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The problem of axial mixing in straight pipes is analyzed by a modification of G. I. Taylor's analysis. The treatment presented here includes the effect of both Schmidt and Reynolds numbers throughout the turbulent-flow range. All applicable data on flow of gases and liquids are found to conlirm the validity of the method.The analysis indicates that axial mixing increases rapidly as the flow approaches the laminar region, especially for liquids, and that pipe roughness causes a relatively small increase in axial mixing. Turbulent eddy diffusion in the axial direction has a negligible effect.The results of the analysis are applicable to those systems wherein the kinematic viscosity of the flowing mixture does not vary greatly from one region to another and in which the concentration region of interest is spread out along a sufllcient length of pipe. These limitations are broad enough to permit most practical problems to be treated by the method.The passage of fluid through a pipe is accompanied by mixing in the axial direction. This effect, which can be observed, for instance, by noting the dispersion of tracers, results in intermixing of products in pipe lines, in decreasing the driving force in tubular reactors, and in diminishing the sharpness of signals in tracer experiments.In unbroken straight pipes axial mixing is due to diffusion in the axial direction because of molecular or turbulent motions and to the relative axial motion of fluid elements at different radial positions. However, the effects of axial molecular and turbulent diffusion are negligible compared with the interpenetration due to relative motion. The latter depends greatly on the shape of the velocity profile and the rate of radial diffusion. The more nearly the velocity profile approaches that for plug flow, the smaller is the amount. of axial mixing. A high rate of radial diffusion tends to keep the concentration radially uniform; the different radial fluid elements then have more nearly the same composition and in moving with respect to one another, cause less severe mixing. Thus axial mixing is pronounced in the case of laminar flow, where the flow is least pluglike and where radial diffusion is small (molecular instead of turbulent).The first analysis of axial mixing based on radial variation of the velocity was made by G. I. Taylor (17 to 19), who treated first the case of laminar flow in capillary tubes and later the case of turbulent flow in pipes. His treatment of turbulent flow is valid only for high Reynolds numbers because he used a velocity profile valid only when the laminar sublayer and transition layers are negligibly small. Experimental results support this treatment for Reynolds numbers greater than 20,000.In the calculations presented here, Taylor's method is refined and extended to cover the whole range of turbulent flows. The chief differences introduced here are the inclusion of the effect of molecular diffusion and the use of experimental velocity profiles rather than a generalized profile. It was necessary to rearrange ...

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A computer program designed to model the turbulent reacting flow in jet-stirred reactors has been developed. In solving the single-phase flow field, a two-equation turbulence closure was used to predict the turbulent eddy viscosity variation in the reactor. The model was used to predict the performance of a real reactor. The predicted results compared favorably with measurements in the field. It was found that the key to the reactor performance is the strength of the recirculating eddy caused by the jet entrainment.