David J. Mason

A computational investigation of transient heat transfer in pneumatic transport of granular particles

Abstract The Distinct Element Method (DEM) has been employed to model a range of gas–solids flow systems such as solids flow in hoppers, gas–solids pipe flow and particulate fluidized bed. But little has been reported on the application of this technique to heat transfer in gas–solids flows. This paper describes a numerical model for gas–solids two-phase flow with heat transfer in pneumatic transport pipes. The gas phase is modelled as a continuum and the solids phase is modelled by DEM. Convective heat transfer between gas and particles and between gas and pipe wall, and conductive heat transfer between particles and between particles and pipe wall are modelled. The influence of particle concentration on the predicted performance of the system has been compared with experimental data. This comparison has shown a good agreement between the DEM simulation and experiment for both pressure drop and pipe wall temperature profile at developed flow region.

The effect of a bend on the particle cross-section concentration and segregation in pneumatic conveying systems

Abstract The effect of a bend on the distribution of particles in a pipe cross section and segregation in pneumatic conveying systems has been investigated numerically. The numerical model solved the finite-volume equations for the conservation of mass and momentum for two phases. The predictions of the numerical model were compared qualitatively with various published experimental data. It was evident that the cross-sectional concentration of the particles a few metres after a bend is not uniform and that the particles tend to concentrate around the pipe wall. Various cross-sectional concentrations of particles were found for different pipe-to-bend radius ratios, particle sizes and direction of gravity (i.e., horizontal-to-vertical flow, and horizontal-to-horizontal flow). Based on the different cross-sectional concentrations for different particle sizes, it was concluded that the paths taken by the particles after the bend were strongly dependent upon their sizes. Since a real particulate phase (i.e., powder, granular material, etc.) is composed of particles with a range of sizes, this would lead to segregation of the particles in the pipe section following a bend. Hence, a better understanding of the segregation process in a pneumatic conveying system was obtained.

APPLICATION OF THE DISCRETE ELEMENT MODELLING IN AIR DRYING OF PARTICULATE SOLIDS

ABSTRACT The Discrete Element Method (DEM) has been widely used as a mathematical tool for the study of flow characteristics involving particulate solids. One distinct advantage of this fast developing technique is the ability to compute trajectories of discrete particles. This provides the opportunity to evaluate the interactions between particle, fluid and boundary at the microscopic level using local gas parameters and properties, which is difficult to achieve using a continuum model. To date, most of these applications focus on the flow behaviour. This paper provides an overview of the application of DEM in gas–solids flow systems and discusses further development of this technique in the application of drying particulate solids. A number of sub-models, including momentum, energy and mass transfer, have been evaluated to describe the various transport phenomena. A numerical model has been developed to calculate the heat transfer in a gas–solids pneumatic transport line. This implementation has shown advantages of this method over conventional continuum approaches. Future application of this technique in drying technology is possible but experimental validation is crucial.

A comparison of analytical and numerical models with experimental data for gas-solid flow through a straight pipe at different inclinations

An analytical model for gas-solid suspension flow through an inclined section of pipe was developed. This model predicts the ratio of the total pressure drop in an inclined pipe to that of a horizontal pipe. The model has been used to predict the critical pipe angle, which is defined as the angle at which the maximum pressure drop for a given solids flow rate is achieved. This angle differs from 90° (found in a single-phase flow) and is directly proportional to the ratio between the gas superficial velocity and the particle terminal velocity. The three-dimensional conservation equations for steady-state two-phase flow in an inclined pipe were solved numerically for constant solids and gas flow rates at different pipe inclinations. This model was based on the continuum theory for describing the mass and momentum balance equations for the fluid and solid phases. A packing model, describing the shear stress of the solid phase as a function of its volume fraction, is suggested in order to limit the maximum value of the solid volume fraction. A new model for particle-wall interaction was developed taking into account the angle of inclination of the pipe. The prediction of the numerical model was compared with experimental data obtained in a specially designed test rig. In general, the agreement between the experimental data and the models was satisfactory. The results of the numerical simulation also confirmed that the critical pipe angle for gas-solid flow is lower than 90°. The assumptions made during the development of the models were assessed in order to explain the differences between the predicted and measured values of the flow parameters for different flow regimes.

A model for non-suspension gas-solids flow of fine powders in pipes

The two-layer concept developed previously for a liquid–solids flow has been adapted to model dense phase transport of powders in pneumatic conveying systems. Many bulk materials of this type are capable of flowing in a non-suspension moving-bed type of flow. A new model for this type of flow in a horizontal pipe has been developed where the flow is modelled as two layers: a dilute gas–solids mixture flowing above a dense gas–solids mixture. For each layer, the conservation equations for mass, momentum and energy were solved for both the gas and solids phases. In addition, mass, momentum and energy transfers between the two layers were modelled. A single pressure was shared between the two layers. The paper describes the sub-models used to describe phenomena, such as the momentum transfer between the gas and solids in a layer. Transfer of mass, momentum and energy between the two layers results in a model that behaves in a similar manner to experimental observations. For example, as the mean flow velocity increases, the depth of the dense layer decreases. The predicted pressure profile for fully developed flow was compared with experimental data. In general, the prediction of pressure profile, and the predicted depth of the dense layer show reasonable agreement with the experimental observations. A parametric study was conducted to assess the relative significance of the initial conditions on the overall behaviour of the model. Variation of the initial conditions for the same total gas and solids mass flow rates was found to have only a small effect on the prediction of fully developed flow.

