Numerical modeling of ideal incompressible fluid flow over a step

Results of calculations of fluid flow over a step located on a channel bottom are given. Numerical modeling is performed for the model of free-boundary potential flows of an ideal incompressible fluid using a finite-difference method with dynamically adaptive grids. The behavior of the free surface in the neighborhood of the step is studied as a function of the incident-flow velocity. The results are compared with experimental data. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 17–22, November–December, 2006.     

Open-channel waves generated by propagation of a discontinuous wave over a bottom step

This paper presents the results of theoretical and experimental studies of open-channel waves generated by the propagation of a discontinuous dam-break wave over a bottom step. The cases where the initial tailwater level is higher than the step height (the step is under water) and where this value is smaller than the step height (at the initial time, water is absent on the step) are considered. Exact solutions are constructed using modified first-approximation equations of shallow-water theory, which admit the propagation of discontinuous waves in a dry channel. On the stationary hydraulic jump formed above the bottom step, the total free-stream energy is assumed to be conserved. These solutions agree with experimental data on various parameters (types of waves, wave propagation velocity, asymptotic depths behind the wave fronts). __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 31–44, January–February, 2008.     

Subcritical flows from beneath a shield

The problem of a two-dimensional stationary flow of an ideal incompressible heavy vortex-free liquid that flows from beneath a shield is studied. The bottom is considered smooth and horizontal, and the flow is assumed to be subcritical. The existence of a solution that is different from a uniform flow is proved in an exact formulation. It is shown that the solution behaves like a Nekrasov wave at infinity. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 54–60, January–February, 1998.     

Two-dimensional sediment transport models for sand-bed rivers

The problem of determining the specific mass flow of sediment entrained by a liquid flow passing above the sand bottom is studied. The boundary-value problem for a two-phase mixture of the liquid and solid particles in the active bottom layer is solved, and a general formula for determining the specific mass flow of sediment is derived. Constraints imposed on the rheological model of a moving mixture, which allow the phenomenological parameter (concentration of particles in the active layer of the mixture) to be eliminated from the model, are found. Within the framework of the proposed rheological model, the equation of riverbed deformations in the case of a sand bottom is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 131–139, May–June, 2009.     

Influence of injection on stabilization of flow over an axisymmetric body with a recess facing into a supersonic oncoming stream

Numerical modeling of supersonic flow over a body with an annular step formed by two coaxial cylinders is performed by the Godunov method within the framework of the model of an ideal gas. Regimes of nonsteady streamline flow and peculiarities of the flow associated with the presence of a cylindrical recess in the nose part of the body are analyzed. The influence of the intensity of injection of an annular wall jet from the bottom of the recess on flow stabilization and the body drag is investigated. The domain of the existence of steady streamline flow is established. Khar'kov Aviation Institute, Khar'kov 310070. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 4, pp. 84–90, July–August, 1998.     

On the existence of three solutions for a supercritical steady flow of a heavy fluid over obstructions

The paper is devoted to the solution of the steady problem of ideal incompressible fluid flow over a semi-circular cylinder located at the bottom. Calculations showed that the problem has at least three solutions for the Froude number. In the absence of an obstruction at the bottom, the proposed algorithm allows one to construct solitary waves up to limiting waves. The paper reports the most important wave characteristics: circulation, mass, and potential and kinetic energy. Analysis of the calculation results leads to the conclusion that all maximum values of the solitary-wave characteristics are attained before the maximum amplitude and the maximum of the mass does not coincide with the maxima of the total energy and the Froude number. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 27–35, January–February, 1999.     

Dam-Break Flows Over a Bottom Step

A single-layer shallow-water model is used to study the solvability of the problem of flows generated by dam break over a bed level discontinuity in the form of a step onto which water flows. Solutions in which the total flow energy is conserved on the step and solutions in which the energy is lost on the step are considered.     

Dispersion and blockage effects in the flow over a sill

The problem of a homogeneous heavy liquid flow over a local obstacle is considered in the long-wave approximation. The steady and unsteady waves in the vicinity of the obstacle are described by second-order models of the shallow-water theory and their hyperbolic approximations. The flow in the vicinity of the leading and trailing edges of bluff bodies (sills and steps) is studied. The solution of the problem of the blocked zone upstream of the step is constructed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 45–58, January–February, 2008.     

Steady temperature field associated with the flow of gassy oil in a porous medium

The steady thermal field associated with the flow of gassy oil through a porous medium is investigated with allowance for the Joule-Thomson and degassing effects. A formula is obtained for estimating the temperature anomalies at the well bottom on oil inflow intervals which correspond to a bottom pressure lower than the saturation pressure. Ufa. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 113–116, January–February, 1994.     

Two-dimensional problem of a uniform flow of a two-layer fluid of finite depth past a circular cylinder

The linear steady problem of an irrotational uniform flow past a horizontal circular cylinder located in the upper or in the lower layer of a two-layer fluid is solved by the multipole-expansion method. The flow is perpendicular to the axis of the cylinder. The fluid is assumed to be inviscid and incompressible, and the flow in each layer is assumed to be potential. The upper layer can be bounded by a free surface or a solid lid, and the lower layer by a rigid horizontal bottom. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 91–101, November–December, 1998.     

