Interfacial Area Density Research Articles

Microstructural path and temperature dependence of recrystallization in commercial aluminum

The isothermal recrystallization of 90% cold-rolled commercial purity aluminum alloy AA1050 was studied by means of quantitative microscopy at four temperatures from 245°C to 280°C. The microstructural properties, V v, the volume fraction recrystallized, S v, the interfacial area density separating recrystallized grains from deformed grains and 〈 λ〉, the mean recrystallized grain free length, were measured stereologically as a function of time. The kinetics, microstructural path, grain boundary migration rates and temperature dependence of recrystallization were quantified experimentally. Based on analysis of all data and microstructural path modelling, recrystallization was determined to be growth (boundary migration rate) controlled; all nucleation occurred in time periods short compared to the earliest annealing times. The activation energy for grain boundary migration was calculated to be 172–183 kJ/mole suggesting that a solute-limited grain boundary migration rate mechanism was operative in the alloy. The recrystallization microstructural path was found to be isokinetic, i.e. identical at all the annealing temperatures studied. Two stages of recrystallization kinetics were observed; an early transient-like stage characterized by decreasing growth rates and a later stage in which the kinetics approached Avrami behavior and the growth rates were approximately constant. The transient-like behavior is attributed to the steep, deformation-induced stored energy gradients surrrounding precipitate particles where the recrystallized grains are nucleated.

Optical Probes for Multiphase Flow Characterization: Some Recent Improvements

Concentration, velocity, size and interfacial area density are key parameters in the design of multiphase processes involving bubbles or droplets. Optical probes provide a relatively simple and cheap mean to measure these quantities. In this paper, recent advances in probe design and signal processing are summarized, and the performances of these systems are discussed. Finally, various applications are presented and known limitations of the technique are underlined.

A study of bubbly flow using resistivity probes in a novel configuration

Among the various methods used for bubbly flow measurements, the double-sensor resistivity probe has been found very effective. Resistivity probes in horizontal and vertical configurations suffer from problems of stability and hydrodynamic resistance, respectively. Better results can be obtained by using an inclined probe. The impact of inclination on the measured bubble size, bubble frequency, local void fraction and interfacial area density concentration has been investigated in this study. For this purpose data from two inclined probes (110° and 145°) has been compared with that from a vertical probe. All three probes were used in a 150 mm diameter flow column. The flow conditions were chosen to develop a discrete two-phase bubbly flow. It was found that probe inclination could have a great effect on the fraction of bubbles captured by both probes, but that the effect on the various measured parameters was less. Among the three probes, the 110° inclined probe gave the best performance.

A transport equation for the interfacial area density applied to bubble columns

A population balance equation is used to describe the evolution of bubble sizes in two-phase flow. New kernel functions for the rate of bubble break-up and coalescence are presented. The model is able to predict the bubble size distribution in bubble columns including the formation of large bubbles at high superficial gas velocities. Applying the concept of self-similarity an approximate analytical solution for the bubble size distribution can be found. With this solution the population balance is reduced to a transport equation for the average bubble volume. We implemented the transport equation in a commercial CFD-code to demonstrate the possibility of combining population balances with CFD. A dynamic two-phase flow model of the Eulerian–Eulerian type is used and calculations for three space coordinates are performed for cylindrical bubble columns.

AN EXPERIMENTAL STUDY OF DISPERSED LIQUID/LIQUID TWO-PHASE UPFLOW IN A PIPE

This paper presents experimental data for dispersed liquid/liquid upflows. Water was the continuous phase and mineral oil was the dispersed droplet phase. For this flow regime reduced gravity bubbly flow phenomena was simulated because the mineral oil and water had almost the same density. The mean velocity and turbulence fields, the size distributions of the oil droplets, the volume fraction, and interfacial area density distribution were measured using fiber optic Laser Doppler Anemometer (LDA) and phase Doppler Anemometer (PDA) systems. Significantly, the results presented in this paper are similar to those for bubbly air/water flows in microgravity conditions (Kamp el at., 1995).

