Behavior of a small single bubble rising in a rotating flow field

A small single bubble was generated with a single-hole nozzle facing upward in a water bath contained in a rotating cylindrical vessel. The bubble size falls in the surface tension force dominant regime. The vertical, radial, and tangential migration velocities of the bubble were measured with two CCD cameras and a high-speed video camera. The tangential velocity component of water flow was measured with particle image velocimetry. A helical motion of the bubble was observed under every experimental condition. The direction of the helical motion was the same as that of the tangential velocity component. This helical motion is associated with the large initial shape deformation of the bubble near the nozzle exit and the subsequent regular shedding of vortices behind it. The period and amplitude of the helical motion were obtained by analyzing the trajectory of the bubble. These quantities were non-dimensionalized by the volume equivalent bubble diameter and the terminal bubble velocity in the vertical direction and correlated as functions of the Eotvos number. Empirical equations were proposed for the period and amplitude. Originally published in the Journal of JSEM, Vol. 4, No. 2, pp. 38–45 (2004).     

Cold-gas experiments to study the flow separation characteristics of a dual-bell nozzle during its transition modes

An experimental investigation has been carried out to study the effect of test environment on transition characteristics and the flow unsteadiness associated with the transition modes of a dual-bell nozzle. Cold-gas tests using gaseous nitrogen were carried out in (i) a horizontal test-rig with nozzle exhausting into atmospheric conditions and, (ii) a high altitude simulation chamber with nozzle operation under self-evacuation mode. Transient tests indicate that increasing δP ₀/δt (the rate of stagnation chamber pressure change) reduces the amplitude of pressure fluctuations of the separation shock at the wall inflection point. This is preferable from the viewpoint of lowering the possible risk of any structural failure during the transition mode. Sea-level tests show 15–17% decrease in the transition nozzle pressure ratio (NPR) during subsequent tests in a single run primarily due to frost formation in the nozzle extension up to the wall inflection location. Frost reduces the wall inflection angle and hence, the transition NPR. However, tests inside the altitude chamber show nearly constant NPR value during subsequent runs primarily due to decrease in back temperature with decrease in back pressure that prevents any frost formation.     

Optimization of the shapes of obstacles in jet-separation flow

The model of an ideal incompressible fluid is used to study the solvability of optimal control problems for the shape of a nozzle which discharges free-boundary fluid flow with and without accounting for gravity (internal aerodynamics) and shape optimization problems for an obstacle with jet separation (external aerodynamics). The qualitative properties of such flows are studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 30–39, May–June, 2007.     

Investigation of a Gas Flow with Solid Particles in a Supersonic Nozzle

A two-phase flow with high Reynolds numbers in the subsonic, transonic, and supersonic parts of the nozzle is considered within the framework of the Prandtl model, i.e., the flow is divided into an inviscid core and a thin boundary layer. Mutual influence of the gas and solid particles is taken into account. The Euler equations are solved for the gas in the flow core, and the boundary-layer equations are used in the near-wall region. The particle motion in the inviscid region is described by the Lagrangian approach, and trajectories and temperatures of particle packets are tracked. The behavior of particles in the boundary layer is described by the Euler equations for volume-averaged parameters of particles. The computed particle-velocity distributions are compared with experiments in a plane nozzle. It is noted that particles inserted in the subsonic part of the nozzle are focused at the nozzle centerline, which leads to substantial flow deceleration in the supersonic part of the nozzle. The effect of various boundary conditions for the flow of particles in the inviscid region is considered. For an axisymmetric nozzle, the influence of the contour of the subsonic part of the nozzle, the loading ratio, and the particle diameter on the particle-flow parameters in the inviscid region and in the boundary layer is studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 65–77, November–December, 2005.     

