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Recently, Ohno proposed a method for computing the correlated color temperature (CCT) of a light source and the shortest distance (with sign) between its chromaticity and that of the Planckian locus (Duv). In Ohno's method, firstly a lookup table is chosen, and then a hybrid method based on the triangular and parabolic solutions is used to predict the CCT and Duv of a given light source. In this article, we found that spline interpolation is better than the parabolic solution for predicting CCT and Duv. Therefore, we propose two new hybrid methods based on the triangular and either spline interpolation or third-order interpolation using two local function values and two local second-order derivative values. Comprehensive tests using the lookup table with both 1% and 0.25% increments relative to the current selected color temperature demonstrate that the proposed methods outperform Ohno's method. [ABSTRACT FROM AUTHOR]

Ventilative drying is an essential drying method to protect natural gas pipeline from corrosion and prevent the formation of hydrate. A mathematical model describing the problem of pipelines drying with dehydrated air is developed based on the fundamental principle of mass, momentum, and species conservation in present work. To enhance the accuracy of the model, a new correlation of the evaporation rate of water in pipeline is introduced by taking interfacial resistance into account. Finite volume method (FVM) is employed to discretize the governing equations with first-order upwind scheme for mass and momentum equations and QUICK scheme for species equations. To reduce calculation load, a new solution strategy of semi-implicit method for Sm-linked equations is proposed to solve the nonlinear algebraic equations after the discretization of mathematical model. The results indicate that average absolute deviation between experimental data and the calculations are 8.8% and 8.2% for two cases, respectively. By analysis of dynamic process of the ventilative drying, it is found that the drying process takes place from the ends toward the center of the pipeline. In addition, the results also demonstrate that the nonuniform distribution of the liquid holdup may reduce the service efficiency of dehydrated air at the late period of drying process. Thus, we suggest that the drying process shifts to soak-test stage when the water vapor at the outlet reaches a minimum set value. Finally, a number of influential factors on the drying process are studied. [ABSTRACT FROM AUTHOR]

Vacuum drying is one of the most effective methods to protect submarine natural gas pipes from blockage caused by hydrate and internal corrosion. This article presents a model for analyzing the mass, momentum, and energy transfer processes in pipeline drying with vacuum drying method. Model of the evaporation rate of liquid water is derived from Hertz–Knudsen–Schrage equation. Finite volume method is employed to discretize the governing equations with an upwind implicit scheme in present work, and 2nd order upwind scheme for energy equation is adopted to weaken numerical dissipation. Non-linear algebraic equations after discretization are solved by Newton-Raphson method. Reliability and accuracy of this model are validated via three experimental cases. Numerical results coincide well with the experimental data, and the relative errors of the calculated drying time are 1.7% in Case 1, 1.2% in Case 2, and 5.5% in Case 3. Finally, the dynamic characteristics of the vacuum drying process are analyzed such as dynamic distributions of pressure, temperature, mass flow rate, and liquid holdup. Mathematical model and algorithm developed in present work provide understanding and insights of the vacuum drying process, which aids in determining cost-effective pipeline drying scheme. [ABSTRACT FROM AUTHOR]

Bubble formation in flowing liquid is an important process for wastewater treatment, processing of molten metals, and biological processes. Based on a global balance of force on the bubble, this report describes a new theoretical model for bubble formation during horizontal gas injection into turbulent liquid flow in a vertical tube. This work highlights the importance of choosing the correct drag law in accordance with the bubble size. Five models for drag coefficient are compared, and of these, model III is recommended. Modified detachment criteria are applicable, depending on the liquid velocity. The new analytical model yields good predictions compared with experimental data. Based on the theoretical model, this study investigates the effects of the direction of liquid flow, liquid velocity, gas velocity, and orifice diameter on the bubble formation behavior. [ABSTRACT FROM AUTHOR]

The de-oiling hydrocyclone is among the most effective devices to recover oil from oily wastewater. In this work, a new model is theoretically developed to predict the separation efficiency of oil droplets in hydrocyclones. According to the analysis of the flow pattern, the droplet dynamics, and oil concentration distribution in the de-oiling hydrocyclone, the differential equation for the new model is established based on the principle of the mass balance of oil droplet. The proposed model can be finally expressed as a simple explicit function including the main geometrical dimensions and operating parameters. The availability of this model is validated by comparison of the calculated grade efficiency with experimental data and other theoretical separation model. [ABSTRACT FROM PUBLISHER]

