平板混合紊流兼具兩類紊流特性，一類是位於中心剪力層流區的剪力紊流(shear turbulence)，另一類是於兩側自由流區的均勻紊流(homogeneous turbulence)。平板混合紊流場沿主流向發展，亦可將其流域區分為近場(near field)發展區，與具有自我保持(self-preserving) 特性的完全發展區。當流場發展至完全發展區時，紊流的產生率(production rate)與消散率(dissipation rate)會達到平衡。
本文以質點影像測速儀(PIV)應用於二維平板混合紊流場之速度量測，並以熱線測速儀的量測結果做為PIV量測之比較基準。因分隔板後方尾流與流場引致之隨機運動會造成追蹤質點(tracers)之不均勻分佈，進而使光學速度量測產生極大誤差。為克服以上問題，本文採用八個參數進行田口式(Taguchi)參數最佳化設計。此八個參數分別為質點探測窗(interrogation window)大小、質點探測窗長寬比(aspect ratio)、數據可驗證率之門檻值(threshold of validation rate)、質點探測窗預偏移量(offset)、影像銳化罩(sharpening filter)、用於計算空間差分之間距值、以及影像柔化罩(smoothing filter)。本研究除了進行單目的參數設計外，並運用多目的參數設計而同時獲得準確的主流向與側向平均速度，以及主流向與側向擾動速度。
為進一步應用多目的參數設計於兩相紊流場速度PIV量測，本研究加入兩組粒徑分佈之SiO2粉末，其中分散相之平均粒徑為175.4 micrometer，連續相之平均粒徑為2.3 micrometer。在此採用不同的亮度篩選並搭配中值濾波器(median mask)在同一張影像中區分連續相(carrier phase)與分散相(dispersed phase)顆粒，此影像辨識法能獲得可靠的連續相與分散相速度量測。其中連續相速度計算仍沿用PIV演算法，但分散相速度計算則使用PTV演算法。流場實驗條件為固定R = 0.67，改變不同的高速側平均速度由8.7至 14.7 m/s，並在高速側加入不同分散相顆粒濃度(a = 0, 1, 3, 5%)，探討其複雜的兩相紊流交互效應。
本文亦藉由二維隨機速度分佈函數發展出一個具有高精確度與可量化之指標，可用來判斷流場到達自我保持特性與否。其偏移角可用於偵測主流向流場的發展趨勢，真圓度可用於區分流域之側向位置位在剪力層流區或是自由流區。本文更進而重新定義一長度尺度，當流場到達自我保持時，此長度尺度隨下游發展會呈現線性擴張。

The incompressible, particle-laden planar turbulent mixing layers are composed of two different flow types in their flow fields, namely a shear layer in the middle region and two free streams in the outer high- and low-speed sides. Turbulent features of the shear layer and free stream regions are of shear and nearly homogeneous turbulence, respectively. A planar turbulent mixing layer which forms at the interface between two uniform streams of different velocities develops streamwisely through successively distinct regions, namely the near-field (developing) region and the self-preserving or self-similar (developed) region in which the production rate of turbulent energy is in equilibrium with its dissipation rate.
Particle image velocimetry (PIV) is used to measure the two-dimensional instantaneous velocity distributions in turbulent mixing layer. Measurements made with a hot-wire anemometry serves as a baseline for identifying the accuracy of the employed PIV diagnostics. To account for the non-uniform tracer distribution, which is attributed to the wake generated behind the trailing edge of the splitting plate, and turbulent random motion, an optimization with the aid of Taguchi method is developed on the basis of eight parameters, including interrogation size, aspect ratio of interrogation window, threshold of data validation, interrogation window offset, sharpening filter, contrast dropout, spatial displacements in estimating the derivatives, and smoothing filter (median mask). Furthermore, multi-objective parametric optimization is employed to deal simultaneously with the mean and fluctuating velocities of both streamwise and transverse velocity components. Two groups of SiO2 powders with different sizes are employed as the tracer (seeding) particles and the dispersed phase. The size of smaller particles (carrier phase) are below 10 micrometer with the mean value of 2.3 micrometer, while the size of larger particles (dispersed phase) are between 100 and 300 m with the mean value of 175.4 micrometer. The high-speed velocities of the two-phase study range from 8.7 ~ 14.7 m/s; and the velocity ratio between high- and low-speed velocities is maintained at R = 0.67. Four mass loadings of dispersed phase are introduced in the high-speed free stream including 0 (single phase), 1%, 3% and 5%.
