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The purpose here is to discuss and review advances in two-phase turbulent modeling techniques and their applications in various gas-solid suspension flow situations. In addition to the turbulence closures, heat transfer effect, particle dispersion and wall effects are partially covered.
Heat transfer coefficients of air-glass, argon-glass, and argon-aluminum suspensions were measured in horizontal and vertical tubes. The glass, 21.6 and 36.0 micron diameter particles, was suspended at gas Reynolds numbers between 11,000 and 21,000 and loading ratios between 0 and 2.5. The presence of particles generally reduced the heat transfer coefficient. The circulation of aluminum powder in the 0.870 inch diameter closed loop system produced tenacious deposits on protuberances into the stream. In the vertical test section, the Nusselt number reduction was attributed to viscous sublayer thickening; in the horizontal test section to particle deposition.
Particle dispersion in confined recirculating turbulent flows has been investigated numerically. The present computational scheme utilizes Eulerian forms of the governing equations and allows two-way coupling between gas and solid phases. A recently developed two-phase closure model based on the multiple-scale turbulence model was used for the estimation of turbulent viscosities and diffusivities. For the particle size and loading considered in this study, the effect of particulate phase on the conveying gas is small, the nonequilibrium between the two phases is significant. Effects of recirculation, expanded chamber size and secondary annular jet momentum on the particle mixing rate are also investigated. In general, the present numerical results are in reasonably good agreement with the available experimental data.
Measurements were performed on dilute flowing gas-solids suspensions and included data, with particles present, on gas friction factors, velocity profiles, turbulence intensity profiles, turbulent spectra, and particle velocity profiles. Glass beads of 10 to 60 micron diameter were suspended in air at Reynolds numbers of 10,000 to 25,000 and solids loading ratios from 0 to 4. Drag reduction was achieved for all particle sizes in vertical flow and for the smaller particle sizes in horizontal flow. The profile measurements in the vertical tube indicated that the presence of particles thickened the viscous sublayer. A quantitative theory based on particle-eddy interaction and viscous sublayer thickening has been proposed.
Modified Runge-Kutta analysis of one-dimensional nozzle flow of gas-solid suspension, noting electrostatic effects
Experimental determination of pressure drop and flow characteristics of dilute gas-solid suspensions in turbulent pipe flow
Heat transfer coefficient, friction factor, and pressure drop analyzed in flow of gas - solid dilute suspension
From both experimental data and theoretical results of the two-phase flow, the complete expression of the interaction force between a gas and solid particles at low Reynolds number flow is obtained. The interaction force contains two terms: one is proportional to the difference between the velocities of the gas and the solid particle with a coefficient as a function of volume fraction Z and the other is proportional to the product of the total pressure of the mixture and the gradient of solid volume fraction. The second term is new. When Z tends to 0, the completion expression of interaction force reduces to the well-known Stokes formula.
Loading ratio, glass particle size, and air Reynolds number effects on pressure drop and flow characteristics of air-solid suspension in turbulent pipe flow
Numerical calculations have been carried out for gas-particle confined turbulent flows using a recently developed two-phase turbulence closure model. The present modeling scheme utilizes Eulerian formulations of the transport equations and accounts for the combined effects of interphase slip and turbulent dispersion of particles. A multiple-scale turbulence model is used for the turbulent field modeling of the underlying fluid flow. For the particle size and particle loading considered in this study, the fluid turbulence transport equations must be modified to include the damping effects of particles. Predictions and comparisons are made in the fully developed gas-solid pipe flow and the confined particle-laden jet. Numerical results are in reasonably good agreement with the published experimental information.
This paper addresses turbulent particle dispersion and modulation effects in dilute gas-particle turbulent flows using the Eulerian and Lagrangian modeling approaches. Gradient diffusion approximations are employed in the Eulerian formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangian formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. For the particle size and loading considered, the turbulence transport equations must be modified to account for the modulation effects. Models are proposed for both Eulerian and Lagrangian schemes. Comparisons and predictions are made in fully developed gas-solid pipe flow and confined coaxial jets laden with particles. For the monodispersed system investigated, Eulerian approach is less expensive and gives more consistent results than the Lagrangian approach. The Lagrangian technique should be further developed to eliminate current inherent inconsistencies especially with regard to the symmetry boundary condition.
Gas-solid particles flow pseudofluid equations, discussing difference of species and partial density and various flow phases
Scaling factors determining various aspects of particle-fluid interactions and the development of physical models to predict gas-solid turbulent suspension flow fields are discussed based on two-fluid, continua formulation. The modes of particle-fluid interactions are discussed based on the length and time scale ratio, which depends on the properties of the particles and the characteristics of the flow turbulence. For particle size smaller than or comparable with the Kolmogorov length scale and concentration low enough for neglecting direct particle-particle interaction, scaling rules can be established in various parameter ranges. The various particle-fluid interactions give rise to additional mechanisms which affect the fluid mechanics of the conveying gas phase. These extra mechanisms are incorporated into a turbulence modeling method based on the scaling rules. A multiple-scale two-phase turbulence model is developed, which gives reasonable predictions for dilute suspension flow. Much work still needs to be done to account for the poly-dispersed effects and the extension to dense suspension flows.
Recent studies in the theory of rarefied gases (kinetic theory, shock structure, molecular forces and interactions, evaporation and condensation, expansions and jets, flow past bodies, gas-solid interactions) are presented along with descriptions of numerous experiments in these areas. Some of the topics covered include: singular limits of solutions of Boltzmann's equations, the Boltzmann and Klimontovich formalisms with reference to turbulent resolution, higher-order kinetic theory for the Lorentz gas, intermolecular potentials from shock structure experiments, cooling of particles in aerosol beams, hypersonic-subsonic transition in spherically symmetric expanding flows, absolute velocity measurements in a rarefied gas flow by an ion time-of-flight technique, the product distribution of gas-solid reactions from absolute rate theory, and relaxation of a gas with internal degrees of freedom. Individual items are announced in this issue.
Heat transfer rates in turbulent flow of heated gas-solid mixtures through converging-diverging nozzle
Mathematical and physical modeling of turbulence phenomena in metals processing, electromagnetically driven flows in materials processing, gas-solid reactions, rapid solidification processes, the electroslag casting process, the role of cathodic depolarizers in the corrosion of aluminum in sea water, and predicting viscoelastic flows are described.
Momentum and energy accommodation for hypervelocity gas particles on crystal surface, using Lennard Jones potential and approximating lattice by system of independent forced harmonic oscillators
The light off transient of catalytic combustion of lean CO-air mixtures in a platinum coated channel of a honeycomb monolith is studied with a model that resolves transient radial and axial gradients in both the gas and the solid. For the conditions studied it is concluded that: the initial heat release occurs near the entrance at the gas-solid interface and is controlled by heterogeneous reactions; large spatial and temporal temperature gradients occur in the solid near the entrance controlled mostly by the availability of fuel; the temperature of the solid near the entrance achieves almost its steady state value before significant heating of the back; heterogeneous reactions and the gas heated up front and flowing downstream heat the back of the solid; the overall transient time is controlled by the thermal inertia of the solid and by forced convection; radiation significantly influences both transient and steady state particularly near the entrance; the oxidation of CO occurs mostly on the catalyst and becomes diffusion controlled soon into the transient.