Alexander Kartushinsky

Distribution characteristics of the mass concentration of coarse solid particles in a two-phase turbulent jet

Abstract In the paper the results of the mathematical modelling a horizontal two-phase turbulent round jet carrying coarse solid particles are presented. The numerical results are compared with the experimental data obtained in our laboratory. The goal of these investigations is to describe the distribution characteristics of the mass concentration of particles moving with a velocity lag which starts from the pipe outlet. These features are based on the intensive diffusion of particles with the rapid decrease of their concentration from the initial stage of the jet (scattering effect) and the less intensive diffusion giving a wave-like distribution of the mass concentration along the axis of the jet (intermediate effect). Such particle distributions in the jet are related to the specific motion of coarse particles in the pipe expressed by their lagging behind the gas. For the mathematical description, an algebraic model for the closure of the equations for the dispersed phase which is based on the inter-particle collision is used since the solid admixture in our experiments is a polydispersed powder. Along with the inter-particle collision, turbulent interaction between the phases resulting in the Reynolds stresses in the dispersed phase is also taken into account. In addition, the Magnus lift force contributes to the model due to the particle rotation and the velocity lag of the particles which enter the jet.

Deposition of solid particles in laminar boundary layer on a flat plate

Results are given of experimental and theoretical investigation of deposition of small solid particles on the surface of a flat plate under conditions of vertical laminar boundary layer. The present investigation is aimed at qualitatively and quantitatively estimating the effect made by the parameters of two-phase flow of the “gas—solid particles” type and by the adhesive properties of particles and surface on the deposition of particles on the plate surface. The flow velocity is 1.5 and 3 m/s. In so doing, the value of Reynolds number along the plate does not exceed 105. Synthetic corundum powders with average sizes of 12, 23, and 32 µm are used as the dispersed phase of two-phase flow. The mass concentration of particles in the flow is 0.01 kg/m3. A flat plate of stainless steel is used as the object of investigation. The distributions of gas velocity and concentration of particles within the boundary layer are measured using laser optical diagnostics. The number of particles deposited along the plate surface is measured by the gravimetric method. The adhesive properties of the “particle-surface” pair are studied using the centrifugal method of detachment of particles from the surface. Logarithmic-normal dependences of the number of adhesion of particles on the force of detachment are obtained. The hydrodynamic parameters of two-phase flow in the vicinity of the plate surface are calculated using the model of two-phase laminar boundary layer.The mathematical expression is suggested for the calculation of the magnitude of deposition of solid particles along the surface of a flat plate, which includes the special features of hydrodynamics of flow, the adhesive properties of the particles and surface, and the probabilistic pattern of the process of entrapment of particles by the surface.

Gas–Solid Particle Flow in Horizontal Channels: Decomposition of the Particle-Phase Flow and Interparticle Collision Effects

This paper examines the turbulent flow of heavy particles in horizontal channels and pipes. Calculations for the fluid are performed within an Eulerian frame of reference, while the particulate phase is considered as several continuous polydisperse media, each constituting a separate phase. The interparticle collisions include two mechanisms: collisions with sliding friction and collisions without sliding friction. The collisions of particles are accounted for, by collisions due to the difference in the average and fluctuating velocities of the several particulate fractions. This work introduces an original model for the closure for the mass and momentum equations based on the collisions as well as an original description of the particle motion in a horizontal channel, by introducing the decomposition of the particle-phase motion into two types of particle phases: falling and rebounding particles. The decomposition allows the correct calculation of the influence of the wall on the motion of particles.

Application of particle tracking velocimetry for studying the dispersion of particles in a turbulent gas flow

A method for the determination of the dispersion of solid particles in a turbulent gas flow has been presented. This method is based on recording the particle trajectories with a high-speed video camera on separate regions of a flow, located at various distances from a point source of particles, and the subsequent processing of the frames. This method has been used to study the dispersion of solid particles under the conditions of turbulence in a horizontal channel with a rectangular cross section of 200 × 400 mm for a measuring region length of 2 m. Turbulence of the gas flow was generated by means of a grid with square meshes of the size of 16 mm. The average velocity of the gas flow in the measuring region was 5.1 m/s. The dispersion of 36-, 56- and 128-micron glass particles of spherical shape was studied in a region 450 mm long from the point source of particles. It has been shown that the dispersion of these particles in the direction of the action of the gravity force is larger than their dispersion in the perpendicular direction to the gravity force. The results of this study have shown that an increase in the size of particles leads to a decrease in the dispersion at small flight times of the particles (short-time dispersion).

Grid-generated turbulence in two-phase flow: The effect of parameters of the carrier medium and particles

Results are given of an experimental investigation of the initial region of decay of grid-generated turbulence in a downward two-phase flow of the “gas-solid particles” type. Optical diagnostic methods are used to obtain the distributions of the dynamic parameters of two-phase flow, namely, averaged and fluctuation velocities of gas, and the curves of decay of turbulence along the flow axis are constructed for grids with square meshes sized 4.8, 10, and 16 mm. The investigation results demonstrate that solid particles 700 μm in size have varying effect on the degree of decay of turbulence. In the case of grids with small mesh sizes of 4.8 and 10 mm, the presence of such particles leads to additional generation of turbulence; in the case of a grid with mesh size of 16 mm, vice versa, the particles suppress the turbulence. Investigations reveal that these tendencies become still more pronounced with increasing concentration of particles. In addition, the investigation of the effect of velocity phase slip reveals that the generation of turbulence increases with the difference between phase velocities. In so doing, variation of the pattern of the effect of particles on turbulence is observed for a grid with large meshes, namely, the suppression of turbulence at low values of velocity slip and generation of turbulence with increasing slip. Based on the results of analysis of experimental data, a criterional parameter is suggested, which defines the effect of particles on the turbulence of two-phase flow, i.e., the ratio of the Reynolds number of particle to the turbulence Reynolds number for gas.

