Thermal stability of a reactive liquid flow

Stability analysis of the solution of the system of differential partial equations describing the thermal state of a reactive liquid flow is based on reducing the infinite-dimensional problem to a finite-dimensional space containing the part of the solution that determines its stability. Within the framework of the projection method, the zero space of the corresponding generating operator is used as the finite-dimensional space. Generally, the zero space of the generating operator of the problem considered consists of its eigenfunctions. Analysis is performed for a combination of liquid-flow parameters such that the generating operator degenerates and to construct its zero space, it is necessary to use vectors generated by the Jordan chain. Calculation results are presented. Technological Institute, Altai State Technical University, Biisk 659305. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 130–137, March–April, 2000.     

Two-dimensional reactive flow dynamics in cellular detonation waves

This investigation deals with the two-dimensional unsteady detonation characterized by the cellular structure resulting from trajectories of triple-shock configurations formed by the transverse waves and the leading shock front. The time-dependent reactive shock problem considered here is governed by a system of nonlinear hyperbolic conservation laws coupled to a polytropic equation of state and a one-step Arrhenius chemical reaction rate with heat release. The numerical solution obtained allowed us to follow the dynamics of the cellular detonation front involving the triple points, transverse waves and unreacted pockets. The calculations show that the weak tracks observed inside the detonation cells around the points of collision of the triple-shock configurations arise from interactions between the transverse shocks and compression waves generated by the collision. The unreacted pockets of gas formed during the collisions of triple points change form when the activation energy increases. For the self-sustained detonation considered here, the unreacted pockets burn inside the region independent of the downstream rarefaction, and thus the energy released supports the detonation propagation. The length of the region independent of the downstream is approximately the size of one or two detonation cell. Received 13 February 1998 / Accepted 13 August 1998     

Two-dimensional flow in porous strata with conductivity varying discontinuously along second-order curves

Solutions of boundary-value problems of two-dimensional flow in a porous medium are obtained on the basis of the theory of axisymmetric generalized analytic functions [1,2] and conversion formulas [3] for a broad class of strata whose conductivity changes abruptly along second-order curves. The singular points of these functions model arbitrary two-dimensional flows. In space the solutions describe the axisymmetric flow in porous media whose homogeneity interfaces are second-order surfaces of revolution. The solutions obtained are applied to new problems associated with environmental protection and the nonpolluting operation of water intakes under complex geological conditions.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 120–128, January–February, 1993.     

Surface instability of an elastic half space with material properties varying with depth

If a body with a stiffer surface layer is loaded in compression, a surface wrinkling instability may be developed. A bifurcation analysis is presented for determining the critical load for the onset of wrinkling and the associated wavelength for materials in which the elastic modulus is an arbitrary function of depth. The analysis leads to an eigenvalue problem involving a pair of linear ordinary differential equations with variable coefficients which are discretized and solved using the finite element method.The method is validated by comparison with classical results for a uniform layer on a dissimilar substrate. Results are then given for materials with exponential and error-function gradation of elastic modulus and for a homogeneous body with thermoelastically induced compressive stresses.     

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.     

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.     

Two-dimensional unsteady flow around a waving plate in wall effects

A new method of nonlinear formulation is presented to analyze the two-dimensional incompressible flow around a flexible plate waving near a rigid wall. A system of differential and integral equations is solved for the velocity field and the wake vortex. A nonlinear unsteady Kutta condition is imposed at the trailing edge in order to treat the case of large amplitude and fast oscillation accurately. The shed vortex sheet is discretized and approximated by a large number of vortex filaments, and their movements are visualized by numerical computation. The lift, thrust, power input and hydrodynamic efficiency are computed for various values of the distance of the waving plate from the wall.     

Blood flow in a muscle capillary cell. Two-dimensional effects

The two-dimensional motion of the blood in a capillary cell is considered, i.e., the calculations take into account not only the main capillaries running along the muscle fibers but also the transverse interconnections [1, 3, 4, 6] for the purpose of estimating their effect on the nonuniformity of the velocity distribution within the cell and on its total hydrodynamic resistance.N. S. Utushkin and V. A. Egorov also participated in this research.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 94–100, September–October, 1989.     

