The next time you scan the shelves in your kitchen looking for something to eat, think about the processes that are used to manufacture the various choices before you. Many food items are manufactured by processes such as extrusion or the mixing of viscous, non-Newtonian substances. Even the packaging from plastic wrap to rigid plastic containers was most likely made using blow molding or film casting. These processes, while mathematically complex to describe, are readily simulated using POLYFLOW, as illustrated here.

A New Twist on Pasta

Pasta comes in a variety of shapes and sizes, many of which involve twists or curls. To manufacture these shapes, pasta dough is extruded through a die. To make the extruded material twist, a torque is required. In the case of shear-thinning pasta dough, a torque can be generated by pinched or sharply curved regions at the edges of the die lip. These regions give rise to increased shear in the dough, which leads to decreased viscosity and increased velocity. A non-uniform velocity profile across the die face can lead to a twisting of the extruded product so that mass will be conserved. An example of a twisted extruded product formed when a substance with the properties of dough is pushed through a die is shown in the figure. This simulation illustrates how CFD can be used to design die shapes that will result in specific extruded shapes, depending upon the rheological properties of the pasta dough.

A Batch of Better Batter

Industrial-strength food mixers are a wonder to observe. The compound rotation of one or two mixing paddles has an uncanny ability to pull, stretch, and fold the contents of the bowl, whether they are liquid-like (cake batter) or solid-like (bread or cookie dough). Using the mesh super-position technique (MST) in POLYFLOW, engineers have simulated this complex transient motion.

DPM-2 Gallon Double Planetary Mixer
Courtesy of Charles Ross & Son Company

To use the MST, two grids are required: one for the tank (or mixing bowl) and another for the paddle. These meshes are superimposed prior to the calculation. In the present example, two intermeshing paddles are used, so a total of three meshes are required. Each paddle is offset from the other by 90 degrees, and each rotates about its axis at 15 rpm. The support to which the paddles are mounted also rotates about the bowl axis at 15 rpm. The bowl is filled with a liquid mixture that has a Reynolds number of 10-4.

During the transient simulation, the MST allows for the steady motion of the paddles through the mixture in the bowl. Despite the fact that the flow is laminar, it has the qualities of chaotic flow, since massless particles released from roughly the same location at the same time follow very different trajectories. The dispersion of 1,000 such particles is illustrated in the figures below during six complete rotations of the paddles. After this period of time, the particles are well dispersed on the horizontal plane from which they were released. Had the paddles contained some twist in their design, the particles would have dispersed axially as well. This point illustrates how helpful numerical simulation can be in the design of mixing equipment used in the food industry.

Particles released from a small cubic region in the mixer are shown after 0, 2, 4, and 6 rotations of the paddles.

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