Criteria analysis of diffusion processes in channels of ventilation systems
DOI:
https://doi.org/10.33216/1998-7927-2022-272-2-62-66Keywords:
ventilation systems, turbulent flow, Diffusion process, Reynolds number, diffusion Peclet number, Schmidt numberAbstract
The process of turbulent diffusionof gas impurities in the channels of the industrial ventilation systems is considered. The stationary diffusion is described by the equation for turbulent diffusion of impurity in homogeneous incompressible medium. It is believed that the actual concentration at each point of the space occupied by the turbulent flow, undergoes random changes in time (pulsating, fluctuating). When solving practical problems about the motion of impurity particles from the actual characteristic, the transition to the average concentration value is applied. In the case of established turbulent motion and stationary external conditions, the time averaging introduced by Reynolds is used.According to the Fick-Boussinesq hypothesis, the averaged values of the multiplications of pulsating velocity components and concentration are accepted proportional to the averaged concentration gradient. The assumption is substantiated that for the operating modes of the industrial ventilation systems, the molecular diffusion coefficient is much lower than the turbulent diffusion coefficient. For the turbulent diffusion coefficient, the well-known empirical dependence for round pipes is used. The hydraulic resistance coefficient to friction under turbulent flow conditions is determined by the universal Altshul formula. To study diffusion processes in the gas flows of the ventilation systems, the equation of turbulent diffusion is reduced to dimensionless form. The dimensionless criteria are introduced into consideration: the Reynolds number, the Schmidt number (or the diffusion Prandtl number), and the diffusion Peclet number. The analysis of the criterion relations for diffusion processes in the cylindrical channels of the ventilation systems is carried out. The dependence of the diffusion Peclet number from the Reynolds number showed that for big values of relative roughness, the Peclet diffusion number does not depend from the Reynolds number. The presence of the self-similar zone in diffusion processes is shown, when the path length for equalizing the impurity concentration will not depend from the gas flow parameters.
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