Showing papers in "Fluid Dynamics in 2009"

Experimental investigation of the role of instability waves in noise radiation by supersonic jets

Abstract: Existing ideas of instability waves as the main dynamic noise sources in supersonic jets are tested for conformity with the data of acoustic measurements of this noise. Methodologically, the problem consists in the verification of the main principles of Tam’s theory of noise radiation by supersonic jets based on the ideology of instability waves in the shear layer of the jet and their key role in noise generation. Technologically, the study is based on a new technique for measuring the noise, namely, the azimuthal decomposition method developed by the authors. It is shown that on the Strouhal number range from 0.03 to 0.35 the theory satisfactorily describes the radiation pattern of the individual harmonics, while the initial amplitudes of the instability waves are in qualitative agreement with the assumption of their uniform distribution near the nozzle edge.

Breaking of Faraday waves and jet launch formation

Abstract: Irregular and breaking Faraday waves are experimentally investigated. Among the irregular waves those with a small depression in the wave crest and periodic triplets are distinguished. In the case of breaking waves the mechanism of jet launch formation on the wave crest is considered. It is experimentally demonstrated that the breaking of standing waves in a rectangular reservoir starts with cavity collapse on the wave crest in process of formation. It is shown that jet launch from the wave crest is preceded by the initiation, development, and collapse of a cavity. A universal power-law dependence governing cavity collapse is obtained. A comparison of the experimental data with an analytical model suggests that cavity initiation is due to the nonlinearity of the waves themselves, namely, the presence of two small disturbances of the free surface traveling counter to one another and forming a cavity. The results obtained underline the importance of the initial stage of wave breaking.

Control of cross flow in the three-dimensional boundary layer using space-periodic body force action

Abstract: The possibility of attenuation of the cross flow in the three-dimensional incompressible laminar boundary layer on a sideslipping wing under the action of body force sources simulating the time-average forces generated by a surface electric discharge is estimated The effect of the distance between the sources and the sideslip angle of the wing on the cross flow velocity is investigated for the source intensity observed experimentally

Three-wave interactions between disturbances in the hypersonic boundary layer on impermeable and porous surfaces

Abstract: The interaction between disturbances in the hypersonic boundary layer on impermeable and porous surfaces is considered within the framework of weakly-nonlinear stability theory. It is established that on the impermeable surface nonlinear interactions between different waves (acoustic and vortex) occur in the parametric resonance regime. The role of pumping wave is played by a plane acoustic wave. The nonlinear interactions take place over a wide frequency range and can lead to the packet growth of Tollmien-Schlichting waves. On the porous surface the analogous interactions are fairly weak and result in a slight decay of the acoustic mode and a slight amplification of the vortex mode. This leads to the dragging out of the laminar flow regime and the regions of linear disturbance growth. In this situation the low-frequency spectrum of the vortex modes may be filled on account of the nonlinear processes occurring in the three-wave systems between the vortex components.

Structure of inertial-admixture accumulation zones in a tornado-like flow

Abstract: The motion of a dispersed inertial admixture in a steady-state axisymmetric 3D viscous incompressible flow formed by a semi-infinite vortex filament interacting with an orthogonally located substrate surface is considered. The carrier-phase parameters are found from the numerical solution of the Navier-Stokes equations under the assumption of flow self-similarity of a known type [1]. Different phase force interaction schemes corresponding to different ratios of the phase densities are considered. For calculating the dispersed-phase continuum parameters, a full Lagrangian approach is used, which makes it possible to calculate the dispersed-phase concentration in particle accumulation zones and regions of intersecting particle trajectories. On the basis of parametric calculations, it is found that in the case of heavy particles (whose density is greater than that of the carrier phase) a “cup-shaped” particle accumulation surface visualizing a high-vorticity region is formed. The dependence of this surface shape on the governing parameters is investigated. It is shown that for different phase density ratios the dispersed-phase concentration fields are qualitatively different.

