Читать книгу Agitator Design for Gas-Liquid Fermenters and Bioreactors - Gregory T. Benz - Страница 46

Froude number is the ratio of a reference rotational speed times a reference velocity divided by the local gravitational acceleration. For similar reasons that we used for Reynolds number, we use N for rotational speed and ND for velocity, resulting in:

(3.9)

Note that g is not a constant; it is the local gravitational acceleration. While it is almost uniform on the Earth’s surface, it will be quite different on other planets. So the same impeller operating at the same speed would have different Froude numbers on Earth, the moon, Mars, and Jupiter. This will be important if we ever build fermenters on another planet.

Conceptually, the Froude number is the ratio of inertial forces to gravitational forces. High Froude numbers mean inertia dominates. This is associated with a choppy surface and vortex formation. Low Froude numbers mean gravity dominates, which is associated with a quiet, flat surface. Froude number, in combination with Reynolds number, impeller type, baffle number, and various geometric factors, can be used to predict mean vortex depth.

In gas–liquid contacting, the impeller gassing factor is a function of Froude number, impeller type, Reynolds number, Aeration number, and geometry factors. That is its principal use for bioreactor design. It is also used in most impeller flooding correlations.