Explicit algebraic relation for calculating Reynolds normal stresses in flows dominated by bubble-induced turbulence

Abstract

Two new algebraic turbulence models for flows dominated by bubble-induced turbulence (BIT) are presented. The first model, referred to as the algebraic Reynolds normal stress model, is derived from a differential Reynolds stress model for bubbly flows. The second model utilizes one two-equation turbulence model to achieve algebraic expressions for $k$ and $ϵ$ in the BIT dominated cases. If both models are combined, it results in a purely algebraic, explicit relation for the Reynolds normal stresses.