A double-discriminating process in terms of gray level and size of image object together with the median mask technique is developed to discriminate the image patterns of the carrier phase (tracers) and the dispersed phase (larger particles but with the same material of the tracers) in the turbulent particle-laden mixing layer. The dispersed-phase velocity measurements are performed by the PTV mode while the carrier-phase velocity by the PIV mode. The inter-particle collisions are appeared in some cases with higher mass loadings. It results in more random motion of dispersed phase and requires a large number of collected samples to attain the meaningful statistics.
Base on the available data in the single-phase flows, it is found that the inclined angle of joint probability density function (PDF) can serve as a precise, quantitative parameter for justifying the achievement of self-preserving state. Furthermore, the evolution from the shear turbulence (shear layer) to the nearly homogeneous turbulence (two outer free stream regions) can be monitored through the variation on roundness of joint PDF. A new definition of the mixing length is suggested by means of the distribution of shear-induced vorticity. With this new definition, the measured mixing length exhibits a linear growth rate right after the achievement of self-preserving state.

1. K.C. Chang, J.C. Yang, and M.R. Wang, On grid-averaged Lagrangian equations of dispersed phase in dilute two-phase flow. AIAA Journal, 2003. 41(7): p. 1292-1303.
2. 楊進成, 兩相紊流場隨機 Eulerian-Lagrangian 計算法之檢視. 2000, 國立成功大學.
3. T. Dreier, S. Blaser, W. Kinzelbach, M. Virant, and H.G. Maas, Simultaneous measurement of particle and fluid velocities in a plane mixing layer with dispersion. Experiments in Fluids, 2000. 29(5): p. 486-493.
4. Y. Yamamoto, M. Potthoff, T. Tanaka, T. Kajishima, and Y. Tsuji, Large-eddy simulation of turbulent gas–particle flow in a vertical channel: effect of considering inter-particle collisions. Journal of Fluid Mechanics, 2001. 442: p. 303-334.
5. 徐明君, 應用大尺度渦流法計算載具顆粒紊流場. 2003, 國立成功大學航空太空研究所博士論文.
6. A. Hussain and M.F. Zedan, Effects of the initial condition on the axisymmetric free shear layer: Effects of the initial momentum thickness. Physics of Fluids, 1978. 21: p. 1100.
7. R.D. Mehta and R.V. Westphal, Near-field turbulence properties of single-and two-stream plane mixing layers. Experiments in Fluids, 1986. 4(5): p. 257-266.
8. P. Bradshaw, The effect of initial conditions on the development of a free shear layer. Journal of Fluid Mechanics, 1966. 26(02): p. 225-236.
9. J.J. Miau and S.K.F. Karlsson, Flow structures in the developing region of a symmetric wake and an unsymmetric wake. Physics of Fluids, 1987. 30: p. 2389.
10. D. Oster and I. Wygnanski, The forced mixing layer between parallel streams. Journal of Fluid Mechanics, 1982. 123: p. 91-130.
11. J. Bell and R. Mehta, Development of a two-stream mixing layer from tripped and untripped boundary layers. AIAA Journal, 1990. 28(12): p. 2034-2042.
12. A.M. Azim and S.A. Islam, Plane mixing layers from parallel and non-parallel merging of two streams. Experiments in Fluids, 2003. 34(2): p. 220-226.
13. S.F. Birch and J.M. Eggers, A critical review of the experimental data for developed free turbulent shear layers. NASA SP-321, 1972. 11: p. 40.
