Aeolian tones of a plate cascade

A model for the aeroacoustic resonance effects (aeolian tones) excited around a plate cascade in a gas flow is suggested. Methods of calculating the frequencies of natural acoustic oscillations near the cascade are developed. The effect of the cascade geometry and the Mach number of the main flow on the frequencies, abundance, and modes of the natural oscillations is investigated. Anomalous acoustic oscillations near a cyclic plate cascade are shown to exist and are studied. It is shown that there always exist no less than two natural oscillation frequencies in the gas flow near any nontrivial cyclic plate cascade. It has been found that the natural oscillation frequencies can be combined in bundles such that in the case where the number of plates in a period is large the frequencies pertaining to each bundle occupy a certain interval with arbitrary density. The natural oscillations are classified with respect to the form of the eigenfunctions; the classification is based on the theory of representations of groups of locally plane symmetries of the cyclic plate cascade in the solution space. The correctness of the proposed model of the aeroacoustic resonance effects (aeolian tones) excited near a plate cascade in a gas flow is supported by a comparison with the available experimental and theoretical data. On the basis of the investigation performed, some previously unknown physical phenomena are predicted. Thus, the existence of frequency zones or main-flow Mach number ranges on which aeroacoustic resonance phenomena exist near a cyclic cascade with a large number of plates in a period is proved; it is shown that for certain frequencies of the natural oscillations near the cyclic plate cascade the resonance oscillations may be localized in the vicinity of the source; and the existence of narrow-band wave packets slowly propagating along the cascade is demonstrated. Novosibirsk, e-mail: sukhinin@hydro.nsc.ru. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 171–186, March–April, 2000.     

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 Low-Dimensional Modeling of Channel Turbulence

We investigate a sequence of low-dimensional models of turbulent channel flows. These models are based on the extraction of the Karhunen–Loève (KL) eigenfunctions from a large-scale simulation in a wide channel with R _*=180 (based on the friction velocity). KL eigenfunctions provide an optimal coordinate system in which to represent the dynamics of the turbulent flow. The hierarchy of KL modes identifies the most energetic independent phenomena in the system. A series of Galerkin projections is then used to derive a dynamical approximation to flows. In order to capture essential aspects of the flow in a low-dimensional system, a careful selection of modes is carried out. The resulting models satisfy momentum and energy conservation as well as yielding the amount of viscous dissipation found in the exact system. Their dynamics includes modes which characterize the flux, rolls, and propagating waves. Unlike previous treatments the instantaneous streamwise flow is time dependent and represented by KL flux modes. The rolls correspond to the streaks observed in experiments in the viscous sublayer. Propagating waves which first appear in the model flow at low Reynolds number (R _*∼ 60) persist through the chaotic regime that appears as the Reynolds number is increased. Statistical measures of the chaotic flows which have been generated by the models compare favorably with those found in full-scale simulations. Received 13 July 1998 and accepted 8 January 1999     

Excitation of subharmonic oscillations in an axisymmetric flow with coherent structures in the regime of aeroacoustic resonance

Conditions of origination of aeroacoustic resonance phenomena near an axisymmetric body in the form of a thick-walled tube in an air flow in a rectangular channel are studied experimentally. Dependences of the eigenfrequency of acoustic oscillations on the model length are determined. By studying the mechanism of origination of oscillations in the wake flow, it is shown that the process of generation of annular coherent structures in resonant regimes is characterized by evolution of nonlinearities including a subharmonic packet. Possible methods of flow control are discussed. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i, Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 59–68, July–August, 2000.     

Numerical simulation of the flow in a variable-section channel with pulsed-periodic energy supply

Results of numerical simulations of a quasi-one-dimensional unsteady flow in a channel considered as an element of an air-breathing engine are presented. The influence of parameters of energy supplied in the pulsed-periodic mode (power, pulse frequency, and distribution of energy sources along the channel) on the characteristics of the flow with Mach numbers M ₀ = 2.4–4.0 at the channel entrance is determined. A channel configuration that allows the energy supply distribution to be found from the condition of restriction of the maximum value of the gas temperature is proposed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 3–11, January–February, 2009.     

Translational nonequilibrium of a gas flow into vacuum in a constant-section channel

A single-species gas flow into vacuum in a constant-section channel is computed by means of the Direct Simulation Monte Carlo method. It is shown that the longitudinal, transverse, and total kinetic temperatures are significantly different in the head part of the flow, which is a consequence of the arising translational nonequilibrium. The flow is almost self-similar in the entire region of flow expansion (except for distributions of the transverse and total kinetic temperatures in the head part of the gas flow), which allows one to predict flow parameters at times greater than those used in simulations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 4, pp. 54–59, July–August, 2006.     

Approximate analytical calculation of the mach configuration of steady shock waves in a plane constricting channel

An approximate analytical model for calculation of the parameters of a steady gas flow inside a plane constricting channel formed by two symmetrically positioned wedges is suggested. A Mach configuration of shock waves (triple point) is formed in the channel when the wedge angles are larger than some critical value. The flow calculation in a constricting channel reduces to the solution of the iterative problem for a system of nonlinear algebraic equations. The configurations of shock waves, the slipstream, and the sonic line are described by the proposed model of a gas flow. A comparison of the results obtained using this model allows a fairly accurate calculation of the Mach stem and the length of the subsonic-flow region. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 52–58, May–June, 1998.     

