On Implementation of the Finite Difference Lattice Boltzmann Method with Internal Degree of Freedom to Edgetone

The lattice Boltzman method (LBM) and the finite difference-based lattice Boltzmann method (FDLBM) are quite recent approaches for simulating fluid flow, which have been proven as valid and efficient tools in a variety of complex flow problems. They are considered attractive alternatives to conventional finite-difference schemes because they recover the Navier-Stokes equations and are computationally more stable, and easily parallelizable. However, most models of the LBM or FDLBM are for incompressible fluids because of the simplicity of the structure of the model. Although some models for compressible thermal fluids have been introduced, these models are for monatomic gases, and suffer from the instability in calculations. A lattice BGK model based on a finite difference scheme with an internal degree of freedom is employed and it is shown that a diatomic gas such as air is successfully simulated. In this research we present a 2-dimensional edge tone to predict the frequency characteristics of discrete oscillations of a jet-edge feedback cycle by the FDLBM in which any specific heat ratio $\gamma$ can be chosen freely. The jet is chosen long enough in order to guarantee the parabolic velocity profile of a jet at the outlet, and the edge is of an angle of $\alpha$=23$^{o}$. At a stand-off distance w, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations resulting from periodic oscillation of the jet around the edge.