By Minye Liu, DuPont Engineering Technology, Wilmington, DE; Arthur Etchells, AWE3 Inc., Philadelphia, PA (DuPont retired); and Richard LaRoche, Fluent Inc.

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DuPont is a science company that delivers a diversity of products that make life better, safer, and easier for people. Their products span the areas of food and nutrition, apparel, home and construction, electronics, transportation, and safety and protection. During production, most of these products pass through a stage where fluid mechanics and mixing play important roles. In a recent project, a team of DuPont engineers improved the yields in one process that involved the mixing of two gases. The key contribution to the improvement came from CFD models of the flow inside the static mixer used.

Molar concentration field (top) and velocity magnitude (bottom) on the center plane of the mixer at one instant in time, computed by the LES model; the mixing of the gas streams is visible in the figures

In the process, two gas streams are fed into a static mixer for homogeneous mixing. The mixture is then fed into a reactor for the next stage of production. The quality of mixing is critical to the reactions, and therefore yields in the reactor. The static mixer used in the production line is a high efficiency vortex (HEV) mixer. In order to improve the performance of the mixer, many different geometry designs and modifications had to be tested. The traditional way of achieving this goal is to test each design on the production line. This method is costly, since production is interrupted each time, and impractical for a large number of designs. The team therefore decided to use CFD to accomplish the goal.

The HEV static mixer used is a round pipe with a number of tabs mounted on the pipe wall. Two gas streams are fed into the pipe upstream of the tabs. In a high Reynolds number turbulent flow, a pair of vortices is generated from the corner tips of each tab at high frequency, generating high efficiency mixing of the two gas streams. Due to production site limitations, the two gas streams have to be fed into the mixer from the side of the pipe through a number of specially designed holes. There are many factors affecting mixing efficiency, such as tab sizes, shapes, angles, the number of tabs, and tab alignment (relative to the other tabs and to the inlet holes).

Geometry of an HEV mixer

The turbulent flow inside the mixer was modeled using both the k-ε and LES turbulence models. To test grid independence, the full 3D flow domain of the mixer was meshed with three grid densities, resulting in models with from 500,000 to 1,200,000 cells. The mixing efficiency was determined using the coefficient of variance (CoV) at the exit of the mixer. With the k-ε turbulence model, a steady flow solution can be obtained while with the LES model, a more computationally demanding time-dependent solution is required to generate enough data for a mixing analysis. A strategy was therefore adopted in which many designs were screened with the k-ε model, and only those that showed promise were modeled with LES. To accelerate the turnover time, the parallel solver was used for all solutions. Along with the CFD work, a test facility was set up at a vendor site to collect data for validation.

Comparisons of the CFD solutions from the k-ε and LES models consistently showed that the k-ε model predicts a much lower CoV, indicating some unphysical diffusion in the solution that may come from Reynolds averaging of the Navier- Stokes equations. On the other hand, CoVs from the LES solutions agreed very well with those taken from lab experiments. The simulations allowed the team to identify design changes that led to better mixing and ultimately, better yields in the downstream reactor, resulting in substantial savings for the company.

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