tailieunhanh - Heat Transfer Mathematical Modelling Numerical Methods and Information Technology Part 11

Tham khảo tài liệu 'heat transfer mathematical modelling numerical methods and information technology part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Particle Scale Simulation of Heat Transfer in Fluid Bed Reactors 389 where Ơ is the Stefan-Boltzmann constant equal to W m2-K4 and spi is the sphere emissivity. Gas radiation is not considered due to low gas emissivities. The parameter Tlocali is the averaged temperature of particles and fluid by volume fraction in a enclosed spherical domain Q given by Zhou et al. 2009 1 kn Tlocali s fTf n 1 - s f -1 T j i 9 kn j 1 where Tf a and ka are respectively the fluid temperature and the number of particles located in the domain Q with its radius of . To be fully enclosed a larger radius can be used. Governing equations for fluid phase The continuum fluid field is calculated from the continuity and Navier-Stokes equations based on the local mean variables over a computational cell which can be written as Xu et al. 2000 ds . . -df v- Sf u 0 10 Ps v PfS fuu -VP - Ffp v Sf1 Pfsf g 11 And by definition the corresponding equation for heat transfer can be written as d pfSfc T kV. f V Pf s f uCpT V CpYVT Qf i Qf wall 12 dt i 1 where u Pf p and Ff kV1ffi AV are the fluid velocity density pressure and volumetric fluid-particle interaction force respectively and kV is the number of particles in a computational cell of volume AV. ris the fluid thermal diffusivity defined by Pt ơT and ƠT the turbulence Prandtl number. Qfi is the heat exchange rate between fluid and particle i which locates in a computational cell and Qf wall is the fluid-wall heat exchange rate. P Vu Vu -1 and Sf 1 - i 1 Vpi AV are the fluid viscous stress tensor and porosity respectively. Vp i is the volume of particle i or part of the volume if the particle is not fully in the cell ue the fluid effective viscosity determined by the standard k-s turbulent model Launder Spalding 1974 . Solutions and coupling schemes The methods for numerical solution of DPS and CFD have been well established in the literature. For the DPS model an explicit time integration method is used to solve the .