Interface between a Polysulfone and Polyamide As Studied by Combined Neutron Reflectivity and Small-Angle Neutron Scattering Techniques

Interfaces between the two phases formed in immiscible polymer pairs were studied by means of neutron reflectivity (NR) combined with small-angle neutron scattering (SANS). The interfacial widths evaluated by the two methods were compared for two systems: a nonreactive system composed of polyamide (PA) and polysulfone (PSU) and a reactive system composed of PA and PSU with a phthalic anhydride reactive end group (PSU-R) in which PSU-b-PA block copolymers can be formed at the interface. SANS measurements were made on bulk mixtures, and the NR measurements were performed on thin film bilayer stacks of PA and PSU or PSU-R. The intrinsic interfacial widths, WI,diffuse, obtained from the two methods were compared for the samples that underwent similar annealing protocols and were quenched below the glass transition temperatures Tg's to room temperature. A consistent result for WI,diffuse can be obtained for the two methods only after taking into account the following important factors: (i) the SANS intensity should be corrected for the frozen density heterogeneities within each phase as well as the frozen thermal composition fluctuations; (ii) the contribution of capillary wave fluctuations to a net (or observed) interfacial width, WI,obs, is more significant for NR than SANS. Without the former correction, the SANS profiles at high scattering vector, q, showed asymptotic behavior of q-n (n < 4), giving an erroneous conclusion on WI,obs. The WI,obs values obtained for the reactive system were found to be larger than those for the nonreactive system for both methods, reflecting block copolymer formation at the interfaces. The interfacial area density, Σ, for the bulk mixture of the reactive system rapidly decreased with time and reached a constant value within ca. 2 min after annealing above the Tg's, while Σ for the nonreactive system kept decreasing with time. This elucidates that the growth of the phase-separating domains in the reactive system was pinned by the formation of block copolymers at the interfaces during early annealing times.

Statistical method to calculate local interfacial variables in two-phase bubbly flows using intrusive crossing probes

This paper presents a statistical method to calculate local interfacial variables in two-phase gas–liquid bubbly flows from data taken with double-sensor intrusive probes. Firstly, one derives the geometrical relationship existing between the apparent and actual bubble velocity for a single spherical bubble flowing in a multidimensional flow field. The apparent variables are obtained from the experimental data when one assumes that the bubble trajectory is aligned with the probe axis. A similar relationship exists for the intersected chord length and bubble diameter. Then, the analysis is extended to a swarm of bubbles. The ratio between the apparent to the actual bubble velocity and the intersected chord length to the bubble diameter appear now as probability density functions. The experimental data were taken for air–water bubbly flow regime in a vertical round pipe with a double tip electrical probe. Processing the phase density function generated by the bubble events, one determines distribution function of the bubble velocity and intersected chord length, termed the apparent distributions. The variables of interest, actual bubble velocity and diameter, come out of the solution of a linear system of equations relating the probability function of the measured and estimated bubble velocity and bubble size ratio. The probability density function of the actual bubble velocity and bubble diameter, plus the bubble frequency, add up to various interfacial properties calculated with this technique: the void fraction, the bubble velocity, the bubble size, the interfacial area density and the interface velocity fluctuation intensity. To validate the method, the paper compares local and area averaged quantities with previously published results, volumetric measurements and extensively used correlation.

Implementation of an Improved Interfacial Mass and Energy Transfer Model in RETRAN-3D

RETRAN-3D-MOD002.0 includes a five-equation flow field model to extend the code’s analytical capabilities to situations in which thermodynamic nonequilibrium phenomena are important. Evaluation of this model’s performance against several depressurization and repressurization transients has shown severe numerical and convergence problems related to the calculation of the interfacial energy and mass transfer. To remove these code limitations, a new interfacial mass and energy transfer model has been developed and implemented in RETRAN-3D. This model calculates the phase change based on the net heat transfer to the liquid-vapor interface at saturation. The heat transfer for each phase is equal to the product of the interfacial area density, a heat transfer coefficient, and the difference between the interface and the bulk temperature of the respective phase. A flow regime map based on the work of Taitel and Dukler is used to identify the flow regime in a control volume and to select the appropriate correlations for these quantities.Assessment of the new model’s performance includes the simulation of an experimental depressurization transient, OMEGA test 9; a turbine trip transient in a BWR/4; and a very fast depressurization transient, the Edwards pipe problem. The results are free from the previous numerical problems and show a good agreement with experimental values.

Interfacial area density in bubbly flow

The interfacial area per unit volume is one of the key parameters in bubbly flow. Momentum, mass and energy transfer occur through the interface between the phases. The functionality of two phase reactors with bubbly flow depends mainly on these three transfer processes. Thus, the design process of a reactor requires the prediction of interfacial area density. In the present work a simple equation for the interfacial area density is derived from the population balance, taking into account the events of coalescence and bubble break-up for each bubble fraction. The system of partial integro-differential equations is simplified. Since the integrals in these equations complicate a numerical treatment. This reduces the balance to one single partial differential equation. An approximate analytical solution is given. If the resulting equation is applied to large gas fluxes, the instability of the coalescence process causes large bubbles and gas plugs to develop. From the instability the volume fraction of the large bubbles and gas plugs may be predicted. Additives may hinder the coalescence process. Experiments show that coalescence hindrance changes the coalescence kernel only by a factor. Calculations are done for bubble columns and vertical pipe flow.

