Disperse multiphase flow turbulence

The recent progress in experimental techniques and applications of DNS and LES for turbulent multiphase flows may lead to new insights necessary to develop better computational models to simulate dispersed multiphase flows with wide particle size distribution in turbulent regimes. Until then, the simulations of such complex turbulent multiphase flow processes have to be accompanied by careful validation (to assess errors due to modeling) and error estimation (due to numerical issues) exercise. Applications of these models to simulate multiphase stirred reactors, bubble column reactors and fluidized bed reactors, are discussed in Part IV of this book. 

Portela LM, Ohemans RVA (2006) Possibilities and Limitations of Computer Simulations of Industrial Turbulent Dispersed Multiphase Flows. Flow Turbulence Combust 77 381-403... 

Balachandar, S. Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annual Review of Fluid Mechanics 42, 111-133. 

PoRTELA, L. M. OuEMANs, R. V. A. 2006 Possibilities and limitations of computer simulations of industrial turbulent dispersed multiphase flows. Flow, Turbulence and Combustion 11, 381 03. 

The description of a dispersed multiphase flow with chemical reactions leads to a complex system of differential and algebraic equations, which can only be solved by specifying appropriate boundary and initial conditions. For the gas phase equations, the boundary conditions are imposed on the gas velocity u, the temperature T, the turbulent kinetic energy k, and its dissipation e. The spray equations require conditions at the nozzle exit and for the interactions of the droplets with the walls. 

The second great limitation of CFD is dispersed, multiphase flows. Multiphase flows are common in industry, and consequently their simulation is of great interest. Like turbulent flows, multiphase flows (which may also be turbulent in one or more phases) are solutions to the equations of motion, and direct numerical simulation has been applied to them (Miller and Bellan, 2000). However, practical multiphase flow problems require a modeling approach. The models, however, tend to ignore or at best simplify many of the important details of the flow, such as droplet or particle shape and their impact on interphase mass, energy, and momentum transport, the impact of deformation rate on droplet breakup and coalescence, and the formation of macroscopic structures within the dispersed phase (Sundaresan et al., 1998). 

Balachandar S, Eaton JK Turbulent dispersed multiphase flow, Annu Rev Fluid Mech 42 111-133, 2010. 

It is the author s conviction that in many (turbulent) dispersed multiphase flows—except probably in very dense multiphase flow systems—the origin of mesoscale structures is in the fluid—particle interaction, with a secondary role for particle-particle interaction (coUisions, coalescence, breakup). Clustering of particles is believed to be intimately connected with the chaotic dynamics of fluid accelerations, as particles converge toward each other where and when the divergence of the acceleration field is positive (Goto... 

Velocity measurement of the dispersed phase in multiphase flow is possible using both PIV and LDV. In PIV, the particles can be masked according to size, and the velocity for each size fraction can be estimated [7]. The turbulent properties, for example, granular temperature, are more difficult to measure because of the low number of particles in the measured volume. With LDV it is also possible to obtain the velocity and size for the dispersed phase, but the turbulent properties for the dispersed phase are still difficult to measure accurately, owing to the low number of particles and also because the position of the particles is not exactly the same aU the time. 

Particle-laden multiphase flows, usually turbulent, cover a wide range of applications, such as pollution control, sediment transport, combustion processes, erosion effects in gas turbines, and so on. One of the most important aspects of particle-laden turbulent flows is the mutual interactions between particles and turbulence. PIV techniques, as a powerful tool other than numerical simulation method and theoretical analysis, have been applied to this research field of particle-laden multiphase flows. Note that, dispersed-phase particles in particle-laden... 

Mashayek, F., F. A. Jaberi, R. S. Miller, and R Givi. 1997. Dispersion and poly-dispersity of droplets in stationary isotropic turbulence. Int. J. Multiphase Flow 23(2) 337-55. 

For multiphase flow processes, turbulent effects will be much larger. Even operability will be controlled by the generated turbulence in some cases. For dispersed fluid-fluid flows (as in gas-liquid or liquid-liquid reactors), the local sizes of dispersed phase particles and local transport rates will be controlled by the turbulence energy dissipation rates and turbulence kinetic energy. The modeling of turbulent multiphase flows is discussed in the next chapter. 

Sommerfeld, M. (1990), Numerical simulation of the particle dispersion in turbulent flow the importance of particle lift forces and particle/wall collision models, in Numerical Methods for Multiphase Flows, Vol. 91, ASME, New York. 

Ahmadi G, Ma D (1990) A thermodynamical formulation for dispersed multiphase turbulent flows-I Basic theory. Int J Multiphase Flow 16 323-340... 

Sha WT, Slattery JC (1980) Local Volume-Time Averaged Equations of Motion for Dispersed, Turbulent, Multiphase Flows. NUREG/CR-1491, ANL-80-51... 

For multiphase flows perturbed by the presence of particles to obtain a turbulence like behavior the local instantaneous velocity of the continuous phase can for example be decomposed adopting the Reynolds averaging procedure (i.e., other methods including time-, volume-, ensemble-, and Favre averaging have been used as well) and expressed as Vg = Vg- - < v >g, where v(. is the fluctuating component of the continuous phase velocity. Introducing the peculiar velocity for the dispersed phase this relation can be re-arranged as ... 

Langlois WE (1964) Slow Viscous Flow. Macmillan, New York Laux H (1998) Modeling of dilute and dense dispersed fluid-particle flow. Dr Ing Thesis, Norwegian University of Science and Technology, Trondheim, Norway Lawler MT, Lu P-C (1971) The role of lift in radial migration of particles in a pipe flow. In Zandi 1 (ed) Advances in Solid-Liquid Flow in Pipes and its Apphcations. Pergamon Press, Oxford, Chap 3, pp. 39-57 Lee SL (1987) Particle drag in a dilute turbulent two-phase suspension flow. Int J Multiphase Flow 13(2) 247-256... 

Rizk MA, Elghobashi SE (1989) A Two-Equation Turbulence Model for Dispersed Dilute Confined Two-Phase Flows. Int J multiphase Flow 15(1) 119-133 Rubinow SI, Keller JB (1961) The transverse force on a spinning sphere moving in a viscous fluid. J Fluid Mech 11 447-459... 

Burns AD, Prank T, Hamill I, Shi J-M (2004) The Favre Average Drag Model for Turbulent Dispersion in Eulerian Multi-Phase Flows. 5th Int Conf Multiphase Flow, Paper No. 392, CD-ROM of ICMF 04, Yokohama, Japan, May 30-June 4... 

Reeks, M. W. 2005a On model equations for particle dispersion in inhomogeneous turbulence. International Journal of Multiphase Flow 31, 93-114. 

It is rather difficult to establish a reasonably accurate mathematical model of a gas-liquid-liquid three-phase reactor for biphasic hydroformylation, because of the complexity in formulating all the necessary mechanisms such as phase dispersion and distribution, multiphase flow, interphase mass transfer, micromixing, and the hydroformylation reaction. Besides, the task is further complicated by turbulence in multiphase flow and the complex domain of stirred-tank reactors. 

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