دانلود رایگان مقاله لاتین حل عددی معادله تعادل جمعیت از سایت الزویر
عنوان فارسی مقاله:
حل عددی معادله تعادل جمعیت با استفاده از روش متوسط سلول اصلاح شده به طور موثر
عنوان انگلیسی مقاله:
Numerical solution of the population balance equation using an efficiently modified cell average technique
سال انتشار : 2016
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مقدمه انگلیسی مقاله:
1. Introduction
Solving the populations balance equation, because of its vast applications in diverse processes, has been a great concern for the researchers. This equation, even in its most simple form, has a non-linear integro-differential nature that makes it intractable to analyze. Another difficulty in solving the PBE numerically is the scarcity of the number of analytically-solved problems that the numerical methods refer to. Most methods are divided into these categories: the pivot-based techniques (Kumar and Ramkrishna, 1996; Kostoglou, 2007; Kumar et al., 2008; Mostafaei et al., 2015), the finite element and finite volume methods (John et al., 2009; Qamar et al., 2009; Ahmeda et al., 2013; Kumar and Kumar, 2013), the Monte Carlo simulation (Lin et al., 2002; Zhao et al., 2007; Xu et al., 2014) and the method of moments (Marchisio and Fox, 2005; Yuan et al., 2012; Bruns and Ezekoye, 2012; Santos et al., 2013). The present method is, in fact, a modified cell average technique which is a fixed-pivot technique (FPT) and a continuation of the previous one (Mostafaei et al., 2015). The problem with most the PBE solvers including modified cell average technique (Mostafaei et al., 2015) and its predecessors cell average technique (Kumar et al., 2008) and FPT (Kumar and Ramkrishna, 1996) is that they cannot be used in high amount of time, because modeling of this region is hard due to its unique condition. For example, in this region the degree of aggregation is high and that is why a little deviance from the actual values may lead to a large error. In the previous work by the authors, a supplemental solver (Fig. 1) was introduced to increase the accuracy of the method by stretching the grid in order to lower the accumulation at the last point. This solver was successful for moderately high amount time, but not in very high amount of time where the accumulation at the lowest part of the internal coordination or the highest part, depending on the process, is high. A new supplemental solver has been incorporated. The goal here is to predict the density function and its zeroth and first moments in this region.
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کلمات کلیدی:
Numerical Solution of the Drop Population Balance Equation Using ... www.tandfonline.com/doi/full/10.1080/01932691.2015.1028550 by J Solsvik - 2016 - Cited by 1 - Related articles Apr 8, 2015 - Keywords: Dispersed flow, finite volume, numerical analysis, population balance equation, spectral orthogonal collocation, weighted residual ... Solution of the Population Balance Equation for ... - ACS Publications pubs.acs.org/doi/abs/10.1021/ie050179s by HM Vale - 2005 - Cited by 31 - Related articles Sep 1, 2005 - By following this approach, it is possible to design a numerical method ... Solution of bivariate population balance equations with high-order ... Solution of the Population Balance Equation for ... - ACS Publications pubs.acs.org/doi/full/10.1021/ie050179s?src=recsys Jump to Numerical Results - Here, we will compare our numerical results with the analytical solutions derived by Gelbard and Seinfeld10 for two different ... [PDF]Numerical Solutions of Population-Balance Models in Particulate ... www2.cs.cas.cz/harrachov/slides/Qamar.pdf Aug 19, 2007 - solving population balance equations (PBEs). Numerical Methods. To solve population balance models we use the high resolution finite ... Numerical solution of population balance equations ... - ResearchGate https://www.researchgate.net/.../223489704_Numerical_solution_of_population_balance... Mar 2, 2017 - This article focuses on the derivation of numerical schemes for solving population balance models (PBMs) with simultaneous nucleation, ... [PDF]Numerical approximations of population balance equations in ... diglib.uni-magdeburg.de/Dissertationen/2006/jitkumar.pdf by J Kumar - 2006 - Cited by 39 - Related articles Discretized Tracer Population Balance Equation. EOC. Experimental ... numerical techniques for solving population balances are discussed. The requirements ... Numerical solution of breakage population balance equations using ... ieeexplore.ieee.org/document/6637381/ by NR Narni - 2013 - Related articles In this paper a new numerical approach is formulated to solve the breakage population balance equations along with its moments. In this approach the breaka.
