tailieunhanh - An Introduction to Modeling and Simulation of Particulate Flows Part 7

Tham khảo tài liệu 'an introduction to modeling and simulation of particulate flows part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 2007 5 15 page 96 e 96 Chapter 8. Coupled particle fluid interaction Figure . A representative volume element extracted from a flow Zohdi 224 . algorithm was adequate for the volume fraction ranges of interest under 30 since the limit of the method is on the order of 38 . Any particles that exited a boundary were given the same velocity now incoming on the opposite boundary. Periodicity conditions were used to generate any numerical derivatives for finite difference stencils that extended beyond the boundary. Clearly under these conditions the group velocity of the particles will tend toward the velocity of the background fluid specified controlled on the boundary. A Boussinesq-type perturbation from an ideal gas relation adequate to describe dense gases and fluids was used for the equation of state stemming from dpf Pf po o Po dPf pf n PfAQf where po Qo Po are reference values APf Pf Po and Aớf Qf Qo. We define the thermal expansion as def 1 dpf Ze pf dQf Pf df Vf dQf and the bulk compressibility modulus by Zcom d f _ Vidf n dPf f dVf Qf PfdPf yielding the desired result 1 Pf Po I 1 Ze Of Z - Pfj leading to Pf Po Zcom 1 Ze Qf Po e ể e Ọ 2007 5 15 page 97 e e . A numerical example 97 where O z0 10 7Z K and 105 Pa O Zcom 1010 Pa. The viscosity is assumed to behave according to the well-known relation ec 0f-1 where A is a reference viscosity 0r is a reference temperature and c is a material constant. As before we introduce the following per unit mass2 decompositions for the key near-field parameters for example for the force imparted on particle i by particle j and vice versa 51 a1ij ã1mimj 2ij Ũ2mimj. One should expect two primary trends Larger particles are more massive and can impact one another without significant influence from the surrounding fluid. In other words the particles can plow through the fluid and make contact. This makes this situation more thermally volatile due to the resulting chemical release at contact. .