Features of solving the problem of condensation of vapor containing solid particles on the edge

Abstract

THE PURPOSE. To evaluate the effect on the condensation process of contaminants contained in the steam and deposited on the surface of the cooled fins, for which to formulate a mathematical model of the process, to investigate its properties and to obtain quantitative estimates of the characteristics.METHODS. The equations of the mathematical model are based on the laws of conservation of energy and mass, their study and evaluation are carried out using analytical methods of the theory of differential equations, methods of similarity theory and dimensions, as well as numerical methods for solving boundary value problems.RESULTS. The formulation of the problem of condensation of vapor containing solid particles on the edge is formulated. The presence of a self-similar solution is revealed, which is represented as a dimensionless function of one variable, uniform for all sets of initial parameters. The relations describing the distributions of the thickness δ(x, τ) of the sediment and the temperature ϑ(x, τ) on a straight edge of unlimited height (l = ∞) with an initially clean surface (h0 = 0) are obtained. These relations also almost accurately describe the initial stage of such a process on a straight edge of a finite height l, until a sediment of noticeable thickness covers the entire surface of the rib, as well as the initial moments in the case of an edge on a round pipe, until the width of the sediment zone with a noticeable thickness is significantly less than the radius of the pipe.CONCLUSION. Using these distributions as the initial ones for edges of limited height instead of, for example, introducing a uniform initial layer h0, will allow achieving high accuracy of numerical calculations without excessive thickening of the grid in coordinate and time.