Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows

Abstract

The interphase transfer of turbulent kinetic energy (TKE) is an important term that affects the evolution of TKE in fluid and particle phases in particle-laden turbulent flow. This work shows that the interphase TKE transfer terms must obey a mathematical constraint, which in the limiting case of statistically homogeneous flow with zero mean velocity in both phases, requires these terms be equal and opposite. In the single-point statistical approach called the two-fluid theory, the interphase TKE transfer terms are unclosed and need to be modeled. Multiphase turbulence models that satisfy this constraint of conservative interphase TKE transfer admit a term-by-term comparison with true direct numerical simulations (DNS) that enforce the exact velocity boundary condition on each particle’s surface. Analysis of three models reveals that not all models satisfy the requirement of conservative interphase TKE transfer. DNS that invoke the point-particle assumption also do not obey this principle of conservative interphase TKE transfer, and this precludes the comparison of model predictions of TKE budgets in each phase with point-particle DNS. This study motivates the development of multiphase turbulence models based on the insights revealed by this analysis, leading to a meaningful comparison of TKE budgets with true DNS.