Spectral properties of helical turbulence

Abstract: The spectral properties of homogeneous stationary turbulence excited by a force that introduces considerable helicity, along with energy, into the flow are considered. It is shown that helicity is transferred on the inertial range as a passive admixture and its spectrum obeys the “−5/3” law much more accurately than the velocity fluctuation spectrum. The helicity is dissipated on the same scales as the energy, though the helicity transfer dynamics on the inertial range are different on the large and small scales. Numerical experiments are performed on the basis of a cascade model developed for describing helical turbulence.

Aerodynamic coefficients of a spinning sphere in a rarefied-gas flow

Abstract: A three-dimensional rarefied-gas flow past a spinning sphere in the transitional and near-continuum flow regimes is studied numerically. The rarefaction and compressibility effects on the lateral (Magnus) force and the aerodynamic torque exerted on the sphere are investigated for the first time. The coefficients of the drag force, the Magnus force, and the aerodynamic torque are found for Mach numbers ranging from 0.1 to 2 and Knudsen numbers ranging from 0.05 to 20. In the transitional regime, at a certain Knudsen number depending on the Mach number the Magnus force direction changes. This change is attributable to the increase in the role of normal stresses and the decrease in the contribution of the shear stresses to the Magnus force with decrease in the Knudsen number. A semi-empirical formula for the calculation of the Magnus force coefficient in the transitional flow regime is proposed.

Inertial migration of sedimenting particles in a suspension flow through a Hele-Shaw cell

Abstract: Within the framework of the model of two interpenetrating continua, a horizontal laminar dilute-suspension flow in a vertical Hele-Shaw cell is investigated. Using the method of matched asymptotic expansions, an asymptotic model of the transverse migration of sedimenting particles is constructed. The particle migration in the horizontal section of the cell is caused by an inertial lateral force induced by the particle sedimentation and the shear flow of the carrier phase. A characteristic longitudinal length scale is determined, on which the particles migrate across the slot through a distance of the order of the slot half-width. The evolution of the particle number concentration and velocity fields along the channel is studied using the full Lagrangian method. Depending on the particle inertia parameter, different particle migration regimes (with and without crossing of the channel central plane by the particles) are detected. A critical value of the particle inertia parameter corresponding to the change in migration regime is found analytically. The possibility of intersection of the particle trajectories and the formation of singularities in the particle number concentration is demonstrated.

Laminar-turbulent flow over wedges mounted on sharp and blunt plates

Abstract: The flow pattern and the heat transfer on sharp and blunt flat plates near a wedge in a Mach 6 stream are experimentally investigated for two Reynolds numbers corresponding to the laminar and transitional states of the undisturbed boundary layer ahead of the wedge. It is shown that, as in a two-dimensional flow, plate bluntness leads to the attenuation of the heat transfer in the boundary layer/shock wave interference zone. However, when a certain threshold value of the bluntness is exceeded, a further increase in the bluntness has almost no effect on the heat transfer. For the first time, an experiment conducted in an intermittent (blow-down) wind tunnel has been based on the comprehensive use of panoramic (global) techniques for measuring the heat transfer and pressure coefficients and a method for visualizing the surface friction employing the luminescence effect after UV irradiation.

Disturbance growth rate in turbulent wall flows

Abstract: Disturbance development in turbulent wall flows is numerically investigated. The flows in a circular tube and in a plane channel are considered. The Navier-Stokes equations subjected to the condition of periodicity along the main flow are integrated in time until a statistically stationary “turbulent” flow regime is attained. Then the solution is disturbed and the further evolution of the disturbance is determined by comparing the two solutions, i.e., with and without the disturbance, which are calculated in parallel. It is shown that in the linear stage on average the solutions diverge exponentially. The main result of the study is that the small disturbance growth rate normalized by the wall time scale turns out to be constant, that is, dependent on neither the Reynolds number on the range considered nor the type of the flow: λ+ ≈ 0.021. The estimate of the disturbance growth rate is consistent with the previously obtained results concerning downstream disturbance growth and the estimate for the highest Lyapunov exponent calculated for turbulent flow in a plane channel.

