本論文主要以傾斜矩形流槽探討重力驅動的顆粒崩塌流場，並在流槽中設置半圓柱阻礙物，以實驗的方式研究不同實驗控制參數(流槽傾角、儲槽開口高度以及半圓柱半徑)對顆粒流撞擊阻礙物之運動行為以及相關物理機制的影響。為了觀察顆粒流體自由表面、側面與底層表面運動時的情形，在透明壓克力製成的滑道上下兩側架設鏡子，從側面拍攝以同時取得三面影像，並使用流體自由表面與底面的速度場來修正側面的速度場，以求得到更準確的體積流率，以及顆粒體積佔有率。
實驗結果顯示阻礙物對流場的影響(如流體深度、速度以及顆粒體積佔有率)程度會隨著上游福祿數增加而增加，且上游福祿數高於某一臨界值後，阻礙物對流場的影響變化會急遽上升；而隨著半圓柱半徑的增加，阻礙物的影響也隨之增加。在低上游福祿數時，流場發生阻流(choked flow)的現象，我們也探討在此流態中的各種運動行為。

The aim of this work is to examine the dynamic behavior of granular flows with granular hydraulic-jumps. The jump is produced by using a fixed semi-circular cylinder obstacle in a rectangular sliding chute. Three different inclined angles combining with three different sizes of the obstacles and four different heights of container opening are tested. Two slender mirrors are installed at the top and the bottom of the transparent chute to reflect the free surface flow and the basal flow image simultaneously to the photographic recording system. Together with the side wall view, image/PIV analysis for the three visible flow fields is performed. With the extra flow profiles and a proposed linear interpolation scheme, we are able to calculate the solid volume fraction along the stream-wise direction in a cost-effective way.
The results show that the effect of the obstacle on the flow field increase both with increasing the Froude number of the upstream flow and the size of obstacle, and rapidly increase when Froude number of the upstream larger than critical value. Moreover, choked flow is occurred at lower Froude number of the upstream flow. The dynamic behaviors in this state are also discussed.

1. Campbell, C. S. and Brennen, C. E., “Chute flows of granular material: some computer simulations,” J. Appl. Mech., Vol. 52, pp. 72-178, 1982.
2. Savage, S. B. and Jeffrey, D. J., “The Stress Tensor in a Granular Flow at High Shear Rates,” J. Fluid Mech., Vol. 110, pp. 255-272, 1981.
3. Jenkins, J. T. and Savage, S. B., “A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Particles,” J. Fluid Mech., Vol. 130, pp. 187-202, 1983.
4. Lun, C. K. K., Savage, S. B., Jeffrey, D. J., and Chepurniy, N., “Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flowfield,” J. Fluid Mech., Vol. 140, pp. 223-256, 1984.
5. Azanza, E., Chevoir, F., and Moucheront, P., “Experimental study of collisional granular flows down an inclined plane,” J. Fluid Mech., Vol. 400, pp. 199-227, 1999.
6. Campbell, C. S., “Rapid granular flows,” Annu. Rev. Fluid Mech., Vol. 22, pp. 57-92, 1990.
7. Silbert, L. E., Ertas, D., Grest, G. S., Halsey, T. C., Levine, D., and Plimptop, S. J., “Granular flow down an inclined plane: Bagnold scaling and rheology,” Phys. Rev. E, Vol. 64, 051302, 2001.
8. Campbell, C. S., “Stress-controlled elastic granular shear flows,” J. Fluid Mech., Vol. 539, pp. 273-297, 2005.
9. Savage, S. B. and Hutter, K., “The motion of a finite mass of granular material down a rough incline,” J. Fluid Mech., Vol. 199, pp. 177-215, 1989.
10. Savage, S. B. and Hutter, K., “The dynamics of avalanches of granular materials from initiation to runout. Part I: Analysis,” Acta Mechanica, Vol. 86, pp. 201-223, 1991.
11. Pitman, E. B. and Le, L., “A two-fluid model for avalanche and debris,” Phil. Trans. R. Soc. A, Vol. 363, pp. 1573-1601, 2005.
12. Chen, K. C. and Tai, Y. C., “Volume-weighted mixture theory of granular materials,” Continuum Mech. Thermodyn., Vol. 19, pp. 457-474, 2008.
13. Nakagawa, M., Altobelli, S. A., Caprihan, A., Fukushima, E., and Jeong, E. K., “Non-invasive measurements of granular flows by magnetic resonance imaging,” Exp. Fluids, Vol. 16, pp. 54-60, 1993.
14. Pugh, J. F. and Wilson, K. C., “Velocity and Concentration Distributions in Sheet Flow above Plane Beds,” J. Hydr. Engrg., Vol. 125, pp. 117-126, 1999.
15. Kawaguchi, T., Tsutsumi, K., and Tsuji, Y., “MRI measurement of granular motion in a rotating drum,” Part. Part. Syst. Charact., Vol. 23, pp. 266-271, 2006.
16. Mantle, M. D., Sederman, A. J., Gladden, L. F., Huntley, J. M., Martin, T. W., Wildman, R. D., and Shattuck, M. D., “MRI investigations of particle motion within a three-dimensional vibro-fluidized granular bed,” Powder Technol., Vol. 179, pp. 164-169, 2008.
