Effect of a Dispersed Admixture on the Flow Pattern and Heat Transfer in a Supersonic Dusty-Gas Flow Around a Cylinder

A mathematical model of two-phase (gas-solid particle) flow which takes into account particle-particle collisions and the feedback effect of the admixture on the gas parameters is proposed. The dispersed phase is described by a kinetic equation of the Boltzmann type and the carrier gas by modified Navier-Stokes equations. Using this model, a supersonic uniform dusty-gas flow past a cylinder is calculated. The fields of the macroparameters of the admixture and the carrier medium are obtained. The dependence of the heat transfer at the stagnation point on the relative particle size and the free-stream admixture concentration is studied in detail. The ranges of these parameters on which particle collisions and the feedback effect of the admixture on the carrier-gas flow are important are found.     

Viscous fluid flow around a semipermeable particle

The problem of hydrodynamic interaction between a laminar flow of a viscous fluid and a partially permeable spherical particle is formulated and solved analytically. The filtration flow inside the particle is assumed to obey the Darcy law. Expressions for the filtration flow velocity, drag, sedimentation velocity, and stream functions are obtained. The effect of the permeability of the particle on the flow characteristics is studied. Stream functions of the flow are constructed. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 48–53, July–August, 2009.     

Effect of particle size on nonlinear wave propagation in a fluidized bed

The effect of particle size (Archimedes number) on the propagation of a kinematic particle concentration wave in a fluidized bed is investigated. The dependence of the characteristic wave velocity on the porosity of the bed (particle concentration) and the Archimedes number (or the Reynolds number for flow past individual particles of the dispersed phase) is determined. The evolution of a nonlinear perturbation of the bed porosity is investigated and the formation of discontinuities in the concentration of the dispersed phase is studied in relation to the particle size (Archimedes number). It is shown, in particular, that, as distinct from a bed of small particles, in a bed of large particles with quadratic interphase interaction only compression discontinuities can be formed. The results obtained can be used to analyze the formation of inhomogeneities (slugs and bubbles) in a fluidized bed in relation to the particle size.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 96–100, May–June, 1987.     

Shock wave interaction in a dusty gas and the appearance of fully dispersed waves

A problem of regular (symmetric and asymmetric) interaction of plane shock waves in a steady-state dusty-gas flow is considered. The possibility of the formation of wave structures is revealed, in which either all or some of the incident or reflected waves degenerate into fully dispersed waves, i.e. zones in which the parameters of both phases vary continuously. Using the Rankine-Hugoniot relations for a one-velocity “effective-gas” model, the ranges of nondimensional governing parameters (the Mach number, the angles between the incident waves and the free stream, the phase specific-heat ratio, and the particle mass concentration) are found, which correspond to different wave configurations. In the framework of a two-fluid dusty-gas model, the flow structure in the region of symmetric interaction of the shocks is calculated numerically for typical configurations containing fully dispersed waves. The flow in the region of a normal fully dispersed wave is also calculated. Good agreement between the calculated wave structure and the data known in the literature is obtained. A range of governing parameters in which the carrier-phase temperature has a local maximum inside the wave structure is found.     

The effect of particles on fluid turbulence in a turbulent boundary layer over a cylinder

The turbulent fluid and particle interaction in the turbulent boundary layer for cross flow over a cylinder has been experimentally studied. A phase-Doppler anemometer was used to measure the mean and fluctuating velocities of both phases. Two size ranges of particles (30μm–60μm and 80μm–150μm) at certain concentrations were used for considering the effects of particle sizes on the mean velocity profiles and on the turbulent intensity levels. The measurements clearly demonstrated that the larger particles damped fluid turbulence. For the smaller particles, this damping effect was less noticeable. The measurements further showed a delay in the separation point for two phase turbulent cross flow over a cylinder. The project supported by the National Natural Science Foundation of China     

Droplet coalescence in the shear flow of model emulsions

During the flow of an emulsion, droplets of the dispersed phase can deform, break up, coalesce or migrate to other regions within the flow field. Understanding these different processes is relevant to morphology development in immiscible polymer blends. Here, emulsions of castor oil in silicone oil were employed to study shear-induced coalescence alone; the conditions chosen were such that drop breakup and drop migration did not occur. A cone-and-plate device and tubes of varying length were used to examine the influence of the average shear rate, the time of shearing, concentration of the dispersed phase, and temperature on the average droplet size. It was found that the extent of “demixing” was not influenced by the spatially non-homogeneous nature of flow in a tube; results correlated very well with the average shear rate. On the other hand, coalescence was significant even when the concentration of the dispersed phase was as low as 0.5%, and it became more important as the concentration was increased. Other results were that the extent of coalescence could be promoted by lowering the shear rate. In quantitative terms, it was found that available coalescence theory gave the correct order of magnitude for the average steady-state droplet size as a function of the imposed shear rate, but the actual variation of drop size with shear rate was gentler than that predicted by theory. An unusual observation was that, under some circumstances, the droplets did not coalesce but simply stuck to each other and maintained their separate identity. Received: 25 March 1999/Accepted: 22 July 1999     

