By Vincent W. Uhl, Joseph B. Gray
ISBN-10: 0123956331
ISBN-13: 9780123956330
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Extra resources for Mixing. Theory And Practice
Example text
In order to obtain a solution to Eq. (47), some assumption or development must be made to obtain a relation between E(k) and T(k). One possible method is to assume that the decay process is independent of T(k); thus, the inertial effects can be assumed to be negligible. Batcheior has analyzed the problem of very low wave numbers or the very large eddies; in essence, his argument can be seen from Fig. 5. The inertial or transfer term, S(k), and the viscous term, k2E(k), fall off more rapidly than does the spectrum function, E(k), as k 0.
However, they would be too large to dissipate energy directly by viscous forces. Thus, these eddies receive energy from the larger ones and then transmit this energy to the small dissipative eddies. Batcheior has shown that the required Reynolds number for the inertial subrange is about twice that required for the equilibrium range to exist. However, if such a range could be realized, then Ψ$η) must be of such a form as to make Eq. (57) or Eq. (58) independent of the kinematic viscosity. The form would be (£77)"^, and Eq.
2. Diffusion in a Packed Bed As mentioned above, mixing can be pictured as a composite of several superimposed diffusional operations. In packed bed systems, the radial and axial bulk diffusion will dictate, to a large extent, the spread of a contaminant. In such a system, one pictures the diffusion as being caused by the rather large, low frequency fluctuations of fluid motion around the particles in the bed, rather than the higher frequency fluctuations of normal pipe turbulence. The spread radially is believed to be due to random displacement of fluid particles as they encounter solid particles in the bed.