Motion and heat and mass transfer in a disperse admixture in turbulent nonisothermal jets of a gas and a low-temperature plasma

The motion and heat and mass transfer of particles of a disperse admixture in nonisothermal jets of a gas and a low-temperature plasma are simulated with allowance for the migration mechanism of particle motion actuated by the turbophoresis force and the influence of turbulent fluctuations of the jet flow velocity on heat and mass transfer of the particle. The temperature distribution inside the particle at each time step is found by solving the equation of unsteady heat conduction. The laws of scattering of the admixture and the laws of melting and evaporation of an individual particle are studied, depending on the injection velocity and on the method of particle insertion into the jet flow. The calculated results are compared with data obtained with ignored influence of turbulent fluctuations on the motion and heat and mass transfer of the disperse phase. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 95–108, May–June, 2008.     

Shallow and deep dynamic stall for flapping low Reynolds number airfoils

We consider a combined experimental (based on flow visualization, direct force measurement and phase-averaged 2D particle image velocimetry in a water tunnel), computational (2D Reynolds-averaged Navier–Stokes) and theoretical (Theodorsen’s formula) approach to study the fluid physics of rigid-airfoil pitch–plunge in nominally two-dimensional conditions. Shallow-stall (combined pitch–plunge) and deep-stall (pure-plunge) are compared at a reduced frequency commensurate with flapping-flight in cruise in nature. Objectives include assessment of how well attached-flow theory can predict lift coefficient even in the presence of significant separation, and how well 2D velocimetry and 2D computation can mutually validate one another. The shallow-stall case shows promising agreement between computation and experiment, while in the deep-stall case, the computation’s prediction of flow separation lags that of the experiment, but eventually evinces qualitatively similar leading edge vortex size. Dye injection was found to give good qualitative match with particle image velocimetry in describing leading edge vortex formation and return to flow reattachment, and also gave evidence of strong spanwise growth of flow separation after leading-edge vortex formation. Reynolds number effects, in the range of 10,000–60,000, were found to influence the size of laminar separation in those phases of motion where instantaneous angle of attack was well below stall, but have limited effect on post-stall flowfield behavior. Discrepancy in lift coefficient time history between experiment, theory and computation was mutually comparable, with no clear failure of Theodorsen’s formula. This is surprising and encouraging, especially for the deep-stall case, because the theory’s assumptions are clearly violated, while its prediction of lift coefficient remains useful for capturing general trends.     

Experiments on the unsteady nature of vortex breakdown over delta wings

 Vortex breakdown location over delta wings is not steady and exhibits fluctuations along the axis of the vortices. Experiments on the nature and source of these fluctuations were carried out. Spectral analysis and other statistical concepts were used to quantify the unsteady behaviour of vortex breakdown location obtained from flow visualization. The fluctuations consist of quasi-periodic oscillations and high-frequency low amplitude displacements. The quasi-periodic oscillations are due to an interaction between the vortices, which cause the antisymmetric motion of breakdown locations for left and right vortices. The oscillations are larger and more coherent as the time-averaged breakdown locations get closer to each other as angle of attack or sweep angle is varied. The frequency of this organized motion is much smaller than the frequency of any other known instabilities. On the other hand, the most probable frequency for the high-frequency small-amplitude fluctuations of breakdown location is in the same range as the frequency of Kelvin–Helmholtz instability of the separated shear layer. A mechanism for the interaction between the vortices causing the oscillations of breakdown location was proposed. When a splitter plate was placed in the symmetry plane of the wing, the large amplitude quasi-periodic oscillations of breakdown location were suppressed. Received: 10 March 1998 / Accepted: 27 October 1998     

Critical gas outflow from nozzles

The possibility of critical gas flow from Laval nozzles in overexpanded regimes behind a bridge shock is investigated theoretically with and without allowance for viscous mixing at the edge of the jet. The influence of the mixing effect and flow separation from the nozzle walls on the critical flow conditions is analyzed. It is shown experimentally that these regimes coincide closely with the displacement of the normal shock to the nozzle exit and cessation of the emission by the jet of a discrete tone. Mariupol. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 180–184, July–August, 1994.     

