TRANSVERSE JET MIXING IN CHEMICAL REACTORS: MIXING PERFORMANCE AND REACTION CHARACTERISTICS

Shaun Kim and Venkat Raman The University of Texas at Austin

Summary

Transverse jets are commonly using in the chemical processing industry to enhance mixing between two fluids. In these systems, a main jet issues into a crossflowing stream initiating the mixing process. In this work, direct numerical simulation of turbulent transverse jets is used to understand the effect of jet exit shape on the near-field mixing characteristics. Four different exit shapes, namely, a circular, a square, and two triangular geometries are considered. A competitive-consecutive reaction system is used to understand the impact of near-field mixing structures on the reaction process. It is found that the primary reaction is dominant on the windward side of the main-jet, and the secondary reaction is dominant in the core of the jet. This spatial separation facilitates the design of transverse jets that minimize secondary product formation.

Keywords Complex reacting flows, Multiscale analysis

IntroductionTransverse jets are common flow configurations used to enhance mixing between two flow streams. In these systems (Fig. 1), a main jet issues into a crossflowing fluid stream initiating the mixing process. Transverse jets entrain more crossflow fluid than corresponding parallel jets, leading to improved mixing. In spite of the simplicity of the flow configuration, transverse jets exhibit a diverse array of vortical flow structures in the near field, which lead to a dominant counter-rotating vortex pair (CVP) further downstream. By controlling the evolution of the near-field structures, it is possible to further improve mixing efficiency. Modifications to the jet exit shape provide an economical means of altering the near-field flow structure. In this work, direct numerical simulations are used to study the effect of jet exit shape on the mixing process. A competitive-consecutive reaction system is used to understand the role of these flow structures on chemical reactions.

Fig. 1 Schematic view of the computational domain

DNS of Transverse Jets The DNS solver was based on a low-Mach number formulation of the Navier-Stokes equations. A second-order energy-conserving scheme was used for the discretizatin of the nonlinear terms, while a central scheme is used for discretizing the viscous/diffusion terms. Fig. 1 shows the computational domain. The ratio of the main jet velocity to the crossflow velocity was set to 1.52. The

Reynolds number based on the main jet velocity and diameter was 3000. The computational grid was chosen so that the smallest turbulence scales are resolved. Based on the Reynolds number, a 512X256X256 grid was used. Grid convergence studies with finer grids showed that the statistics considered here did not differ significantly from the baseline grid. The computations were carried out on 512 processors using MPI-based parallelism. Four different exit shapes, namely, a circle, a square, and two triangles were considered. The triangles were oriented such that either their apex (case III) or base (case IV) faced on the oncoming crossflow. A fully developed laminar flow profile was used as the inlet condition. The velocity boundary condition was imposed on the Cartesian using a trilinear interpolation method. The crossflow was assumed to be laminar as well with a boundary layer thickness equal to 0.7D, where D is the equivalent jet diameter. The competitive-consecutive reactions were implemented by solving for three scalars, namely, mixture fraction and two reaction progress variables. The main jet fluid reacts with crossflow to produce the primary product. The primary product can then react with the jet fluid to form the secondary product. The reaction rate constant of the main reaction is set to be 10 times the rate constant for the secondary reaction. The scalars were evolved using a third order upwind scheme.

Impact of Exit Shape on Scalar Mixing The near field flow structure contained similar vortical structures for all orifice shapes considered. However, the relative strengths of the structures varied between the different configurations. For instance, Fig. 2 shows the near-field vortical structures for the jet issuing through a square orifice. The most prominent near-field feature is the hanging vortices emanating from the sides of the square orifice. The interaction of the crossflow with the jet creates upstream spanwise roller vortices. At the same time, the hanging vortices create lee-side spanwise vortices (not

seen in the figure), which coalesce with the upstream vortices at several jet diameters downstream of the inlet. In addition, near-vertical wake vortices with a wall-normal orientation are formed through the interaction of the lee-side boundary layer with the main jet. Although the crossflow and the main jet are laminar, the flow quickly transitions to a turbulent flow, as evidenced by randomly oriented smaller vortical structures downstream of the inlet.

Fig. 2 Coherent structures in square jet in crossflow

The most important effect of the jet orifice shape appears to be the modification of the upstream spanwise vortices and the hanging vortex. For instance, a circular jet exhibits weaker hanging vortices compared to the triangular cases. This impacts the formation of the CVP structure downstream. To understand mixing performance, inert scalar composition was extracted in planes normal to the mean jet trajectory (Fig. 3). The surface integral of scalar variance on these planes is a good measure of small-scale mixing. It was found that this plane averaged variance decayed fastest along the jet trajectory for triangle (case III) configuration.

Fig. 3 Mean mixture fraction field in square jet in crossflow

Reaction Structure in Transverse Jets The competitive consecutive reactions were used to study the reaction structure (Fig. 4). For all the orifice shapes considered, the primary reaction was initiated on both the jet lee-side and the upstream shear layers. The hanging vortices cause crossflow fluid to be entrained into the jet-core. As the jet-core breaks down, a secondary reaction zone is formed on the windward side due to shear-based fluid entrainment. The secondary reaction between the jet fluid and the primary product occurs in the lee-side, indicating a spatial separation of reaction zones.

Secondary product

Primary product

Fig. 4 Instantaneous view of reaction structures. Contours indicate

primary product concentration. Isosurface of primary product (blue) and secondary product (gray) are shown.

The different orifice shapes had minimal impact on the reaction zone. However, triangle 2 produced locally high concentration of the secondary product. This is primarily due to the insufficient jet breakdown associated with this configuration. Additional studies with faster secondary reactions and crossflow fluid based secondary reactions are being carried out. References (1) Lim, T.; New, T.H.; Luo, S. On the development of large-scale structures of a jet normal to a cross flow, Phys. of Fluids 2001, 13, 770-775. (2) Yuan, L. L.; Street, R. L.; Ferziger, J. H. Large-eddy simulations of a round jet in crossflow, J. Fluid Mech. 1999, 379, 71-104. (3) Muppidi, S.; Mahesh, K. Study of trajectories of jets in crossflow using direct numerical simulations, J. Fluid Mech. 2005, 530, 81-100. (4) Fric, T. F. Structure in the Near Field of the Transverse Jet, Ph.D. Thesis, California Institute of Technology, 1990. (5) Salewski, M.; Stankovic, D.; Fuchs, L. Mixing in Circular and Non-circular Jets in Crossflow, Flow Turbulence Combust. 2008, 80, 255-283. (6) Gutmark, E. J.; Grinstein, F. F. Flow control with noncircular jets, Annu. Rev. Fluid Mech. 1999, 31, 239-272. (7) Muppidi, S.; Mahesh, K. Direct numerical simulation of passive scalar transport in transverse jets, J. Fluid Mech. 2008, 598, 335-360.