Предложена математическая модель расчета распределения средних по сечению концентраций водорода по высоте конвективной колонки, образующейся над источником его натекания в помещение. Показано, что расход воздуха, вовлекаемого в колонку, определяется с использованием угла полураскрытия колонки. Из анализа результатов сопоставления расчетов по предложенной модели с экспериментальными данными, приведенными в литературных источниках, получена зависимость угла полураскрытия от числа Фруда. Представлены результаты численных экспериментов по определению зависимостей высоты начала и окончания участков колонки от уровня источника натекания водорода, приходящихся на пожаро- и взрывоопасные водородно-воздушные смеси, от числа Рейнольдса на выходе из отверстия, через которое водород поступает в помещение. Показано, что при турбулентном режиме истечения угол полураскрытия колонки и безразмерные длины пожаро- и взрывоопасной зон практически не зависят от числа Рейнольдса.
Introduction. During leakage of hydrogen in the room convection column is formed over the source of leakage under the influence of buoyancy forces and the pressure drop between ones in the vessel with hydrogen and in the room. Ambient air is mixed with hydrogen unevenly along vertical axis of the column. To determine the lengths of the column sections, falling on flammable and explosive dangerous hydrogen-air mixtures, it is necessary to calculate the concentration field. In general, this problem is highly unsteady and three-dimensional and requires a numerical solution of the original system of equations. In this paper, we consider a model task of hydrogen concentration distribution in the area of the convective column formed over the source of leakage. Materials and methods. There are used methods of gas dynamics and heat and mass transfer for calculating the parameters of the gas mixture during free convection. Theory and calculation. A physics and mathematical model for calculating the distribution of average concentrations of hydrogen in the cross section along the height of the convective column during free convection is proposed. The flow of the hydrogen-air mixture inside the convection column is considered as a steady, one-dimensional and isothermal one. Air flow involving in the column is determined by using the half-angle of column expansion. In similar articles air flow is calculated using the empirical coefficient of flows mixing. Results. The dependence between the half-angle of convective column and the Froude number is obtained from comparison the results received by using the proposed model with the experimental data presented in the literature. There are presented the results of numerical experiments to determine the dependence between the heights of start and end points of the column falling on flammable and explosive hydrogen-air mixtures, and Reynolds number. The turbulent and laminar flow regimes at the exit of the hole through which hydrogen is supplied to the room are considered. Discussion. In laminar and transitional flow conditions at the exit of the hole through which hydrogen is supplied to the room, the half-angle of the column and the dimensionless length of fire and explosive dangerous zones of the column substantially dependent on hydrogen flow rate and the equivalent diameter of the above mentioned hole. In the case of turbulent regime above mentioned parameters practically does not depend on the Reynolds number. Conclusions. In turbulent conditions the dimensionless sizes of fire and explosive dangerous zones and the half-angle of the convection column expansion are practically constant. For a more accurate assessment of the spread of hydrogen in the convection column it must take into account the three-dimensional non-stationary convection that occurs when leakage of hydrogen in the room takes place.
The authors declare that there are no conflicts of interest present.