be experimentally obtained from particle tracking velocimetry of finite-sized colloidal particles suspended in a liquid. The first method employs additional unpatterned reference channels where the liquid flow can be calculated theoretically and a relationship between the velocity of the particles and the liquid is obtained. The second method takes advantage of a time-dependent pressure drop that leads to an exponential decrease in the particle velocity inside a porous structure. From the corresponding decay time, the permeability can be calculated independently of the particle size. Both methods lead to results comparable with permeabilities derived from numerical simulations.     

Wetting boundary conditions in numerical simulation of binary fluids by using phase‐field method: some comparative studies and new development

We studied several wetting boundary conditions (WBCs) in the numerical simulation of binary fluids by using phase‐field method. Five WBCs, three using the linear, cubic, and sine form surface energy (LinSE, CubSE, and SinSE), the other two using the geometric formulation (Geom) and the characteristic interpolation (CI), were compared through the study of several problems: (1) the static contact angle (CA) of a drop; (2) a Poiseuille flow‐driven liquid column; (3) a wettability gradient (WG)‐driven liquid column; and (4) drop dewetting. It was found that while all WBCs can predict the static CA fairly accurately, they may affect the simulation outcomes of dynamic problems differently, depending on the CA. For the flow‐driven problem with a CA near 90°, using different WBCs had almost no effect on the flow characteristics over a large scale. For the WG‐driven problem, to use different WBCs may lead to different steady drop velocities, and all WBCs except LinSE can give reasonably consistent prediction between the drop velocity and dynamic CAs. For drop dewetting, Geom led to the most violent drop motion, whereas CubSE caused the weakest motion. For several problems, CubSE and SinSE gave almost the same results, and those by Geom and CI were also close, possibly due to similar consideration in their design. Besides, a new implementation that may be used for all WBCs was proposed to mimic the wall energy relaxation and control the degree of slip. This new procedure made it possible to allow the simulations to match experimental measurements well. Copyright © 2014 John Wiley & Sons, Ltd.