Turbulent Flow in Converging Nozzles Part Ⅰ——Boundary Layer Solution
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摘要: 应用边界层积分法,研究锥形喷嘴入口区域中湍动涡流的发展.球面坐标系中的控制方程,通过边界层的假定得到简化,并对边界层进行了积分.应用4阶Adams预测校正法求解该微分方程组.入口区域的切向和轴向速度,分别应用自由涡流和均匀速度分布来表示.由于缺乏收缩喷嘴中涡流的实验数据,需要用数值模拟对该发展模式进行逆向验证.数值模拟的结果证明,该解析模型在预测边界层参数中的能力,例如边界层的生长、剪切率和边界层厚度,以及不同锥度角时的涡流强度衰减率等.为所提出的方法引进一个简明而有效的程序,用以研究几何形状收缩设备内的边界层参数.Abstract: In this research the boundary layer integral method was used to investigate the development of turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system were simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations were then solved by the forth-order Adams predicto-rcorrector method. The free vortex and uniform velocity profiles were applied for tangential and axial velocities at the inlet region respectively. Due to the lack of experimental data for swirling flow in converging nozzles, the developed model was validated against the numerical simulations. The results of numerical simulations demonstrate the capability of the analytical model in predicting boundary layer parameters, such as boundary layer growth, shear rate and boundary layer thickness, as well as the swirl intensity decay rate for different cone angles. The proposed method introduces a simple and robust procedure in order to investigate the boundary layer parameters inside converging geometries.
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[1] Algifri A H, Bhardwaj R K, Rao Y V N. Eddy viscosity in decaying swirl flow in a pipe[J]. Applied Scientific Research, 1988,45(4):287-302. doi: 10.1007/BF00457063 [2] Najafi A F. Investigation of internal turbulent swirling flow, single phase and two phase flow[D]. Ph D dissertation. Sharif University of Technology, 2004:24-30. [3] Gul H. Enhancement of heat transfer in a circular tube with tangential swirl generators[J]. Experimental Heat Transfer, 2006, 19(2): 81-93. doi: 10.1080/08916150500318422 [4] Chang F, Dhir V K. Mechanisms of heat transfer enhancement and slow decay of swirl in tubes using tangential injection[J]. International Journal of Heat and Fluid Flow, 1995, 16(2): 78-87. doi: 10.1016/0142-727X(94)00016-6 [5] Thambu R, Babinchak B T, Ligrani P M, Hedlund C R, Moon H K, Glezer B. Flow in a simple swirl chamber with and without controlled inlet forcing[J]. Experiments in Fluids, 1999, 26(4): 347-357. doi: 10.1007/s003480050298 [6] Zaherzade N H, Jagadish B S. Heat transfer in decaying swirl flow[J]. International Journal of Heat and Mass Transfer, 1975, 18(7/8): 941-944. doi: 10.1016/0017-9310(75)90187-8 [7] Yilmaz M, Yapici S, Jomakli O, Sara O N. Energy correlation of heat transfer and enhancement efficiency in decaying swirl flow[J]. Heat and Mass Transfer, 2002, 38(4/5): 351-358. doi: 10.1007/s002310100207 [8] Steenbergen W, Voskamp J. The rate of decay of swirl in turbulent pipe flow[J]. Flow Measurement and Instrumentation, 1998, 9(2): 67-78. doi: 10.1016/S0955-5986(98)00016-8 [9] Cakmak G, Yildiz C. The influence of the injectors with swirling flow generating on the heat transfer in the concentric heat exchanger[J]. International Communication in Heat and Mass Transfer, 2007, 34(6): 728-739. doi: 10.1016/j.icheatmasstransfer.2007.03.007 [10] Martemianov S, Okulov V L. On heat transfer enhancement in swirl pipe flows[J]. International Journal of Heat and Mass Transfer, 2004, 47(10/11): 2379-2393. doi: 10.1016/j.ijheatmasstransfer.2003.11.005 [11] Taylor G I. The boundary layer in the converging nozzle of swirl atomizer[J]. The Quarterly Journal of Mechanics and Applied Mathematics, 1950, 3(2): 129-139. doi: 10.1093/qjmam/3.2.129 [12] Weber H E. The boundary layer inside a conical surface due to swirl[J]. Journal of Applied Mechanics, 1956, 23: 587-592. [13] Kreith F, Margolis D. Heat transfer and friction in turbulent vortex flow[J]. Applied Scientific Research, 1959, 8(1): 457-473. doi: 10.1007/BF00411769 [14] Rochino A, Lavan Z. Analytical investigations of incompressible turbulent swirling flow in stationary ducts[J]. Journal of Applied Mechanics, 1969, 36: 151-158. doi: 10.1115/1.3564602 [15] Akiyama T, Ikeda M. Fundamental study of the fluid mechanics of swirling pipe flow with air suction[J]. Industrial and Engineering Chemistry