By Gregorio Millán Barbany
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Extra resources for Aerothermochemistry
11] above and associated discussion), with v substituted for D. In fact this is exactly what's going on: the Reynolds number is a Peclet number for the diffusion of momentum, and measures the square of the ratio between the size of a system and the momentum diffusion length. When Re is large, momentum diffuses ineffectively, and velocities may vary wildly from one part of the system to another (re-circulating and turbulent flows). When Re is small, momentum diffuses rapidly across the chamber or other region of interest, and velocity varies in a simple fashion from one location to another (creeping and laminar flows).
If the residence time is very long compared to the diffusion time, then everything in the chamber reaches a sort of steady state during the time gases are present: concentrations are likely to be some sort of linear function of position determined mostly by boundary conditions and not gas flows. 3 39 Lengths, Times, and Dimensionless Numbers The diffusion length is our first introduction into a characteristic scale for a problem. Chemical engineers like to divide a characteristic length (like the reactor size, for example) by such a characteristic scale for a physical process, to obtain a dimensionless number.
A) Definition of plug flow reactor dimensions (b) Boundary conditions Finally, we use a simple trick: we travel along with the gas. This is easy because the velocity is constant everywhere. The concentration as a function of x and y in the moving gas is exactly the same as the concentration encountered in a stationary slice of gas as a function of position y and time t, if we let t be the "streamtime" tst = x/U (figure 3-14). Solving the (x, y) problem is thus the same as the problem we've already examined: the concentration in a one-dimensional slice of gas as a function of time, with transport due to diffusion within the gas, where diffusion is taken to occur in the y direction.
Aerothermochemistry by Gregorio Millán Barbany