On the influence of the diffusion effect on the accuracy of a fluid flow measurement via the Lagrangian particle tracking method

Abstract

By solving a one-dimensional scalar transport equation with diffusion, it is shown that the diffusion effect can lead to an overestimation of the velocity determined by the Lagrangian particle tracking method, which consists in measuring the time of passage of a flow tracer between two sensors located in the channel. To obtain model signals, the transport equation was solved numerically for different initial scalar distributions, after which the scalar values at two spatial points were recorded. It is shown that in liquid metals characterized by high electrical and thermal conductivity, the effect can be noticeable. The limiting Peclet number, starting from which diffusion effects do not introduce error into measurements, was determined. It is shown that for high-frequency signals the diffusion effect will not manifest itself due to the rapid attenuation of perturbations. The paper provides estimates of Peclet numbers with turbulent transfer coefficients taken into account. It is shown that in developed turbulent flows the diffusion effect can appear due to a significant contribution of small-scale turbulence.