Boundary conditions for direct numerical simulations of free jets

Abstract

State-of-them-t In the present study, behavior of classical non-reflecting boundary conditions for unsteady flows is investigated by using a software package which provides numerical solutions to the compressible three-dimensional Navier-Stokes equations. Despite the use of non-reflecting boundary conditions, aeroacoustic coupling phenomena are clearly identified in the simulation of twoand three-dimensional unsteady free jets. A new “sponge layer” approach is proposed and is shown to completely remove the acoustic coupling. This new approach appears then to be an adequate candidate for Direct Numerical Simulations of spatially evolving turbulent flows. Introduction Most DNS or LES performed to date make use of the incompressibility assumption1~2. Databases provided-by DNS have been used to study turbulence models3,4 and characterize turbulent structure9. On the other hand, the study of compressible turbulent flows is less mature. Passot et al 6 studied compressible isotropic homogeneous turbulence, later Blaisdell et aZ7 considered homogeneous shear turbulence, Leles, mixing layers and more recently Coleman et aP, supersonic channel flow. All these computations correspond to simple geometries because homogeneity is invoked to use periodic conditions in two or three directions. In the other direction, a well-defined no-slip condition over a flat plate is imposed. For the last decade, the constant increase of performance of computers has allowed the development of a new approach based on the Direct Numerical Simulation (DNS) of flows. In this kind of simulation, one resolves the full unsteady Navier-Stokes equations without any modelling of turbulence. It is thus necessary to-resolve all the time and length scales present inside the flow, which often results in quite huge computations. Most flows considered by DNS have been extremely simple: isotropic homogeneous turbulence; channel flow, boundary layers, which have become then common test cases for flow solvers. The next step for DNS is to address more complex flows: this means to compute compressible turbulent flows in complex geometries, with various inflow and outflow boundary conditions. This task requires the development of new numerical schemes providing a sufficiently good accuracy on arbitrary meshes as ml1 as new treatments to handle inflow and outflow boundary conditions and acoustic waves (for compressible cases). This paper deals with this latter point. After a short review of the state-of-the-art about this topic, we will describe briefly the compressible three dimensional flow solver AVBP used for the computations. A specific presentation of the boundary conditions available will be added. Results obtained for the case of the two-dimendional free jet with and without the sponge layer will be discussed. More relevant simulations deal with spatially evolving turbulent flows such as boundary layerslO, square jet ii or plane jet. These computations are more expensive because a larger domain must be computed to ensure that the upstream conditions do not influence the results. They are also more complex because of the need to prescribe unsteady boundary conditions for inflow and outflow. Even in cases where physical waves are not able to propagate upstream from the outlet (incompressible or supersonic flows), numerical waves may do so and interact with the flow. Moreover, in the case of a subsonic exit one has to account for the entering acoustic wave properly to minimize the numerical production of sound in the computational domainr2-‘4. To our knowledge, no boundary treatment exists at the moment, which can efficiently let a vortex structure leave the domain without generating a reflected acoustic wave. This introduces an artificial coupling between any sensitive region of the flow that is of interest (for example the vicinity of a trailing edge) and the exit of the vortices generated in this region15. A way to reduce this coupling is to enlarge the size of the computational domain in order to increase the distance between the boundary conditions and the unstable zones of the flow. -Thus the possibility to do this without dramatically increasing the number of grid points appears to be attractive.