64
3 A Structuring Regime to Control Bubbling Beds
Therefore, I r approaches one in the case of a highly structured flow, as the separation
remains unchanged. Given such conditions, I r is nevertheless only applicable to
evaluate a well-structured flow, in which bubbles are horizontally aligned and paired.
In a chaotic flow, bubbles are closely deposited, and pairs are hard to be distinguished.
Subsequently, I r simply represents the homogeneity of bubble flows, and it is found
significantly sensitive to many factors, such as bubble size as well as the position
and size of the artificial sampling area.
Alternatively, model-based pattern recognition and quantification can be applied
given prior knowledge of the structure. For example, the appearance of structured
flows is known as triangular lattice, or hexagonal arrays in deeper beds, and the
orientation pattern is predefined, as it propagates upward. The degree-of-order for
structured flow can be determined by fitting an experimental bubble arrangement to
a normal triangle tessellation. It evaluates the regularity by considering the crosscorrelation of spatiotemporal positions of bubbles, independent of bubble size and
shape. Based on this principle, a model-based pattern recognition algorithm for
computing pattern intensity of the structured flow has been developed at the Centre
for Nature Inspired Engineering (CNIE) of University College London. The steps
are summarised in the block diagram (Fig. 3.1).
Firstly, apart from extracting the size of bubbles, it loops through every single
bubble in the domain over time and extracts the relative positions, such as distance
r and polar angle θ, by pairing with the rest, as shown in Fig. 3.2.
The overall extracted bubbles position from the experimental domain over time
and space can be simply presented in a single reference frame. The fitted model of a
normal triangle tessellation is constructed with three parameters: pattern wavelength,
angle and variability. To compute the degree-of-order, the fitted model is then imposed
to approximate the experimental bubble pattern, as shown in Fig. 3.3.
In the step of reconstructing the corresponding randomised arrangement of
bubbles, the extracted experimental bubbles in each frame are relocated randomly
without overlaps to approximate a possible unstructured flow pattern. In such a
way, it accounts for the size of bubbles, preventing from generating any unphysical
arrangement, as shown in Fig. 3.4.
The probability of these triangle tessellation models (red dots in Fig. 3.3) fitting
to the experimental (black dots in Fig. 3.3) and the random bubble distributions (blue
dots in Fig. 3.4) are then computed, respectively, with increasing model variability.
Therefore, a pattern intensity Λ can be determined as the maximum difference in the
fitting probability between the two, as shown in Fig. 3.5. Similarly, Λ approaches one
when experimental bubbles are perfectly deposited in a form of normal triangular
lattices, whereas Λ approaching zero represents a statistically random pattern of
bubbles.
The MB approach determines the index by the fitting of experimental bubble positions to normal triangle tessellation grids. In the current method, the fitted model is
constructed and optimised with the measured pattern wavelength, pattern angle, and
variability. More sophisticated optimisation method can be applied to determine the
model. An alternative way is to employ Lenstra-Lenstra-Lovász (LLL) algorithm
3 A Structuring Regime to Control Bubbling Beds
Therefore, I r approaches one in the case of a highly structured flow, as the separation
remains unchanged. Given such conditions, I r is nevertheless only applicable to
evaluate a well-structured flow, in which bubbles are horizontally aligned and paired.
In a chaotic flow, bubbles are closely deposited, and pairs are hard to be distinguished.
Subsequently, I r simply represents the homogeneity of bubble flows, and it is found
significantly sensitive to many factors, such as bubble size as well as the position
and size of the artificial sampling area.
Alternatively, model-based pattern recognition and quantification can be applied
given prior knowledge of the structure. For example, the appearance of structured
flows is known as triangular lattice, or hexagonal arrays in deeper beds, and the
orientation pattern is predefined, as it propagates upward. The degree-of-order for
structured flow can be determined by fitting an experimental bubble arrangement to
a normal triangle tessellation. It evaluates the regularity by considering the crosscorrelation of spatiotemporal positions of bubbles, independent of bubble size and
shape. Based on this principle, a model-based pattern recognition algorithm for
computing pattern intensity of the structured flow has been developed at the Centre
for Nature Inspired Engineering (CNIE) of University College London. The steps
are summarised in the block diagram (Fig. 3.1).
Firstly, apart from extracting the size of bubbles, it loops through every single
bubble in the domain over time and extracts the relative positions, such as distance
r and polar angle θ, by pairing with the rest, as shown in Fig. 3.2.
The overall extracted bubbles position from the experimental domain over time
and space can be simply presented in a single reference frame. The fitted model of a
normal triangle tessellation is constructed with three parameters: pattern wavelength,
angle and variability. To compute the degree-of-order, the fitted model is then imposed
to approximate the experimental bubble pattern, as shown in Fig. 3.3.
In the step of reconstructing the corresponding randomised arrangement of
bubbles, the extracted experimental bubbles in each frame are relocated randomly
without overlaps to approximate a possible unstructured flow pattern. In such a
way, it accounts for the size of bubbles, preventing from generating any unphysical
arrangement, as shown in Fig. 3.4.
The probability of these triangle tessellation models (red dots in Fig. 3.3) fitting
to the experimental (black dots in Fig. 3.3) and the random bubble distributions (blue
dots in Fig. 3.4) are then computed, respectively, with increasing model variability.
Therefore, a pattern intensity Λ can be determined as the maximum difference in the
fitting probability between the two, as shown in Fig. 3.5. Similarly, Λ approaches one
when experimental bubbles are perfectly deposited in a form of normal triangular
lattices, whereas Λ approaching zero represents a statistically random pattern of
bubbles.
The MB approach determines the index by the fitting of experimental bubble positions to normal triangle tessellation grids. In the current method, the fitted model is
constructed and optimised with the measured pattern wavelength, pattern angle, and
variability. More sophisticated optimisation method can be applied to determine the
model. An alternative way is to employ Lenstra-Lenstra-Lovász (LLL) algorithm