TAILIEUCHUNG - An Introduction to Modeling and Simulation of Particulate Flows Part 8

Tham khảo tài liệu 'an introduction to modeling and simulation of particulate flows part 8', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | e . Multiple scatterers 115 _ . - 2007 5 15 page 115 Figure . Top to bottom and left to right the progressive movement of rays making up a beam L and n 10 . The lengths of the vectors indicate the irradiance Zohdi 219 . e ể Ọ 2007 5 15 page 116 e e 116 Chapter 9. Simple optical scattering methods for particulate media A f L n an ensemble averaging procedure is applied whereby the performances of a series of different random starting scattering configurations are averaged until the ensemble average converges . until the following condition is met 1 M 1 1 M y n A -1 y n i A M 1 y M y i 1 i 1 TOL 1 M 1 y IICA- M 1 i 1 where index i indicates a different starting random configuration i 1 2 . M that has been generated and M indicates the total number of configurations tested. Similar ideas have been applied to determine responses of other types of randomly dispersed particulate media in Zohdi 208 - 213 . Typically between 10 and 20 ensemble sample averages need to be performed for n to stabilize. Remark. As before in order to generate the random particle positions the classical random sequential addition algorithm was used to place nonoverlapping particles into the domain of interest Widom 200 . This algorithm was adequate for the volume fraction ranges of interest under 30 . Remark. It is important to recognize that one can describe the aggregate ray behavior described in this work in a more detailed manner via higher moment distributions of the individual ray fronts and their velocities. For example consider any quantity Q with a distribution of values Qi i 1 2 . Nr rays about an arbitrary reference value denoted Q as follows MQi d f EN i- Q p f Qi - Q p where _ SiE. f 7 Nr and A Qi. The various moments characterize the distribution for example I MQi-A measures the first deviation from the average which equals zero II MQi-0 is the average III MQi -A is the standard deviation IV MQi-A is the skewness and V MQi-A is the kurtosis. The higher .

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