Longwave approximation model for gas shear flow in a channel of varying area

An approximate system of equations that describe unsteady flow of an inviscid non-heat-conducting gas in a narrow channel of varying area is derived. Generalized characteristics and hyperbolicity conditions are obtained for this system of equations. In connection with characteristics theory, the average Mach number and the flow criticality condition are introduced. Exact solutions that describe steady transonic channel flows are investigated. 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. 15–27, January–February, 1998.     

Rarefied flow in a channel and a periodic system of channels

the steady two-dimensional isothermal rarefied flow in a channel formed by two parallel flat plates of finite length is studied on the basis of the numerical solution of a linearized kinetic problem. The channel may either be isolated or constitute a cell of a periodic cascade consisting of zero-thickness plates arranged one above the other. As the channel length increases, the flow in it approaches the asymptotic one-dimensional Poiseuille flow. It is shown that the asymptotic dependence of the gas flow rate on the low Knudsen number corresponding to an infinitely long channel is already attained for a channel of length equal to several channel widths, if the flow rate is referred to the pressure gradient at the middle of the channel rather than to the mean pressure difference at the channel ends. The effect of the boundary conditions imposed on the channel entrance is investigated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 166–175, May–June, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 98-01-00443).     

Simple waves on a shear gas flow in a channel of constant cross section

The plane-parallel unsteady-state shear gas flow in a narrow channel of constant cross section is considered. The existence theorem of solutions in the form of simple waves of a set of equations of motion is proved for a class of isentropic flows with a monotone velocity profile over the channel depth. The exact solution described by incomplete beta-functions is found for a polytropic equation of state in a class of isentropic flows. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 36–43, January–February, 1999.     

On Low-Dimensional Galerkin Models for Fluid Flow

In this paper some implications of the technique of projecting the Navier–Stokes equations onto low-dimensional bases of eigenfunctions are explored. Such low-dimensional bases are typically obtained by truncating a particularly well-suited complete set of eigenfunctions at very low orders, arguing that a small number of such eigenmodes already captures a large part of the dynamics of the system. In addition, in the treatment of inhomogeneous spatial directions of a flow, eigenfunctions that do not satisfy the boundary conditions are often used, and in the Galerkin projection the corresponding boundary conditions are ignored. We show how the restriction to a low-dimensional basis as well as improper treatment of boundary conditions can affect the range of validity of these models. As particular examples of eigenfunction bases, systems of Karhunen–Loève eigenfunctions are discussed in more detail, although the results presented are valid for any basis. Received 10 September 1999 and accepted 13 December 1999     

Mixed Convection in a Vertical Porous Channel

A numerical study of mixed convection in a vertical channel filled with a porous medium including the effect of inertial forces is studied by taking into account the effect of viscous and Darcy dissipations. The flow is modeled using the Brinkman–Forchheimer-extended Darcy equations. The two boundaries are considered as isothermal–isothermal, isoflux–isothermal and isothermal–isoflux for the left and right walls of the channel and kept either at equal or at different temperatures. The governing equations are solved numerically by finite difference method with Southwell–Over–Relaxation technique for extended Darcy model and analytically using perturbation series method for Darcian model. The velocity and temperature fields are obtained for various porous parameter, inertia effect, product of Brinkman number and Grashof number and the ratio of Grashof number and Reynolds number for equal and different wall temperatures. Nusselt number at the walls is also determined for three types of thermal boundary conditions. The viscous dissipation enhances the flow reversal in the case of downward flow while it counters the flow in the case of upward flow. The Darcy and inertial drag terms suppress the flow. It is found that analytical and numerical solutions agree very well for the Darcian model. An erratum to this article is available at .     

Parametric analysis of two-phase flow instability in a channel with inlet and outlet hydraulic resistances

The mechanism of low-frequency self-oscillating instability of a one-dimensional two-phase flow in a channel with inlet and outlet hydraulic resistances is considered. The mechanism is based on the sensitivity of the inlet flow rate of the liquid to the pressure variation inside the channel and the sensitivity of the pressure to the variation of the outlet gas flow rate (with a constant mass rate of the liquid-gas phase transition per unit volume). A spectral analysis of the stability of the steady solution of the boundary-value problem for a hyperbolic-type nonlinear system of equations is performed within the framework of a two-velocity model of a gas-liquid flow. Parametric boundaries of the region of instability are obtained. The existence of self-oscillations in this range of parameters is supported by a numerical solution of the unsteady boundary-value problem. Institute of Catalysis, Siberian Division Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 1, pp. 47–53, January–February, 1998.     

