Non-dispersive path mapping approximation for the analysis of ambient species diffusion in laminar jets

作者：Schmidt Bleker Ansgar^*; Reuter Stephan; Weltmann Klaus Dieter

来源：Physics of Fluids, 2014, 26(8): 083603.

DOI：10.1063/1.4893573

The present work for the first time presents an analytical approximation capable of describing the diffusion of surrounding species into laminar fluid jets in the near-field with a known (but arbitrary) velocity field. The diffusive transport of ambient air into fluid jets is studied analytically and numerically on the basis of a convection-diffusion equation with a predefined velocity field and diffusion coefficient. It is shown that the majority of particles entering a jet flow in an artificial uniform velocity field can only reach the axis in the near-field following narrow straight paths. This is exploited in the here-proposed non-dispersive path mapping approximation, where these paths and the underlying solution for the uniform velocity field are mapped according to the flow field. Dispersion is assumed to be negligible for every single path if the velocity profile does not vary significantly over the width of the path. The resulting formula for the on-axis density can easily be evaluated using a pocket calculator. The analytical model is compared to numerical studies of diffusion in jet flows with different geometries and shows good agreement.

• 出版日期2014-8