A novel experimental technique for the investigation of gas-solids flow in pipes

Abstract An experimental rig was designed and commissioned to simulate the flow of gas–solid mixtures in pneumatic-conveying systems at industrial scales. In the rig, the flow rates and pressures of the gas and solid can be closely controlled by predefined control variables or by feedback from a measured system parameter. This technique overcomes the problems of scale experienced in most research laboratories and vendor test centres. It also permits a wide range of operating conditions to be simulated in a short period of time using a small volume of the bulk material and hence reducing costs. Experiments with different modes of flow were compared with each other and with the works of other researchers. The advantages and current limitations of this approach are discussed.

Numerical Simulation of Cavitation Flows Based on Their Hydrodynamic Similarity

Abstract Hydrodynamic similarity of cavitation flows in nozzles of different scales has been observed experimentally. In this paper a model of cavitation has been developed, taking into account the bubbly nature of cavitation and assuming local homogeneity of the vapour-liquid flow. The model of cavitation is built from correlations for evaporation and condensation, based on bubble dynamics theory, and an equation for the number density of cavitation bubbles, derived by assuming hydrodynamic similarity of cavitation flows. Compared with conventional models of cavitation, which fix the number density of cavitation bubbles, the present model takes into account the effect of liquid tension on the number density of active cavitation nuclei. The model has been implemented within the VECTIS computational fluid dynamics code and applied to the simulation of cavitating flows in nozzles.

A simulation system for pneumatic conveying systems

Pneumatic conveying systems provide a highly flexible means of transporting dry bulk particulate materials. The main problem encountered when designing, optimising, or uprating these systems is the determination of the air supply necessary to achieve a particular duty (solids mass flow rate). Many correlations exist to predict the pressure drop necessary to drive the flow, and the gas velocities necessary for successful operation. Unfortunately, the design methods that incorporate these correlations are limited in terms of their flexibility. The development of this simulation resulted from the desire to increase the flexibility of the design method, and the need to employ more than one pressure drop correlation. As a result of these two requirements the problem of simulating the operation of a pneumatic conveying system was re-evaluated.

Drying of wet solid particles in a steady-state one-dimensional flow

Abstract A mathematical model for mass, momentum and heat transfer in a one-dimensional two-phase flow is presented. This model was applied to the drying process of wet coal particles in a gas flow. The coal particles were assumed to have a wet core and a dry oute crust. The evaporation process of liquid from a particle was assumed to be governed by diffusion through the particle crust and convection into the gas medium. As evaporation proceeds, the wet core shrinks as the particle dries. The drying process is assumed to stop when: the moisture content of a particle falls to a predefined value; or the crust temperature reaches the ignition temperature: or break-up of the particle, caused by a pressure rise in the wet core, has occurred. The model was based on the one-dimensional balance equations for mass, momentum and energy of the gas and the dispersed phases. The system of the governing equations was represented by first-order differential equations and solved simultaneously by a numerical method. The model permitted calculation of the mass transfer ratio, change of the core diameter, and change of the average temperatures of the core and the crust. Four operating conditions were simulated using the model: isothermal: adiabatic: fixed wall temperature: and known heat flux. The model is also capable of simulating a dispersed gas-solids flow, without mass or heat transfer, in a one-dimensional transport system. The prediction of the numerical simulation, for the last case, was compared with experimental results of coal-nitrogen conveying in high pressure systems.

An investigation of the flow structure through abrupt enlargement of circular pipe

Abstract There are many examples of flow of gas, with or without solids, where an abrupt change of cross-sectional area has to be implemented. A typical example is long distance pneumatic conveying where single bore pipeline normally requires high pressure drop which consequently results in high gas and solids velocities towards the end of pipeline. In those cases, stepped pipeline is used in order to reduce both gas and solids velocity whenever they reach unacceptable level. The flow structure through an abrupt enlargement of a conduit can be very complex, specially in the case of gas–solids flow. Both velocity and pressure fields are very important for the analysis and design of the overall flow characteristics. The compressible flow of gas through an abrupt enlargement was modelled using both a 1-D analytical model and 3-D numerical model. A summary of the analytical 1-D model of compressible flow through an abrupt enlargement and the results obtained for the flow through stepped pipe (81 to 105 mm) for several flow conditions are presented in this paper. Those results have been compared with the 3-D numerical model which solves basic conservation equations and very good agreement was found. Finally the same 3-D numerical model was applied to several regimes of gas–solids flow in order to investigate the structure of gas and solids velocity field, as well as pressure distribution along the pipe. Special attention has been paid to the pressure recovery downstream from the enlargement due to its important role in the design of stepped pipeline pneumatic conveying system.