Mathematical modeling of balloon systems for storage and rate control of gas
DOI:
https://doi.org/10.34185/1562-9945-3-128-2020-08Keywords:
сжатый газ, инертный газ, баллон высокого давления, температура газа, изотермическая фильтрация газа, асимптотический метод, аналитическое решение, космический летательный аппарат, длительный полетAbstract
Modern techniques and technologies often require constant or controlled gas supply for their functionality. Especially difficult this problem appears in transport systems, where a gas source must be transported by the same system, for example, in aviation vehicles and space vehicles. The long-time flight usually takes place in the last case. Processes of gas outflow from high-pressure balloon using for gas-supply of space vehicle in long-time flow are considered in the work. To provide an enough small discharge, a porous insertion is applied as a rate control tool in the balloon. It is necessary to note, that mathematical models of such constructions is not developed yet, nevertheless huge amount of investigations concerning filtration flows. It is assumed that the inertial gases are used, which are enough good satisfied to ideal gas state equation. The well-known mathematical model of isothermal gas filtration is used to describe a filtration process. Taking into account slow outflow, it is managed to apply an asymptotic approach for analysis of the mentioned filtration model. Such trick is completely necessary to overcome difficulties of multiscale problem solution, arising due to smallness of filtration flow rate. As a rule, the obtained asymptotic sequence of problems can be restricted by only zero-th approximation because of the mentioned smallness of filtration flow rate and thus smallness of the constructed small parameter used in asymptotic expansion. As a result, a description of filtration process is reduced to boundary-value problem for second order ordinary differential equation. It is managed to integrate the obtained boundary-value problem in quadrature and to reduce an initial problem to quadratic equation with respect to the pressure in the balloon. It is shown, that the temperature inside the balloon and gas pressure on the porous insertion outlet can be used as control parameters for the process of gas outflow from high-pressure balloon through porous insertion. Thus a new asymptotic approach is developed for specific kind of strongly nonlinear problems. The recommendations concerning heating and cooling of the balloon are formulated. The results of the work can be recommended for using in space-missile technique and other field, connected with pressured gas storage.
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