Pulsating motion of an inhomogeneous solid sphere in a vibrating liquid

The problem of rotational vibrations of an inhomogeneous solid body (a sphere) in a uniformly vibrating ideal liquid under gravity is considered. New hydromechanical effects are reported.     

Change of regime in supersonic flow past an obstacle preceded by a thin channel of reduced density

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 146–151, September–October, 1989.     

Pulsating flow in a heat exchanger

The problem of heat transfer in industrial processes, heat exchangers, and combustion chambers is formulated for a case where flow inside the chamber consists of a periodic motion imposed on a fully developed turbulent flow. It is shown that the velocity pulsations induce harmonic oscillations in temperature, thus breaking the temperature field into a steady mean part and a harmonic part. The interaction between the velocity and temperature oscillations introduces an extra term into the energy equation which reflects the effect of pulsations in producing higher heat transfer rates. The analysis shows that when the mean temperature is fully developed with constant heat flux at the wall, there is no effect of the velocity pulsations on the total heat transfer rate along the chamber. For the case where the mean temperature profile is not fully developed, analytical solutions are obtained for asymptotic values of the pulsations frequency. The results show the temperature gradient and its dependence on the frequency. These results are used to evaluate the feasibility of pulsating the flow in a heat exchanger for obtaining higher rates of heat transfer.     

Pulsating liquid flow past a spherical body in an infinite cylinder

The problem of determination of the hydrodynamic characteristics of an ideal incompressible liquid moving with constant velocity past a spherical body in an infinite circular cylinder is considered. It is assumed that the cylinder axis passes through the mass center of the spherical body. The total liquid potential has been constructed both in spherical and cylindrical coordinate systems. The hydrodynamic characteristics of the flow in the cylinder were researched based upon comparison with the corresponding characteristics of the liquid flow of a spherical body in a boundless medium. S. P. Timoshenko Mechanics Institute, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 6, pp. 27–31, June, 1999.     

Pulsating turbulent pipe flow in the current dominated regime at high and very-high frequencies

The paper presents Direct Numerical Simulations of sinusoidal pulsating turbulent flow, at low bulk Reynolds numbers, with high frequency, in a straight pipe. Our objective is to study pulsating flow considering it as the superposition of a temporal unsteadiness on a mean current, and from this viewpoint, to decompose the flow in a mean and an oscillating part. Firstly, we examine the time-averaged statistics, which show that the parent flow retains its properties. Then, we analyze the oscillating part of the flow, and confirm the notion that for rapidly pulsating flow, the amplitude of the streamwise velocity and the phase lag at different radial locations follow the solution of the laminar Stokes problem. In addition, we find that the modulation of the turbulent fluctuations follows approximately the sinusoidal form of the imposed pulsation, and that the ratio of the frequency parameter to the amplitude of the streamwise velocity can be used as a scaling factor. We investigate the effects of the amplitude and the frequency of the imposed unsteadiness on the modulation of the time-averaged properties and the turbulence statistics, through a systematic analysis. Finally, we examine the time evolution of the mean velocity and the turbulent fluctuations. These results indicate that a lower limit for the high frequency regime can be identified, based on the level of conformity of the phase-averaged profiles on their steady-state counterparts. For very high frequencies, we find that that the flow behavior does not change, indicating the absence of an upper limit for the high frequency regime.     

Stability of an inhomogeneous vibrationally-nonequilibrium flow in a waveguide

The stability of an inhomogeneous subsonic vibrationally-nonequilibrium flow is examined in the linear approximation. It is shown that the nonequilibrium flow stability is reduced with increase in the initial flow velocity and the energy pumping zone width. This is attributed to the effect of the feedback due to acoustic disturbances propagating counter to the flow. Calculations are carried out for different pumping models.     

Separation zone in fluctuating flow past an obstacle in a channel

The results of an experimental investigation of hydrodynamic processes in separated turbulent flows in the presence of superimposed flow-rate fluctuations are presented. A sharp shortening of the separation zone in the fluctuating flow is found to exist in the vicinity of Sh = 1. The dependence of the separation zone length on the superimposed fluctuation frequency is the same in the cases in which the obstacle is located in the regions of antinodes of both the flow velocity and the pressure.     

Asymptotic theory of the flow around an obstacle by a sonic flow

The first investigation of the problem of the flow around an obstacle by a gas flow whose velocity is equal to the speed of sound at infinity was carried out in [1, 2], where it is shown in particular that the principal term of the appropriate asymptotic expansion is a self-similar solution of Tricomi's equation, to which the problem reduces in the first approximation upon a hodographic investigation. The requirement that the stream function be analytic as a function of the hodographic variables on the limiting characteristic was an important condition determining the selection of the self-similarity exponent n (xy^–n is an invariant of the self-similar solution). The analytic nature of the velocity field everywhere in the flow above the shock waves, which arise from necessity upon flow around an obstacle, follows from this condition. The latter was found in [3], where one of the branches of the solution obtained in [1] was used in the region behind the shock waves. The principal and subsequent terms of the asymptotic expansion describing a sonic flow far from an obstacle were discussed in [4], where the author restricted himself to Tricomi's equation. Each term of the series constructed in [4] contains an arbitrary coefficient (we will call it a shape parameter) which is not determined within the framework of a local investigation, and consideration of the problem of flow around a given obstacle as a whole is necessary in order to determine these shape parameters. It follows from the results of [4] that the problem of higher approximations to the solution of [1] coincides with the problem, of constructing a flow in the neighborhood of the center of a Laval nozzle with an analytic velocity distribution along the longitudinal axis (a Meyer-type flow). Along with the Meyer-type flow in the vicinity of the nozzle center, which corresponds to a self-similarity exponent n=2, two other types of flow are asymptotically possible with n=3 and 11, given in [5]. The appropriate solutions are written out in algebraic functions in [6]. The results of [5] show that the condition that the velocity vector be analytic on the limiting characteristic in the flow plane is broader than the condition that the stream function be analytic as a function of the hodographic variables, which is employed in [1, 2, 4]. Therefore, the necessity has arisen of reconsidering the problem of higher approximations for the obstacle solution of F. I. Frankl'. It has proved possible for the region in front of the shock waves to use a series which is more general than in [4], which implies the inclusion of an additional set of shape parameters. The solution is given in the hodograph plane in the form of the sum of two terms; the series discussed in [4] corresponds to the first one, and the series generated by the self-similar solution with n=3 or with n=11 corresponds to the second one.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 99–107, May–June, 1979.The authors thank S. V. Fal'kovich for a useful discussion.     

