Research on particle settling in rectangular ducts under effect of walls
Tang Fuping1, Shi Yan1, Guo Jiaojiao1, Xue Jianquan2, Zhang Guodong2
1.Zhundong Oil Production Plant of Xinjiang Oil Field Company, Fukang, Xinjiang 831511, China; 2.College of Petroleum Enginee-ring, China University of Petroleum, Qingdao, Shandong 266580, China
Abstract：In order to characterize wall effect of rectangular ducts on particle settling, a prediction method of wall factor was presented using Artificial Neural Network(ANN). Extracted ρf, ρp, d, d/a, a/b, K and n as feature parameters, which substantially affect particle settling velocity.Culled 70 data of Machac′s paper to train and test the models, and compared predicted results of ANN with the calculated results of Miyamura correlation and Liu Malin correlation.The results show that, the accurate of ANN predicted results is great, the error is less than 7.5% for 90% calculated results. Comparing to Miyamura correlation and Liu Malin correlations, the ANN model has high engineering accuracy in parallel plate and rectangular ducts, and the application range of ANN has broader scope of application,and can meet complex engineering needs.
[1]Chhabra R P, Uhlherr P H T. Wall effect for high Rey-nolds number motion of spheres in shear thinning fluids[J]. Chemical Engineering Communications, 1980, 5(1/2/3/4): 115-124.[2]Chhabra R P. Wall effects on free-settling velocity of non-spherical particles in viscous media in cylindrical tubes[J]. Powder Technology, 1995, 85(1): 83-90.[3]Chhabra R P. Wall effects on terminal velocity of non-spherical particles in non-Newtonian polymer solutions[J]. Powder Technology, 1996, 88(1): 39-44.[4]Chhabra R P, Uhlherr P H T, Richardson J F. Some further observations on the hindered settling velocity of spheres in the inertial flow regime[J]. Chemical Engineering Science, 1996, 51(19): 4531-4532.[5]Di Felice R, Gibilaro L G, Foscolo P U. On the hindered settling velocity of spheres in the inertial flow regime[J]. Chemical Engineering Science, 1995, 50(18): 3005-3006.[6]Chhabra R P, Agarwal S, Chaudhary K. A note on wall effect on the terminal falling velocity of a sphere in quie-scent Newtonian media in cylindrical tubes[J]. Powder Technology, 2003, 129(1): 53-58.[7]Faxén H. Der Widerstand gegen die Bewegung einer starren Kugel in einer zähen Flüssigkeit, die zwischen zwei parallelen ebenen Wänden eingeschlossen ist[J]. Annalen der Physik, 1922, 373(10): 89-119.[8]Kawase Y, Ulbrecht J J. The influence of walls on the motion of a sphere in non-Newtonian liquids[J]. Rheologica Acta, 1983, 22(1): 27-33.[9]Song D, Gupta R K, Chhabra R P. Wall effects on a sphere falling in quiescent power law fluids in cylindrical tubes[J]. Industrial & Engineering Chemistry Research, 2009, 48(12): 5845-5856.[10]Miyamura A, Iwasaki S, Ishii T. Experimental wall correction factors of single solid spheres in triangular and square cylinders, and parallel plates[J]. International Journal of Multiphase Flow, 1981, 7(1): 41-46.[11]Machac I, Lecjaks Z. Wall effect for a sphere falling through a non-Newtonian fluid in a rectangular duct[J]. Chemical Engineering Science, 1995, 50(1): 143-148.[12]Wang J, Qi H, You C. Experimental study of sedimentation characteristics of spheroidal particles[J]. Particuo-logy, 2009, 7(4): 264-268.[13]Malhotra S, Sharma M M. Settling of spherical particles in unbounded and confined surfactant-based shear thinning viscoelastic fluids: An experimental study[J]. Chemical Engineering Science, 2012,84:646-655.[14]刘磊, 廖红伟, 周芳德. 砂粒与复杂流体压裂液在裂缝中的流动特性研究[J]. 工程热物理学报, 2008, 29(1): 102-104. Liu Lei, Liao Hongwei, Zhou Fangde. Flow perfor-mance of particles suspended in complex fracturing flui-ds in a rectangular fracture[J]. Journal of Engineering Thermophysics, 2008, 29(1): 102-104.(in Chinese)[15]刘马林. 三维矩形槽道中颗粒沉降的数值模拟[J]. 应用数学和力学, 2011, 32(9): 1071-1083. Liu Malin. Numerical simulation of particle sedimentation in a 3D rectangular channel[J]. Applied Mathematics and Mechanics, 2011, 32(9): 1071-1083.(in Chinese)[16]Brown P P, Lawler D F. Sphere drag and settling velocity revisited[J]. Journal of Environmental Engineering, 2003, 129(3): 222-231.[17]Werbos P J. Backpropagation and neurocontrol: A review and prospectus[C]//Proceedings of International Joint Conference on IEEE, 1989: 209-216.[18]Rumelhart D E, McClelland J L, PDP Research Group. Parallel Distributed Processing[M]. Cambridge: MIT Press, 1995.[19]Fletcher D, Goss E. Forecasting with neural networks: An application using bankruptcy data[J]. Information & Management, 1993, 24(3):159-167.