14. A.A. Townsend, The Structure of Turbulent Shear Flow. 1976: Cambridge, London.
15. P.E. Dimotakis, The mixing transition in turbulent flows. Journal of Fluid Mechanics, 2000. 409: p. 69-98.
16. B. Dziomba and H.E. Fiedler, Effect of initial conditions on two-dimensional free shear layers. Journal of Fluid Mechanics, 1985. 152: p. 419-442.
17. M.M. Rogers and R.D. Moser, Direct simulation of a self-similar turbulent mixing layer. Physics of Fluids, 1994. 6(2): p. 903.
18. L.J.S. Bradbury, The structure of a self-preserving turbulent plane jet. Journal of Fluid Mechanics, 1965. 23(01): p. 31-64.
19. P. Druault, J. Delville, and J. Bonnet, Experimental 3D Analysis of the Large Scale Behaviour of a Plane Turbulent Mixing Layer. Flow, Turbulence and Combustion, 2005. 74(2): p. 207-233.
20. J. Westerweel, Fundamentals of digital particle image velocimetry. Measurement Science and Technology, 1997. 8(12): p. 1379-92.
21. R.J. Adrian, Particle-imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics, 1991. 23(1): p. 261-304.
22. S.D. Hall, M. Behnia, C.A.J. Fletcher, and G.L. Morrison, Investigation of the secondary corner vortex in a benchmark turbulent backward-facing step using cross-correlation particle imaging velocimetry. Experiments in Fluids, 2003. 35(2): p. 139-151.
23. A. Cenedese, G. Doglia, G.P. Romano, G. De Michele, and G. Tanzini, LDA and PIV velocity measurements in free jets. Experimental Thermal and Fluid Science, 1994. 9(2): p. 125-134.
24. H. Kawanabe, K. Kawasaki, and M. Shioji, Gas-flow measurements in a jet flame using cross-correlation of high-speed-particle images. Measurement Science and Technology, 2000. 11(6): p. 627-32.
25. P. Lavoie, G. Avallone, F. De Gregorio, G.P. Romano, and R.A. Antonia, Spatial resolution of PIV for the measurement of turbulence. Experiments in Fluids, 2007. 43(1): p. 39-51.
26. J. Mi, P. Kalt, G.J. Nathan, and C.Y. Wong, PIV measurements of a turbulent jet issuing from round sharp-edged plate. Experiments in Fluids, 2007. 42(4): p. 625-637.
27. S. Yoshioka, S. Obi, and S. Masuda, Turbulence statistics of periodically perturbed separated flow over backward-facing step. International Journal of Heat and Fluid Flow, 2001. 22(4): p. 393-401.
28. M. Piirto, P. Saarenrinne, H. Eloranta, and R. Karvinen, Measuring turbulence energy with PIV in a backward-facing step flow. Experiments in Fluids, 2003. 35(3): p. 219-236.
29. R.D. Keane and R.J. Adrian, Optimization of particle image velocimeters. I. Double pulsed systems. Measurement Science and Technology, 1990. 1(11): p. 1202-1215.
30. R.D. Keane and R.J. Adrian, Theory of cross-correlation analysis of PIV images. Applied Scientific Research, 1992. 49(3): p. 191-215.
31. J. Westerweel, D. Dabiri, and M. Gharib, The effect of a discrete window offset on the accuracy of cross-correlation analysis of digital PIV recordings. Experiments in Fluids, 1997. 23(1): p. 20-28.
32. H. Nobach and C. Tropea, Improvements to PIV image analysis by recognizing the velocity gradients. Experiments in Fluids, 2005. 39(3): p. 614-622.
33. R.C. Gonzales and R.E. Woods, Digital Image Processing Second Edition. 2002: Prentice Hall.
34. S. Kida and H. Miura, Identification and analysis of vortical structures. European Journal of Mechanics/B Fluids, 1998. 17(4): p. 471-488.
