Acoustic oscillations of a gas near nested thin-walled cylindrical obstacles in a channel

The frequencies of eigenoscillations of obstacles axisymmetrically arranged in a channel are found as functions of the obstacle lengths and locations with the use of a mathematical model that describes eigenoscillations of a gas near several thin-walled cylindrical obstacles in a channel. The velocity field and gas density distribution in the channel are found for the first mode of eigenoscillations.     

Eigenoscillations near a plate in a channel

Acoustic eigenoscillations of a gas near a plate in a rectangular channel, i.e., the eigenfrequency of oscillations as a function of the chord length and the position of the plate in the channel, and the form of the eigenfunctions are studied in a two-dimensional formulation. A mathematical model of eigenoscillations near a plate in a channel has been proposed and substantiated, and the dependence of the eigenfrequency of oscillations on the geometric parameters is studied numerically with the use of this model. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 2, pp. 78–90, March–April, 1998.     

On Compactness, Domain Dependence and Existence of Steady State Solutions to Compressible Isothermal Navier–Stokes Equations

The steady state system of isothermal Navier–Stokes equations is considered in two dimensional domain including an obstacle. The shape optimisation problem of minimisation of the drag with respect to the admissible shape of the obstacle is defined. The generalized solutions for the Navier–Stokes equations are introduced. The existence of an optimal shape is proved in the class of admissible domains. In general the solutions are not unique for the problem under considerations.     

Experimental study of the reverse flow in the forward separation region in a pulsating flow around a spiked body

The flow with a free-stream Mach number M _∞ = 6 around a cylindrical body with a sharp spike is studied. The existence of a supersonic reverse flow for one of the phases of the pulsating flow regime is experimentally validated. A range of spike lengths is determined, which ensures a region of a supersonic reverse flow near the side surface of the spike. The time of existence of the supersonic reverse flow region is shown to be 0.15 of the period of pulsations if the spike length equals the model diameter. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 30–39, July–August, 2007.     

Flow regimes of a high-viscosity polymer mass bounded by the free surface in the region of drastic expansion of a channel

Flow regimes of the polymer mass filling cylindrical variable-section molds are studied by means of the numerical solution of the problem of a nonlinear viscoplastic fluid flow with a free surface in cylindrical channels of geometrically complicated shapes. A mathematical formulation of the problem is given, and factors affecting the molding process are analyzed. Numerical experiments performed in a wide range of problem parameters make it possible not only to elucidate the specific features of the hydrodynamic behavior of the free surface of the moving polymer mass, but also to establish the existence of two flow regimes depending on the ratio of the generalized Reynolds number to the Froude number. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 81–88, January–February, 2008.     

Supersonic flow past a cylindrical body with transverse jets at large angles of attack

Supersonic flow past a cylindrical body with a system of transverse jets ejected from its surface at angles of attack α=60–120^o is characterized by a complicated gasdynamic flow pattern [1]. The body surface is affected by both the oncoming flow and the ejected jets which shield a portion of the surface from the external flow. This results in considerable transverse and longitudinal pressure gradients appearing on the body surface. The experimental pressure distributions over a cylindrical model with four transverse jets at a Mach number M=4 and α=60°, 90°, and 120° make it possible to study the specific features of the flowfield and derive correlations for the "jet obstacle" dimensions. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 179–183, January–February, 1998.     

Cylindrical shock waves generated by a spark discharge and their interaction with the shock waves from a pulsed induction discharge

An experimental investigation of a spark discharge in argon is described. The existence of a shock wave and a following thermal wave is demonstrated. The experimental law of propagation of the thermal wave front is obtained. The effect of the discharge parameters on the dynamics of both waves is studied. The interaction between the cylindrical shock waves generated by a pulsed induction discharge and the shock waves formed in a spark discharge is considered. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 166–170, January–February, 1994.     

Special features of self-sustained oscillations in a supersonic underexpanded jet impinging on an obstacle with a restricted cross-section

Effect of the obstacle size on the flow structure and the transient conditions arising in a supersonic underexpanded jet normally impinging on a flat restricted obstacle is studied. Baltic State Technical University, St. Petersburg 198005. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 4, pp. 143–149, July–August, 1999.     

