А.N. Tarasova - Assistant Professor, Department of Engineering Graphics, Moscow Aviation Institute (National Research University). E-mail: msannik@yandex.ru А.S. Kurbatov - Ph.D. (Eng.), Chief Researcher, State Scientific Center «M.V. Keldysh Research Cen-ter». E-mail: .defunt@inbox.ru А.N. Astapov - Ph.D. (Eng.), Associate Professor, Department of Material Sciences, Moscow Aviation Institute (National Research University). E-mail: Lexxa1985@inbox.ru

The main goal of this study is the mathematical modelling of the sorption processes during the experimental simulation of the rege-neration of atmosphere of hermetic closed capsules such as spatial vehicles and stations, submarines etc. The description of the test stand as well as the principles of its operation is presented. A mathematical model of the dynamics of the carbon dioxide-s non-equilibrium isothermal adsorption during the incompressible gas filtration through the axisymmetric adsorbing static bed is constructed. The assumption about the isothermal behavior of the adsorbing bed allows one to find out the influential parameters effect on the mass transfer without coupling with heat effects. It is shown that the obtained system of ordinary differential equations is stiff because of qualitative different speeds of the observing physical processes. A numerical simulation algorithm is developed on the basis of the longitudinal variant of the method of lines used together with the method of solution-s continuation along the best parameter as well as the implicit multi-step backward differentiation formulae with order and step value adaptive control. The main feature of the mentioned algorithm is its use of the analytic λ-transform that refines the spectral properties of the considered equations - system, therefore the problem stiffness can be significantly reduced. The numerical implementation of the proposed algorithm as well as the results - visualization are performed on the basis of the MATLAB software. The algorithm is tested on the system of the model problems allowing the analytical solutions. It is shown that the maximum absolute error have the order of the MATLAB-s system variable AbsTol and does not exceed the value 10-6. A numerical simulation needed to study the dependence of the carbon dioxide-s process on the variation of influential parameters is planned and realized on the groundwork of the expert information and the results of the physical experiments performed using the test stand. The parametric investigation of the carbon dioxide-s sorption by the sorbent on the basis of the ferric hydroxide is carried out varying the input gas concentration, the gas filtration speed, and the kinetic adsorption factor. The analysis of the obtained results has shown that the input concentration rising decreases the time of adsorption saturation of the bed due to the growth of density current of the substance delivered to the sorbent. Therefore the concentration profiles of both free and adsorbed carbon dioxide move steeper and the slopes of output curves rises (the time dependence of CO2 concentration in the exit air stream). The growth of the speed of the incoming flow results the same effects that the growth of the input concentration; this phenomenon can be interpreted by the current density growth, but for this particular case the principal distinction exists. For the fixed bed-s thickness and the certain minimum velocity level the cumulative breakthrough is observing: the substance strikes the unsaturated adsorbing bed and is not adsorbing due to the supercritical velocity; the output curves begin from the finite concentration value. The growth of the kinetic adsorption factor rises the slope of concentration profiles as well as the output curves. For the fixed thickness of the adsorbing bed the small values of the kinetic adsorption factor result the concentration breakthrough similar to the one observed for the high velocities of the flow. The constructed mathematical apparatus and algorithm were verified and validated using the obtained experimental data. It is shown that the numerical simulation allows one the accurate replication of the main specificities of the observed isothermal adsorption process. The maximum relative error does not exceed 12% for all the input parameters - range. The non-isothermal behavior of adsorbing beds will be the main goal of the perspective studies of the sorption process.

 

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