Vertical Buoyant Jet Analysis in an Enclosure Using ITM and LES

Abstract

The objective of this study is to investigate vertical buoyant jets in an enclosure using Large Eddy Simulation (LES) methods with no sub-grid scale model. This type of methodology is called Implicit Turbulent Modeling (ITM). Two different boundary conditions are applied at the inlet, being a uniform and periodic forcing velocity distribution. To accomplish this goal, a numerical solver was written, named DREAM®, which is capable of solving three dimensional, transient flows using an accurate monotonic upwinding scheme. The three-dimensional Navier-Stokes equations are solved in Cartesian coordinates, with the control volume approach being implemented on a staggered grid. The numerical scheme uses a fractional time step method, Crank-Nicolson, with the overall spatial and temporal accuracy being second order. In ITM simulations, there is no explicit subgrid-scale model (SGS) used for the modeling of the small scale vortical structures. ITM simulations assume that through strict conservation of the fluxing quantities in and out of the cell, the grid resolution is fully capable of capturing the important scales of the flow. The control volume averaging techniques used in the ITM methods acts as an implicit subgrid-scale model, and the resolvable scales of the flow are only dependent on the grid resolution within the domain. The available experimental data, as well as simulations that used SGS models, compare favorably to the ITM simulations from DREAM® in most cases as long as an “adequate” grid resolution is maintained. Results show that the density stratification tends to accelerate the jet and increase the amount of turbulence present within the flow. Perturbation of the inlet boundary condition ensures a sooner onset of turbulence, which is faster than the non-perturbed inlet boundary condition. A similarity solution is achieved at approximately 8 and 13 inlet diameters downstream of the inlet for the perturbed and uniform inlet boundary condition. Comparison between the vertical buoyant jet simulations to the available experimental data shows good agreement for the jet width and buoyant path centerline locations based on the internal densimetric Froude number. The application of these methods to immiscible fluids shows a new dimension to ITM and allows for a high resolution of the resulting flow field without the need for an explicit SGS model.