IV Journeys in Multiphase Flows (JEM2015)March 23-27, 2015 - Campinas, Brazil

Copyright c© 2015 by ABCMPaperID: JEM-2015-0054

GRANULAR FLOWS IN PRESSURIZED SILOS: JANSSEN EFFECTVERSUS HYDROSTATIC PRESSURE

Erick de Moraes FranklinNewton Silva de AndradeFaculty of Mechanical Engineering, University of Campinas - UNICAMPfranklin@fem.unicamp.brnewton1103@gmail.com

Abstract. Granular matter is present in nature and industry. When in the presence of lateral walls, pressure distributionalong the granular material saturates due the existence of contact lines. This saturation is known as Janssen effect andcan be responsible for clogging the flow or even for bursting silos. In cases where granular matter is flowing in denseregime in a pressurized silo (or tube) with a cocurrent water flow, the pressure distribution is given by the fluid pressure(within the fluid flow) and by the mechanical redistribution caused by grains (Janssen effect). This paper investigatesexperimentally the influences of hydrostatic pressure and granular redistribution in a pressurized granular flow in a silo.

Keywords: Granular matter, pressurized silo, granular flow, Janssen effect

1. INTRODUCTION

Granular materials occupy an important place in our quotidian. For instance: arid regions (soil composed of sand andof other solid fragments) occupy 20% of Earth emerged surfaces; the world annual production of grains and aggregatesis approximately ten billion metric tons; and the processing of granular media consumes roughly 10% of all the energyproduced worldwide (Duran, 1999). This kind of material is a discrete medium whose rheology is unknown.

As grains constitute a discrete medium, their statics and dynamics depend on the contact points. One example is theJanssen Effect: the mechanical saturation of the forces at the low end of containers filled with grains due to the redirectionof forces at the contact points (Duran, 1999; Sperl, 2006; Bertho et al., 2003; Courrech du Pont et al., 2003). In manyindustrial applications, such as in mining and food industries, descending granular flows occur in ducts and hoppers. Inthese cases, the pressure at the duct low end may saturate due to the redirection of forces. Any additional force exerted atthe upper end is redirected towards the lateral walls, which may clog the flow or even burst the duct.

In the case of gravitational dry granular flows (i.e., fluid drag is negligible) in ducts, silos and hoppers, Janssen effectis present and pressure at the low end is saturated. As a result, the flow rate of grains does not depend on the upper endpressure (Aguirre et al., 2010). However, if a fluid flows cocurrently with grains, the slip between phases changes thedistribution of mechanical forces at the duct low end. As a result, the flow rate of grains can increase with the inlet fluidpressure.

If many previous studies were devoted to dry granular flows in ducts, the same is not true for dense granular flows ofgranular columns with a cocurrent fluid flow. There is a lack of information concerning how the slip between phases andpressure saturation operate on the flow rate of grains.

This paper presents an experimental study on descending vertical flows of grains in dense regime and liquids in a silo.The influences of hydrostatic pressure and forces redistribution are investigated. The experimental results contribute tobetter understand the roles of the fluid flow and of the mechanical contacts in the flow rate of grains.

2. EXPERIMENTAL SET-UP

The experimental device is presented in Fig. 1. It consists basically of a silo immersed in water, a return line, a waterpump, and an inlet pressure port. The silo is a 50mm ID and 500mm long tube with a hopper at its low end. For thepresent experiments, the diameter of grains, the height of the granular column in the silo, the exit aperture and the waterpressure at the silo entrance were varied. Figure 2 presents a photo of the immersed silo.

The liquid phase consisted of city (tap) water and the granular matter consisted of glass beads with specific mass ofρs = 2500 kg/m3. Two different granulometries were employed: diameter in the ranges 500µm ≤ d ≤ 600µm and106µm ≤ d ≤ 212µm. At the silo’s lower end two different apertures were used: da = 4mm and da = 6mm.Pressure at the silo’s upper end was fixed by controlling the water level as well as the pressure at the inlet port (connectedto an air compressor). Gauge pressure varied between 0.78Pa and 80 kPa. Finally, the granular column was variedbetween 70mm and 200mm.

For each grain type, column heigh, exit aperture and inlet pressure, the flow rate of grains was computed from acquiredimages. It was employed a 16Mpx digital camera operating in sequential mode, and the images were post-processed with

Franklin, E.M. and Andrade, N.S.Granular Flows in Pressurized Silos: Janssen Effect vs. Hydrostatic Pressure

Figure 1. Experimental device

Figure 2. Immersed silo

the GIMP software. Figure 3 presents an example of acquired images during an experimental run.

3. RESULTS

One example of the slip velocity effect, i.e., the variation of the flow rate of grains with the inlet pressure is shown inFig. 4. This Figure presents the flow rate of grains Q as a function of the entrance gauge pressure Pman. Grains werein the 500µm ≤ d ≤ 600µm range and the aperture was of 6mm. All the other tests showed the same tendency of alinear relation between Q and Pman. This indicates that slip velocity and grains entrainment follows the Darcy law forflow through a porous media.