Sediment-discharge vector in a turbulent flow above an eroded bottom

The problem of determination of sediment discharge by a turbulent flow of a fluid above an eroded surface of an arbitrary relief with a finite slope of the bottom is considered. The surface of the bottom separates a stationary granular medium (sand) from a moving two-phase mixture of a fluid and solid particles. The medium is set into motion under the action of shear stress of the fluid. The medium obeys Coulomb's friction law for a granular medium and Prandtl's law of turbulent friction of the fluid. As a result of solving the boundary-value problem for the motion of a two-phase mixture of a fluid and solid particles, a generic formula for sediment discharges is derived. The sediment-discharge vector is expressed through the vector of shear stress on the bottom, the vector of the slope of the bottom, and the distribution function of the solid particles in the bottom layer for an arbitrary relief of the bottom with a finite slope. It is shown that the sediment discharge depends weakly on the detailed distribution of particles in the bottom layer. Conditions of failure of the bottom surface are obtained. The sediment-discharge formula allows one to derive a closed system of equations that determines the process of bottom erosion in the river or channel bed. Institute Problems of Mechanics, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 102–112, March–April, 2000.     

Oil low to a lateral well in the presence of bottom water

Exact solutions are obtained for a number of two-dimensional problems of steady-state fluid flow to a lateral hole in a reservoir with a quiescent bottom fluid of higher density or with a fluid of lower density at the reservoir top __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 114–126, September–October, 2008.     

Gas-condensate flow in the vicinity of a hydraulic fracture

The problem of gas-condensate flow in the vicinity of a production well with a hydraulic fracture is considered. In the matrix, the flow is assumed to be three-dimensional, and at the fracture, it is assumed to be two-dimensional. It is shown that, for steady-state flow, the problem is split into a physicochemical problem (of phase transitions) and a filtration problem (of determining the pressure field). Numerical solutions are constructed for a rectangular fracture with finite and infinite conductivities. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 128–136, May–June, 2008.     

Circulation flow around airfoils by a steady plane-parallel flow of a heavy liquid of finite depth with a free surface

Steady problems of a circulation flow around bodies by a flow of a heavy liquid bounded by a free surface and a straight bottom are solved. The method of complex boundary elements is used, which is based on the integral Cauchy formula written for a complex-conjugate velocity. Results of numerical calculations of the flow around a circular contour and the Joukowski airfoil are presented. Shapes of the free surface and the most important hydrodynamic characteristics of the process (velocity circulation over the airfoil and the lifting force and its moment relative to the sharp edge of the airfoil) are given. Kemerovo State University, Kemerovo 650043. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 101–110, May–June, 2000.     

Kinematically Excited Stokes Flow in a Right-Angle Wedge (Plane Problem)

An exact solution is obtained for a Stokes flow in a right-angle wedge. The flow is kinematically excited at the bottom edge and discontinues at the corner point __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 60–69, September 2005.     

Buckling analysis of an elastic bar using the Bubnov-Galerkin method

The factors responsible for the errors often encountered in the stability analysis of elastic systems are found by testing the Bubnov-Galerkin method for the buckling problem of a single-layer flexible elastic bar. Refined formulas are obtained for the maximum deflection of a longitudinally compressed hinged three-layer bar. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 148–156, January–February, 2008.     

Gravity-induced spreading of a drop of a viscous fluid over a surface

The unsteady-state nonlinear problem of spreading of a drop of a viscous fluid on the horizontal surface of a solid under the action of gravity and capillary forces is considered for small Reynolds numbers. The method of asymptotic matching is applied to solve the axisymmetrical problem of spreading when the gravity exerts a significant effect on the dynamics of the drop. The flow structure in the drop is determined at large times in the neighborhood of a self-similar solution. The ranges of applicability of the quasiequilibrium model of drop spreading with a dynamic edge angle and a self-similar solution are found. It is shown that the transition from one flow model to another occurs at very large Bond numbers. Institute of Mechanics of Multiphase Systems, Siberian Division, Russian Academy of Sciences, Tyumen’ 625000. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 59–67, May–June, 1999.     

Friction and Heat Transfer in a Laminar Separated Flow behind a Rectangular Step with Porous Injection or Suction

Results of a numerical study of a laminar separated flow behind a rectangular step on a porous surface with uniform injection or suction are described. Two cases are considered: an unconfined flow past a step and flow evolution in a confined channel (duct). It is shown that mass transfer on the surface causes strong changes in the flow structure and substantially affects the position of the reattachment point, as well as friction and heat transfer. More intense injection leads first to an increase in the separation-zone length and then to its rapid vanishing due to boundary-layer displacement. Vice versa, suction at high Reynolds numbers Re _s > 100 reduces the separation-zone length. The duct flow has a complicated distribution of friction and heat-transfer coefficients along the porous surface owing to the coupled effect of the transverse flow of the substance and changes in the main flow velocity due to mass transfer. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 18–28, January–February, 2006.     

Pressure oscillation on a plane upstream of an obstacle in a supersonic flow

The levels and spectra of pressure oscillation on a plane upstream of a vertical cylinder and a step in an M=3 supersonic flow are measured in the presence of a turbulent boundary layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 69–74, January–February, 1998.     

Subcritical and supercritical shear flows above an uneven bottom

The concepts of subcritical and supercritical flows are introduced for the long-wave approximation model describing stationary free-boundary rotational flows of an ideal incompressible fluid. Shear flows of a fluid layer above an uneven bottom are analyzed. Exact solutions describing different flow regimes are constructed, and the flow properties are studied as a function of the flow regime. Flows with backward streamlines are considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 26–38, July–August, 2006. An erratum to this article is available at .