A novel state-space based method for direct numerical simulation of particle-laden turbulent flows

particle-laden flows;kernel-density method;Box scheme;collocated method;incompressible flow

Ranjan, Reetesh

关键词: particle-laden flows;    kernel-density method;    Box scheme;    collocated method;    incompressible flow;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/42247/Reetesh_Ranjan.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

We developed a novel state-space-based numerical method for evolution of the particle density function, that describes particle-laden flows. The problem is stated purely in a deterministic Eulerian framework. The method is coupled to an incompressible three-dimensional Navier-Stokes solver. We focus on dilute suspensions where the volume fraction and mass loading of the particles in the flow are low enough so that the approximation of one-way coupling remains valid. The transport equation for the particle density function is derived from the governing equation of the particle dynamics described in a Lagrangian frame, by treating position and velocity of the particle as state-space variables and referring to the Liouville equation. The particle-density function is approximated as a discrete mixture of parametric density functions, in the least-squares kernel density method. The method generates the governing equations for the parameters of the kernel density functions. The resulting system of hyperbolic equations are solved using a high-order accurate numerical method for non-conservative hyperbolic equations. The numerical framework results in an efficient implementation where realizability and conservation properties are satisfied. The method is validated by comparing the results obtained from the Lagrangian particle tracking method for various flows, which include a one-dimensional manufactured flow, the Taylor-Green vortex flow, a two-dimensional manufactured nonstationary flow and a three-dimensional flow. Finally, simulation of a particle-laden decaying isotropic turbulent flow is performed. The focus on turbulent flow is dictated by the knowledge that even in isotropic turbulent flows, the distribution of particles is not uniform. For example, heavier-than-fluid particles tend to accumulate in regions of low vorticity and high strain rate. This leads to large regions in the flow where particles appear to be sparsely distributed. The new approach can capture the statistics of the particle in such sparsely distributed regions in an accurate manner compared to other numerical methods and presents substantial advancement over alternative established methods.