17. Pouliquen, O., “Scaling laws in granular flows down rough inclined planes,” Phys. Fluid, Vol. 11, pp. 542-548, 1999.
18. Hanes, D. M. and Walton, R., “Simulations and physical measurements of glass spheres flowing down a bumpy incline,” Powder Technol.,Vol. 109, pp. 133-144, 2000.
19. Kruyt, N. P. and Verël, W. J. Th., “Experimental and theoretical study of rapid flows of cohesionless granular materials down inclined chutes,” Powder Technol., Vol. 73, pp. 109-115, 1992.
20. Ahn, H., Brennen, C. E., and Sabersky, R. H., “Measurements of velocity, velocity fluctuation, density and stresses in chute flows of granular materials,” J. Appl. Mech., Vol. 58, pp. 792-803, 1991.
21. Gray, J. M. N. T., Tai, Y. C., Noelle, S., “Shock waves, dead zones and particle-free regions in rapid granular free-surface flows,” J. Fluid Mech., Vol. 491, pp. 161-181, 2003.
22. Gray, J. M. N. T. and Cui, X., “Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows,” J. Fluid Mech., Vol. 579, pp. 113-136, 2007.
23. Tai, Y. C., Gray, J. M. N. T., Hutter, K., and Noelle, S., “Flow of dense avalanches past obstructions,” Annals of Glaciology, Vol. 32, pp. 281-284, 2001.
24. Pudasaini, S. P., Hutter, K, Hsiau, S. S., Tai, S. C., Wang, Y., and Katzenbach, R., “Rapid flow of dry granular materials down inclined chutes impinging on rigid walls,” Phys. Fluid, Vol. 19, pp. 053302, 2007.
25. Pudasaini, S. P. and Kröner, C., “Shock waves in rapid flows of dense granular materials: Theoretical predictions and experimental results,” Phys. Rev. E, Vol. 78, 041308, 2008.
26. Faug, T., Beguin, R., and Chanut, B., “Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows,” Phys. Rev. E, Vol. 80, 021305, 2009.
27. Chanut, B., Faug, T., and Naaim, M., “Time-varying force from dense granular avalanches on a wall,” Phys. Rev. E, Vol. 82, 041302, 2010.
28. Faun, T., Naaim, M., Bertrand, D., Lachamp, P., Naaim-Bouvet, F., “Varying Dam Height to Shorten the Run-Out of Dense Avalanche Flows: Developing a Scaling Law from Laboratory Experiments,” Surv. Geophys., Vol. 24, pp. 555-568, 2003.
29. Faug, T., Gauer, P., lied, K., and Naaim, M., “Overrun length of avalanches overtopping catching dams: Cross-comparison of small-scale laboratory experiments and observations from full-scale avalanches,” J. Geophys. Res., Vol. 113, F03009, 2008.
30. Hákonardóttir, K. M., Hogg, A. J., Jóhannesson, T., Kern, M., and Tiefenbacher, F., “Large-scale avalanche braking mound and catching dam experiments with snow: A study of the airborne jet,” Surv. Geophys., Vol. 24, pp. 543-554, 2003.
31. Hákonardóttir, K. M., Hogg, A. J., and Batey, J., “Flying avalanches,” Geophys. Res. Lett., Vol. 30, 2191, 2003.
32. Hákonardóttir, K. M. and Hogg, A. J., Johannesson, T., and Tomasson, G. G., “A laboratory study of the retarding effects of braking mounds on snow avalanches,” J. Glaciol., Vol. 49, pp. 191-200, 2003.
33. Jain, S. C., “Open-channel flow,” John Wiley & Sons 2001.
34. Brennen, C. E., Sieck, K., and Paslaski, J., “Hydraulic jumps in granular material flow,” Powder Technol., Vol. 35, pp. 32-27, 1983.
35. Buchholtz, V. and Pöschel, T., “Interaction of a granular stream with an obstacle,” Granular Matter, Vol. 1, pp. 33-41, 1998.
36. Pudasaini, S. P., Hsiau, S. S., Wang, Y. Q., Hutter, K., “Velocity measurements in dry granular avalanches using particle image velocimetry technique and comparison with theoretical predictions,” Phys. Fluids, Vol. 17, 093301, 2005.
37. Adrian, Ronald J. “Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry,” Applied Optics, Vol. 25, pp. 3855-3858, 1986.
38. Nobach, H., Tropea, C., “Improvements to PIV image analysis by recognizing the velocity gradients,” Experiments in Fluids, Vol. 39, pp. 612-620, 2005.
39. Tai, Y. C., and Lin, Y. C., “A focused view of the behavior of granular flows down a confined inclined chute into the horizontal run-out zone,” Phys. Fluids, Vol. 20, 123302, 2008.
40. Vreman, A.W., Al-Tarazi, M., Kuipers, J. A. M., Sint Annaland van, M., and Bokhove, O., “Supercritical shallow granular flow through a contraction: experiment, theory and simulation,” J. Fluid Mech., Vol. 578, pp. 233-269, 2007.