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.     

Calculation of spatial flow past an inclined flat plate with a detached shock wave

The results of a numerical analysis of a supersonic underexpanded jet impinging on an inclined flat plate are presented. The effects of the angle between the plate and the jet symmetry axis, the distance from the nozzle exit section, the exit Mach number, and the off-design conditions on the distribution of the gasdynamic parameters in the jet flowfield and on the plate surface are demonstrated. Specific features of the compressed layer and obstacle surface flows are revealed. The three-dimensional flow is simulated using the large particle method on the basis of the nonstationary Euler equations written in the cylindrical coordinate system. The calculated results are compared with experimental data. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 31–35, January–February, 1997.     

Experimental and numerical analysis of the jet dispersion from a bent chimney around an obstacle

An experimental study and a numerical modelling analysis were carried out simultaneously to study the flow field structure issuing from a chimney around an obstacle. The main purpose of this study is to evaluate the impact of the jet emitted from a chimney (bent or straight) on the dynamics and the turbulent features of the surrounding flow. The consideration of these features is particularly pertinent to the understanding of mixing between the interacting flows which may be very important in controlling pollutant dispersion in the atmosphere. The experimental data are depicted by means of a PIV technique; whereas the numerical three-dimensional model is simulated through the resolution of the different governing Navier–Stokes equations. The volume finite method, together with the second order turbulent closure model (RSM), was adopted. Variations in obstacle form (cylindrical or parallelepiped) and chimney configuration (bent or straight) were tested and features studied were: the global jet plume, the windward and leeward jet spread; the size, location and magnitude of the reverse flow region; the penetration and the deflection of the jet trajectory around the obstacle. All these considerations allowed us to characterize well the impact of the injection of the jet emitted from the chimney within the crossflow, and its spreading around the obstacle and within the whole domain. Such characterization is very important with regard to pollutant dispersion and consequently to the environmental impact. Indeed, the different species contained within the emitted fumes are mainly directed by the velocity components and their mixing and progression within the domain and around the obstacle are closely related.     

The propagation mechanism of high speed turbulent deflagrations

The propagation regimes of combustion waves in a 30 cm by 30 cm square cross–sectioned tube with an obstacle array of staggered vertical cylindrical rods (with BR=0.41 and BR=0.19) are investigated. Mixtures of hydrogen, ethylene, propane, and methane with air at ambient conditions over a range of equivalence ratios are used. In contrast to the previous results obtained in circular cross–sectioned tubes, it is found that only the quasi–detonation regime and the slow turbulent deflagration regimes are observed for ethylene–air and for propane–air. The transition from the quasi–detonation regime to the slow turbulent deflagration regime occurs at (where D is the tube “diameter” and is the detonation cell size). When , the quasi–detonation velocities that are observed are similar to those in unobstructed smooth tubes. For hydrogen–air mixtures, it is found that there is a gradual transition from the quasi–detonation regime to the high speed turbulent deflagration regime. The high speed turbulent deflagration regime is also observed for methane–air mixtures near stoichiometric composition. This regime was previously interpreted as the “choking” regime in circular tubes with orifice plate obstacles. Presently, it is proposed that the propagation mechanism of these high speed turbulent deflagrations is similar to that of Chapman–Jouguet detonations and quasi-detonations. As well, it is observed that there exists unstable flame propagation at the lean limit where . The local velocity fluctuates significantly about an averaged velocity for hydrogen–air, ethylene–air, and propane–air mixtures. Unstable flame propagation is also observed for the entire range of high speed turbulent deflagrations in methane–air mixtures. It is proposed that these fluctuations are due to quenching of the combustion front due to turbulent mixing. Quenched pockets of unburned reactants are swept downstream, and the subsequent explosion serves to overdrive the combustion front. The present study indicates that the dependence on the propagation mechanisms on obstacle geometry can be exploited to elucidate the different complex mechanisms of supersonic combustion waves. Received 5 November 2001 / Accepted 12 June 2002 / Published online 4 November 2002 Correspondence to: J. Chao (e-mail: jenny.chao@mail.mcgill.ca) An abridged version of this paper was presented at the 18th Int. Colloquium on the Dynamics of Explosions and Reactive Systems at Seattle, USA, from July 29 to August 3, 2001.     