A mechanical separation process in a de-oiling hydrocyclone is described in which disperse oil droplets are separated from a continuous water phase. This separation process is influenced by droplet breakage and coalescence. Based on experimental data and simulation results in a stirred tank, a modified breakage model, which can be applied to droplet breakage in the de-oiling hydrocyclone, is developed. Then, a simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics (CFD) with population balances. The homogenous discrete method and the inhomogeneous discrete method are applied for solving the population balance model (PBM). The investigations show that the numerical results obtained by the simulation model coupled with the modified PBM using the inhomogeneous discrete method are in good accordance with experimental data under a high flow rate. According to this simulation model, the effect of three different inlet designs on the separation efficiency of the de-oiling hydrocyclone has been discussed. The results indicate that the separation efficiency of the de-oiling hydrocyclone can be improved with an appropriate inlet design. [ABSTRACT FROM AUTHOR]

Water-in-oil (W/O) emulsions are very common in the petroleum industry, and their viscosities are the principle parameters for the operation design. Typical correlations composed by one or two factors cannot always fit the apparent viscosity of W/O emulsions very well, especially when applied to the crude oil/water emulsions. The viscosities of W/O emulsions, which were made from three kinds of crude oil, were measured by Anton Paar MCR302 viscometer at atmospheric pressure with different temperatures as well as shear rates. The experiment results indicate that W/O emulsion would exhibit Newtonian characteristic when water content is no higher than 0.2 and non-Newtonian characteristic otherwise. According to the experimental data, a modified correlation based on the Broughton–Squires model and Ronningsen model was introduced to predict the viscosity of W/O emulsions, and the comparison results showed that the new modified correlation has better accuracy than the original models. [ABSTRACT FROM PUBLISHER]

The SOR-like method with two real parameters ω and α is considered for solving the augmented system. The new method is called the modified SOR-like method (MSOR-like method). The MSOR-like method becomes the SOR-like method when α = 0. The functional equation relating the parameters and eigenvalues of the iteration matrix of the MSOR-like method is obtained. Hence the necessary and sufficient condition for the convergence of the GSOR-like method is derived. It is shown that when α is negative, the convergence domain for the parameter ω for the MSOR-like method is larger than that for the SOR-like method. Finally, a numerical computation based on a particular linear system is given which clearly shows that the MSOR-like method outperforms the SOR-like method. [ABSTRACT FROM AUTHOR]

A new iterative method is given for the augmented system of equations. Similarly to the GSOR and SOR-like methods, the new method involves two iteration parameters and one preconditioning matrix. The convergence analysis and the determination of the optimum parameters are studied first. Then the explicit formulae for the optimum parameters and the associated spectral radius are derived. Finally, numerical computations are presented which show clearly that the new method has a very good numerical performance and is much faster than the SOR-like method. [ABSTRACT FROM AUTHOR]

There are several proposals for the generalization of Young’s successive over-relaxation (SOR) method to solve the saddle-point problem or augmented system. The most practical version is the SOR-like method (G.H. Golub et al ., BIT , 41, 71–85, 2001), which was further studied by Li et al . ( Int. J. Comput. Math. , 81, 749–765, 2004) who found that the iteration matrix of the SOR-like method has no complex eigenvalues only under certain conditions. Motivated by the results of Li and co-authors, we consider the Chebyshev acceleration of the SOR-like method (GSOR-SI). First, the convergence of the GSOR-SI method is given. Secondly, it is shown that the asymptotic rate of the convergence of the GSOR-SI method is much larger than that of the SOR-like method, which indicates that the GSOR-SI method has a faster rate of convergence than the SOR-like method. Finally, numerical comparisons are given which show the GSOR-SI method is indeed faster than the SOR-like method. [ABSTRACT FROM AUTHOR]

Recently, several proposals for the generalization of Young's SOR method to the saddle point problem or the augmented system has been presented. One of the most practical versions is the SOR-like method given by Golub et al. , [(2001). SOR-like methods for augmented systems. BIT , 41 , 71-85.], where the convergence and the determination of its optimum parameters were given. In this article, a full characterization of the spectral radius of the SOR-like iteration matrix is given, and an explicit expression for the optimum parameter is given in each case. The new results also lead to different results to that of Golub et al. Besides, it is shown that by the choices of the preconditioning matrix, the optimum SOR-like iteration matrix has no complex eigenvalues, therefore, it can be accelerated by semi-iterative methods. [ABSTRACT FROM AUTHOR]

In this article, the accelerated over-relaxation (AOR) method is generalized for solving the saddle point problem or the augmented system. The successive over-relaxation (SOR)-like method is the special case of the generalized AOR (GAOR) method. The connection between the parameters and the eigenvalues of the iteration matrix of the GAOR method is given. Therefore, a necessary and sufficient condition for the convergence of the GAOR method is derived. Numerical examples are also given to show that the GAOR method is better than the SOR-like method in certain cases. [ABSTRACT FROM AUTHOR]