5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
Wet Particles in Granular Sheared Flows
Wen-Lung Yang1, Shu-San Hsiau2
1: Dept. of Mechanical Engineering, National Central University, Chung-Li, Taiwan, ROC,
2: Dept. of Mechanical Engineering, National Central University, Chung-Li, Taiwan, ROC,
Abstract We have studied the transport properties of wet granular materials in shear cell apparatus. If the particles of flows are wet, the flows become more viscous and the liquid bridges between particles. The dynamic liquid bridge forces are considered as the cohesive forcesbetween particles to restrict the movements of particles. The cohesive forces make the particles stick tighter with each other and hamper the movements of particles. The mixing and transport properties are influenced seriously due to the amount of moisture in the flow. This paper discusses a series of experiments performed in a shear cell device with five different moisture contents using3-mm glass spheres as granular materials. A high-speed camera recorded the motions of the granular materials. Using the image processing technology and particle tracking method, the average and fluctuation velocities in the streamwise and transverse directions could be measured. The self-diffusion coefficient could be found from the history of the displacements of particles. The self-diffusion coefficients and fluctuations in the streamwise direction were much higher than those in the transverse direction. Three bi-directional stress gages were installed to the upper wall to measure the normal and shear stresses along the upper wall.For the wetter granular material flows, the fluctuation velocities and the self-diffusion coefficients were smaller.
1. Introduction
Granular materials are collections of discrete solid particles dispersed in a vacuum or interstitial fluid. The voids between particles are filled with a fluid such as air or water. Therefore, the flow behaviors of granular material can be treated as a multiphase flow. Granular flows are widely found in nature, such as ice flow, soil liquefaction, landslides and river sedimentation. In industries, granular flows are widely found in the mixing and transport processes of foodstuffs, coal, pellets, metal mine and so on. In chemical industry more than 30％ of products are formed as particles (Shamlou, 1988). All granular flows are highly dissipative. The energy supplied to a granular flow, through vibration, gravity, or shearing is rapidly dissipated into heat. Thus, work must constantly be done on the system to maintain a granular flow.
The dominant mechanism affecting the flow behavior is the random motions of particles resulted from the interactive collisions between particles (Campbell, 1990). Because of the random motion of particles in a granular flow is analogous to the motion of molecules in a gas, the dense-gas kinetic theory (Savage and Jeffrey, 1981; Jenkins and Savage, 1983; Lun and Savage, 1984; Jenkins Richman, 1985) and molecular dynamic simulations(Campbrll, 1989; Lan and Rosato, 1995) are borrowed to analyze and model the granular flow behavior.
Due to the difficulty in measurement of granular temperature, there were relatively few experimental studies about this important quality. Fiber-optic probe technology was employed by Ahn, Brennen and Sabersky (1991) and Hsiau and Hunt (1993) to measure the fluctuation, but only in the bulk flow direction. The image technology and the autocorrelation method were used by Natarajan, Hunt and Taylor (1995) to study the two-dimensional granular temperatures of granular material flows in a vertical channel. Hsiau and Jang (1998) used the similar technology to measure the flow behavior in a shear cell. The anisotropic distribution of fluctuations were clearly demonstrated in the above three experimental studies.
The presence of small amount of interstitial fluid in the system introduces another degree of complexity due to the cohesive forces between particles in addition to the core repulsion force and the friction force present for dry granular matter. An increase in repose angle is the most well known effect of the presence of interstitial fluid in a granular system and has become a topic of current interest (Tegzes et al., 1999; Halsey and Levine, 1998). The interstitial fluid also alters the percolation of particles, and the particles tend to behave as clumps rather than individual grains. The research about wet particles is more important at present. When the particles have a little amount of water, they would gather together and hinder the movements of themselves. There are plenty of indications, both in laboratory and in industrial situations, that other perturbations can complicate thing and consume our ability to model the behavior of “dry granulars” as we have defined them earlier (Hsiau and Shieh, 1999). Ambient humidity, for instance, can cause serious disruptions by creating clumps of particles that are more or less mobile. We know from common experience that wet sands could be fairly cohesive, whereas dry sands crumble apart readily.Due to the appearance of liquid bridge between particles, the capillary force should be considered as an important force effecting the motion behaviors of the granular system. Calculating the capillary force that keeps two wet spheres in contact is far from trivial. Several methods have been proposed to avoid the difficulties associated with solving the Laplace-Young equation (Erle et al., 1971; Lian et al., 1993).
