The Dispersion of Matter in Turbulent Pipe Flows

The dispersion of matter in fully developed turbulent pipe flow is described by the transient diffusion equation with an eddy diffusivity approximation. G. I. Taylor’s [16] analysis for asymptotically long dispersion times started a revival of publications on this problem. The moment method of Aris [2], which is well suited to computer methods, is used to solve the mass conservation equation for dispersion near the injection source. The governing equations are converted to a tractable system of equations which is solved mainly by numerical methods with the aid of a digital computer, for the zeroth, first, second, third, and fourth moment of the longitudinal concentration distribution. The utility of the moment method is enhanced by use of Hermite polynomials to express the longitudinal concentration distributions. The present results agree with the asymptotic predictions of Taylor for long dispersion times. The computational convenience of the suggested solution is demonstrated for specific examples where experimental data are available.