Flow determination and observation of granular flow have become an important task in many industrial conveying processes. Especially for dilute phase granular flow, determination of particle velocities and velocity profiles is crucial for an appropriate dimensioning of conveyor systems and for safe conveying with minimum damage to the conveyor pipe and the conveyed material. Abrasive material conveyed at high velocities and unpredictable fluctuations in flow properties make a non-invasive measurement principle with on-line velocity determination desirable. Optical non-invasive approaches to determine granular material flow, such as Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV), have been used. Cross-correlation flow meters work on a different principle: Properties of the material flow are measured in two flow cross-sections separated by a certain distance. Natural or artificial fluctuations in the flow are detected and signals from the two layers are correlated. In dilute-phase granular flow processes, a conveyed particle, passing the first measurement plane, causes a significant change in the measured signal in this layer. Depending on the conveying velocity, the same particle will appear in the downstream measurement plane after a certain time delay, again causing a significant signal form. Good signal correlation is possible only if the material behaviour is similar in the two measurement planes. For very small distances, the flow appears similar in the two planes. This results in a good match between the two derived signals but a bad resolution for velocity calculation. For larger inter-layer distances and time delays, the resolution is better. But curved particle trajectories, such as due to the omnipresent gravity effects, can cause the flow in the two pipe cross-sections to look different. This results in a weak cross-correlation function. The optimum inter-layer distance is a trade-off between reliable cross-correlation function and usable resolution for velocity calculation.

This paper presents the necessary considerations and preparatory work for the development of a light attenuation based cross-correlation flowmeter. To determine the optimum inter-layer distance for this sensor principle, Computational Fluid Dynamics (CFD) simulations have been carried out to study particle trajectories in dilute phase flow. These trajectories provide necessary information on how to dimension the sensor geometry.

CFD SIMULATIONS

The steady-state flow simulations were carried out using the CFD package CFX (version 5.7.1). The flow region of interest is the 230 mm long sight-glass portion of the pipe. This was chosen as the computational domain for the simulation. This domain is divided into a number of non-overlapping tetrahedral cells, forming the computational mesh. These cells are non-uniformly distributed, with denser cell population in regions where steep gradients in the flow parameters are expected, such as the pipe wall. Partial differential equations expressing continuity and momentum balances, and those for the turbulent kinetic energy and its dissipation rate for the continuous fluid medium are integrated over the volume of each cell to obtain discretised (algebraic) versions. These algebraic equations are solved iteratively until balances are achieved for each cell. Since the cells are contiguous, this implies a balance over the entire computational domain. In the present 'cold flow' simulation, solution of the thermal energy equation is not needed. The computational domain is enclosed by three surfaces: Inlet, Outlet, and Wall. The no-slip wall boundary condition is applied to the pipe wall, and zero gauge pressure condition at the outlet. Parametric CFD simulations were carried out in order to provide more general guidelines relevant to dilute-phase pneumatic conveying, for different flow conditions. It was found that the optimum distances are very insensitive to different particle sizes and densities, but very strong functions of the conveying gas velocities.

EXPERIMENTS

Practical experiments using plastic pellets and two banks of six light dependent resistors were conducted with varying inter-layer distance. The granular material was pneumatically conveyed in a horizontal pipe with a sight-glass section. The particle loading was small enough for the process to be classified as dilute-phase pneumatic conveying. Average air velocities, measured by Pitot-Static tubes, ranged from about 15 m/s to 35 m/s. The practical experiments show good accordance with the CFD simulation results.

In a non-intrusive method for measuring particle velocities in dilute-phase particle-gas flows in pipes, estimation of the optimum distance between the upstream and downstream measurement planes is possible using the latest techniques in CFD. This combination of CFD and the cross-correlation measurement principle will be particularly useful in dilute-phase pneumatic conveying processes prevalent in many industries. In this paper, this will be demonstrated by calculating the trajectories of conveyed particles. Their simulated descent under the action of gravity is validated against experimental measurements. Parametric simulation studies are carried out to arrive at estimates of the maximum allowable and optimum distances between measurement planes used in the CCF technique.