Process Design and Development, 1986, 25(4): 907-913. doi: 10.1021/i200035a012 [16] Yajnik K S, Subbaiah M V. Experiments on swirling turbulent flows—part 1: similarity in swirling flows[J]. Journal of Fluid Mechanics, 1973, 60(4): 665-687. doi: 10.1017/S0022112073000406 [17] Kitoh O. Experimental study of turbulent swirling flow in a straight pipe[J]. Journal of Fluid Mechanics, 1991, 225: 445-479. doi: 10.1017/S0022112091002124 [18] Algifri A H, Bhardwaj R K, Rao Y V N. Turbulence measurement in decaying swirl flow in a pipe[J]. Applied Scientific Research, 1988, 45(3): 233-250. doi: 10.1007/BF00384689 [19] Alekseenko S V, Kuibin P A, Okulov V L, Shtork S I. Helical vortices in swirl flow[J]. Journal of Fluid Mechanics, 1999, 382: 195-243. doi: 10.1017/S0022112098003772 [20] Lucca-Negro O, O′Dohery T. Vortex breakdown: a review[J]. Progress in Energy and Combustion Science, 2001, 27(4): 431-481. doi: 10.1016/S0360-1285(00)00022-8 [21] Talbot L. Laminar swirling pipe flow[J]. Journal of Applied Mechanics, 1954,21: 1-7. [22] Kreith F, Sonju K. The decay of a turbulent swirl in a pipe[J]. Journal of Fluid Mechanics, 1965, 22(2): 257-271. doi: 10.1017/S0022112065000733 [23] Yu S C M, Kitoh O. A general formulation for the decay of swirling motion along a straight pipe[J]. International Communications in Heat and Mass Transfer, 1994, 21(5): 719-728. doi: 10.1016/0735-1933(94)90073-6 [24] Harris M J R. The decay of swirl in a pipe[J]. International Journal of Heat and Fluid Flow, 1994, 15(3): 212-217. doi: 10.1016/0142-727X(94)90040-X [25] Najafi A F, Saidi M H, Sadeghipour M S, Souhar M. Boundary layer solution for the turbulent swirling decay flow through a fixed pipe: SBR at the inlet[J]. International Journal of Engineering Science, 2005, 43(1/2): 107-120. doi: 10.1016/j.ijengsci.2004.08.010 [26] Maddahian R, Kebriaee A, Farhanieh B, Firoozabadi B. Analytical investigation of boundary layer growth and swirl intensity decay rate in a pipe[J]. Archive of Applied Mechanics, 2010, 81(4): 489-501. [27] Burden R L, Faires J D. Numerical Analysis[M]. 7th ed. Belmont: Brooks/Cole, 2000: 297-300. [28] Ashraf A I. Comprehensive study of internal flow field and linear and nonlinear instability of an annular liquid sheet emanating from an atomizer[D]. Ph D dissertation. University of Cincinnati, 2006: 32-49. [29] Schlichting H. Boundary Layer Theory[M]. 7th ed. New York: McGraw-Hill, 1973: 47-223. [30] Farhanieh B, Davidson L. Manual of CALC-BFC[M]. Gothenburg, Sweden: Chalmers University of Technology, 1991. [31] Maddahian R, Farhanieh B. Numerical investigation of thermo fluid mechanics of differentially heated rotating tubes[J]. Heat Transfer Engineering, 2010, 31(3): 201-211. doi: 10.1080/01457630903304376 [32] Patankar S V. Numerical Heat Transfer and Fluid Flow[M]. Washington DC:Taylor & Francis, 1980: 113-135. [33] Rhie C M, Chow L W. Numerical study of the turbulent flow past an airfoil with trailing edge separation[J]. AIAA J, 1983, 21(11): 1527-1532. [34] Slack M D, Prasad R O, Bakker A, Boysan F. Advances in cyclone modeling using unstructured grids[J]. Chemical Engineering Research and Design, 2000, 78(8): 1098-1104. doi: 10.1205/026387600528373 [35] De Souza J, Silveria-Neto A. Preliminary results of large eddy simulations of a hydrocyclone[J]. Thermal Engineering, 2004, 3(2): 168-173. [36] Cullivan J C, Williams R A, Cross C R. Understanding the hydrocyclone separator through computational fluid dynamics[J]. Chemical Engineering Research and Design, 2003, 81(4): 455-466. doi: 10.1205/026387603765173718 [37] Cullivan J C. Williams R A, Dyakowski T, Cross C R. New understanding of a hydrocyclone flow field and separation mechanism from computational fluid dynamics[J]. Minerals Engineering, 2004, 17(5): 651-660. doi: 10.1016/j.mineng.2004.04.009 [38] Nowakowski A F, Dyakowski T. Investigation of swirling flow structure in hydrocyclones[J]. Chemical Engineering Research and Design, 2003, 81(8): 862-873. doi: 10.1205/026387603322482103 [39] Launder B E, Reece G J, Ro di W. Progress in the development of a Reynolds-stress turbulence closure[J]. Journal of Fluid Mechanics, 1975, 68(3): 537-566. doi: 10.1017/S0022112075001814
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