Deposition of Fine Solid Particles in Laminar Flat-Plate Boundary Layers

A method for the assessment of the deposition of fine solid particles in a vertical two-phase laminar flat-plate boundary layer is presented. The method is based on a probabilistic approach to the particles deposition and takes into account both the hydrodynamics of the flow past the plate and the adhesive properties of particles and the plate surface. Electrocorundum powders with particle sizes of 12, 23 and 32 μm were used for the investigations. A stainless steel hollow conical shape was used as a prototype surface for the particles deposition. The experimental investigation used the centrifugal technique for the deposition of particles and examined pairs of particles and surfaces for the characteristics of the deposition process. The results exhibited the typical log-normal distributions of the dependence of the deposition/adhesion process. An overall expression for the particles deposition flux was derived. The expression includes the normal to the surface velocity of the particles, the particle mass concentration observed immediately close to the surface of the plate and the surface of the plate. The hydrodynamic properties of the dispersed phase in the vicinity of the plate surface, namely the normal velocity and the particle mass concentration, were calculated by the mathematical model of the flat-plate laminar boundary layer elaborated in [1]. The validation of the proposed method of assessment of deposition was accomplished by comparing the deposition flux calculated along the plate with experimental data obtained in [2]. A small discrepancy between the numerical and experimental results was observed, which may be attributed to neglecting the microphysics of adhesion, such as the influence of the electric charges and humidity during the experiments.Copyright

RSTM Numerical Simulation of Channel Particulate Flow with Rough Wall

Turbulent gas-solid particles flows in channels have numerous engineering applications ranging from pneumatic conveying systems to coal gasifiers, chemical reactor design and are one of the most thoroughly investigated subject in the area of the particulate flows. These flows are very complex and influenced by various physical phenomena, such as particle-turbulence and particle-particle interactions, deposition, gravitational and viscous drag forces, particle rotation and lift forces etc.

3D RANS-RSTM Numerical Simulation of Channel Turbulent Particulate Flow with Wall Roughness

3D Reynolds stress turbulence model based on 3D Reynolds-averaged Navier-Stokes equations has been elaborated for the horizontal and vertical downward turbulent particulate flows in the channels of rectangular and square cross-sections with smooth and rough walls.

Mathematical Modelling of the Motion of Dust-Laden Gases in the Freeboard of CFB Using the Two-Fluid Approach

Fluidized beds are the units designed to provide fluid-solid contacting by the fluid flow through a bed of particles (Andrews and Arthur 2007). A number of thermal processes in technology take advantage of the importance of gas-solid interaction in fluidized beds to carry out gas-solid reactions, heterogeneous catalysis and particle drying. The gas-solid fluidization process in circulating fluidized beds is widely applied in many industrial branches. Characterization of the gas-solid particle flow in a circulating fluidized bed (CFB) riser is important for the process optimization. The particle size distribution has significant influence on the dynamics of gas-solid flow (He et al., 2008) along with another important property of the giving system, such as difference in the physical densities of the used materials. The gas-fluidized beds consist of fine granular materials that are subject to the gas flow from below giving the transport velocity that is large enough to overcome the gravity by the viscous drag force and thus the particles can suspend and be fluidized. When in the fluidized state, the moving particles work effectively as a mixer resulting in a uniform temperature distribution and high mass transfer rate, which are beneficial for the efficiency of many physical and chemical processes (Wang et al., 2005). For this reason the gasfluidized beds are widely applied in different industries: thermal, energy, chemical, petrochemical, metallurgical, and environmental industries in large-scale operations involving adhesion optimized coating, granulation, drying, and synthesis of fuels and base chemicals (Kunii & Levenspiel, 1991). In general, the lack of understanding of fundamentals of the dense gas–particle flows has led to severe difficulties in design and scale-up of these industrially important gas-solid contactors (van Swaaij, 1985). In most cases, the design and scale-up of fluidized bed reactors is a fully empirical process based on preliminary tests on pilot-scale model reactors, which is a very time consuming and thus expensive activity. Clearly, computer simulations can be a very useful tool to aid this design and scale-up process. In the CFB furnaces the ash solids and inert materials like sand particles are mainly used as a solid heat carrier – separated in a hot cyclone and cooled after that in a heat exchanger

The RANS, PDF and TBL Simulations of Turbulent Gas-Solid Particle Flow in Vertical Pipe

The numerical simulation of turbulent gas-solid particle flow in vertical round pipe is performed & analyzed by three different approaches: RANS 2D modeling, PDF approach (Zaichik’s model 2001) & by two-phase TBL (turbulent boundary layer approach). The given performances include all relevant force factors imposed on the motion of solid phase (two-fluid model is considered): particle-turbulence, particle-particle, particle-wall interactions, two-lift the Magnus & Saffman forces and buoyancy (gravitational) force. The dispersed phase is considered as a polydispersed phase composed of finite number of particle fractions and the mass & momentum equations are closed with the help of implementation of original “collision” model (Kartushinsky & Michaelides, 2004). The two/four-way coupling model of Gillandt & Crowe (1998) is accounted for turbulence modulation. The numerical results show that retaining of second diffusion terms in both directions (in streamwise & transverse directions) aligns the average x-velocity components of gas and dispersed phases as well as the particle mass concentration and k-profiles across the flow in case of both PDF and RANS 2D approaches that versus the distributions of parameters obtained by two-phase TBL approach. This is reasonable due to additional effect of fluxes diffusion of the carrier fluid & solid phase in the main direction derived from turbulence fluctuation and inter-particle collision which smoothes the profile shapes.Copyright