Interaction of a circular turbulent jet with a flat target

Large eddy simulations are performed for an unsteady flow and heat transfer in the region of interaction of a circular turbulent jet with a normally positioned flat obstacle (target). Space-filtered Navier-Stokes equations are closed by the RNG model of eddy viscosity, which takes into account the curvature of streamlines in the region of flow turning. The computations are performed for different dimensionless distances between the nozzle exit and the target and for different Reynolds numbers. The dependence between the Nusselt number distribution over the target surface and the vortex structure of the jet is analyzed. The local and integral characteristics of the flow are compared with the data of a physical experiment. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 55–67, January–February, 2007.     

Some Properties of a New Model for Slow Flow of Granular Materials

Some properties of a new continuum model for the bulk flow of a dense granular material in which neighbouring grains are in contact for a finite duration of time and in which the contact force is non-impulsive – the so called slow flow regime – are presented. The model generalises both the plastic potential and double-shearing models and contains an additional kinematic quantity – the intrinsic spin. The stress tensor is, in general, non-symmetric and separate yield conditions govern translational and rotational yield. We consider homogeneous, quasi-static loadings for the symmetric part of the stress and dynamic loading for the anti-symmetric part of the stress. A solution for the stress state in terms of a single parameter, namely the major principal direction of the symmetric part of the stress, is presented. This direction itself is determined by a consideration of the flow equations in the context both dilatant and isochoric simple shear flows. These simple flows are used to complete the characterisation of the relationship between the anti-symmetric part of the stress and the intrinsic spin.     

Effect of the plenum-chamber diameter on the turbulent characteristics of a supersonic jet

The effect of the flow character in the plenum chamber of a nozzle on the high-frequency boundary of the spectrum of fluctuations at the boundary of a supersonic, strongly underexpanded jet of nitrogen exhausted from a circular sonic nozzle into the ambient space was experimentally studied. The Reynolds number in the plenum chamber of the nozzle with a given throat area was varied by changing the diameter of the subsonic region. The high-frequency boundary of the spectrum of turbulent fluctuations was evaluated on the basis of two-point correlation functions of time. The technique for measurement of these functions was based on molecular scattering of light. Radiation of two pulse lasers with a controlled delay between the pulses was used as a source of light. It follows from experimental results that the high-frequency boundary of the spectrum of turbulent fluctuations and the spectrum itself vary significantly depending on the Reynolds number of the flow in the plenum chamber. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 69–72, November–December, 1999.     

Oscillating annular liquid membranes

Summary The response of annular liquid membranes to sinusoidal mass flow rate fluctuations at the nozzle exit is analyzed as a function of the amplitude and frequency of the axial velocity fluctuations at the nozzle exit and thermodynamic compression of the gas enclosed by the membrane. It is shown that both the pressure of the gases enclosed by the annular membrane and the axial distance at which the annular membrane merges on the symmetry axis are periodic functions of time which have the same period as that of the mass flow rate fluctuations at the nozzle exit. They are also nearly sinusoidal functions of time for small amplitudes of the mass flow rate fluctuations at the nozzle exit, and exhibit delay and lag times with respect to the sinusoidal axial velocity fluctuations at the nozzle exit. Both the delay and the lag times are functions of the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit and the polytropic exponent. The amplitudes of both the pressure of the gases enclosed by the annular liquid membrane and the convergence length increase and decrease, resp., as the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit, resp., are increased. They also increase as the polytropic exponent is increased.