Convective stability of a rotating conducting fluid layer in an external magnetic field

Abstract: The stability of the rest state of a conducting incompressible fluid forming a horizontal layer with rigid dielectric boundaries heated from below and rotating about a vertical axis, with a vertical magnetic field superimposed, is studied in the Boussinesq approximation. With increase in the Rayleigh number, depending on the relationship between the problem parameters (Taylor, Chandrasekhar and kinematic and magnetic Prandtl numbers), the eigenvalue of the critical mode of the linearization operator may be zero or imaginary, so that the instability of the rest state may be monotonic or oscillatory. The effect of the parameter values on the instability mode is investigated. In particular, the parameter ranges on which the critical eigenvalue is zero or imaginary are found.

Three-dimensional magnetohydrodynamic description of the process of collision of a solar wind shock wave and the Earth’s bow shock

Abstract: The propagation of a solar wind shock wave along the surface of the Earth’s bow shock is investigated within the framework of an ideal magnetohydrodynamic model in the three-dimensional non-plane-polarized formulation. The most characteristic values of the solar wind parameters and the interplanetary magnetic field strength are considered for the plane front of a solar wind shock wave moving at various velocities along the Sun-Earth radius. The global three-dimensional pattern of the interaction is constructed as a function of the angle of inclination of the surface of the bow shock to the solar wind velocity and the azimuthal angle along the curve of intersection of the fronts of the interacting shock waves. The evolution of the flow developed in the neighborhood of the bow shock is investigated and the parameters of the medium and magnetic field are calculated.

Numerical investigation of supersonic plate flutter using the exact aerodynamic theory

Abstract: In classical investigations of panel flutter it is usually assumed that the gas pressure acting on the plate can be calculated within the framework of the piston theory, an approximation exact for high Mach numbers. The loss of stability revealed in these investigations is of the “coupled” type, involving the interaction of two oscillation modes. Recently, the use of asymptotic methods revealed another single-mode type of stability loss, which cannot be obtained within the framework of the piston theory. In the present study this type of stability loss is investigated numerically using the Bubnov-Galerkin method.

Filling of channels with a non-Newtonian fluid in the gravity field

Abstract: The flow of a pseudoplastic fluid with a free surface realized during the filling of a channel at a constant flow rate in the entry section is modeled. The fluid flow direction coincides with that of gravity. The mathematical problem is formulated on the basis of the complete equations of motion. A numerical technique for solving the problem in the two-dimensional formulation is developed on the basis of the SIMPLE algorithm and the method of invariants. A parametric investigation of the free surface evolution is carried out for different values of the governing criteria and rheological parameters. Three filling regimes are found to exist, namely, a complete filling regime, a transitional regime characterized by air cavity formation, and a jet regime. Criterial dependences separating these regimes are presented.

Phase velocity spectrum of internal waves in a weakly-stratified two-layer fluid

Abstract: The problem of steady-state internal waves in a weakly stratified two-layer fluid with a density that is constant in the lower layer and depends exponentially on the depth in the upper layer is considered. The spectral properties of the equations of small perturbations of a homogeneous piecewise-constant flow are described. A nonlinear ordinary differential equation describing solitary waves and smooth bores on the layer interface is obtained using the Boussinesq expansion in a small parameter.

Oscillating laminar fluid flow in a cylindrical elastic pipe of annular cross-section

Abstract: The coupled elastohydrodynamic problem based on the dynamic equations for a viscous incompressible fluid and for two closed finite-length cylindrical elastic shells, inner and outer, described using the Kirchhoff-Love hypotheses is formulated and solved with the corresponding boundary conditions for harmonic variation of the pressure at the inlet and outlet of an elastic annular pipe. From the solution of this problem the flow parameters and the elastic shell displacements are found. The amplitude and phase frequency characteristics and resonant frequencies of the shells are found. The cases of shells simply supported and with fixed ends are considered. The effect of the support mode and the fluid characteristics on the resonant frequencies and the amplitude frequency characteristics of the shells is investigated.

Numerical modeling of gravity currents in inclined channels

Abstract: The mixing and wave formation processes in gravity currents induced by the rupture of a vertical dam initially separating a heavy and a light liquid are studied for different channel inclination angles. The calculations are performed using the LES and RANS models. It is shown that when the heavy liquid moves down the channel slope, the longitudinal and transverse internal waves break and form turbulent mixing zones. When the heavy liquid ascends the slope, the wavy motion mode predominates.