Computational Modeling of the Structure of a High-Current Discharge in a Magnetogasdynamic Channel

A two-dimensional computational model is proposed to calculate radiative-convective heat transfer in gas flows with large gradients of physical properties. The model is based on the numerical solution of the unsteady dynamic equations for a compressible inviscid gas and the radiative transfer equations. Flow calculations for the magnetogasdynamic channel of a rail accelerator show that the dynamics of the process is substantially affected by the flow in the discharge region and hydrodynamic instability, resulting in the nonstationarity and nonuniformity of the flow and discharge structure. During the process, the discharge can exist both in the form of several current-carrying channels and in the form of a unified plasma formation. Results of the numerical calculations agree qualitative with experimental data. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 5–13, November–December, 2005.     

Gravity-flow structure in a miscible fluid

Steady-state density flows in a horizontal channel are studied based on a two-layer shallow water model, developed by the author, with allowance for the mixing between the layers. The structure of a gravity flow and the intensity of mixing in the flow head are shown to depend significantly on the channel depth. Conditions behind the flow front, which determine the basic characteristics of a gravity flow, are found. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 3, pp. 79–85, May–June, 1998.     

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.     

Peripheral explosion in a self-gravitating gas ball and dynamic explosion of star equilibrium

The problem of peripheral explosion in a star initially at equilibrium is solved for an exponential density distribution. Qualitatively new flow modes, such as recurrent ejection of the star shell and partial scatter of its matter in interstellar space, are obtained. The critical energies corresponding to various flow modes are determined. Calculations conducted over a wide range of the determining parameters allow certain conclusions to be drawn concerning the possibility of explaining the phenomena occurring in the interior of pulsing and variable stars. The problem of dynamic explosion of star equilibrium, followed by the formation of a detonation wave travelling through a gravitating gas at rest, is also considered. It is shown that various solutions involving detonation may be constructed by choosing the adiabatic exponent and the exponent of the power density distribution. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 157–163, May–June, 1998.     

Dynamic film thickness between bubbles and wall in a narrow channel

The present paper describes a novel technique to characterize the behavior of the liquid film between gas bubbles and the wall in a narrow channel. The method is based on the electrical conductance. Two liquid film sensors are installed on both opposite walls in a narrow rectangular channel. The liquid film thickness underneath the gas bubbles is recorded by the first sensor, while the void fraction information is obtained by measuring the conductance between the pair of opposite sensors. Both measurements are taken on a large two-dimensional domain and with a high speed. This makes it possible to obtain the two-dimensional distribution of the dynamic liquid film between the bubbles and the wall. In this study, this method was applied to an air–water flow ranging from bubbly to churn regimes in the narrow channel with a gap width of 1.5 mm.     

Direct numerical simulation of a liquid sheet in a compressible gas stream in axisymmetric and planar configurations

A thin liquid sheet present in the shear layer of a compressible gas jet is investigated using an Eulerian approach with mixed-fluid treatment for the governing equations describing the gas–liquid two-phase flow system, where the gas is treated as fully compressible and the liquid as incompressible. The effects of different topological configurations, surface tension, gas pressure and liquid sheet thickness on the flow development of the gas–liquid two-phase flow system have been examined by direct solution of the compressible Navier–Stokes equations using highly accurate numerical schemes. The interface dynamics are captured using volume of fluid and continuum surface force models. The simulations show that the dispersion of the liquid sheet is dominated by vortical structures formed at the jet shear layer due to the Kelvin–Helmholtz instability. The axisymmetric case is less vortical than its planar counterpart that exhibits formation of larger vortical structures and larger liquid dispersion. It has been identified that the vorticity development and the liquid dispersion in a planar configuration are increased at the absence of surface tension, which when present, tends to oppose the development of the Kelvin–Helmholtz instability. An opposite trend was observed for an axisymmetric configuration where surface tension tends to promote the development of vorticity. An increase in vorticity development and liquid dispersion was observed for increased liquid sheet thickness, while a decreasing trend was observed for higher gas pressure. Therefore surface tension, liquid sheet thickness and gas pressure factors all affect the flow vorticity which consequently affects the dispersion of the liquid.      

Mass transfer of aerosols with axial diffusion in narrow rectangular channels

The problem of mass transfer of aerosols with axial, as well as radial, diffusion in laminar flow in a narrow rectangular channel is studied. Two cases are investigated. The first case is where all particles enter the channel inlet and none form within the channel; and the second, where no particles enter the channel, and “formation in flight” occurs within the channel. For each case, analyses are made for both slug and Poiseuille flows. The first twenty modes of the eigenvalues, the eigenfunctions, and the coefficients of series expansion are obtained for several diffusion Péclet numbers, Pe. The first twelve of them are presented for Pe=1, 5, 10, 100, and ∞. Asymptotic expressions for the eigenvalues and the eigenfunctions are also given. The effects of axial diffusion on the local particle concentration, the bulk concentration, the Sherwood number, and the fraction of aerosols arriving at any cross-section of the channel are studied for various diffusion Péclet numbers. It was found that, for diffusion with or without formation in flight, the effect of axial diffusion may be neglected at an axial distance from the channel inlet greater than one and a half times that of the channel height for 1<Pe<100.