Theoretical study of partially return air flows in vertical mine shafts

Abstract This paper is concerned with a theoretical study of the conditions for occurrence of partially return air flows in vertical mine shafts. Such problem arises when the temperature of the air rising in the vertical mine shaft is much higher than the temperature of the shaft walls. This situation can occur during the construction of mine shafts using artificial freezing of surrounding rocks. The uncontrolled return air flows in the shaft under construction may cause an accumulation of harmful impurities released during drilling and blasting operations and a deterioration of microclimate parameters in the atmosphere of mine shafts. We investigate here a two-dimensional, fully turbulent, unsteady air flow in a vertical domain. In accordance with the Boussinesq approximation, the air density is specified as a function of temperature. The results of simulations show that a significant change in the transverse air velocity profile and the occurrence of return air flows are observed at Rayleigh numbers (dimensionless temperature difference) of order of 109. We propose two criteria for quantitative analysis of the flow structure: the critical Rayleigh number which denotes the occurrence of return flows in the cross section of the shaft and the transforming Rayleigh number which serves as indicator of significant changes in the velocity profile. Numerical dependences of the critical and transforming Rayleigh numbers on the Reynolds number of the airflow in the shaft are determined.