Mixed convection in a vertical channel with discrete heat sources at the wall

Abstract: The mixed convection in a vertical plane-parallel channel with two heat sources of finite dimensions located at the wall is analyzed on the basis of a two-dimensional numerical simulation. The effect of the distance between the heat sources on the flow pattern and the temperature field is studied. Calculations are performed on the Grashof and Reynolds number ranges from 0–105 and 0–10, respectively, at a Prandtl number of 0.7. The mathematical model is based on the time-dependent Navier-Stokes equations in the Boussinesq approximation. The problem is solved by the finite element method.

Simulation of hydrogen adsorption in carbon nanotubes

Abstract: The processes of physical hydrogen adsorption by carbon nanotubes are simulated by considering the molecular dynamics. The interactions are described by the Lennard-Jones potential and quantum effects are neglected. The dependences of the relative mass content of adsorbed hydrogen on the pressure and temperature are obtained. The formation of a second adsorption layer at low temperatures is detected. This leads to a higher stored hydrogen content.

Stability of a steady-state discontinuity of a fluid layer on the surface of an immiscible fluid

Abstract: A new stable structure of the three-phase system formed by a gas, a horizontal liquid layer with a free upper surface and an underlying immiscible liquid substrate is investigated experimentally and theoretically. When the upper layer has a greater surface tension than the lower layer and its thickness is fairly small, a local deformation of its surface can lead to the development of a steady-state concentric discontinuity within whose limits the lower layer os in contact with the gas. The conditions of stability of such a phase system with a steady-state discontinuity are studied and the dependences of the discontinuity parameters on the vessel diameter, the upper layer thickness, and the liquid surface tensions are obtained for various pairs of liquids. The formulation of the analytic problem of the layer discontinuity is discussed. The experimental data are compared with the results of calculations carried out for a model of a discontinuity in an infinite layer.

Calculation of particle concentration in the problem of aerosol aspiration into a thin-walled tube

Abstract: A mathematical model of the problem of aerosol aspiration into a thin-walled tube from a moving gas is developed and particle concentration fields are calculated. In the absence of a particle effect on the gas flow, the carrier medium is calculated in the potential-flow and viscous-flow approximations for an incompressible gas, using boundary-element and finite-volume methods. For the viscous-flow model, a numerical solution is found using the FLUENT program. The particle motion equations are complemented with equations for calculating the concentration along the particle trajectories. The spatial distributions of the particle concentration near and inside the sampler are studied for different ratios of the wind and aspiration velocities and for different Stokes numbers. The effect of nonuniformity of the particle concentration distributions on the aspiration coefficient is discussed.

Statics of a magnetic fluid containing magnetic field concentrators

Abstract: Various static surface shapes of a magnetic fluid containing bodies made of easily magnetizable materials (magnetic field concentrators) in a uniform applied magnetic field are numerically calculated with account for the gravity force, surface tension, and the dependence of the magnetic-fluid magnetization on the magnetic field strength. The possibility of a sudden change in surface shape is shown. Hysteresis in the surface shape with a cyclic increase and decrease in the applied field is predicted.

Seepage effects of dissolving rock by acid action on carbonate oil-bearing formations

Abstract: The displacement of oil by an aqueous acid solution in the neighborhood of a well and a hydraulic fracture is considered with allowance for the kinetics of acid dissolution of a carbonate rock. The penetration of the active admixture and the variation of the seepage characteristics of the reservoir in the course of the reactant injection and after stoppage for reaction are investigated on the basis of the model proposed. The effect of the acid treatment, the reaction time, and the depth of penetration of the solution into the formation are estimated. Analytic estimates and numerical calculations are carried out for real examples.

Flow past a plate with a moving surface

Abstract: On the basis of a numerical solution of the unsteady Navier-Stokes equations, the flow past a finite plate with an upstream-moving surface is investigated. For the Reynolds numbers Re =102−104, the flow past the plate is analyzed as a function of the relative plate surface velocity. On the basis of this analysis a limiting mathematical model of the flow as Re → ∞ is proposed.

