Practical sizing and bubble velocity processing

Commercial DynamicStudio software package was used for image acquisition and analysis for Particle Image Velocimetry (PIV) and particle sizing. The software also has tools for acquisition, configuration, analysis, and post processing of acquired data. This software has been used for detecting and measuring particle sizing but in this investigation, it was used to measure bubble sizes and velocities within two-phase flow in the simulated gas lift column. The software can provide information about fluid behaviours, such as bubble sizes (average, maximum, minimum and equivalent bubble diameters), velocity of bubbles, bubble area and bubble count, which are important for the distribution of bubbles. In addition, this package has an interesting feature known as shadow processing. It is capable of detecting bubbles’ shapes and edges and has an adaptive PIV function to show bubbles’ velocity profiles. This

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feature captured and showed details and observations about the interactions between bubbles, especially when bubbles were forming and collapsing. This fluid dynamic process was achieved statically and dynamically. This means, the software allows the user to capture bubble sizes and their velocities in one frame and double frames. This feature allow the user to connect all frames together to give continuous flow. Finally, there are several steps that must be followed to distinguish between gas phase (air bubbles) and liquid phase (water) and capture bubble sizes and their velocities in the simulated test section. These steps are summarised and shown in Figure 3.9.

(a) Model Calibration (b) Image min/max

(c) Image arithmetic Image (d) Image masking

(e) Image processing library & double frame (F) Shadow processing & sizing

64 The following briefly describes these steps:

a) Model calibration

The calibration of the model is an important step, because the conditions of recording videos and digital camera positions can be changed from time to time during the experiment. Therefore, when frames are imported to the model, the first frame can be used as a starting point for other remaining frames. Thus, the calibration of this frame and measuring its scale factor are essential, and subsequently these calibration settings can be applied for the remaining frames. For velocity measurements, the scale factor has to be determined. This can be achieved by using the calibrated first frame then duplicating to locate two points – A for the starting point and B for ending point – located at the measuring tape, and then the program will calibrate and calculate the measure scale factor for the remaining frames. Therefore, the velocity can be calculated for every bubble flowing from point A to point B. In addition, dewarping method is also useful to validate and/or verify the parameters, since dewarping one or more of the calibration images should produce a de-warped image where calibration markers are well aligned.

b) Image Min/ Mean/Max

This feature is useful to distinguish between phases (air and water). The 'Image Min/Mean/Max' method is located in the "Image Processing" category in the software settings. It is used to compute power mean greyscale values from a series of images. The Power Mean (or generalised mean) 𝑀_𝑃with exponent 'p' of the positive real numbers 𝑥_1,…….,𝑥_𝑛 is defined as:

𝑀_𝑃 = (𝑥_1,……..𝑥_𝑛) = (1 𝑛∑ 𝑥𝑖 𝑝 𝑛 𝑖=1 ) 1 𝑝 (3.1) Where

P = approaching minus infinity will return the minimum of all x-values and for p approaching plus infinity will return the maximum.

M1 (p=1) is the conventional (arithmetic) mean, and in the limit of p approaching 0 we get the geometric mean:

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𝑀₀ (𝑥_1,……..,𝑥_𝑛) = √∏𝑛 𝑛_𝑖=1𝑥_𝑖 (3.2)

The recipe supports already known p-values of:

P = +∞ (Maximum) ,P = 2 (Quadratic Mean), P = 1 (Arithmetic Mean), P = 0 (Geometric Mean), P = -1 (Harmonic Mean), P = -∞ (Minimum).

The Power means for a given series of values can be ordered as follows: Maximum > = Quadratic > = Arithmetic > = Geometric >= Harmonic > = Minimum The formula for power mean is defined with positive x-values in mind, but Maximum, Quadratic, Arithmetic and Minimum can be computed for negative values as well. The Geometric and Harmonic mean has been designed to return zero if just a single non-positive grey value is found among the input grey values.

c) Image arithmetic

As the name implies, this method enables arithmetic on pixel values and it can be performed on any type of image (for example 8-, 10- or 12-bit images) as well as floating point images, and can be applied to both single- and double-frame images.

There are four types of operation that can be performed in this method: i. Addition and subtraction

ii. Multiplication and division And the two operand types:

iii. Image as operand

iv. Constant value as operand

It is possible to combine the two operands, so for example subtract another image and then add the constant value. Finally, there is an option to perform data clamping on the result. This is useful to limit the output to a certain range.

d) Define mask

Define mask enables the user to define a mask for regions or areas of specific interest on the frame and avoid any regions not required for these investigations, which may affect the analysis and results.

66 e) Image masking

This method is used to mask images by assigning specific grey-values in regions defined by the software user as being of no interest. In order to apply this function, a mask has to be defined using the analysis method "Define Mask". The mask ensemble must contain either one static mask or N dynamic masks, where N equals the number of images.

f) Image processing library (IPL)

The filters featured in the IPL module can be used to smooth images (Low-pass), detect the bubbles’ edges (High-pass), and enhance image contrast (Low-pass & Morphology) as well as for non-linear calculations (Signal processing). It also includes various image-processing tools (Utility and Threshold). Finally, a Custom filter is available to allow filtering with user- defined filter kernels. The following are brief descriptions of some filters available in the image processing library:

i. Low pass filter

This filter is the simplest linear, local filter used to smooth images. This filter does not take spatial gradients inside the kernel into consideration, as shown in Figure 3.10. Thus, for applications related to fluid mechanics, kernel sizes of (3x3) or (5x5) are recommended. Larger kernel sizes may significantly increase numerical diffusion.

Figure 3-10: Low pass filter

67 3x3 1 1 1 /9 1 1 1 1 1 1 5x5 1 1 1 1 1 /25 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

ii. Morphology filters

Morphology filters are a class of nonlinear filters, which in their most basic form correspond to the minimum and maximum filters as shown in Figure 3.11. Combining these in different ways can however produce results that are more advanced.

 Dilation & erosion filters

 Opening & closing filters

 Tophat & blackhat filters

68 g) Shadow size processing

The package also includes the Shadow Sizing Processing as well as various filtering procedure that described above. The shadow size processing is a method where bubbles’ edges are detected and measured as shown in Figure 3.12. This feature provides detailed measurements, such as different bubble sizes, the bubbles’ positions, the shape of bubbles and the velocity of bubbles. According to Dentec Company 2015, this technique has no limitations in measuring sizes and shapes of bubbles or droplets, and it can be used both with transparent and opaque bubbles, as well as droplets.

Figure 3-12: Shadow-sizing technique