Geometric similarity means that our scale-up length ratio of 84/11.5 = 7.3 will multiply all of the length dimensions. In this particular case, a combination of experience, literature research and experimentation leads us to believe that the tip speed should be held constant when we scale-up and that torque-per-volume may represent mixing intensity.Īs a first step in our scale-up calculation, we will use geometrical similarity to do a scale-up from our 11.5 in.-dia. As we will see while doing the calculations, the tank geometry and impeller type both change in the scale-up process. tank with a 3,000 gal capacity using four-blade, pitched-blade turbines. Now suppose we want to duplicate our process results in an 84.0 in.-dia. (Power number corrections differ with type of impeller.) This additional step to correct power number should be done for each subsequent step in the scale-up process if the Reynolds number suggests that such a correction is necessary. Had the Reynolds number been less than 900, we would have to make an appropriate correction to the power number and use that corrected number to calculate power and torque characteristics of the mixer. For simplicity, let’s assume that the power number does not begin to increase until the Reynolds number drops below 900. For a pitched-blade turbine the power number, which remains constant in the turbulent range, will begin to increase in the transition and viscous regime. At these conditions, the Reynolds number of 995 would suggest that the mixer is operating in the transition regime, which applies for 1 < N Re < 20,000. With this information, we can calculate the operating conditions that exist in our pilot-scale experiment (see table). While corrections can be made for bottom shape and tank internals, for simplicity we will ignore these corrections here. In the real world, the tank may have a dished bottom and the internals typically will occupy 2% to 5% of the volume for this type of reactor. liquid level assumes that the tank bottom is flat and the tank internals (impellers, shaft, baffles, etc.) do not take up any space. Derivations and details on the various equations for geometric scale-up and mixer evaluation appear in many references such as widely available handbooks. The sidebar gives formulas for calculating mixing variables in conventional U.S. Other criteria, such as equal blend time or surface motion are difficult to scale-up because of the rapidly increasing mixing intensity for large-scale tanks. Most of the practical scale-up rules for geometric similarity, including equal solids suspension, fall in the speed range between equal tip speed and equal power per volume. For geometric similarity and turbulent conditions, torque per volume reduces to the same scale-up formula as equal tip speed (Eq. While torque is just power divided by speed, torque per volume is similar to momentum transfer and is closely related to the effective motion created by the mixer. Another important mixing characteristic is torque per volume, which often represents mixing intensity, in terms of fluid velocities.
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