35. J. Jeong and F. Hussain, On the identification of a vortex. Journal of Fluid Mechanics, 1995. 285: p. 69-94.
36. G. Haller, An objective definition of a vortex. Journal of Fluid Mechanics, 2005. 525: p. 1-26.
37. V. Kolář, Vortex identification: New requirements and limitations. International Journal of Heat and Fluid Flow, 2007. 28(4): p. 638-652.
38. R. Gore and C. Crowe, Effect of particle size on modulating turbulent intensity. International Journal of Multiphase Flow, 1989. 15(2): p. 279-285.
39. M.R. Wang and D.Y. Huang, Measurements of <u′giu′pi> in Mixing-Layer Flow with Droplet Loading. Atomization and Sprays, 1995. 5(3): p. 305-328.
40. A.A. Mostafa and H.C. Mongia, On the interaction of particles and turbulent fluid flow. International Journal of Heat and Mass Transfer, 1988. 31: p. 2063-2075.
41. E. Wallner and E. Meiburg, Vortex pairing in two-way coupled, particle laden mixing layers. International Journal of Multiphase Flow, 2002. 28(2): p. 325-346.
42. J. Hinze, Turbulent fluid and particle interaction. Prog. Heat Mass Transfer, 1971. 6: p. 433-452.
43. K. Hishida, A. Ando, and M. Maeda, Experiments on particle dispersion in a turbulent mixing layer. International Journal of Multiphase Flow, 1992. 18(2): p. 181-194.
44. S. Elghobashi and G.C. Truesdell, On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Physics of Fluids A: Fluid Dynamics, 1993. 5: p. 1790.
45. A.M. Al Taweel and J. Landau, Turbulence modulation in two-phase jets. Int. J. Multiphase Flow, 1977. 3: p. 341-351.
46. P. Saarenrinne, M. Honkanen, T. Parssinen, and H. Eloranta, Digital Imaging and PIV methods in Multiphase Flows. 2004.
47. D.P. Towers, C.E. Towers, C.H. Buckberry, and M. Reeves, A colour PIV system employing fluorescent particles for two-phase flow measurements. Measurement Science and Technology, 1999. 10(9): p. 824-30.
48. J. Sakakibara, R.B. Wicker, and J.K. Eaton, Measurements of the particle-fluid velocity correlation and the extra dissipation in a round jet. International Journal of Multiphase Flow, 1996. 22(5): p. 863-881.
49. Y. Hassan, S.J. CH, C. RE, and B. TK, Simultaneous velocity measurements of both components of a two-phase flow using particle image velocimetry. Int. J. Multiphase Flow, 1992. 18: p. 371-395.
50. K.T. Kiger and C. Pan, PIV technique for the simultaneous measurement of dilute two-phase flows. Journal of Fluids Engineering, 2000. 122: p. 811.
51. T. Oakley, E. Loth, and R. Adrian, A two-phase cinematic PIV method for bubbly flows. Journal of Fluids Engineering, 1997. 119: p. 707.
52. G. Rottenkolber, J. Gindele, J. Raposo, K. Dullenkopf, W. Hentschel, S. Wittig, U. Spicher, and W. Merzkirch, Spray analysis of a gasoline direct injector by means of two-phase PIV. Experiments in Fluids, 2002. 32(6): p. 710-721.
53. M.L. Jakobsen, W.J. Easson, and C. Greated, Particle image velocimetry: simultaneous two-phase flow measurements. Measurement Science and Technology, 1996. 7(9): p. 1270-80.
54. M. Stanislas, K. Okamoto, and C. Kahler, Main results of the First International PIV Challenge. Meas. Sci. Technol, 2003. 14(10): p. R63-R89.
55. M. Stanislas, K. Okamoto, C.J. Kahler, and J. Westerweel, Main results of the Second International PIV Challenge. Experiments in Fluids, 2005. 39(2): p. 170-191.
56. M. Stanislas, K. Okamoto, C.J. Kahler, J. Westerweel, and F. Scarano, Main results of the third international PIV Challenge. Experiments in Fluids, 2008. 45(1): p. 27-71.