Effect of Interphase Heat Transfer on the Stability of a Turbulent Multicomponent Flow in a Vortex

The parameters of an axisymmetric turbulent two-phase swirling flow of a viscous heat-conducting gas containing a liquid dispersed phase in the presence of water vapor condensation on the particles are calculated. For the dispersed phase, a model taking into account the variation of the vapor concentration and the particle size due to condensation or evaporation is proposed. The distributions of the parameters of the basic unperturbed flow obtained numerically are used in the numerical solution of the linear problem of hydrodynamic stability within the time-dependent formulation. The parameters of small-amplitude harmonic perturbations propagating along the vortex axis are investigated in the linear formulation. A significant effect of heat release in the gas due to water vapor condensation on the parameters of the neutral perturbations and the neutral-stability curves is detected.     

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.     

PIV measurements in a liquid–liquid system at volume percentages up to 10% dispersed phase

In this study the effect of the volume percentage dispersed phase on the flow structure in an immiscible liquid–liquid system is investigated. A model system, consisting of two refraction index matched liquids, is presented along with velocity measurements of the continuous phase utilising the particle image velocimetry technique. Velocity fields at three locations have been measured inside a baffled cylindrical tank, stirred with a six-bladed Rushton turbine. The experiments show that this technique is applicable for volume fractions of up to 10% of dispersed phase. The magnitudes of velocity and turbulence are clearly affected by the level of the dispersed volume fraction.     

Modeling of the unsteady force for shock–particle interaction

The interaction between a particle and a shock wave leads to unsteady forces that can be an order of magnitude larger than the quasi-steady force in the flow field behind the shock wave. Simple models for the unsteady force have so far not been proposed because of the complicated flow field during the interaction. Here, a simple model is presented based on the work of Parmar et al. (Phil Trans R Soc A 366:2161–2175, 2008). Comparisons with experimental and computational data for both stationary spheres and spheres set in motion by shock waves show good agreement in terms of the magnitude of the peak and the duration of the unsteady force.      

Measurements of concentration per size class in a dense polydispersed jet using planar laser-induced fluorescence and phase Doppler techniques

In dense two-phase flows, it is well known that phase Doppler anemometry is not well suited for the measurement of concentration and mass flux. Laser diagnostics based on fluorescence can provide the dispersed phase concentration but without discrimination between size classes. We present a new method of coupling the two techniques, in order to extract the local value of concentration and flux per size class. The method is applied to an axisymmetric turbulent jet, laden with polydispersed droplets 1–90 μm. Droplet concentration profiles are obtained in the development zone (x/d ₀ < 20) of the dense jet and are used to study droplet dispersion. The results are then introduced into the momentum transport equations to analyze the influence of droplets on the carrier phase. We show that the local decrease of the rate of variation of mean momentum with mass loading is due both to an increase in interfacial transfer rate and to a decrease in turbulent diffusion effects. Received: 20 November 2000 / Accepted: 3 April 2001     

Turbulent Flow and Dispersion of Inertial Particles in a Confined Jet Issued by a Long Cylindrical Pipe

In this work we examine first the flow field of a confined jet produced by a turbulent flow in a long cylindrical pipe issuing in an abrupt angle diffuser. Second, we examine the dispersion of inertial micro-particles entrained by the turbulent flow. Specifically, we examine how the particle dispersion field evolves in the multiscale flow generated by the interactions between the large-scale structures, which are geometry dependent, with the smaller turbulent scales issued by the pipe which are advected downstream. We use Large-Eddy-Simulation (LES) for the flow field and Lagrangian tracking for particle dispersion. The complex shape of the domain is modelled using the immersed-boundaries method. Fully developed turbulence inlet conditions are derived from an independent LES of a spatially periodic cylindrical pipe flow. The flow field is analyzed in terms of local velocity signals to determine spatial coherence and decay rate of the coherent K–H vortices and to make quantitative comparisons with experimental data on free jets. Particle dispersion is analyzed in terms of statistical quantities and also with reference to the dynamics of the coherent structures. Results show that the particle dynamics is initially dominated by the Kelvin–Helmholtz (K–H) rolls which form at the expansion and only eventually by the advected smaller turbulence scales.     

Effect of the boundary layer on the base pressure in a two-dimensional flow with a Mach number M = 5

New data on the base pressure in a two-dimensional ow with a Mach number M = 5 are obtained for a wide range of variation of the normalized boundary-layer thickness in the flow-separation cross section. The test results are compared with Tanner’s theory, and a conclusion is made that this numerical model has to be corrected. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 23–28, May–June, 2005.     