Post-treatment for phase detection probes in non uniform two-phase flows

The question of the demodulation of raw information delivered by phase detection probes is reconsidered. The standard procedure providing the size distribution from chord measurements is extended along various directions. For spherical inclusions, the presence of flow inhomogeneities is accounted for, both in the case of totally correlated or completely uncorrelated sizes and velocities. Also, the number density, its flux, as well as the mean interfacial area density, become available. Two-phase flow regions close to walls are also considered. It is shown that, using multiple point measurements, the number density flux can be reconstructed with acceptable accuracy. However, the number density and average inclusion velocity relative to centres seem to be out of reach when using only phase detection probes.

Structure and Strength of Multilayers

Nanometer-scale multilayer materials exhibit a wealth of interesting structural and mechanical property behaviors. Physical-vapor-deposition technology allows almost unlimited freedom to choose among elements, alloys, and Compounds as layering constituents and to design and produce materials with compositional and structural periodicities approaching the atomic Scale. These materials have tremendous interface area density, approaching 106 mm/mm3, so that a Square centimeter area of a one-micron-thick multilayer film with a bilayer period of 2 nm has an interface area of roughly 1,000 cm2. Hence interfacial effects can dominate multilayer structure and properties leading to unusually large strains and frequently stabilization of metastable structures. The atomic-scale layering of different materials also leads to very high hardnesses and good wear resistance. These materials are a test-bed for examination of the fundamental aspects of phase stability and for exploring mechanical strengthening mechanisms. They are also becoming increasingly interesting for applications such as hard coatings, x-ray optical elements, in microelectromechanical Systems (MEMS), and in magnetic recording media and heads.In this article, we review some of the interesting structures and mechanical properties that have been observed in nanometer-scale artificial multilayer structures.Superlattice thin films are readily deposited by vapor-phase techniques such as sputter deposition, evaporation, and chemical vapor deposition, as well as by electrochemical deposition. Superlattice deposition Systems are similar to conventional film deposition Systems, except for the provision to modulate the fluxes and thereby produce alternating super-lattice layers.

Light extinction technique for void fraction measurements in bubbly flow

The analysis of the scattering induced by a dispersion of gas bubbles in a liquid medium on a collimated, monochromatic light beam, traversing the two-phase flow, allows for the direct measurement of the 2-D distribution of the line-average of the interfacial area density. The 2-D distribution of the line-average of the void fraction is deduced from that of the interfacial area density through an image processing algorithm. To demonstrate the technique, experiments are performed in a pool of water injected with air and illuminated with a CW argon ion laser. Since the bubble diameters range from a fraction of a millimeter to a few millimeters, the scattering processes are entirely in the Mie range. The limits of applicability of the technique and the measurement uncertainty are discussed. The results compare favorably with level-swell based measurements used as a reference.

A first order relaxation model for the prediction of the local interfacial area density in two-phase flows

Many energy production and chemical processes involve vapor/liquid two-phase flows. Mass and energy are often exchanged between the vapor and the liquid phases, and the fluid mechanics of the two-phase system is strongly influenced by the exchange of momentum between each phase. Significantly, the transport of mass, energy and momentum between the phases takes place across interfaces. Therefore the interfacial area density (i.e. the interfacial area per unit volume) has to be accurately known in order to make reliable predictions of the interfacial transfers. Indeed, the interfacial area density must be known for both steady and transient two-phase flows. It is the purpose of this paper to present a first order relaxation model which is derived from the Boltzmann transport equation, and which accurately describes the evolution of interfacial area density for bubbly flows. In particular, the local, instantaneous interfacial area densities and volume fractions are predicted for vertical flow of a vapor/liquid bubbly flow involving both bubble clusters and individual bubbles.