57. G. Taguchi and Y. Yokoyama, Taguchi Methods: Design of Experiments. 1993: ASI Press.
58. A. Melling, Tracer particles and seeding for particle image velocimetry. Measurement Science and Technology, 1997. 8(12): p. 1406-16.
59. J.S. Bendat and A.G. Piersol, Random Data: Analysis & Measurement Processing. 2000, Wiley-Interscience Publication, John Wiley and Sons, New York.
60. M. Raffel, C.E. Willert, S.T. Wereley, and J. Kompenhans, Particle Image Velocimetry: A Practical Guide. Second Edition. 2007: Springer Berlin.
61. U. Shavit, R.J. Lowe, and J.V. Steinbuck, Intensity Capping: a simple method to improve cross-correlation PIV results. Experiments in Fluids, 2007. 42(2): p. 225-240.
62. R. Theunissen, F. Scarano, and M.L. Riethmuller, An adaptive sampling and windowing interrogation method in PIV. Measurement Science and Technology, 2007. 18(1): p. 275-287.
63. B.J. Lazaro and J.C. Lasheras, Particle dispersion in a turbulent, plane, free shear layer. Physics of Fluids A: Fluid Dynamics, 1989. 1: p. 1035.
64. K.T. Kiger and J.C. Lasheras, The effect of vortex pairing on particle dispersion and kinetic energy transfer in a two-phase turbulent shear layer. Journal of Fluid Mechanics, 1995. 302: p. 149-178.
65. R.N. Parthasarathy and G.M. Faeth, Turbulence modulation in homogeneous dilute particle-laden flows. Journal of Fluid Mechanics, 1990. 220: p. 485-514.
66. S. Horender and Y. Hardalupas, Turbulent particle mass flux in a two-phase shear flow. Powder Technology, 2009. 192: p. 203-216.
67. K.D. Driscoll, V. Sick, and C. Gray, Simultaneous air/fuel-phase PIV measurements in a dense fuel spray. Experiments in Fluids, 2003. 35(1): p. 112-115.
68. W. Kosiwczuk, A. Cessou, M. Trinite, and B. Lecordier, Simultaneous velocity field measurements in two-phase flows for turbulent mixing of sprays by means of two-phase PIV. Experiments in Fluids, 2005. 39(5): p. 895-908.
69. E. Delnoij, J. Westerweel, N.G. Deen, J.A.M. Kuipers, and W.P.M. van Swaaij, Ensemble correlation PIV applied to bubble plumes rising in a bubble column. Chemical Engineering Science, 1999. 54(21): p. 5159-5171.
70. D.A. Khalitov and E.K. Longmire, Simultaneous two-phase PIV by two-parameter phase discrimination. Experiments in Fluids, 2002. 32(2): p. 252-268.
71. J. Uozumi and T. Asakura, First-order intensity and phase statistics of Gaussian speckle produced in the diffraction region. Applied Optics, 1981. 20(8): p. 1454-1466.
72. C. Li, K. Chang, and M. Wang, PIV measurements of turbulent flow in planar mixing layer. Experimental Thermal and Fluid Science, 2009. 33(3): p. 527-537.
73. P. Davidson, Turbulence: an introduction for scientists and engineers. 2004: Oxford University Press, USA.
74. M. Shah, M. Agelinchaab, and M. Tachie, Influence of PIV interrogation area on turbulent statistics up to 4th order moments in smooth and rough wall turbulent flows. Experimental Thermal and Fluid Science, 2008. 32(3): p. 725-747.
75. M. Sommerfeld, Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence. International Journal of Multiphase Flow, 2001. 27(10): p. 1829-1858.
76. C.H. Hsu and K.C. Chang, A Lagrangian modeling approach with the direct simulation Monte-Carlo method for inter-particle collisions in turbulent flow. Advanced Powder Technology, 2007. 18(4): p. 395-426.