Behavior of the unsteady jet of a mixture of a pressurized gas and dispersed particles discharged from a circular duct into the atmosphere

The unsteady axisymmetric jet produced by discharge of a mixture of a pressurized gas and dispersed particles from a circular duct into the atmosphere is studied within the framework of two-velocity, two-temperature gas dynamics. An attempt is undertaken to allow for the effective pressure due to random particle motion. The collision mechanism is found to be essential to radial expansion of the flow. Experimental data that support the results obtained are reported. Mozhaiskii Military Spacecraft Engineering Academy, St. Petersburg 197082. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 151–157, January–February, 1999.     

Optimal disturbances of a dusty-gas plane-channel flow with a nonuniform distribution of particles

The classical stability theory for multiphase flows, based on an analysis of one (most unstable) mode, is generalized. A method for studying an algebraic (non-modal) instability of a disperse medium, which consists in examining the energy of linear combinations of three-dimensional modes with given wave vectors, is proposed. An algebraic instability of a dusty-gas flow in a plane channel with a nonuniform particle distribution in the form of two layers arranged symmetrically with respect to the flow axis is investigated. For all possible values of governing parameters, the optimal disturbances of the disperse flow have zero wavenumber in the flow direction, which indicates their banded structure (“streaks”). The presence of dispersed particles in the flow increases the algebraic instability, since the energy of optimal disturbances in the disperse medium exceeds that for the pure-fluid flow. It is found that for a homogeneous particle distribution the increase in the energy of optimal perturbations is proportional to the square of the sum of unity and the particle mass concentration and is almost independent of particle inertia. For a non-uniform distribution of the dispersed phase, the largest increase in the initial energy of disturbances is achieved in the case when the dust layers are located in the middle between the center line of the flow and the walls.     

Shock-induced Near-wall Two-phase Flow Structure Over a Micron-sized Particles Bed

The present paper studies numerical modelling of near-wall two-phase flows induced by a normal shock wave moving at a constant speed, over a micron-sized particles bed. In this two-fluid model, the possibility of particle trajectory intersection is considered and a full Lagrangian formulation of the dispersed phase is introduced. The finiteness of the Reynolds and Mach numbers of the flow around a particle as well as the fineness of the particle sizes are taken into account in describing the interactions between the carrier- and dispersed-phases. For the small mass-loading ratio case, the numerical simulation of flow structure of the two phases is implemented and the profiles of the particle number density are obtained under the constant-flux condition on the wall. The effects of the shock Mach number and the particle size and material density on particle entrainment motion are discussed in detail. The obtained results indicate that interphase non-equilibrium in the velocity and temperature is a common feature for this type of flows and a local particle accumulation zone may form near the envelope of the particle trajectory family.     

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.     

Experimental investigation of the active compensation of the electric charge of a body in a flow with ions and charged drops

Results of experimental investigation of the problem of active control of the charge acquired by a body (sphere) in flow with an electrically charged component (ions) and electrically charged dispersed phase (water drops) are obtained and analyzed. This situation is not uncommon during aircraft flight in a cloud front. Previous experimental studies have mainly considered flows without a dispersed phase. The required flow was created by introducing in a turbulent air-steam jet a corona discharge on whose ions “electric” condensation developed and on the growing drops that arose a charge was accumulated due to diffusion processes and directional ion motion in the electric field. On the sphere which was introduced in the charged jet a discharger (active compensator) with an autonomous high-voltage power source creating a potential difference between the discharger corona needle insulated from the body and the body surface was mounted. Measurements of the size and concentration of the drops ahead of the critical point of the sphere were performed. The electric currents to elements of the experimental electric system and the floating potential of the body were measured for various corona charge parameters and various voltages on the active compensator. An active control of the sphere charge, its complete removal and the recharge of the sphere, is realized.     

Experimental studies on heat transfer and friction factor characteristics of CuO/water nanofluid under laminar flow in a helically dimpled tube

An experimental investigation on the convective heat transfer and friction factor characteristics in the plain and dimpled tube under laminar flow with constant heat flux is carried out with distilled water and CuO/water nanofluids. For this, CuO nanoparticles with an average size of 15.3 nm were synthesized by sol–gel method. The nanoparticles are then dispersed in distilled water to form stable suspension of CuO/water nanofluid containing 0.1, 0.2 and 0.3% volume concentration of nanoparticles. It is found that the experimental Nusselt numbers for 0.1, 0.2 and 0.3% volume concentration of CuO nanoparticles are about 6, 9.9 and 12.6%, respectively higher than those obtained with distilled water in plain tube. However, the experimental Nusselt numbers for 0.1, 0.2 and 0.3% volume concentration of CuO nanoparticles are about 3.4, 6.8 and 12%, respectively higher than those obtained with distilled water in dimpled tube. The friction factor of CuO/water nanofluid is also increased due to the inclusion of nanoparticles and found to increase with nanoparticle volume concentration. The experimental results show that there exists a difference in the enhancement levels of Nusselt numbers obtained with nanofluids in plain tube and dimpled tube. Hence it is proposed that the mechanism of heat transfer enhancement obtained with nanofluids is due to particle migration from the core of fluid flow to tube wall.