Numerical Investigation of Coaxial Turbulent Jet

Abstract

Implantation of the 3D compressible parallel code to study a compressible turbulent coaxial jet at higher number of Reynolds. The model of large eddy simulation used. In this model, only the larger structures are computed, and the effects of smaller scales are taken into account via a sub-grid scale model. The code was parallelized using the Message Passing Interface (MPI) library. The resolution full Navier Stokes equations are based on the compute the fluxes. In order to compute the fluxes, the fluxes were split into viscous fluxes and convective fluxes. Viscous fluxes are computed from the second order central differences in space. The convective fluxes are evaluated using the approximate Riemann solver. Approximate Riemann solver based on the linearization of the differential relations along the characteristic curves of the one-dimensional hyperbolic conservation laws. The solution was advanced in time using a two-stage explicit McCormack time-marching method, this method is accurate, efficient and simple to implement on parallel computers. The mean flow field and turbulence intensities of the coaxial jet have been calculated and analyzed. The results obtained in our simulation are found to be in very good agreement with the available experimental data of coaxial jet at similar flow conditions. Key-Words: Coaxial jet, Large Eddy Simulation, Riemann solver, MUSCL Coaxial jets are present in various industrial devices: they effectively provide an effective means of mixing species for combustion applications. They are also used in aero-acoustics. The noise produced by a single jet can indeed be reduced through the addition of a coaxial surrounding flux. There are two types of coaxial jets: those where the velocity of the primary jet is greater than the velocity of the secondary and those where the velocity of the primary jet is lower than the velocity of the secondary jet. The coaxial jet is defined by many initial parameters, such as the primary jet expansion rate and its temperature, the secondary jet expansion rate and its temperature, the ratio of the velocities between the secondary and the primary jet. As well as the ratio between the diameters of the secondary and primary stream. Experimental work of Ko and Kwan [1] distinguished the development of the jets in three zones: the initial region, the intermediate region, and the fully merged zone. The initial region is located between the nozzle, and the end of the outer core potential. Immediately downstream is the intermediate region which ends at the reattachment point, and finally is found the fully merged zone. The work of Champagne and Wygnanski [2] showed that coaxial jets had two distinct shear layers, one forming between the primary and secondary jets, and the second between the secondary jet and the environment. Forstall and Shapiro [3], identified that the ratio of the velocity of the secondary jet and the primary jet defined by was then the determining parameter of the coaxial jets. Later, Favre-Marinet and CamanoSchettini [4, 5] showed that this was actually the ratio of momentum fluxes, (where and are the densities of the fluid from the secondary jet and the primary jet respectively. Williams et al. [6], Dosanjh et al. [7] it was concluded that the noise produced by a single jet could be substantially reduced by the addition of a low velocity annular jet. The measurements made by Kwan and Ko [8] revealed two distinct peaks corresponding to the passage of vortices from the WSEAS TRANSACTIONS on HEAT and MASS TRANSFER Nabil Belkacem Safer, Abdelhadi. Beghidja E-ISSN: 2224-3461 98 Volume 14, 2019 inner shear layer and the passage of those from the outer shear layer. They deduce from their experimental results on the mean and fluctuating velocity distributions that the structure of the coaxial jet flow could be described by considering the independent shear layers. A number of previous works have focused on the instabilities that are developing in the coaxial jets. A special case interesting is the experimental configuration by Dahm et al. [9]. Studied the interaction between the coherent structures evolving in the two shearlayers. Wicker and Eaton [10] noted that the coaxial jet developed axi-symmetric mode instability, and beyond a certain value of the Reynolds number below which the instability is sinuous. Frequencies dominates in the near field of coaxial jets have also been explored in several works Au and Ko [11], Gladnick et al. [12], and Wicker and Eaton [10]. Theirs measurements show that as in the case of simple jets, a preferential mode of jet exists beyond the core potential. Camano-Schettini [13] illustrated the presence of longitudinal vortices. Zawacki et al. [14] were the first to highlight presences of a return flow. This recirculation region (which we will also call recirculation bubble) exists for quite high velocity ratios. According to Rehab and al. [15], the value of seems to be between 5 and 8, depending on the shape of the injector. Rehab [16] was also interested in the behavior of this bubble. In his experiments with high Reynolds number, he showed that this re-circulation bubble oscillates at a low frequency leading to a Strouhal number of the order of 0.035. In comparison with the simple jets, we find much less fundamental studies informing, us on the turbulence of these flows. In this work attempts to simulate the unsteadiness of coaxial jets, and to study the evolution of coherent structures, this is one of the objectives in this work. This nevertheless takes place in the case of monophasic coaxial jets, and velocity of the primary jet is greater than that of the secondary jet, using the model Large Eddy Simulations (LES). 2 Governing Equation The full Navier–Stokes equations for twodimensional fluid motion are written in conservative form. In Cartesian coordinates, we have: