We consider the motion of non-Newtonian behavior in the inter-disk space of the liquid separator. The shared medium is supplied from the periphery of the disks and moves to the center of the machine. Under the influence of centrifugal force the particles of the dispersed phase are precipitated to the bottom surface of the top disk to form a thin layer of precipitate, which moves toward the periphery of the disk. The equations of motion are solved by the equal-discharge-increments method. In this case, the flow field is introduced surfaces of equal costs for the continuous phase, which are determined by the conditions of constant flow velocity of the medium between them. To determine the locations of input surfaces, the recurrent type differential equations are recorded. The equations of motion, recorded on the flow lines, are simplified and take the form of ordinary differential equations in the longitudinal coordinate. The term, takes into account the effect of viscous friction in the equation of motion, contains the partial derivatives of the transverse coordinate. For their computation, a grid solution can be represented as a series expansion in the complete system of basis functions, satisfying the boundary condition. The presence of moving sediment layer and the centrifugal force influence causes the asymmetry of the flow in the dispersion medium in the inter-disk space. In this work the basic functions that take into account the asymmetry of the flow were constructed. In order to determine the type of basis functions, the Poiseuille flow in a conical slit with a moving wall was considered. An algebraic equation for calculating the extremum point of the function of speed made up. It is shown, that for the power fluid in the areas of increasing and decreasing functions, there are different solutions. The studies proposed a system of basis functions for the approximation of the grid solutions. It is shown, that the proposed features provide continuity of the viscous stress tensor in the whole flow area.
inter-disk space, non-Newtonian medium, equation of motion, asymmetric flow, approximation of velocity.
При проектировании и эксплуатации жидкостных тарельчатых сепараторов важным является правильный расчет гидродинамики потока в межтарелочном пространстве. Несмотря на большое количество работ, посвященных исследованию гидродинамики жидкостных тарельчатых сепараторов, данная проблема остается актуальной. Недостаточно изученным остаются течение и разделение неньютоновских сред с учетом входного участка и наличия движущегося слоя осадка.
Пусть дисперсная среда подается во вращающуюся щель толщиной hс периферии тарелок и под действием перепада давления движется к центру аппарата [1]. Под действием центробежной силы частицы дисперсной фазы осаждаются к нижней поверхности верхней тарелки и образуют тонкий слой осадка, который движется к периферии тарелки [2, 3]. В качестве реологической модели дисперсной среды выберем степенной закон Оствальда де Виля. Предположим, что течение среды является ламинарным и установившимся. Тогда уравнения сохранения массы и импульсов многофазной среды запишутся в виде
1. Romankov P.G., Plyushkin S.A. Zhidkostnye separatory. [Liquid separators]. - L.: Mashinostroenie, 1976. - P. 256.
2. Akhmadiev F.G., Ibyatov R.I. Description of two-phase media flows in the centrifugal separators considering the rheological state of sludge. [Opisanie techeniya dvukhfaznykh sred v tsentrobeznykh separatorakh s uchetom reologicheskogo sostoyaniya osadka] // Inzhenerno-phizicheskiy zhurnal. - Engineering Physics Journal. - 1984. - Volume 47, № 5. - P. 857-858. Full text is deposited in All-Russian Institute of Scientific and Technological Information on 06.06.84 № 3725-84.
3. Kogan V.M., Zhukov V.N., Plyushkin S.A. Dynamics of sediment movement along the disk of liquid separator. [Dinamika dvizheniya osadka po tarelke zhidkostnogo separatora] // Teoreticheskie osnovy khimicheskoy tekhnologii. - Theoretical Foundations of Chemical Engineering. - 1976. - Volume 10, №5. - P. 740-745.
4. Kholpanov L.P., Shkadov V.Ya. Gidrodinamika i teploobmen s poverkhnostyu razdela. [Hydrodynamics and heat exchange with the interface]. - Moscow: Nauka, 1990. - P. 271.
5. Ibyatov R.I. Mathematical modeling of multiphase heterogeneous medium velocity on permeable tube. [Matematicheskoe modelirovanie techeniya mnogofaznoy geterogennoy sredy po pronitsemoy trube] / R.I. Ibyatov, L.P. Kholpanov, F.G. Akhmadiev, I.G. Bekbulatov // Teoreticheskie osnovy khimicheskoy tekhnologii. - Theoretical Foundations of Chemical Engineering. - 2005. - Volume 39, №5. - P. 538-541.
6. Ibyatov R.I., Kholpanov L.P., Akhmadiev F.G., Bekbulatov I.G. Mathematical modeling of multiphase heterogeneous medium velocity on permeable channel. [Matematicheskoe modelirovanie techeniya mnogofaznoy geterogennoy sredy po pronitsemomu kanalu] // Teoreticheskie osnovy khimicheskoy tekhnologii. - Theoretical Foundations of Chemical Engineering. - 2007. - Volume 41, №5. - P. 514-523.
7. Akhmadiev F.G, Bekbulatov I.G., Ibjatov R.I. Filtering Two-Phase Medium in Pipes and Channels on the Entrance Part of Flow // Journal of Chemistry and Chemical Engineering. - 2011. - Vol. 5, Num. 6. - P. 544-548.
8. Ibyatov R.I., Kholpanov L.P., Akhmadiev F.G., Fazylzyanov R.R. Mathematical modeling of multiphase medium bundle process. [Matematicheskoe modelirovanie protsessa rassloeniya mnogofaznoy sredy] // Teoreticheskie osnovy khimicheskoy tekhnologii. - Theoretical Foundations of Chemical Engineering. - 2006. - Volume 40, № 4. - P. 366-375.
9. Ibyatov R.I., Kholpanov L.P., Akhmadiev F.G. Multiphase medium flow along permeable surface to form a precipitate. [Techenie mnogofaznoy sredy po pronitsaemoy poverhnosti s obrazovaniem osadka] // Inzhenerno-phizicheskiy zhurnal. - Engineering Physics Journal. - 2005. - Volume 78, № 2. - P. 65-72.
