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Atomization and Sprays

Impact factor: 1.235

ISSN Print: 1044-5110
ISSN Online: 1936-2684

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Atomization and Sprays

DOI: 10.1615/AtomizSpr.v16.i7.70
pages 807-826


M. G. Pai
Department of Mechanical Engineering, Iowa State University, Ames, IA 50011
Shankar Subramaniam
Iowa State University


Modeling turbulent multiphase flows, such as sprays, is a major challenge owing to droplet (or solid-particle) interactions with a wide range of turbulence length and time scales. In a broad class of Lagrangian-Eulerian models, the instantaneous Lagrangian dispersed-phase velocity evolves on a time scale that is proportional to the particle response time τp = (ρddp2)/ (ρf18νf). Numerical simulations of a model from this class reveal a nonmonotonic and unphysical increase of the turbulent kinetic energy (TKE) in the dispersed phase kd that is not seen in direct numerical simulations (DNS) of decaying, homogeneous turbulence laden with solid particles. Analysis of this class of models shows that for a linear drag law corresponding to the Stokes regime, the entire class of models will predict an anomalous increase in kd for decaying turbulent flow laden with solid particles or droplets. Even though the particle response time is the appropriate time scale to characterize momentum transfer between sub-Kolmogorov-size dispersed-phase particles and the smallest turbulent eddies (for droplet/particle Reynolds number of < 1), it is incapable of capturing the range of time- and length-scale interactions that are reflected in the evolution of kd. A new model that employs a time scale based on a multiscale analysis is proposed. This model succeeds in capturing the dispersed-phase TKE and fluid-phase TKE evolution observed in DNS. The model also correctly predicts the trends of TKE evolution in both phases for different Stokes numbers.