The Couette granular flow was the simplest and very suitable for fundamental research. Some examples of the related experimental studies are Savage and Mckeown (1983), Savage and Sayed (1984), Hanes and Inman (1985), Johnson and Jackson (1987), and Wang and Campbell (1992). Most earlier experiments measured only the averaged stresses by transducers and assumed that the flow in the cell is a simple shear flow.However, the assumption should not be truein a shear cell because of gravitational force as demonstrated in the study of Hsiau and Shieh (1999). In our earlier research (Hsiau and Yang, 2002; Hsiau and Yang, 2004), we started to use the bi-directional stress gages to measure the normal and shear stresses along the upper wall. We studied the granular flows with different wall friction coefficients and solid fractions. The self-diffusion coefficients of granular flows increase with increasing the wall friction coefficients. However, they are decrease with increasing the solid fractions. This paper focuses on the effect of the presence of moisture. We performed experiments in a shear cell device that suppliedby a constant external energy with five different moisture contents.The present paper employedthe image technology and particle tracking method to investigate thegranular flow transport properties in the shear cell. Three bi-directional stress gages were buried in the upper wall to measure the normal and shear stresses of granular materials along the surface. The dependence of the measurements on the moisture content will be discussed.
2. Setup
The experiment materials in this study are soda lime beads which have an average diameter dp of 3 mm (standard deviation of 0.04 mm and particle density of 2490 kg/m3). There are 5% identical red soda lime beads serving as tracers. The average solid fraction of the test is calculated from the particle mass (1.5 kg in this paper) divided by the particle density and the test section volume.In this study, we control the average solid fraction to a value of 0.6285. A certain amount of water and tested particles were weighted by an electronic scale with accuracy of 0.001g. The water and the particles were put into a sealed jar. Then, we shook the sealed jar to mix the water and particles. The wet particles were put into the shear cell apparatus. We also measured the weight of sealed jar before and after putting the wet particles. Therefore, we know how much water in the granular flow and control the moisture content. The accurate values of the masses of water and particles which were put in the shear cell could be decided. The moisture content V* would be calculated.
In this study we use the annular shear cell apparatus which schematically shows in Fig.1. The experimental setup has arotation bottom disk (outside diameter: 45.00 cm; thickness of 4.50 cm) which is driven by a 3 hp AC-Motor.A tachometer we used to measure and control the rotation speed of the bottom disk. In this study, the AC-Motor supplies a constant energy into the shear cell. The bottom disk is made of plexiglass for visualization purposes. An annular trough (inside diameter: 31.67 cm; outside diameter: 42.02 cm) was cut in the bottom disk. The stationary upper disk was inserted into the trough after the wet granular materials were put in the test section. A dial indicator is installed in the apparatus to measure the adjustable height h of the test section.
Fig.1.Schematic drawing of the Couette shear cell experimental apparatus.
There are three bi-directional stress gages been installed along the upper wall to measure the normal and shear stresses, shows as Fig. 1. The detecting surfaces of the stress gages are even with the upper wall. The idea of the stress gage is based on a simple ring dynamometric element which is provided with semiconductor strain gages. The normal and shear stresses are realized by two different wiring systems of the strain gages, and we can measure the normal and shear stresses in the same time in this study.
The stress gage utilizes two different full bridge semiconductor strain circuits to measure both stress components simultaneously and independently. The diameter of the measuring surface of the gage is 2.0 cm. The measuring surface can be replaced with the same wall material as the upper surface of the test section. A stable voltage of 10 Volts is supplied to each stress gage by a DC power supply. When the stress gages sense the normal and shear forces from the granular materials, the voltage signals are translated from the gages to a personal computer through a data acquisition card (Advantech PCL-818HG). A series of calibration tests were carefully done in two directions through dead weights and then the calibration lines (straight lines) representing the dependences of the output voltage signals on the normal and the tangential loads on the gages can be determined. The accuracy of the pressure gages is over 99%. The normal and shear stresses are then determined from the average of the signals from the three stress gages.
In this study, the influence of the moisture conditions on the flow behaviors is investigated. The friction coefficients between particles and walls and among particleswere measured by a commerial Jenike shear tester. Plotting for each of these the shear stress against the normal pressure determines the straight lines through the origin of which the slopes define the internal friction angle and wall friction angle.However the straight line of the internal friction angle will touch the y-axis and indicate a value. The value is the cohesive force between particles.
The granular flow in the test section is assumed to be two-dimensional with streamwise (horizontal) direction as x-axis and transverse (vertical) direction as y-axis (upwards is positive). Because of the visualization limitation, only the flows adjacent to the outer surface of the annular trough in the bottom disk could be recorded and analyzed. The velocity of the lower wall u0 could be calculated from the product of the rotational speed of the bottom disk and the outside radius of the trough.In this paper, we controlled the input energy been a constant and measured the rotational speed. The rotational speed u0was fixed at 0.88 m/s.
