In this thesis, we established a laboratory-scale facility to study the interaction force between a steady granular flow and a obstacle on an inclined chute. The experimental facility (see figure 2.1) includes a reservoir of packing width W and height H, an inclined chute at angle θ, high-speed image acquisition system, and load cell sensing modules. Two types of load cell modules developed and calibrated individually in this work: one measuring only the normal force to determine an overall mass flow rate and the duration of a steady flow; the other acting as an obstacle on the incline and sensing both the shear and the normal force as the bulk impacted and crossed it (see figure 2.3 and 2.4).
We recorded the sphere motions by high-speed image acquisition system from the side and developed an image processing routine to measure individual sphere motion. This routine integrates the circular Hough transformation to locate sphere center in each image followed by the nearest neighbor method to pair the same spheres in two consecutive images to achieve particle tracking velocimetry (PTV).
The errors in locating and matching spheres were estimated and provided in table 3.1 and table 3.2, respectively.
We installed the load cell module on the chute at a streamwise distance 100 cm
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away from the reservoir and prepared chute of different inclination angles θ and two depths, h. We released granular mass from the reservoir of fixed gate opening and let steady flow develop on the chute and run over the load cell module. We received signals from different components in the load cell module and compared the data to the 2D image control volume analysis. At θ=20° and h=4.8 cm, the granular flow cannot climb over the load cell module but accumulated in front of the impact surface, producing a clear impact force of 4~5N but zero normal and shear force. At θ=20°and h=2.4 cm, the flow developed two distinctive packing configurations in front of the impact surface and for the one in random configuration, a ‘jammed and collapsed’
cycle was observed during and little granular mass crossed the module during the
‘collapsed’ phase. Fluctuating impact force of 3~6N was measured and the resulting normal and shear force loadings are highly unsteady and of nearly zero magnitude.
These load cell data at low inclination angle (θ=20°) and the images of different packing configurations are given in figures 5.2, 5.3, and 5.4. For shallow flow (h=2.4cm) at higher inclination angle, θ=23° and 26°, the resulting flow is composed of fierce sphere bouncing motion over the load cell box giving a rather steady load cell signal over time in figures 5.5 and 5.6: about 1N impact force in the front load cell and 0.2N normal loading on the rear load cell. A nearly zero shear force was detected due to short contact time. For thicker flows with h=4.8cm at θ=23°
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and 26°, steady flows developed across the load cell module with a noticeable stationary zone of height around 7~9D in front of the impact plate (see Figure 5.7).
The running spheres formed a thin layer—of averaged depth around 3D—over the rear shear- and the normal-loading plates. The impact force magnitudes fell nicely in the range of 5~7N and the shear and normal forces remained slightly below 0.1N and around 0.2N, respectively. These steeper and thicker flow data are shown in figures 5.8, 5.9, and 5.10.
We then applied two-dimensional control volume analysis to the bulk momentum using the captured lateral images to estimate the interaction force with the obstacle (load cell module). The obtained 2D data was multiplied by the chute width to obtain an equivalent 3D force component which was compared to the three-dimensional in-situ load cell measurements for evaluation. We only compared steeper and thicker flows (with h=4.8cm and θ=23°, 26°) since the bouncing sphere motions in the steep shallower flow invalidated the current PTV matching algorithm.
The mild flows at θ=20° were not considered since no steady flow could develop across the load cell module. The methodology of control volume analysis is described in section 5.3. We compared the impact force first and found out that the control volume analysis results matched reasonably well with the in-situ load cell measurements when the largest control volume width (~35D) was employed.
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However, when we shrank the CV width towards the impact surface to 1/3 and 2/3 original value, severer fluctuations were obtained. This phenomenon was speculated to result from erroneous PTV data for more dilute and chaotic flow near the load cell.
We thus conducted manual matching and much improved results were obtained. The relevant results are shown in figures 5.13~5.18. We also examined the shear and normal loadings and obtained agreeing results for the normal loading but total failure for the shear loading (see figures 5.19 and 5.20). We repeated manual PTV at a few chosen moments (see table 5.1) and the results now fell nicely in the range of in-situ load cell data. We thus conclude that the current image analysis is capable of granular force estimation only when the flowing spheres are in dense configuration.
Apart from interaction forces from a steady flow, we also studied the discharging characteristics of reservoir materials in different packing geometries.
We placed the reservoir at small 4 degrees on a horizontal hoister with a fixed gate opening of 10cm height. Experimental POM spheres of nearly identical diameter were packed to different widths, W, and heights, H. To quantify a total mass flow rate, we put a plastic container to receive the discharged spheres. The accumulated sphere total weight was monitored over time by the aforementioned load cell module with its measuring surface laid at the center of the container base. The temporal profile of accumulated weight was employed to identify a steady discharge and we found out
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that enlarging the packing width (W) and height (H) could extend the steady duration (see figure 4.2).We further defined “deviation time” to denote the termination of steady discharge from a specific packing geometry (see section 4.2.1). The following unsteady discharge was also analyzed the difference from an steady discharge and a peculiar deviating temporal profile for unsteady discharge was revealed for the flow from the narrowest packing. For the narrowest, the deviation from the steady
discharge scales with e3.25t0.25 but a much milder deviation, e1.25t0.45, was detected for all the flows from thicker packing widths (W=12cm, 18cm, and 24cm).
As an attempt to understand the discharge nature, a high-speed camera was installed to record the sphere motions by the side of the connection guide that where the spheres flowed from the reservoir gate to the container (or the chute). The sphere motions and hence the bulk flow properties were analyzed at three streamwise locations—at the reservoir gate, at the guide center, and by the guide exit—with a 7-cm separation (see figure 4.1). We examined the instantaneous depth profiles for bulk velocity and solid volume fraction in figure 4.7 to figure 4.10. We also computed the corresponding depth-averaged values using equations 4.3(a) and 4.3(b) for flows from each packing geometry and their temporal variations are compared (see figures 4.12 and figure 4.14). We noticed that the narrowest packing gave distinctive temporal profiles for the depth-averaged bulk velocity and solid volume fraction. The instant
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when a depth-averaged solid volume fraction drops was found to coincide with when the depth-averaged velocity changed dramatically.
For future perspectives, we would like to examine a wide range of flow conditions to see whether the findings of this thesis are universal to other dry granular flows. Flow conditions that may be explored include: thinner W and H, spheres of different density and sizes, chute widths, heights, and inclination angles, and where to install the load cell obstacle.
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