The present level of understanding of turbulent mixing has come from extensive measurements undertaken over the last few years. The need now is to develop a quantitative characterization of mixing processes for modeling. However, the mixing process is complex and has not allowed an adequate numerical representation by computational fluid mechanics methods. Even the simplest case, reactive mixing of soluble fluids, can be regarded as a combination of four nonlinear coupled spatially distributed processes: convection, stretching, diffusion,and chemical reaction. Convection moves portions of material from one location to another, promoting global uniformity by redistributing initially segregated components. Stretching transforms portions of material into elongated striations,increasing the contact area. Diffusion, which is generated by the thermal energy of individual molecules, induces uniformity at small scales. These processes typically generate partially mixed structures that exhibit strong variability in local composition. Chemical reactions taking place in this inhomogeneous milieu often exhibit spatially dependent rates. Given this level of complexity, it is not surprising that reactive mixing processes have so far eluded detailed quantification and that inefficient mixing can have large negative effects on the performance of a wide spectrum of industrial processes: desired reactions are slowed and sometimes stopped before reaching completion, selectivity is affected, and the yield is decreased.Many facets need to be addressed to improve modeling that is now available.First, an understanding of the physics is needed and must be incorporated into the models, and second, the dynamics of such systems must be taken into account. The existence of low frequency, unsteady dynamical motions has not been incorporated into any of the commercial model efforts. Currently,such models are steady state computations and do not allow unsteady motions.

Our work involves a unique interactive combination of computational and experimental efforts. In brief, the key is the realization that if a full simulation can reproduce the experimental flow field that controls mixing, then by such a calculation (which is currently not of engineering practicality), we can obtain measures of the individual terms in the Navier-Stokes equations on scales down to a small multiple of the grid size. These estimates can then be used to help test other simpler models and can even be used to improve engineering type calculations. Such an effort is fundamental to the entire field of fluid mechanics and of considerable industrial importance.

There are a definable series of steps that can be undertaken to improve the situation. Our first step is to use a direct numerical simulation (DNS) approach for the opposed jet configuration.This approach solves the full, three - dimensional Navier-Stokes equations with appropriate boundary conditions. There are several reasons for the selection of the opposed jet geometry. Two of these are associated with unaddressed problems associated with DNS calculations in the past on channel,pipe, and boundary layer flows. The first problem is the boundary conditions at the entry to the flow. In the standard approach, the inlet turbulent conditions are unknown and one assumes that the inlet conditions are the same as that obtained from the computation at the exit. This is called cyclic boundary conditions. The second problem is associated with the initial turbulent field in the entire volume. What is sometimes done is to use a representation of the average turbulent velocity profile with an added random component to represent the turbulence. In contrast, the opposed jet system operates with laminar flow inlets, even for conditions where the jets are unstable. Cyclic boundary conditions are not needed. To solve the problem associated with the initial conditions of the field, we have the full-field, time-resolved velocity-vectors measured and can give the computation experimentally measured initial conditions. Finally, there are no rotating parts, as in an impeller mixer, that would require the used of a sliding mesh grid. The question to be answered by the research is how long do the statistical measures obtained from experiments and DNS computations track one another. We are sure that one cannot match results on an instantaneous basis; however, by tracking important statistics, we can evaluate the approach for engineering purposes. We hope to prove, once and for all, that those measures, that are consider critical for subsequent mixing, do remain similar for one or more tank turnovers or residence times.

We first tested our DNS calculations by doing a study to simulate a complex off-center mixer (vortex lamp). This geometry has a stable vortex that parallels the unsteady vortex that exists in mixing vessels. This completed work has verified that the numerical simulations can be used for the mixing problem. The full details are available. The vortex lamp (see slide 9) with its stable low frequency vortex is an ornamental light stand made of a glass cylinder, approximately 3" in diameter and 6" long,containing water and illuminated by a small lamp at the bottom. A small impeller with three short vanes, driven by an electric motor, rotates at an eccentric position close to the bottom. The water contains tiny colored beads lighter than water. As the rotor rotates, the water in the cylinder rotates and a tornado-like cyclone is formed with the vortex center near the top of the water at an eccentric location. The beads are trapped in the cyclone and form a colorful chain, which goes down slowly through the center of the cyclone till it reaches the outer edge of the impeller rotor.The beads are then propelled to some distance by the water flowing from the rotor outward rotationally and ascend near the outer wall of the cylinder.In the two identical hurricane lights shown in the figure, the shapes of the cyclones are not identical, although time average of the shapes would agree well. A code to solve the unsteady incompressible Navier-Stokes equations in the strong conservation form was used. A moving mesh system was developed (see slide 10). Shown is only the overall mesh. The rotating mesh was a small cylinder at the bottom and off center about 2/3 of the way to the wall. The computational simulation successfully captured the formation of a cyclone that starts at an eccentric location at the top surface and reaches an edge of the rotor, with a good qualitative agreement to the experimentally visualized flow (see slide 11).

Some preliminary comparisons between DNS and LES are also available for the opposed jet geometry (see slide 30). The LES approach is based on a low-resolution DNS computation with the finer scales being modeled by a knowledge of a physical understanding of the flow. The LES modeling technique has only a few assumptions that can be modified to provide a match between the experimental statistical measures and the LES results. The advantage of LES is that it is far less computer demanding than DNS, so that the computations can be pushed to higher Reynolds number flows. The problem is to decide which,if any, of the subgrid models and filtering techniques are adequate to represent the data. As in the DNS effort, one is not going to be able to match the data on an instantaneous basis; however, by tracking important statistics basic to the mixing process, we can evaluate the approach. Once this step is resolved, then the LES results can be used as the basis for the development of new methods of engineering modeling (Reynolds averaged Navier-Stokes or RANS) that would have broad practical importance in industries that use such mixing systems.

The opposed jet measurements are completed, as they required a fixed camera view. For the rotating mixing vessel, the convective view allows measurement of time-resolved, three-dimensional velocity-vectors in a mixing vessel, even at high Reynolds numbers. More fundamental and local parameters (e.g., local turbulent kinetic energy) can be obtained that describe inhomogeneities that are of importance in mixing vessels and can be used to describe trailing impeller vortex structures, baffle-fluid interactions, etc. Such measures can be contrasted with overall global parameters as the power per unit volume. Local motions must be used to allow prediction of mixing, especially where selectivity is of importance.These measurements must be made under true dynamic conditions where superimposed larger scale motions can influence finer scale mixing processes.