A high-speed camera recorded the motions of the granular materials. Using the image processing technology and particle tracking method, the average and fluctuation velocities in the streamwise and transverse directions could be measured.The flow motions were recorded by a high-speed camera. In this study, the images were grabbed at a speed of 500 frames per second. The autocorrelation technique was employed to process the stored images and to decide the shift of each tracer particle in every two consecutive images. The details of the autocorrelation process can be referred to the paper by Hsiau and Shieh (1999).
The height of test section was divided into 10 regions. The ensemble average velocities in horizontal and vertical directions, <u> and <v> in each region were averaged from about 250 tracer particles (8500 frames):
(1)
(2)
where k represented the kth tracer particle, N was the total number of velocities used for averaging the mean values, and uk and vk are the velocities of the kth tracer particle measured from the two consecutive images containing the kth tracer particle. The fluctuation velocities in the two directions were calculated by:
(3)
(4)
Since the current study followed the auto-correlation technique developed by Hsiau and Shieh (1999) which took into consideration of the correlation values of gray level derivatives, the experimental errors of the velocities were reduced within 1.5%.
The Granular Bond Number Bog was defined as the ratio of the maximum capillary force Fc and the weight of the particle, W (Nase et al., 2001). It was somewhat reminiscent of the Bond Number in fluid mechanics, so by analogy was referred to as the Granular Bond Number Bog,
(5)
where R was the radius of particle (R = 0.0015 m), the fluid surface tensionγwas a value of 7.34*10-2 N/m (Munson et al., 2002), and ρp was the density of the solid (ρp = 2490 kg/m3). In this study, the Granular Bond Number was a constant (Bog = 2.003256). The cohesive effect should be considered with Granular Bond Number greater than 1 (Bog > 1)(McCarthy, 2003) In McCarthy’s research, the Collision Number Co was defined as the ratio of the maximum cohesive force Fc and the collisional force FBg,
(6)
where λ2 was a constant and du/dy represented the shear rate. We could know the degree of collision from the Collision Number.
The velocity fluctuations induce the self-diffusion in granular shear flows. Einstein (1956) first employed the concept for analyzing the diffusive phenomena of suspended particles undergoing Brownian motion in a liquid. This technique was used by Savage and Dai (1993) and Campbell (1997) to investigate the diffusive behavior of granular flow systems through computer simulation. The self-diffusion coefficient was defined as
(7)
where xi and xj are the diffusive displacements in directions i and j. Similar concept was employed by Natarajan et al. (1995) to study experimentally the granular self-diffusion in a 1-m-high vertical channel. However, it was very difficult to record the movements of the tracer particles in a rotated shear cell since the particles moved out of the view window of the CCD camera in a very short time. The idea of “periodic cell” used in computer simulation (Campbell and Brennen, 1985) was introduced in the experiments by Hsiau and Shieh (1999). In this experiment, when a tracer particle moved out of one image, the time counter for this particle was paused. The computer program would then search the following images, until the other tracer particle was found in the inlet with the same channel height and the same velocities as the former tracer. The path of this new tracer particle from the image inlet was then treated as the continuous movements of the former tracer particle. The mean-square diffusive displacements <xx>, <yy> and <xy> were averaged from about 200 tracer particles taken from 7000 to 9000 frames. The experimental errors were mainly resulted from the uncertainty in determining the centroid of a particle. The errors of diffusion coefficients Dxx and Dyy were estimated beyond 2% and 5% respectively.
3.Results
The five tests in this study were done for a total granular mass of 1.5 kg and a fixed channel height of 1.6 cm. The average solid fraction of the current setup was 0.6285. We controlled the input energy been a constant. The lower wall velocity u0 was fixed at 0.88 m/s. The dimensionless liquid bridge volume, V* = Vl/(Vl +Vp), was used as a control parameter in this paper, where Vl was the volume of water and Vp was the volume of the particles. In this paper, we used fivemoisture contents (V* = 0, 0.008, 0.017, 0.025 and 0.033). Fig.2(a) shows the distributions of the ensemble average velocities in the streamwise and transverse directions, <u> and <v>, with different moisture contents. The transverse velocities are close to 0 as expected because there is no vertical bulk motion in the channel. The streamwise velocity decreases with the height and is greater for the case with wetter granular flows (greater V*). Slip velocities exist at the lower and upper walls. The upper slip velocities are about 61% to 80% of the lower wall velocities. Due to the gravity effect, there exists a “solid-like region” (Zhang and Campbell, 1992) in the lower half of the channel with faster and more uniform velocities in the streamwise direction. The shear rate is higher in the upper section where is called the “fluid-like region” (Zhang and Campbell, 1992) or “shear layer” (Aidanpää et al., 1996). From Fig.2(a), the values of the shear rates in this region deviated significantly with different moisture contents. For the test with greater moisture content, V*, the velocity gradient is lower since the wetter particles (greater V*) can generate higher cohesive forces between the particles resulting in the lower shear rate. The energy of flow is dissipated highly due the frictional forces between the particles.