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Oszilierende rotationsschalenförmige Flüssigkeitsmembranen

Übersicht Untersucht wird das Verhalten rotationsschalenförmiger Flüssigkeitsmembranen in Abhängigkeit von der Amplitude und Frequenz der axialen Geschwindigkeitsschwankungen an der Düsenmündung und der thermodynamischen Verdichtung des eingeschlossenen Gases, wenn sich der Massestrom an der Düsenmündung sinusförmig ändert. Es wird gezeigt, daß der Druck des eingeschlossenen Gases und der axiale Mündungsabstand des Scheitels der geschlossenen Membran periodische Zeitfunktionen mit der Frequenz der Masseflußschwankung am Düsenaustritt sind. Für kleine Amplituden des Massestroms ist ihr Zeitverhalten ebenfalls fast-sinusförmig, wobei sie bezüglich der sinusförmigen axialen Geschwindigkeitsschwankungen an der Düsenmündung eine Ansprechzeit und Phasenverschiebung aufweisen. Ansprechzeit und Phasenverschiebung sind Funktionen von Amplitude und Frequenz der Massestromschwankung sowie des polytropen Exponenten. Die Amplitude von Gasdruck und Abstand des Membranscheitels von der Düse wächst bzw. fällt mit wachsender Amplitude und Frequenz des Massestroms. Beide nehmen außerdem mit dem polytropen Exponenten zu.

     

Hysteresis phenomena in a plane rotatable nozzle

The flow in a rotatable nozzle is calculated within the framework of the Reynolds equations and the Spalart-Allmaras turbulence model on the pressure difference range 1.1 < π < 5 for four configurations of the nozzle with the area ratio ε = 1.52 and two angles of the nozzle axis rotation. The flow structure is determined and the thrust characteristics and the angles of the thrust vector rotation are obtained. It was found that in the overexpansion regime the flows in plane symmetric and rotatable nozzles involve hysteresis phenomena due the Coanda effect and the interaction between the boundary layer and a shock generated within the nozzle on its supersonic walls. The hysteresis phenomena detected provide an up-to-4% divergence in the thrust coefficient for the same problem parameters. The results of the numerical modeling are compared with the experimental data and the results of calculations in accordance with Sekundov’s model.     

Numerical Investigation of Unsteady Transitional Flows in Turbomachinery Components Based on a RANS Approach

This paper presents results of the numerical simulation of periodically unsteady flows with focus on turbomachinery applications. The unsteady CFD solver used for the simulations is based on the Reynolds averaged Navier–Stokes equations. The numerical scheme applies an extended version of the Spalart–Allmaras one-equation turbulence model coupled with a transition correlation. The first example of validation consists of boundary layer flow with separation bubble on a flat plate, both under steady and periodically unsteady main flow conditions. The investigation includes a variation of the major parameters Strouhal number, amplitude, and Reynolds number. The second, more complex test case consists of the flow through a cascade of turbine blades which is influenced by wakes periodically passing over the cascade. The computations were carried out for two different blade loadings. The results of the numerical simulations are discussed and compared with experimental data in detail. Special emphasis is given to the investigation of boundary layers with regard to transition, separation and reattachment under the influence of main flow unsteadiness. This revised version was published online in July 2006 with corrections to the Cover Date.     

Three-dimensional supersonic turbulent flows past conical bodies

The results of the numerical simulation of supersonic three-dimensional flow past sharp-nosed cones with circular and elliptic cross-sections in the turbulent shock-layer flow regime are presented. The calculations are performed in the local conical approximation using the system of Reynolds equations and the differential one-equation turbulence model. The numerical solutions are obtained by means of an implicit constant-direction finite-difference scheme. The emphasis is placed on the investigation of the transverse flow separation and the flow features associated with the turbulent flow regime. St.Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 99–105, January–February, 2000. The study was carried out with the support of the Russian Foundation for Basic Research (project No. 99-01-00735).     

