Modelling of turbulence modulation in particle- or droplet-laden flows

Addition of particles or droplets to turbulent liquid flows or addition of droplets to turbulent gas flows can lead to modulation of turbulence characteristics. Corresponding observations have been reported for very small particle or droplet volume loadings ${\Phi }_{v} $ and therefore may be important when simulating such flows. In this work, a modelling framework that accounts for preferential concentration and reproduces isotropic and anisotropic turbulence attenuation effects is presented. The framework is outlined for both Reynolds-averaged Navier–Stokes (RANS) and joint probability density function (p.d.f.) methods. Validations are performed involving a range of particle and flow-field parameters and are based on the direct numerical simulation (DNS) study of Boivin, Simonin & Squires (J. Fluid Mech., vol. 375, 1998, pp. 235–263) dealing with heavy particles suspended in homogeneous isotropic turbulence (Stokes number $\mathit{St}= O(1{\unicode{x2013}} 10)$ , particle/fluid density ratio ${\rho }_{p} / \rho = 2000$ , ${\Phi }_{v} = O(1{0}^{- 4} )$ ) and the experimental investigation of Poelma, Westerweel & Ooms (J. Fluid Mech., vol. 589, 2007, pp. 315–351) involving light particles ( $\mathit{St}= O(0. 1)$ , ${\rho }_{p} / \rho \gtrsim 1$ , ${\Phi }_{v} = O(1{0}^{- 3} )$ ) settling in grid turbulence. The development in this work is restricted to volume loadings where particle or droplet collisions are negligible.