**4. Experimental procedure**

The experimental studies were performed using a specifically designed and constructed pseudo-2D fluidized bed. The bed was 0.32 m wide, 1.2 m high and 0.02 m thick and almost 2D thus allowing visual observations of bubble dynamics within the bed. The front and back sides were made of polycarbonate plastic in order to allow easy drilling of holes for assembly of the simulated tubes and allow full transparency of light. Bubble properties were calculated with the help of a Digital Image Analysis Technique (DIAT). DIAT was seen as a powerful method especially for the analysis of bubble properties as it provides rigorous and detailed information about the flow structure of the whole bed without interfering the flow dynamics. With the help of MATLAB Image Processing Toolbox, an in-house software was developed to fully automate the image acquisition and data processing procedure for the analysis of bubble properties for fluidized bed with and without immersed tubes. Detail description of the procedure was presented in our previous publication and interested readers are referred to it (Asegehegn et al., 2011b). The in-house software was developed to handle simulation results as well.

Once the bubbles are delineated and identified their projected areas AB, horizontal and vertical coordinates of their centroids and horizontal and vertical extremes are measured. Then the bubble properties (bubble aspect ratio, diameter, rise velocity and location of the rise velocity) are calculated using equations 27 to 30 respectively.

The bubble aspect ratio, AR, is defined as:

244 Computational Simulations and Applications

Fig. 1. Bed geometries: left - without immersed tubes (NT) and right with staggered tube

40

150

40

20

40

20

1200

NT S6

The experimental studies were performed using a specifically designed and constructed pseudo-2D fluidized bed. The bed was 0.32 m wide, 1.2 m high and 0.02 m thick and almost 2D thus allowing visual observations of bubble dynamics within the bed. The front and back sides were made of polycarbonate plastic in order to allow easy drilling of holes for assembly of the simulated tubes and allow full transparency of light. Bubble properties were calculated with the help of a Digital Image Analysis Technique (DIAT). DIAT was seen as a powerful method especially for the analysis of bubble properties as it provides rigorous and detailed information about the flow structure of the whole bed without interfering the flow dynamics. With the help of MATLAB Image Processing Toolbox, an in-house software was developed to fully automate the image acquisition and data processing procedure for the analysis of bubble properties for fluidized bed with and without immersed tubes. Detail description of the procedure was presented in our previous publication and interested readers are referred to it (Asegehegn et al., 2011b). The in-house software was developed to

Once the bubbles are delineated and identified their projected areas AB, horizontal and vertical coordinates of their centroids and horizontal and vertical extremes are measured. Then the bubble properties (bubble aspect ratio, diameter, rise velocity and location of the

rise velocity) are calculated using equations 27 to 30 respectively.

arrangement (S6). All dimensions are in mm.

320

**4. Experimental procedure** 

handle simulation results as well.

$$AR = \mathbf{d\_y/d\_x} \tag{27}$$

Where dy and dx are the vertical and horizontal extremes shown in Fig. 2.

Fig. 2. Bubble dimensions.

The bubble diameter was calculated from the area equivalent AB as:

$$d\_B = \sqrt{4A\_B/\pi} \tag{28}$$

The rise velocity was calculated from the difference in the vertical-coordinate of the centriod between consecutive time frames and dividing by the time interval between the frames.

$$
\Delta u\_B = \left( \mathbf{y\_g(t + \Delta t) - y\_g(t)} \right) / \Delta t \tag{29}
$$

Where yg is the vertical component of the centre of gravity of the bubble, t is the time and t is the time delay between consecutive frames of the images, 1/50 s in this case. The velocity is attributed to the mean vertical height according to:

$$h = \left(\mathbf{y\_g(t + \Delta t) + y\_g(t)}\right) / 2\tag{30}$$

Once the instantaneous bubble properties at each section of the bed are calculated, a number averaging was used to calculate the time-averaged bubble properties with bed height.

$$\Theta = \begin{array}{c} \Sigma^n\_{l=1}(\Theta\_l)/N \end{array} \tag{31}$$

Where is any of the bubble property such as aspect ratio, diameter, rise velocity, and N is total number of bubble properties recorded during the total averaging time considered.