Characterization of a massive transformation by microstructural analysis

Quantitative metallography was employed to investigate experimentally the nucleation behavior and growth rates in a quenched Ag + 50 at. pct Cd alloy undergoing an isothermal massive transformation at 373 K (100 °C). The experimental characterization of the massively transforming microstructure as a function of time was accomplished by the stereological measurement of the microstructural variables, Vv, the volume fraction transformed, Sv, the parent/daughter interfacial area density, and λmax, the largest intercept-free nodule length of the newly forming daughter phase. These data were compared to statistically derived geometrical models of the microstructure formulated on various nucleation and growth premises and expressed in terms of these same variables. A model was found which matched the data in all respects, and this allowed certain nucleation characteristics, the interface migration rates, and the nodule shapes of the daughter phase to be deduced.

Relaxation Process of Thermal Non-Equilibrium in Boiling Two-Phase Flow, (I)

The thermo-hydraulics in a thermal non-equilibrium state, which may appear during a postulated loss-of-coolant accident, is one of phenomena which have never been understood enough. In this paper, accelerating boiling two-phase flow is dealt with which realizes thermal non- equilibrium conditions in a steady state in order to clarify the relaxation process of superheated liquid. The following insight is clarified from the results; Jones' model cannot explain the underpressure and relaxation time unless an empirical constant is changed. Therefore, the effect of interfacial area density on the macroscopic relaxation inception is experimentally investigated by adding artificially bubbles in accelerating boiling two-phase flow in order to offer a fundamental data base for modeling the relaxation process of superheated liquid. It is made clear that the macroscopic relaxation inception can be evaluated by a relationship between the integration of liquid superheating by the travelling time and the initial interfacial area density.

Analysis of the bubbly/slug flow regime transition

An extended two-fluid model that includes the dynamics of bubble cluster formation and breakup was developed and used successfully to predict the bubbly/slug flow regime transition. In particular, a linear void wave stability analysis of the extended two-fluid model was performed and it was found that an instability of the void wave associated with the bubble clusters triggers a bubbly/slug flow regime transition. The predictions obtained for the change in sign of the void wave damping coefficient of this model, and thus for the onset of flow regime transition, agreed very well with the available experimental data. Another important result of this work is that it provides a mechanistic transport model for the prediction of interfacial area density, bubble number density, and mean bubble radius, parameters which are required for closure of two-fluid models.

Relaxation Process of Thermal Non-Equilibrium in Boiling Two-Phase Flow, (I). Experimental Results.

The thermo-hydraulics in a thermal non-equilibrium state, which may appear during a postulated loss-of-coolant accident, is one of phenomena which have never been understood enough. In this paper, accelerating boiling two-phase flow is dealt with which realizes thermal non- equilibrium conditions in a steady state in order to clarify the relaxation process of superheated liquid. The following insight is clarified from the results; Jones' model cannot explain the underpressure and relaxation time unless an empirical constant is changed. Therefore, the effect of interfacial area density on the macroscopic relaxation inception is experimentally investigated by adding artificially bubbles in accelerating boiling two-phase flow in order to offer a fundamental data base for modeling the relaxation process of superheated liquid. It is made clear that the macroscopic relaxation inception can be evaluated by a relationship between the integration of liquid superheating by the travelling time and the initial interfacial area density.

Late stage spinodal decomposition in binary fluids: comparison between computer simulation and experimental results

Abstract We present detailed comparisons of results on the late stage dynamics of spinodal decomposition obtained by the computer simulation of the time-dependent Ginzburg-Landau equation with hydrodynamic interaction and experiments of a polymer mixture of polybutadiene and polyisoprene. We show that the temporally linear domain growth law, which is characteristic for viscous fluids, is observed in both simulation and experiment in the late stage. Some quantities obtained in such a hydrodynamic domain growth region, such as the interface area density and the scaling function, are compared in detail. Especially, we show that the scaling functions for the two systems are in quantitative agreement.

Interfacial area density, mean radius and number density measurements in bubbly two-phase flow

This paper presents a new experimental method for measuring the local interfacial area density, average bubble radius and number density for bubbly two-phase flow. Experiments were performed using a KfK dual-sensor resistivity probe. The results obtained for interfacial area density using this method agreed with other methods previously proposed, except for high void fractions, close to the transition to slug flow, where prior methods are known to no longer be valid.

Impedance imaging relative to gas-liquid systems

Determining interfacial area density in two-phase, gas-liquid flows is one of the major elements impeding significant development of predictive tools based on the two-fluid model. Currently, these models require coupling of liquid and vapor at interfaces using constitutive equations which do not exist in any but the most rudimentary form. This paper describes the theory of impedance imaging of two-phase mixtures and summarizes bench-type experiments utilized in its development, testing, and feasibility evaluation.