MATHEMATICAL MODEL OF A CIRCULAR LATTICE OF PROFILES WITH A VORTEX SOURCE High potential is shown of the proposed energy flow control method in the inter-blade channels of impeller to increase the operational efficiency, aerodynamic loading and adaptability of mine radial fans An original patented technical solution for construction of impeller blades of shaft radial fan is suggested with realization in it of energy flow control method which uses a part of the main fan flow as a source-drain. A mathematical model is constructed in the form of a system of equations that establish the dependence of aerodynamic loading of shaft radial fan, angle of outflow from its impeller and position of effective critical point of blade profile on the energy characteristics of the source-drain. On basis of the principle of hydrodynamic analogs, the position of critical points of profiles of circular grating and the angle of flow exit from it is determined. The construction of a mathematical model is based on the principle of hydrodynamic analogy, method of conformal transformations, theory of residues and mathematical theory of singular equations. The aim of the work is to construct a mathematical model of aerodynamics of a circular grid of profiles with drain-sources for a purposeful search for ways of increasing the aerodynamic loading and adaptability of mine radial fans. A way of adaptation of the conformal transformations method is proposed, using the hydrodynamic analogy principle for calculation of mine radial fans aerodynamics, the impeller blades profiles are presented in the form of segments of logarithmic spirals in a circular lattice.
The articles presents results of a profound comprehensive analysis of dynamics of ventilation performance in dead mine workings as well as the urgency of development of fans for local ventilation with the increased aerodynamic loading and adaptability.
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