* Choose TWO problems from below. Assignment #01 Due date : 2nd November 2018 * Choose TWO problems from below. 1. (One-fluid approach) Solve the famous “broken dam problem” in the next slide. See Appendix-01 for details. Compare calculation results with experimental data. 2. (Two-fluid approach) Solve the fluidized bed problem in the reference by Guenther and Syamlal (2001). See Sec. 10.4 in the Tryvasson’s text book and Appendix-02. Compare results for low-order scheme (e.g. 1st order upwind) and any higher order scheme. 3. (Surface tension) Solve the fluidized bed problem in the reference by Guenther and Syamlal (2001). See the Sec.7.3 in the reference book by Trygvasson (see the PDF file on the right) Choose one case from the static case (pressure inside a stationary droplet) and another one case from the dynamic case (capillary oscillation of droplet). Compare your results with results in the reference book. (General notes on the report) Use any code and proper modeling. Summarize your result in a PPT slide, max 10 pages total (including cover). Your report must include, i) Problem definition, ii) Numerical methods, iii) Results & discussion and iv) conclusion (plus References if there’s any)

Appendix 01: Broken dam Removed at t = 0 H y W x (a) Broken dam problem Initially a water column with W = 0.06 m wide and H = 0.12 m high is in a rest. All the boundaries are solid walls. Under the effect of the gravity g = 9.81 m/s2, the column collapses. Removed at t = 0 W H y x The experimental results of Martin and Moyce* for the front position x/W and the height of the column y/H with respect to the dimensionless time are available for your comparison. Front position Column height 0.41 1.11 0.84 1.22 1.19 1.44 1.43 1.67 1.63 1.89 1.83 2.11 1.98 2.33 2.2 2.56 2.32 2.78 2.51 3 2.65 3.22 2.83 3.44 2.97 3.67 3.11 3.89 3.33 4.11 4.02 5 4.44 5.89 1 0.77 0.89 1.08 0.78 1.46 0.67 1.84 0.56 2.21 0.44 2.7 0.33 3.44 0.22 Examine slip condition as well as the non-sip condition (See Hirt and Nichols, 1981) * J. C. Martin and W. J. Moyce, Part IV. An experimental study of the collapse of liquid columns on a rigid horizontal plane , Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 244, No. 882 (Mar. 4, 1952), pp. 312-324

Appendix 02: Fluidized bed Fluidized beds : Problem definition (Gidaspow*, 1994, see also Trygvasson’s book) Drag modeling Collision modeling Assume constant αparticle, t=0 = 0.55 For ideal gas model Gas property Grid