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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

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

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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

History Force Model Formula Expensive to calculate – E.g. expand for three time steps ( Rostami et al ) 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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

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 = / NETL Workshop on Multiphase Flow Science, August, 2015 Morgantown, WV, 26508

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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

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

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

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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

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

(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

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

(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 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

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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

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 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 26508

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

Validation: Settling spheres 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, Run #Re p,term d(mm)  p (kg/m 3 )  f (kg/m 3 ) f (m 2 /s)  d (s) Moorman (1955) e e e e e e e e Mordant and Pinton (2000) CASE e CASE e Ten Cate et. al. (2002) E e E e E e

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

Validation: Bouncing spheres 2015 NETL Workshop on Multiphase Flow Science, August 12, 2015 Morgantown, WV, 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 10A B-11B C D A C D