Investigation of hot-fluid cavitating flow through an obstacle in a pipeline

The results of investigating hot-fluid cavitating flow in a pipe with a local contraction are presented for a broad temperature interval (water from cold to near-boiling) and various cavitation regimes — from the initial (bubble) to the supercavitation regime. Experimental relations for the amplitudes of the fluctuations and the fundamental frequencies are presented for a Venturi tube with various diffusers and for diaphragms of various dimensions. A flow model which takes into account the fluctuations of the vapor pressure in the cavity and, moreover liquid-cavity mass transfer effects is presented. It is shown that for a given flow geometry there is a limiting Jakob number below which the self-oscillating regime is impossible at any cavitation numbers.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.4, pp. 124–133, May–June, 1993.     

Anomalous two-layer flow regimes over an obstacle

Journal of Applied Mechanics and Technical Physics -     

Pulsating slurry flow in pipelines

An experimental study on pulsating turbulent flow of sand-water suspension was carried out. The objective was to investigate the effect of pulsating flow parameters, such as, frequency and amplitude on the critical velocity, the pressure drop per unit length of pipeline and hence the energy requirements for hydraulic transportation of a unit mass of solids. The apparatus was constructed as a closed loop of 11.4 m length and 3.3 cm inner diameter of steel tubing. Solid volumetric concentrations of up to 20% were used in turbulent flow at a mean Reynolds number of 33,000–82,000. Pulsation was generated using compressed air in a controlled pulsation unit. Frequencies of 0.1–1.0 Hz and amplitude ratios of up to 30% were used. Instantaneous pressure drop and flow rate curves were digitized to calculate the energy dissipation associated with pulsation. The critical velocity in pulsating flow was found to be less than that for the corresponding steady flow at the same volumetric concentration. Energy dissipation for pulsating flow was found to be a function of both frequency and amplitude of pulsation. A possible energy saving was indicated at frequencies of 0.4–0.8 Hz and moderate amplitudes ratios of less than 25%.List of symbols A cross-section area of the tube (m²) - C _D drag coefficient of sand particles - C _v volumetric concentration (%) - D inner diameter of test-section pipe (m) - F frequency (Hz) - f friction factor - g gravitational constant (m/s²) - J energy dissipation of suspension (W/m)/(kg/s) - J _p energy dissipation of pulsating suspension (W/m)/(kg/s) - J _s energy dissipation of steady component of suspension (W/m)/(kg/s) - J _w energy dissipation of pure water (W/m)/(kg/s) - L length of test-section (m) - m mass flow rate (kg/s) - P pressure drop in test-section (N/m²) - S specific gravity of sand - V instantaneous flow velocity (m/s) - V _c steady flow critical velocity (m/s) - V _cp pulsating flow critical velocity (m/s) - V _F settling velocity of particles (m/s) - V _s steady component of mean flow velocity (m/s) - dynamic viscosity (g/cm sec) - _m mean density of suspension (kg/m³) - angular velocity (rad/sec) - amplitude ratio (V — V _s)/V - nondimentional factor equal to - nondimentional factor equal to (V–V _s/V - NI nondimentional factor equal to (V ²C _d/g D(S – 1)) - Re Reynolds number (V ²C _d/C _v g D(S – 1))     

Vortex flow adjacent to a stationary surface

The radius of transition from an inner core of solid body rotation to an outer free vortex motion was determined via the momentum integral method.     

Pressure oscillation on a plane upstream of an obstacle in a supersonic flow

The levels and spectra of pressure oscillation on a plane upstream of a vertical cylinder and a step in an M=3 supersonic flow are measured in the presence of a turbulent boundary layer. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 69–74, January–February, 1998.     

Foam flow around an obstacle: simulations of obstacle–wall interaction

The flow of a two-dimensional foam around an obstacle provides a benchmark experiment in which to study the transition from discrete to continuous properties of this complex fluid. The interaction between the obstacle and the walls of the channel is simulated using the Surface Evolver. The lift and drag forces on a circular obstacle are measured and the contributions to the total force of the film network and the bubble pressures are assessed. As the distance of the obstacle from the wall decreases, the lift force is found to increase significantly whereas the drag force does not vary greatly.A paper presented at the AERC 2005     

Pulsating motions of a solid particle in turbulent flow

The relations governing the transverse pulsations of a spherical particle in a turbulent flow are examined. On the basis of the resulting relations an estimate is made of the effect of several factors on the intensity of the velocity pulsations of the solid component in dispersed flow through a conduit.