One example of the flow rate of grains in the presence of Janssen effect is shown in Fig. 5. This figure presents theflow rate of grains Q as a function of granular column hgraos. Grains were in the 500µm ≤ d ≤ 600µm range and theaperture was of 4mm. Gauge pressure was of Pman 40 kPa. All the other tests showed the same behaviour: the flow rateof grainsQ does not varies with the granular column hgraos. This indicates the presence of Janssen effect: the mechanicalsaturation of the forces at the low end of the silo due to the redirection of forces at the contact points. This constant force

IV Journeys in Multiphase Flows (JEM2015)March 23-27, 2015 - Campinas, Brazil

Figure 3. Sequence of images during a test.

Figure 4. Flow rate of grains Q as a function of the entrance gauge pressure Pman. Grains were in the 500µm ≤ d ≤600µm range and the aperture was of 6mm.

(and pressure) at the silo exit for different columns implies a constant flow rate of grains.

Figure 5. Flow rate of grains Q as a function of granular column hgraos. Grains were in the 500µm ≤ d ≤ 600µmrange and the aperture was of 4mm. Gauge pressure was of Pman 40 kPa.

Figure 6 presents the flow rate of grains Q as a function of granular column hgraos for different inlet pressures. Grainswere in the 500µm ≤ d ≤ 600µm range and the aperture was of 4mm. Different symbols correspond to different

Franklin, E.M. and Andrade, N.S.Granular Flows in Pressurized Silos: Janssen Effect vs. Hydrostatic Pressure

entrance pressures and they are indicated in the figure. This figure summarizes the effects of entrance pressure and forcesredistribution for the 500µm ≤ d ≤ 600µm, 4mm aperture case. It shows that the flow rate of grains increases withthe inlet hydrostatic pressure while it does not vary with the heigh of the granular column. The first is a consequence ofthe slip between phases while the latter is due to the Janssen effect. However the combination of the two effects is notsimple and requires further investigation.

Figure 6. Flow rate of grains Q as a function of granular column hgraos for different inlet pressures. Grains were in the500µm ≤ d ≤ 600µm range and the aperture was of 4mm.

Figure 7 presents the flow rate of grains Q as a function of granular column hgraos for different inlet pressures. Grainswere in the 106µm ≤ d ≤ 212µm range and the aperture was of 4mm. Different symbols correspond to differententrance pressures and they are indicated in the figure. This figure summarizes the effects of entrance pressure and forcesredistribution for the 106µm ≤ d ≤ 212µm, 4mm aperture case. Although noisier than in the case of Fig.6, Fig 7also shows that the flow rate of grains increases with the inlet hydrostatic pressure while it does not vary with the heighof the granular column. As in the precedent figure, the combination of the two effects is not simple and requires furtherinvestigation.

Figure 7. Flow rate of grains Q as a function of granular column hgraos for different inlet pressures. Grains were in the106µm ≤ d ≤ 212µm range and the aperture was of 4mm.

4. CONCLUSIONS

This paper presented an experimental study on descending vertical flows of liquids and grains in a silo. The influencesof hydrostatic pressure and forces redistribution were investigated for different grain types, column heighs, exit aperturesand inlet pressures. The results showed that the granular flow rate increases with the inlet hydrostatic pressure in a linearmanner, while it does not vary with the heigh of the granular column. The first is a consequence of the slip betweenphases while the latter is due to the Janssen effect. The combination of the two effects is not simple and requires furtherinvestigation.

IV Journeys in Multiphase Flows (JEM2015)March 23-27, 2015 - Campinas, Brazil

5. ACKNOWLEDGEMENTS

The authors are grateful to FAPESP (grants no. 2012/19562-6 and no. 2013/04175-0) and to FAEPEX/UNICAMP(conv. 519.292, projects AP0008/2013 and 0201/14) for the provided financial support.

6. REFERENCES

Aguirre, M.A., Grande, J.G., Calvo, A., Pugnaloni, L.A. and Géminard, J.C., 2010. “Pressure independence of granularflow through an aperture”. Phys. Rev. Lett., Vol. 104, p. 238002.

Bertho, Y., Giorgiutti-Dauphiné, F. and Hulin, J., 2003. “Dynamical janssen effect on granular packing with movingwalls”. Phys. Rev. Lett., Vol. 90, p. 144301.

Courrech du Pont, S., Gondret, P., Perrin, B. and Rabaud, M., 2003. “Wall effects on granular heap stability”. EurophysicsLetters, Vol. 61, No. 4, p. 492.

Duran, J., 1999. Sands, powders and grains: an introduction to the physics of granular materials. Springer, 2nd edition.Sperl, M., 2006. “Experiments on corn pressure in silo cells - translation and comment of janssen’s paper from 1895”.

Granular Matter, Vol. 8, No. 2, pp. 59–65.

7. RESPONSIBILITY NOTICE

The authors are the only responsible for the printed material included in this paper.