Investigations on the formation and stability of plugs at dense-phase pneumatic conveying

Gerhard Niederreiter1, Martin Strauss2, Karl Sommer1, Hans Herrmann2

1 Lehrstuhl für Maschinen- und Apparatekunde, Technische Universität München/Weihenstephan, Germany 2 Institut für Computeranwendungen, Universität Stuttgart, Germany

ABSTRACT For many industrial applications dense phase pneumatic conveying is the preferred transport mode for granular media. There exists several models derived from material laws and valid for granular bulks or fluidized beds. However, pneumatic transport predictions often prove to be inaccurate. Further knowledge on plug flow is needed to be able to implement more sophisticated models. This paper introduces an approach to gain access to details of plug flow, which have been up to now unavailable. Therefore a sensor has been developed to measure in situ stresses and pressure drop of individual plugs and a simulation has been implemented and experimentally validated to provide access to experimentally unreachable properties like porosity and plug dynamics on particle scale.

1 INTRODUCTION Pneumatic conveying is one of the most common methods used for the internal transportation of bulk solids. One differentiates between dilute and dense phase conveying. Plug conveying, which dominates the transport in the dense phase regime, is gaining importance due to its gentle treatment of the bulk solid and the lower wear rate on pipelines. For this mode of conveying the design of plants is based on extensive tests on pilot plants. Experimental diagrams are generated which represent the correlation of pressure loss, velocity of the conveying gas and mass flow rate for a special material conveyed in a predetermined pilot plant.

So far no satisfactory theoretical model exists to predict exactly the pressure loss or the conveying ability of the material as a function of particle and bulk properties. Further investigations on the internal dynamics and properties of plugs are needed to develop a more sophisticated conveying model.

This paper provides the first results of experiments and simulations done to obtain a more detailed understanding of the characteristics of plug flow.

2 METHODS 2.1 Simulation

For our computer simulations we use a combination of a discrete element method, molecular dynamics, with a differential diffusion equation for the gas pressure [1, 2]. All simulations are done in 3D. The molecular dynamics simulation considers Coulomb friction between contacts, rotation, and polydispersity. Static friction is neglected. The gas simulation includes pressure drop; the inertia of the gas is neglected. The differential equation for the gas pressure is based on the mass conservation of the gas and the granular particles (Eq. 1).

( ) 0vt

=ρ⋅∇+∂ρ∂ rr

(1)

Using the ideal gas equation, this can be reduced to a differential pressure equation depending on the porosity ε, the velocity of the gas and the velocity of the granular material. The relative velocity between gas and granulare material can be obtained by D'Arcy's law.

Puv granulargas ∇ηκ

−=rr

(2)

After expansion around the atmospheric pressure P0the resulting pressure equation depends only on the local porosity and velocity of the granular material, which both are obtained by the molecular dynamics simulation (Eq. 3).

( )( ) granular00 uP

PP

tP rrrr

∇ε

−∇εεκ∇ε⋅η

=∂∂

(3)

The particles of the molecular dynamics simulation are driven by the local pressure gradient. Up to now only preliminary simulation results are available. As observed in experiments, plug flow occurs for a wide range of parameters. Experimentally measurable properties, such as wall shear stress, normal stress, pressure drop, etc. show comparable behavior.

2.2 Experimental Setups

In this context, a sensor was constructed to measure directly normal stress, wall shear stress, and pressure drop at a conveyed plug concurrently (Figure 1). The stresses of the bulk solid plug are transferred over a sealed, mobile pipe element to two perpendicularly arranged piezoelectric force sensors. The piezoelectric force sensors allow the

measurement of the forces acting on the pipe element and the calculation of the appearing stresses over the surface of the pipe element. The piezoelectric force sensors are located in a sealed chamber, in which the same pressure prevails as in the conveying pipe. This is realized by a bypass. So the sensor can measure the wall shear stress as well as the normal stress of a moving plug during the conveying process but not the pressure difference between the conveying line and the sensor chamber. But factors that influence the measurements must be considered. During the calibration of the sensor the interaction of the piezoelectric sensors has to be quantified. Actually the sensor should only detect forces in its recording direction and no shear forces. But occurring moments let the sensor for the axial stress detect stresses by an radial stress and vice versa. Also changes in temperature influence the sensor. During measurements the temperature must be constant in the chamber. Further influence factors are pressure dependency in the chamber and the electric discharge of piezoelectric sensors at static loading. But these influence factors can be detected and considered in the data processing. Additionally a ledge of six miniature pressure sensors are integrated to detect the pressure drop along the plugs at the same time as the mechanical stresses.

Figure 1: Isometric view of the sensor

To apply the measuring. method to continuous, vertical plug conveying, a test rig was constructed and built up (Figure 2). The test rig consists of a dosing unit, a screw feeder and a vertical conveying pipeline of 6 meter, including the bulk solid stress sensor. A CCD camera and photos taken by the CCD camera support the interpretation of the measuring results. The conveying air is dosed exactly with a mass flow measuring instrument [3].

