1. DEVELOPMENT AND VALIDATION OF A NEW HISTORY FORCE MODEL WITH COLLISION TREATMENT 2015 NETL W ORKSHOP ON M ULTIPHASE F LOW S CIENCE Husam Elghannay & Danesh Tafti Department of Mechanical Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia 24061 1 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

2. Outline Motivation Model formulation – Re p <<1 – Finite Re p – Collision handling Validation – Settling spheres – Bouncing Spheres Computational resources Summary and Conclusions 2 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

3. Particle EOM Drag; viscous dissipation exerted by fluid Gravity; particle weight Added mass; acceleration of surrounding fluid by the particle History force; accounts for temporal evolution of viscous region in the vicinity of the particle Fluid Stress; Effects of gradients of fluid occupied by particle Lift force; due to velocity gradients across particles 3 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

4. History Force Model Formula Expensive to calculate – E.g. expand for three time steps ( Rostami et al. 2 006) Memory storage; – 1.2GB are required to store 4- byte-digit of relative velocity information for 100k particles for 1000 time steps (Dorgan & Loth 2007) Can make the calculation impractical with large number of particles 4 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

5. Reduction Techniques Gonzalez et al. (2006) – Use of fractional- derivative approach – Concept of memory time period – Saves 10-30% of simulation time Dorgan & Loth (2007) – Window Model – Can saves up to 2-Orders of magnitude of CPU-time per time step 5 Log(  h ) for Re p =1000 -2 -1/2 2015 NETL Workshop on Multiphase Flow Science, August, 2015 Morgantown, WV, 26508

6. Motivation and Objectives Goal: To develop an efficient history force model to be used in CFD-DEM – Should not be expensive since large number of particles is usually involved in simulating industrial and natural systems – Used for finite Reynolds numbers – Proper handling of particle-wall particle-particle interactions 6 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

7. Model Formulation (Re p <<1) 7 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

8. Decay Function 8 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

9. Model Formulation (Finite Re p ) Not as straight forward as for Re p <<1 Suggested fit function when history time is exceeded; – g 2 (n)= 1.53.n -2 Final form 9 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

10. Collision Handling 10 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

11. (S~2.47, Re p ~1-6) (S~3.7, Re p ~30-180) 11 Validation: Settling spheres 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

12. ( Re p ~30, S~2.5-9.2) 12 Validation: Settling spheres (S~1.16, Re p ~2-12) 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

13. (Re p,i ~15-400, S~8) 13 Validation: Bouncing spheres 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

14. 14 Validation: Bouncing spheres (Re p,i ~100, S~1.5-16) 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508, S~8

15. Computational Resources Two Mock sub-routines to calculate the History force using Window Model and traditional calculation using Basset Kernel (less expensive) Moorman RUN#27 (Re p,term ~29) was tested 15 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

16. Summary A new formulation of History force along w/ method of handling collisions was presented and validated for large range of Re p and density ratios The model compares well with experimental measure -ments of settling spheres and shows reasonably good agreement with bouncing sphere experiments The use of the model and the fit function reduces both memory resources and CPU time required to calculate the history force 16 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

17. Thank You 17 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508 Comments?

18. Validation: Settling spheres 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508 Run #Re p,term d(mm)  p (kg/m 3 )  f (kg/m 3 ) f (m 2 /s)  d (s) Moorman (1955) 1031.511.17782.2850.42.7e-40.4553 1918115.883076.8834.97.2e-53.502 21679.513076.8834.97.2e-51.256 22286.373076.8834.97.2e-50.56363 272912.713076.81247.21.48645e-41.0868 2966.373076.81247.21.48645e-40.273 303.86.373076.81252.41.877e-40.216 310.96.373076.81257.54.4872e-40.0904 Mordant and Pinton (2000) CASE-1410.5256010001e-60.25 CASE-42800.8771010001e-60.64 Ten Cate et. al. (2002) E11.51511209703.85e-40.585 E24.11511209652.2e-41.024 E311.61511209621.17e-41.915 18

19. Validation (Mordant and Pinton) 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508 19

20. Validation: Bouncing spheres 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508 Gondret et al. (2001) experiments were selected Drag Model used is the same as of Gondret Soft sphere collision model was used (k=800 N/m) Spheres released from height equal to rebound height and their restitution coefficient was set to 1 Forces where activated just before the collision is completed Fig # Re p,i d p (mm)  s (kg/m 3 )  f (kg/m 3 )  f (m 2 /s)  d (s) Re p,reb Gondret 10A394578009200.005 4.6 369 10B-11B106678009530.02 1.7154 83.48 10C55478009530.02 0.7624 39 10D15678009650.01 0.3474 7 11A1085149709530.021.1912596.2 11C119625009350.01 3.366 45.5 11D91514109200.005 4.6 14.8 20