The MATLAB code was written by Dr. Luke Fullard, and automates the process of find- ing the thicknesses of the active layers and the passive region. This allowed the PIV data to be more accurately and rapidly interrogated than it would have been possible to do by hand.
The code draws a series of lines radially from a user-defined point, which in the case of this study should be the point marking the centre of the drum. The angle between each line is also user-definable: for this study the lines were spaced 5° apart. The edge of the drum is defined by the radius and matched to the image being processed by the
4.3. AUTOMATED LAYER THICKNESS ANALYSIS 71 calibration set during the PIV analysis of the footage. The code then looks for the point along each line where the angular velocity flips sign, i.e., the point at which the flow goes from downhill to uphill, which is used in this study as the boundary between the active layers and passive region. Finding the position of the free surface is a slightly more complex process, as for parts of the footage the point at which the free surface meets the back wall of the drum is visible along with the desired point at which the free surface meets the glass door. The image is converted into binary, i.e., black if below a certain grey scale value, or white if above that same value (see Figure 4.3.3). As the visible free surface is brighter than the bulk material involved in the experiment (due to being lit from above, see Section 3.2.1), correct choice of a critical grey scale value can have the visible free surface marked in white, while the bulk material will be black. The code then just looks for the point along the line from the centre of the drum to the outer edge where the white region returns to black. If no such change from black to white to black again is detected, the code assumes there’s no material that intercepts that radial line, and the data are discarded. The final data are output as a comma separated value (.csv) file type (chosen for its interoperability across multiple spreadsheet applications and computer operating systems) or in Excel format (.xlsx) for more complex data sets, which can then be analysed. The thicknesses of each layer are output in metres. To obtain dimensionless measurements, the thicknesses are added together and then the thickness in question becomes the numerator in a ratio with the drum radius.
4.3.1 Area of Active and Passive Regions
The areas of the active and passive regions (these regions are illustrated in Figure 2.6.1) were also found using the code. The profile lines can be spaced at a known angle: where the profile lines met the free surface, the passive/active interface, and the drum wall created a series of trapezoidal regions whose areas are relatively simple to find. For small angles, the difference between these straight-edge trapezoids and ones tak- ing into account the curvature of the the drum wall is minimal. The sum of the ar-
eas of these trapezoids gives the area of each layer with a reasonable amount of accu- racy.
As the distinction between the active and passive regions becomes less obvious at the edges of the material, the edges were ignored for the purposes of finding the areas of the regions, see Figure 4.3.2. This was done by eye, using the velocity vector maps to find the end of the distinct active and passive regions, and on a case-by-case basis. As each velocity will cover different amounts of the drum interior, cases would have a different number of profile lines. The author considers this approach valid as the trend in layer areas would be correct even without the less distinct edges if they are ignored in the same manner, and because the edges of the material represent artefacts of the experiments being undertaken in a drum, rather than "true" parts of the active and passive layers. (A geological granular flow would not display these end regions, for example.)
4.3.2 The Centre of Mass/Dynamic Angle of Friction
The code written by Dr. Luke Fullard also finds the centre of mass of the material in the drum. It finds the angle of the line which bisects the area of the material in two from the vertical. Using the same techniques outlined above to find the free surface and the edge of the drum, the code is also capable of finding the midpoint of the bisecting line - this point then represents the centre of mass for a material. The angle of the centre of mass for a flowing material is also the definition for the dynamic angle of friction. The dynamic angle of friction is used in this thesis across materials and velocities (both static and dynamic) to compare the properties of the materials involved.