Mixed convection from a cylinder oscillating vertically in a quiescent fluid

 The problem of heat convection from a vertically oscillating cylinder in a quiescent fluid is investigated. The governing equations of motion and energy are solved numerically in a non-inertial frame of references to determine the flow field and heat transfer characteristics under different conditions. The main dominating parameters are Keulegan–Carpenter number, KC, frequency parameter, β, Grashof number, Gr and Prandtl number, Pr. The ranges considered for these parameters are KC ≤ 10, β≤40 and Gr ≤ 10⁵ while Prandtl number is kept constant. The study revealed that the effect of amplitude and frequency of oscillation on heat transfer is strongly influenced by the Grashof number range. In the forced convection regime (Gr = 0), the increase of KC creates extensive vortex motion at all cylinder positions that leads to a significant increase in heat transfer. A similar trend, but with a lesser extent, is also observed for the increase of β. However, at high Grashof numbers, the effect of oscillation on heat convection is only significant at large values of KC. Received on 5 June 2000 / Published online: 29 November 2001     

Calculation of a transport current from a nozzle with two-phase flow in the presence of a corona discharge

The operation of a source of charged aerosol particles which consists of a supersonic nozzle, a corona-forming needle-shaped electrode, and a device for injecting liquid droplets into a gas flow is considered. A theoretical model for two-dimensional, two-phase flow in the nozzle is considered. An algorithm of numerical calculation of such a flow is developed, and results of calculations of the electric transport current from the nozzle are given. Institute of Mechanics, Moscow State University, Moscow 117192. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 6, pp. 102–109, November–December, 1998.     

Wall pressure fluctuations and topology in separated flows over a forward-facing step

Laboratory measurements of wall pressure fluctuations and aerodynamic fields were made in separated flows over a forward facing step (h = 30, 40 and 50 mm with U _e = 15–40 m/s). An array of 16 off-set pressure probes extending in the streamwise and the spanwise directions was especially developed for sensing the wall pressure fluctuations. The flow field was also investigated by wall flow visualizations and PIV to analyze the flow topology in an open section wind tunnel. The results show a different behavior of the flow depending on the aspect ratio l/h and δ/h for high Reynolds numbers. The space time correlations between the wall pressure and the velocity fields were highlighted. The results show that high levels of these correlations are located at the top of the recirculation bubble, mainly in the shear layer and are extended downstream of the re-attachment point. Indeed, the results indicate that the flapping motion at the separation is important in the flow organization at the re-attachment point.     

Investigation of the flow in a circular cavity using stereo and tomographic particle image velocimetry

The turbulent flow over a circular cavity with an aspect ratio of D/H = 2 is investigated by multi-planar stereoscopic particle image velocimetry and with tomographic particle image velocimetry (PIV). The main aim of the study is the flow topology and the turbulent structure of the asymmetrical flow pattern that forms inside the cavity at these specific conditions. The flow field is measured in the vertical symmetry plane to describe the overall recirculation pattern in the cavity and the turbulent shear layer developing from the separation point. In this specific regime the shear layer fluctuations are recognized as those caused by instabilities together with the effect of the incoming boundary layer turbulence. Additional observations performed at several wall-parallel planes at different height inside the cavity allow to further evaluate the secondary flow circulation generated by this asymmetric regime. The observed flow pattern consists of a steady vortex, occupying the entire cavity volume and placed diagonally inside the cavity such to entrain the external flow from one side, capture it into a circulatory motion and eject it from the opposite side of the cavity. The spatial distribution of the turbulent fluctuations also reveals the same structure. The tomographic PIV measurement returns a visual inspection to the instantaneous three-dimensional structure of the turbulent fluctuations, which at the investigated height exhibit a low level of coherence with slightly elongated vortices in the recirculating flow inside the cavity.     

Effect of external flow on the flow rate of a gas discharged through an orifice

The dependence of the flow coefficient of a gas jet ejected from an orifice/nozzle into a subsonic/transonic cross-flow on the flow and the jet Mach numbers, the off-design ratio, the nozzle inclination angle, β, and other determining parameters is considered. The physical nozzle flow pattern is constructed on the basis of experimental data obtained for 0.3< M_∞<1.75 and β=60°, 90°, and 120°. The results of measuring the pressure upstream and downstream of the orifice and on the windward and leeward orifice generators are presented. It is shown that the flow rate coefficient of a jet ejected into a cross-flow may exceed that of a similar jet outflowing into a flooded space. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 65–70, May–June, 1998.