Numerical Simulation of Instantaneous Images of the Smoke Released from a Chimney

Abstract

Instantaneous images of the smoke released to the unstable surface boundary layer from a chimney are simulated numerically.The characteristic patterns of instantaneous images are formed by introducing spatial correlation of velocity. Trajectories correlated spatially are obtained by use of random variables correlated spatially in a Markov chain equation. In order to generate the field of random variables correlated spatially, a random number is given for each region divided by a length corresponding to the scale of turbulence.Empirical profiles of the mean and fluctuation of wind velocity are used in the Markov chain. The scale of turbulence is estimated from these profiles. Numerical simulations of the diffusion released from a source of 60 m height were carried out. Under certain atmospheric conditions, some samples of image are formed. The results with irregular patterns seem to be realistic. The spatial correlation of velocity was detected from the results of simulation, which is smaller than that of the given random variable.