Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet

This paper describes the implementation of the instability analysis of wave growth on liquid jet surface, and maximum entropy principle (MEP) for prediction of droplet diameter distribution in primary breakup region. The early stage of the primary breakup, which contains the growth of wave on liquid–gas interface, is deterministic; whereas the droplet formation stage at the end of primary breakup is random and stochastic. The stage of droplet formation after the liquid bulk breakup can be modeled by statistical means based on the maximum entropy principle. The MEP provides a formulation that predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. The deterministic aspect considers the instability of wave motion on jet surface before the liquid bulk breakup using the linear instability analysis, which provides information of the maximum growth rate and corresponding wavelength of instabilities in breakup zone. The two sub-models are coupled together using momentum source term and mean diameter of droplets. This model is also capable of considering drag force on droplets through gas–liquid interaction. The predicted results compared favorably with the experimentally measured droplet size distributions for hollow-cone sprays.     

A feature in deriving the Gibbs distribution from the entropy maximum principle

It is proved that, in the general case, the Gibbs distribution may not provide an entropy maximum.     

Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop

The mechanisms of acceleration-induced breakup of liquid drops are reviewed briefly. Data on acceleration-induced fragmentation of liquid drops have been collected from the literature and are presented on a consistent basis. Included are critical Weber number data, breakup time data, velocity history data and fragment size data. A triangular relationship based on the concept of a critical Weber number, breakup time data and velocity history data is presented which permits prediction of the maximum size of stable fragments.     

A procedure to determine the viscosity function from experimental data of capillary flow

The accurate calculation of the viscosity η as function of the shear rate &γdot; from capillary viscometry is still a matter of debate in the literature. In fact, this problem involves the inversion of an integral equation, which leads to multiple solutions due to the unavoidable noise present in the experimental data. The purpose of this work is to develop an efficient procedure to determine the viscosity function from experimental data of capillary flow without presenting the difficulties inherent in other methods discussed previously in the literature. The system identification procedure is used here to estimate the parameters of a viscosity model, which is appropriately selected for the fluid under study through preliminary calculations involving the apparent shear rate – shear stress data. Once the model is chosen by satisfying criteria for the fit goodness and its parameters are evaluated, a smooth and continuous function η(γdot;) is obtained in the range of experimental shear rates. The procedure proposed is also applicable to fluids in shear flow that present two Newtonian plateaus, as it is typically found in macromolecular dilute solutions. The mean value theorem of continuous functions is used to reduce significantly the computational time. Received: 15 November 1999 Accepted: 7 November 2000     

Luminescence technique for the measurement of local concentration distribution in thin liquid films

Experimental data of the concentration field with high spatiotemporal resolution is required for the comprehension of mass transfer increasing kinetic phenomena in falling liquid films. For this purpose a non-invasive measuring method based on luminescence indicators is developed. It is used to determine the concentration distribution and the local film thickness simultaneously. First results are presented for the oxygen absorption into a laminar-wavy water film flowing down a plane with an inclination angle of 4° and a liquid side Reynolds number of 177. With the measured concentration distributions the effective diffusion coefficients are calculated at three points in a single wave of the film.     

Application of the laser beam deflection to the study of temperature fields in Rayleigh–Benard convection

An optical integral and unobtrusive method is developed to determine the temperature gradient field by measurement of laser beam deflection induced by optical index changes. The technique is inexpensive and easy to perform. It allows the study of the temperature gradient at a large number of points simultaneously (over 400/cm²). This technique is particularly adapted to two-dimensional convection flow in both unsteady and steady conditions. For illustration purposes, such a technique is applied to the roll pattern of Rayleigh-Bénard convection. The agreement between theory and experiments is fair.     

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.     

The recrystallization technique for local plastic-zone observation in type 304 stainless steel in the temperature range of −196° to 950° C

The recrystallization technique has been extended for direct observation of plastic zone in Type 304 stainless steel in the temperature range of ?196° to 950°C. It can reveal plastic deformation with plastic strain above 0.02 in the range of ?196° to 850° C and that with plastic strain above 0.06 at 950°C. Results of plastic-zone observation in notched specimen in the range of ?196° to 950° C are presented to illustrate the technique's capability.     

On the influence of local fluctuations in volume fraction of constituents on the effective properties of nonlinear composites. Application to porous materials

Composite materials often exhibit local fluctuations in the volume fraction of their individual constituents. This paper studies the influence of such small fluctuations on the effective properties of composites. A general asymptotic expansion of these properties in terms of powers of the amplitude of the fluctuations is given first. Then, this general result is applied to porous materials.As is well-known, the effective yield surface of ductile voided materials is accurately described by Gurson's criterion. Suitable extensions for viscoplastic solids have also been proposed. The question addressed in the present study pertains to nonuniform distributions of voids in a typical volume element or in other words to the presence of matrix-rich and pore-rich zones in the material. It is shown numerically and analytically that such deviations from a uniform distribution result in a weakening of the macroscopic carrying capacity of the material.     

Application of a POD-Galerkin based method to time resolved and time unresolved data for the determination of the Convective Velocity of Large-Scale Coherent Structures in High Speed Flows

Motivated by the aero-acoustic feedback loop phenomenon in high speed free jets and impinging jets, a thorough examination of a POD (Proper Orthogonal Decomposition)-Galerkin method to determine the average convection velocity of coherent structures in the shear layer is presented in this paper. The technique is shown to be applicable to both time resolved as well as time unresolved data, if the data set meets certain requirements. Using a detailed sensitivity analysis on a synthetic data set, a quantitative estimate on the required time resolution for the technique has been found, which can be useful for both experimental, as well as numerical studies investigating the aero-acoustic feedback loop in high speed flows. Moreover, some innovative ways to apply the technique are also demonstrated using a simulated data set, showing the effectiveness of the technique to any general problem in supersonic jets, heat transfer, combustion or other areas in fluid mechanics, where an advection process can be identified.