Newton region

For Reynolds numbers > 1000, the flow is fully turbulent. Inertial forces prevail and becomes constant and equal to 0.44, the Newton region. The region in between Re = 0.2 and 1000 is known as the transition region andC is either described in a graph or by one or more empirical equations. 

As the Reynolds number increases further, vortex shedding takes place (Figure 1.13) in what is known as the Newton region, in the range 500 < Re <2 X where the drag coefficient has a value of approximately 0.44. Consequently equation 1.28 gives the drag force as... 

Richardson (1971) summarises a mefhod of predicting minimum fluidizing velocify as a function of the terminal falling velocify of a particle. This requires the terminal falling velocify Ut to be expressed in terms of fhe Galileo number. Thus, treating the Stokes, transition and Newton regions in turn ... 

Finally, for the Newton region, at Reynolds numbers greater than... 

Finally, substituting = 0.44, for the Newton region the following relation is obtained ... 

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

All other cases are between the extreme limits of Stokes s and Newton s formulas. So we may say, that modeling the free-falling velocity of any single particle by the formula (14.49), the exponent n varies in the region 0.5 s n < 2. In the following we shall assume that k and n are fixed, which means that we consider a certain size-class of particles. 

It uses a linear or quadratic synchronous transit approach to get closer to the quadratic region of the transition state and then uses a quasi-Newton or eigenvalue-following algorithm to complete the optimization. 

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