Flows Resulting from the Incidence of a Discontinuous Wave on a Bottom Step

The solvability of the problem of the flows resulting from the incidence of a discontinuous wave on a bottom step is studied using a single-layer shallow water model. Solutions in which the total energy of the flow is conserved at the step and those in which it is lost at the step are considered. Regions of double and triple hystereses in the obtained self-similar solutions are found. An analogy is drawn with the problem of single-layer flow over a bottom obstacle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 8–22, March–April, 2006.     

Nonlinear vibrations of viscoelastic cylindrical shells taking into account shear deformation and rotatory inertia

The vibration problem of a viscoelastic cylindrical shell is studied in a geometrically nonlinear formulation using the refined Timoshenko theory. The problem is solved by the Bubnov–Galerkin procedure combined with a numerical method based on quadrature formulas. The choice of relaxation kernels is substantiated for solving dynamic problems of viscoelastic systems. The numerical convergence of the Bubnov–Galerkin procedure is examined. The effect of viscoelastic properties of the material on the response of the cylindrical shell is discussed. The results obtained by various theories are compared.     

Explosive projection of liquid from a thick-walled cylindrical container

The process of projection of a layer of an ideal liquid enclosed into a cylindrical elastoplastic shell by products of instantaneous detonation of a high explosive charge is studied numerically in a two-dimensional plane formulation. The processes of shell fracture and liquid exhaustion through the resultant slots are considered. Numerical results are analyzed, and analytical relations for angular distributions of radial velocity and mass of the liquid escaping through the slots are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 56–63, 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.     

Existence of solutions of Kraiko's problem

Three initial-boundary-value problems for the equations of gas dynamics are formulated. Successive solution of these problems yields a solution of Kraiko's problem of the isentropic transition of an ideal gas from a homogeneous state of rest to another state of rest with higher or lower density. Solutions are constructed for plane, cylindrical, and spherical layers of an ideal gas. The existence of locally analytic solutions is proved. Ural State Academy of Service, Ekaterinburg 620034. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 48–55, May–June, 2000.     

Existence of a new type of irregular shock-wave interaction

Several types of plane shock-wave interactions [1–5], realized in various cases of practical importance, are now known. In [7] the possibility of the existence of a new type of shock-wave interaction was demonstrated by numerically solving the axisymmetric boundary-value problem. Here, the corresponding two-dimensional boundary-value problem of the interaction between a shock wave and a plane shock is numerically studied, a theoretical basis is obtained for the region of existence of the shock-wave interaction detected, and its principal properties are investigated. Moscow, Dnepropetovsk. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 181–183, September–October, 1988.     

Antiplane strain of a body undergoing large-rotations

Antiplane strain of a cylindrical elastic body undergoing large rotations under surface load in the absence of body loads is studied. The form of the elastic potential corresponding to this strain is found. The stresses, the strains, and the displacement are expressed in terms of pressure and two independent strains and the pressure is expressed in terms of the linear strain invariant. For the strains and displacement, nonlinear boundary-value problems are formulated and their ellipticity conditions are given. The linear problem for the displacement is obtained by transformation of variables. An example of determining the displacement is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 191–198, May–June, 2007.     

Breaking of waves of limiting amplitude over an obstacle

Homogeneous heavy fluid flows over an uneven bottom are studied in a long-wave approximation. A mathematical model is proposed that takes into account both the dispersion effects and the formation of a turbulent upper layer due to the breaking of surface gravity waves. The asymptotic behavior of nonlinear perturbations at the wave front is studied, and the conditions of transition from smooth flows to breaking waves are obtained for steady-state supercritical flow over a local obstacle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 3–11, May–June, 2006.