Figure 2: Schematic construction of the pilot plant

First experimental tests were made with granular plastic material. Table 1 shows the characteristic bulk solid properties. Table 1. bulk solid properties particle diameter 3 mm

solid density ϕS 899 kg/m³

bulk density ϕB 533 kg/m³ wall friction angle ϕW(stainless steel) 17.4°

3 RESULTS The experimental investigations yield the following results: The sensor can detect wall shear stress, normal stress as well as the pressure drop along the conveyed plug. Figure 3 shows the values of a conveyed plug. The photos of the conveyed plug, recorded with a frequency of 30 photos/sec, allow the determination the plug velocity and the acceleration of the plug. Therefore less than one percent by weight of the granular material are colored black. The plug velocity is calculated by the distance that an observed particle travels between two photos (Figure 4). Any electrostatic problems are removed by coating the granular material with an static inhibitor, ATMER 129 Ciba/Basel. At the same time the porosity along the conveyed plugs can be indirectly calculated with the measured pressure drop, the plug velocity and therewith the relative gas velocity.

pressure sensor

sensor cap

piezoelectric sensors

conveying pipe

pipe element

seal

connecting strap

Figure 3: Pressure drop, wall shear stress and normal stress of a pneumatically conveyed plug

Figure 4: Velocity and acceleration of a moving plug

Figure 5: Porosity distribution along a pneumatically conveyed plug

Investigations of the pressure loss of compact bulk solid columns verified, that the Ergun-Equation is the best description of the pressure loss. For the

theoretical description of the experimental results, the original Ergun-Equation is extended with the isothermal change of gas. The application of the modified Ergun-Equation can be documented also at a higher porosity of 0.475 [4].

At first the experimental results serve to verify the computer simulation and to get more information about the formation and the stability of single plugs. Therefore first experimental tests are made with spheres in an acryl glass pipe with an inner diameter of 7 mm. Figure 7 shows the comparison of pictures of the molecular dynamics simulation and the experimental tests.

Figure 6: Comparison of simulation with experimental results in pneumatic conveying

The pictures below are time series of pneumatic transport within a circular tube simulated by using molecular dynamics for the granular material and a diffusion equation for the gas. The particles with a restitution coefficient and coulomb friction of 0.5 are driven upwards by air flow. The color shows the relative velocity of the particles. Figure 7 shows the changes of the particle density profile of a plug over time. The density is represented with colors from black (0.0) to yellow (0.6). Time advances from left to right. The vertical axis corresponds to the vertical position of the plug in the pipe. In the experimental investigations the wall friction angle ϕW is 12.8° measured on acryl glass. Nevertheless the bulk solid plugs show a similar behavior of transportation. Among the visualization further values can be calculated, like the wall shear stress. Figure 8 and figure 9 show the experimental values of wall shear stress in comparison with the calculated values. Due to the different parameters a direct comparison of the values is not yet possible. Therefore the individual parameters have to be adjusted to get a validation of the simulation. If the

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/--

porosity between pressure sensor 1 and 2porosity between pressure sensor 2 and 3porosity between pressure sensor 3 and 4porosity between pressure sensor 4 and 5porosity between pressure sensor 5 and 6

simulation can confirm the experimental measurements, the simulation give more information about experimentally unreachable characteristics of the plug, like the radial porosity distribution.

Figure 7: Particle density profile of a single plug

Figure 8: Simulation results of wall shear stress along a moving plug

Figure 9: Experimental values of wall shear stress along a pneumatically conveyed plug

4 CONCLUSION A measuring method was developed to measure wall shear stress, normal stress and the pressure drop of a pneumatically conveyed plug at the same time while continuous, vertical dense phase conveying in a build up test rig. For the computer simulation we combined a discrete element method, molecular dynamics, with a differential diffusion equation for the gas pressure. First, the computer simulation will be verified with the experimental results. Than the results of the simulation will give more information about the experimentally unreachable characteristics of the plug, like the radial distribution of porosity, gas velocity or the reason of wall shear stress, if the plug is fluidized. Additionally the radial porosity distribution or the radial speed distribution can be analyzed with the simulation. Based on these results the stability, the formation and the constitution within pneumatically conveyed plugs can be explained. The aim of these studies is to develop a model relevant to the practice for the calculation of the pressure loss of plug conveying, which will be confirmed empirically. Constitutive on this theoretical model a reliable Scale-up method can be derived.

REFERENCES [1] Sean McNamara, Eirik G. Flekkøy, Knut Jørgen Måløy, Grains and gas flow: Molecular dynamics with hydrodynamic interactions, Physical Review E, Vol. 61 (2000) pp. 4054 – 4059

[2] Eirik G. Flekkøy, Sean McNamara, Knut Jørgen Måløy, Damien Gendron, Structure Formation and Instability in a Tube of Sand, Physical Review Letters, Vol. 87, No. 13, (2001)

[3] Gerhard Niederreiter, Karl Sommer, Modeling and Experimental Validation of Pneumatic Plug Conveying, Proceedings of the 4th International Conference for Conveying and Handling of Particulate Solids, Budapest/Hungary 2003

[4] Gerhard Niederreiter, Karl Sommer, Investigations on Formation and Stability of Plugs at Dense Phase Conveying, Proceedings of the World Congress on Particle Technology 4, Sydney/Australia 2002

ACKNOWLEDGMENT This research was supported by DFG within grants SO 118/31-1, SO118/31-3, HE 2732/2-1 and HE 273/2-3.