Interactions of a propeller with a stator-induced circumferentially varying flow

The interactions of a circumferentially varying stator cascade and a downstream fixed pitch propeller were investigated experimentally. The global performance of the components and the coupled system were systematically investigated through force and moment measurements on the propulsor model in a water tunnel. In addition, the wake of the cyclic stator cascade with and without the propeller was investigated downstream from a propulsor model using the Stereoscopic PIV technique. A cyclic distribution of the stators’ deflections resulted in non-axisymmetric distributions of the flow field downstream of the stator array. The stator distribution alone produced a significant side force that increased linearly with stator pitch amplitude. When a propeller was incorporated downstream from the cyclic cascade, the side force from the stator cascade was reduced, but a small normal force and pitching moment were created. The generation of these secondary forces and moments can be related to the redistribution of the tangential flow from the cyclic cascade into the axial direction by the retreating and advancing blade states of the fixed pitch propeller.     

Heat transfer by laminar flow of an elastico-viscous liquid in a circular cylinder with linearly varying wall temperature

Summary The heat transfer by laminar flow of elastico-viscous liquids in a circular cylinder with linearly varying wall temperature has been studied by using the constitutive equation of motion for elastico-viscous liquids and energy equation. The flow phenomenon are characterized by two parameters R _c and S. The presence of the elastic elements in the viscous liquid considerably affects the velocity and temperature distributions.     

Two-dimensional flow in a fractured medium

Transport processes within a liquid-filled fractured reservoir can be modelled using a double-diffusive mechanism in fracture and block. Then it is commonly assumed that the flow in the block is purely one-dimensional (e.g. vertical). Lateral flow within the block will, however, become significant at long times. Avdonin has given an analytic solution for the pressure response in an infinite fissure bounded by two homogeneous half-spaces, allowing vertical flow only in the blocks. We extend this solution to include horizontal flow in the blocks. There are significant qualitative differences between the two cases. In particular, we find that if fluid is injected at a constant rate into the fissure and horizontal flow in the blocks is allowed, then the long-time pressure response of the fissure/block assembly has the same character as that due to a line source in a homogeneous anisotropic porous medium.     

Linear stability in the flow of a liquid film concurrent with a gas flow

The two-phase flow of liquid films are often encountered in practice, but the number of theoretical papers devoted to this problem is limited. The problem of the linear stability of a viscous liquid film subjected to a gas flow has been formulated in [1] and, in somewhat different form, in [2]. The linear stability of plane-parallel motion in films has been studied analytically in [1–8] for some limiting cases. The range of validity of the analytic approaches remains an open question. Therefore, an exact numerical analysis of flow stability over a fairly broad range is required. In the present paper a separate solution of the problem for the gas and the liquid is shown to be possible. The Orr-Sommerfeld equation has been integrated numerically, and the results are compared to the results of analytic calculations.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 143–146, January–February, 1976.The author is grateful to É. É. Markovich for directing the work and to V. Ya. Shkadov for his interest in the work and many useful comments.     

Wave flow of a liquid film together with a flow of gas

The wave flow of a thin layer of viscous liquid in conjunction with a flow of gas was considered in a linear formulation earlier [1, 2]. In this paper the problem of the wave flow of a liquid film together with a gas flow is solved in a nonlinear setting. On this basis relationships are derived for calculating the parameters of the film and the hydrodynamic quantities.Ivanovo. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 12–18, January–February, 1972.     

Measurements of a stator-induced circumferentially varying flow

The flow physics associated with the generation of both axisymmetric and non-axisymmetric swirl by various deflection patterns of a stator array was investigated experimentally through surface pressure and Stereoscopic Particle Image Velocimetry measurements. A three-dimensional rendering technique was developed to reconstruct the flow field around the model and in its wake. The three-dimensional fluid volume was reconstructed from multiple two-dimensional measurement planes. A cyclic distribution of the stators’ deflections resulted in non-axisymmetric distributions of the surface pressure and the flow field downstream of the stator array. The addition of a shroud had an amplifying effect: accelerating the flow through the stator array while reducing the non-uniform tangential velocity component generated by the stators. In the model near wake the flow field is associated with secondary flow patterns in the form of coherent streamwise vortical structures that can be described by potential flow mechanisms. The collective pitch distribution of the stators produces a flow field that resembles a potential Rankine vortex, whereas the cyclic pitch distribution generates a flow pattern that can be described by a potential vortex pair in a cross-flow.