Purpose. The scientific paper involves the development of quick computing numerical model for prediction of output parameters of aeration tank. The numerical model may be used in predicting the effectiveness of aeration tank under different regimes of work. Methodology. To simulate the process of biological wastewater treatment in aeration tank numerical models were developed. The flow field in the aeration tank is simulated on the basis of potential flow model. 2-D transport equations are used to simulate substrate and sludge dispersion in the aeration tank. To simulate the process of biological treatment simplified model. For the numerical integration of transport equations implicit difference scheme was used. The difference scheme is built for splitting transport equations. Splitting of transport equation into two equations is carried out at differential level. The first equation of splitting takes into account the sludge or substrate movement along trajectories. The second splitting equation takes into account the diffusive process of substrate or sludge. To solve the splitting equations implicit difference scheme was used. For the numerical integration of potential flow equation the implicit scheme of conditional approximation was used. On the basis of constructed numerical model computer experiment was performed to investigate the process of biological treatment in aeration tank. Findings. Quick computing numerical model to simulate the process of biological treatment in the aeration tank was developed. The model can be used to obtain aeration tank parameters under different regimes of work. The developed model takes into account the geometrical form of the aeration tank. Originality. The numerical model which takes into account the geometrical form of aeration tank and fluid dynamics process was developed; the model takes into account substrate and sludge transport in aeration tank and process of biological treatment. Practical value. Efficient numerical model, so called «diagnostic models» was proposed for quick calculation of biological treatment process in aeration tank.

метою статті є розробка багатофакторних камерних моделей для експрес-оцінки ефективності роботи реакторів біологічного очищення стічних вод. Методика. Для комп'ютерного моделювання процесу біологічного очищення стічних вод розроблено дві чисельні камерні моделі. В основу моделей покладено закон збереження маси для субстрату та активного мулу. Моделі є нуль-вимірними. У першій камерній моделі процес окислення забруднювача розраховують на базі реакції першого порядку. У другій камерній моделі для розрахунку окислення забруднювача використано модель Monod. Для чисельного інтегрування моделювальних рівнянь використано метод Ейлера. Моделі дозволяють під час розрахунку біореактора, враховувати зміну з часом концентрації активного мулу, субстрату, що потрапляють до реактора для біологічного очищення стічних вод. Результати. Здійснено програмну реалізацію розроблених чисельних моделей. Наведено результати комп'ютерних експериментів із дослідження ефективності очищення стічних вод у реакторах біологічного очищення для різних умов експлуатації споруд. Наукова новизна. Розроблено дві комп'ютерні камерні моделі, що дозволяють швидко оцінити ефективність роботи біореактора для очищення стічних вод. Практична значимість. Моделі можуть бути корисні під час проведення розрахунків у випадку проєктування споруд біологічного очищення або під час реконструкції наявних біореакторів для їх перспективної роботи в нових умовах. Ключові слова: очищення води; чисельне моделювання; біореактор; водокористування

Purpose. Efficiency determination of the aeration tank at the stage of design or reconstruction of bioreactors in which biological wastewater treatment is carried out requires the use of special mathematical models and calculation methods. The main purpose of the article is to develop CFD models for evaluating the operation efficiency of aeration tanks. Methodology. A numerical model has been developed for the computer calculation of the biological wastewater treatment process in aerotanks, taking into account hydrodynamics. The model is based on two-level mass conservation equations for the substrate and activated sludge and the velocity potential equation. The process of biological transformation of the substrate is calculated based on the Monod model. For the numerical integration of the mass transfer equations of activated sludge and substrate, the alternating-triangular difference splitting scheme is used. In this case, the basic equations are divided into two equations of a more simplified form. For the numerical integration of the equations for the velocity potential, it is split into two one-dimensional equations. Further, each equation is solved according to explicit scheme. For the numerical integration of equations that describe the process of substrate transformation based on the Monod model, the Euler method is used. Findings. The software implementation of the constructed numerical model has been carried out. The results of a computational experiment on the study of the wastewater treatment process in an aeration tank with plates are presented. This leads to the conclusion that the quality control of wastewater treatment in aeration tanks is possible with the help of plates. Originality. A multivariate CFD model has been developed, which makes it possible to quickly assess the efficiency of the aeration tank. A feature of the model is the ability to evaluate the operation of the aeration tank, taking into account its geometric shape and location of additional plates in the construction. Practical value. The constructed numerical model can be used during calculations in the case of designing aeration tanks, or in determining the efficiency of wastewater treatment under new operating conditions.

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Purpose. The main purpose of the article is to develop a numerical model for the analysis of the process of biological wastewater treatment in a reactor with a mobile biocenosis. Methodology. For mathematical modeling of the process of biological wastewater treatment in a reactor with a moving biocenosis, a hydrodynamic model of a non-viscous vortex-free flow is used. We calculated the boundary conditions for the modeling equation on the surfaces of the bioreactor, solid walls, and the upper surface; at the inlet boundary; at the outlet boundary from the building. To calculate the process of movement of activated sludge and substrate in the bioreactor, a mass transfer model is used, which takes into account the convective-diffusion movement of the substrate and activated sludge. The process of biological water purification in that part of the bioreactor where there are no mobile biocenosis carriers will be calculated based on the Monod model. The process of biological water purification in the part of the bioreactor where there are mobile carriers is calculated on the basis of an empirical model in three stages. The first stage is determined using the Harremoes model. At the second stage, the rate of substrate «consumption» in the biofilm is calculated. At the third stage, the change in the substrate concentration in the zone where the biocenosis carriers are located is determined due to convective movement, substrate diffusion in the flow and its destruction in the biofilm on the carriers. The chaotic motion of biocenosis carriers in the reactor is modeled based on the parabolic diffusion equation. Finite-difference schemes are used for numerical integration of modeling equations. Findings. The software implementation of the constructed numerical model is carried out. A computational experiment to determine the efficiency of biological wastewater treatment in different parts of the bioreactor was conducted. Originality. An effective multifactorial numerical model has been created, which allows quick analysis of the efficiency of biological wastewater treatment in an aeration tank with mobile biocenosis carriers. Practical value. The created two-dimensional numerical model can be used for serial calculations at the stage of designing biological wastewater treatment systems and analysis of the efficiency of bioreactors under different operating conditions.