Lagrangian Solver Research Articles

Direct numerical simulations of a planar jet laden with evaporating droplets

A direct numerical simulation (DNS) study is conducted on the various aspects of phase interactions in a planar turbulent gas-jet laden with non-evaporative and evaporative liquid droplets. A compressible computational model utilizing a finite difference scheme for the carrier gas and a Lagrangian solver for the droplet phase is used to conduct the numerical experiments. The effects of droplet time constant, mass-loading and mass/momentum/energy coupling between phases on droplet and gas-jet fields are investigated. Significant changes in velocity, temperature, density and turbulence production on account of the coupling between the liquid and gas phases are observed in non-isothermal jets with evaporating droplets. Most of these changes are attributed to the density stratification in the carrier gas that is caused by droplet momentum and heat transfer.

A level set approach to Eulerian–Lagrangian coupling

We present a numerical method for coupling an Eulerian compressible flow solver with a Lagrangian solver for fast transient problems involving fluid–solid interactions. Such coupling needs arise when either specific solution methods or accuracy considerations necessitate that different and disjoint subdomains be treated with different (Eulerian or Lagrangian) schemes. The algorithm we propose employs standard integration of the Eulerian solution over a Cartesian mesh. To treat the irregular boundary cells that are generated by an arbitrary boundary on a structured grid, the Eulerian computational domain is augmented by a thin layer of Cartesian ghost cells. Boundary conditions at these cells are established by enforcing conservation of mass and continuity of the stress tensor in the direction normal to the boundary. The description and the kinematic constraints of the Eulerian boundary rely on the unstructured Lagrangian mesh. The Lagrangian mesh evolves concurrently, driven by the traction boundary conditions imposed by the Eulerian counterpart. Several numerical tests designed to measure the rate of convergence and accuracy of the coupling algorithm are presented as well. General problems in one and two dimensions are considered, including a test consisting of an isotropic elastic solid and a compressible fluid in a fully coupled setting where the exact solution is available.

Vortex simulation of unsteady shear flow induced by a vortex ring

A hybrid Eulerian–Lagrangian solver for unsteady shear flow induced by vortex ring/wall interactions is presented and discussed herein. Normal and oblique impacts of a vortex ring on a plane surface involve strong interactions between and external and the induced boundary layer, which undergoes separation and explosive growth, leading to the ejection of vorticity. For an oblique ring impact, the interaction is shown to be highly asymmetric. The development of the primary vortex ring and the pattern of the secondary vorticity generation can be seen clearly and the effects of the helical vortex lines around the primary ring also observed. The main features of the oblique impingement of a vortex ring on a wall are captured quite well and comparison is made with the experimental results. At the higher Reynolds number of 1000, the helical winding of vortex lines is however much more pronounced, and the secondary vortex structure has a thicker core. The results reveal detailed phenomena and provide physical insight into the flow mechanisms of vortex ring/wall interaction.

LAGRANGIAN FLOW SIMULATION WITH SUB-PARTICLE-SCALE TURBULENCE MODEL

A Lagrangian solver of the Navier-Stokes equation, or the MPS method, is extended by installing the sub-particle-scale (SPS) turbulence model. The momentum equation for the particle-scale (PS) flow is derived through the filtering operation of the Navier-Stokes equation. The effect of the SPS turbulence is found as the Reynolds stress terms in the PS momentum equation. The Reynolds stress terms are described by introducing the Smagorinsky model, which is frequently used in Eulerian LES. The MPS method has the advantage in the calculation of the free-surface flow against the Eulerian one, because it is free from the numerical diffusion due to the discretization of advection terms. While, in this paper, the MPS method with the SPS turbulence model is applied to the turbulent mixing layer, or the jet, to show its performance on the simulation of the turbulent flow with a simple structure. The mean velocity profile is compared with the previous experiments. The unsteady behavior of the jet and the mixing process at the interface of the jet and the still water are displayed as the snapshots of the particle motion.