Effect of Nozzle Exit Turbulence on the Column Trajectory and Breakup Location of a Transverse Liquid Jet in a Gaseous Flow

This study examines the effect of fully developed turbulent flow at the exit of nozzle/injector on the trajectory and column breakup location of a liquid jet injected transverly into a gaseous crossflow. Liquid jet trajectory and column breakup for different nozzle geometries at different velocities of liquid jet and crossflow are analytically and experimentally Investigated. Shadowgraph imaging technique is used to determine the jet trajectory and breakup location of a transverse liquid jet in a uniform airflow. Particle image velocimetry (PIV) is used to measure the near-field velocity profile of a liquid jet discgarged into a quiescent atmosphere. The experimental results show a higher penetration and breakup height for the liquid jet ensuing from a nozzle with a smaller length to diameter ratio. This is due to the surface irregularities of the liquid column of a turbulent jet, which breaks up and consequently follows the cross airflow sooner. In order to capture the effect of turbulence, the analytical trajectory correlation developed in our previous studies is modified to account for the discharge coefficient of a nozzle. The discharge coefficient is estimated indirectly by comparing the liquid column trajectory predicted by the modified analytical correlation with that determined experimentally. The indirectly determined discharge coefficient is then used in the analytical correlation for predicting the breakup height of a transverse liquid jet. The results predicted using this approach are in good agreement with the experimental data of the present study at standard temperature and pressure (STP) test conditions.     

Scattering by random rough surfaces: Study of direct and inverse problem

In order to study the problems of scattering by rough metallic surfaces, we have used Maxwell’s equations in covariant form within the framework of a non-orthogonal coordinates system adapted to the geometry of the problem. Electromagnetic fields are written in Fourier’s integral form. The solution is found by using a perturbation method applied to the smooth surface problem; this is fully justified when the defects are of small magnitude.For the direct problem, the mean value of diffraction intensity is obtained for random rough surfaces of finite conductivity by computer simulation.In the case of the inverse problem, the reconstruction of the profile of the metal surface from values of the diffraction intensity, obtained by simulation, is found using an iterative algorithm.     

Orthogonal sets: The axiom of choice and proof of a fixed point theorem

In this paper, we prove some fixed point theorem on orthogonal spaces. Our result improve the main result of the paper by Eshaghi Gordji et al. [On orthogonal sets and Banach fixed point theorem, to appear in Fixed Point Theory]. Also we prove a statement which is equivalent to the axiom of choice. In the last section, as an application, we consider the existence and uniqueness of a solution for a Volterra-type integral equation in L ^p space.     

The simplest proof of Lieb concavity theorem

In this paper, by applying jointly concavity and jointly convexity of generalized perspective of some elementary functions, we give the simplest proof of the well-known Lieb concavity theorem and Ando convexity theorem.     

A fuzzy multidimensional multiple-choice knapsack model for project portfolio selection using an evolutionary algorithm

Project portfolio selection problems are inherently complex problems with multiple and often conflicting objectives. Numerous analytical techniques ranging from simple weighted scoring to complex mathematical programming approaches have been proposed to solve these problems with precise data. However, the project data in real-world problems are often imprecise or ambiguous. We propose a fuzzy Multidimensional Multiple-choice Knapsack Problem (MMKP) formulation for project portfolio selection. The proposed model is composed of an Efficient Epsilon-Constraint (EEC) method and a customized multi-objective evolutionary algorithm. A Data Envelopment Analysis (DEA) model is used to prune the generated solutions into a limited and manageable set of implementable alternatives. Statistical analysis is performed to investigate the effectiveness of the proposed approach in comparison with the competing methods in the literature. A case study is presented to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms.     

Note On a Comparative Evaluation of Nine Well-Known Algorithms for Solving the Cell Formation Problem in Group Technology

Over the last three decades, numerous algorithms have been proposed to solve the work-cell formation problem. For practicing manufacturing managers it would be nice to know as to which algorithm would be most effective and efficient for their specific situation. While several studies have attempted to fulfill this need, most have not resulted in any definitive recommendations and a better methodology of evaluation of cell formation algorithms is urgently needed. Prima facie, the methodology underlying Miltenburg and Zhang's (M&Z) (1991) evaluation of nine well-known cell formation algorithms seems very promising. The primary performance measure proposed by M&Z effectively captures the objectives of a good solution to a cell formation problem and is worthy of use in future studies. Unfortunately, a critical review of M&Z's methodology also reveals certain important flaws in M&Z's methodology. For example, M&Z may not have duplicated each algorithm precisely as the developer(s) of that algorithm intended. Second, M&Z's misrepresent Chandrasekharan and Rajagopalan's [C&R's] (1986) grouping efficiency measure. Third, M&Z's secondary performance measures lead them to unnecessarily ambivalent results. Fourth, several of M&Z's empirical conclusions can be theoretically deduced. It is hoped that future evaluations of cell formation algorithms will benefit from both the strengths and weaknesses of M&Z's work.     

Normal spectral emissivity of platinum in the red and in the green in vacuum and helium

The spectral emissivity of platinum for λ=0.645 μm and λ=0.546 μm has been measured by using a De Vos blackbody in ultrahigh vacuum and in helium. Changes in enissivity brought about by heat treatment and changing ambiences, are illustrated and discussed and the results are compared with previously published data. The emissivities determined turned out to be appreciably lower than the measurements of previous investigators. The determined values for 1100<T(K)<1800 are for 0.645 μ between 0.237 and 0.249 in vacuum, and between 0.185 and 0.290 in helium; and for 0.546 μm between 0.250 and 0.312 for vacuum and between 0.219 and 0.321 in helium.