Numerical modeling of a viscous incompressible unsteady separated flow past a rotating cylinder

Abstract: For studying unsteady flow past a rotating circular cylinder the Navier-Stokes equations are used. The numerical algorithm is based on an artificial-compressibility method, an implicit three-layer second-order scheme with subiterations with respect to time, a third-order scheme with splitting of the flux vectors for the convective terms, and a central-difference scheme for integrating the viscous terms. The calculated velocity profiles, the vorticity fields, the Strouhal numbers, the distribution of the pressure and friction coefficients over the cylinder surface, and the coefficients of the drag and lift forces for the laminar flow regime are analyzed.

Electrization and liquid glow in a coaxial channel with dielectric walls

Abstract: Dielectric-liquid flows in narrow channels with walls composed of different dielectrics are investigated experimentally. It is revealed that at a certain flow velocity, as a result of electrization, on the interface between the dielectrics the liquid begins to glow. The glow is discrete in the form of frequent pulses and is accompanied by electromagnetic noise on the radio-frequency range. It is shown that with decrease in the channel thickness the glow appears at smaller flow velocities. The glow is accompanied by heating of the liquid in the wall region to temperatures that may reach several tens of degrees. The electrization potential reaches more than 100 kV. The mechanisms of electrization and liquid glow are discussed.

Structure and bifurcations of plane shock waves in a vibrationally excited gas with an external pumping source

Abstract: The structure of the density profiles in stationary plane shock waves in a vibrationally excited gas is investigated. For self-similar solutions a bifurcation diagram is plotted in the parametric “traveling wave velocity—degree of nonequilibrium” plane. The bifurcation boundaries of the domains of existence of the structures of different types are analytically derived. It is shown that weak plane shock waves are unstable, accelerate, and break down into a sequence of pulses or-at a fairly high pumping rate-waves with nonzero asymptotics, whose amplitude and propagation velocity are independent of the initial disturbance and are determined by the parameters of the medium itself.

Possible classification of the self-oscillatory spouting regimes of plane vertical submerged jets of a heavy fluid

Abstract: New results of an experimental investigation of self-oscillatory regimes of plane vertical jet spouting from beneath the free surface of a heavy incompressible fluid are discussed. The experiments were performed on a setup with discharge over a weir. The range of dimensionless jet submergence values on which bifurcation change of spouting regime is observable is studied. It is established that on the Froude number and dimensionless jet submergence ranges considered in the study six characteristic spouting regimes differing in free surface shape and self-oscillation frequency can exist. It is shown that these regimes can be subdivided into three typical groups with respect to the dependence of the self-oscillation period on the jet flow rate. A dimensionless parameter that makes it possible to identify the boundaries of the bifurcation change in spouting regimes is obtained for each of these groups. For certain spouting regimes without the formation of free jets numerical calculations are carried out using the STAR-CD software package; the calculated results are in good agreement with experimental data.

Effect of the freestream turbulence scale and the leading edge shape on boundary layer laminar-turbulent transition

Abstract: The effect of the leading edge shape and the turbulence scale on laminar-turbulent transition in the flat-plate boundary layer due to grid turbulence is investigated. In the experiments, the turbulence scale was changed by a factor of three and the bluntness radius of the edge by a factor of four, all other factors being fixed. It is shown that on the plate with a sharp edge the fluctuation growth rate and the laminar-turbulent transition point depend nonmonotonically on the turbulence scale. On the blunt plate transition occurs considerably earlier than on the sharp plate.

Effect of vaporizing droplets on the structure of a submerged spray

Abstract: Heat and mass transfer in a gas-droplet spray is investigated numerically using the Eulerian description of both phases. The system of averaged equations for the dispersed phase is based on the kinetic equation for the probability density function of the particle coordinates, velocity, and temperature. With increase in the particle concentration and size, the spray becomes narrower and longer. However, for evaporating sprays, particularly with small droplets, the turbulence suppression and mixing effects are less pronounced than for jets without phase transitions. The strongest turbulence suppression is detected in the initial spray region, where the droplet concentration is maximum and the droplet size is only slightly reduced due to vaporization.