Froude criterion

In order to simulate the action of a flow on an adhering particle we must maintain geometric, kinematic (velocity ratio), and dynamic (mass and force) similarity. We cannot choose these conditions in detail. We can only note that for river-type flows the Froude criterion Fr = v /gZ ensures d5mamic similarity and the Reynolds criterion Re = vd/ v kinematic similarity. Since the forces of gravity prevail over viscosity, the decisive factor in simulating river flows will be the Froude criterion. 

Similarly it may be shown that, at the critical conditions, the flowrate is a maximum for a given value of the specific energy J. At the critical velocity, (ir/gD) is equal to unity. This dimensionless group is known as the Froude number Fr. For velocities greater than the critical velocity Fr is greater than unity, and vice versa. It may be shown that the velocity with which a small disturbance is transmitted through a liquid in an open channel is equal to the critical velocity, and hence the Froude number is the criterion by which the type of flow, tranquil or rapid, is determined. Tranquil flow occurs when Fr is less than unity and rapid flow when Fr is greater than unity. 

It is thus seen that the velocity of an elementary wave is equal to the critical velocity, at which the specific energy of the fluid is a minimum for a given flowrate. The criterion for critical conditions is therefore that the Froude number, (u2/gD), must be equal to unity. 

In an early attempt to differentiate between the conditions leading to particulate or aggregative fluidisation, Wilhelm and Kwauk suggested using the value of the Froude number (u f/gd) as a criterion, where ... 

On the other hand, since the film is accelerating in this initial zone, it follows that the Froude number of the flow, which may be taken as the criterion for gravity-wave instability, increases from some very small value at the inlet to its equilibrium value for the particular flow rate and channel slope. Depending on the flow conditions, it is possible for the Froude number of the flow to reach the critical value before the end of the acceleration zone is reached. In this case it can be supposed that waves could occur before the end of the acceleration zone if some triggering mechanism were available. This appears to be the case in fact, for Tailby and Portalski (T5) have noted that when an adjacent gas stream (either cocurrent or countercurrent) is present, the length of the smooth entry zone decreases markedly. 

Convective bulk transport is also an extremely important factor in the suspension of solids in a stirred tank (this is also responsible for the flow pattern at the tank bottom). P/V cannot be used as a scale-up criterion in this process either. Measurements have shown that the minimum rotational speed, ncrit, of the stirrer which is necessary for the suspension (whirling-up) of particles in the turbulent regime is given by the appropriate Froude number ... 

Because the Froude number is the scale-up criterion here, we formulate it for a given material system by P/V as follows ... 

Froude Number has been described for powder blending and was suggested as a criterion for dynamic similarity and a scale-up parameter in wet granulation. The mechanics of the phenomenon was described as interplay of the centrifugal force (pushing the particles against the mixer wall) and the centripetal force produced by the wall, creating a compaction zone. ... 

Froude number (Fr) is the ratio of the centrifugal acceleration to the gravitation constant (g). It can be used as a criterion for dynamic similarity of granulators ... 

The approximate criterion to estimate the transition from bubbling to smooth fluidization is expressed in terms of the dimensionless Froude number at minimum fluidization. This is presented in Equation (18.1) in terms of the minimum fluidization velocity,, the catalyst diameter, dp, and the acceleration due to gravity, g, as ... 

SCALE-UP AND TESTING OF MIXERS 971 Criterion 2 Keep Froude numbers constant ... 

Archimedes number Criterion of stokes Streamlines The backward jet The Froude number The path of corpuscles The rotoklon... 

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