3.1. Gray Distribution of Image
The experimental images of the gas-liquid flow in the mixing zone are composed of a large number of pixels. The gray distribution of the experimental images can be obtained by counting the light and shade degree of each pixel. Therefore, the gray distribution is actually the statistical result of the brightness and darkness of the experimental image.
When the working conditions of the nozzle change, as the gas-liquid flow pattern in the nozzle gradually changes from flow focusing to flow blurring, the liquid cone in the mixing zone gradually distorts and finally breaks, and the mixing degree of gas-liquid two-phase fluid increases. Under different conditions, the distribution of the gas and liquid fluid in the mixing zone is different, and the density and other physical parameters of the fluid in different positions of the mixing zone are different. The most important thing is that the size, quantity and distortion degree of the gas-liquid interface in different positions of the mixing zone are different. The difference of these parameters makes the transmission, refraction and reflection ability of the gas-liquid flow to the light at different positions in the mixing zone different, resulting in different gray distribution of the experimental images. This makes it possible to use the gray distribution of the experimental images to study the two-phase flow in the mixing zone under different conditions.
In this section, the basic concept of the gray distribution of the experimental images is described. And in
Section 3.2, the relationship between the gray distribution of the experimental images and the flow patterns (flow characteristics) inside the nozzle is qualitatively analyzed through several cases. Through the qualitative relationship between the flow patterns (flow characteristics) and the gray distribution curves, we can study the gas-liquid flow and mixing inside the flow focusing/blurring nozzle.
For each pixel, the gray scale is divided into 0 to 255, total 256, gray levels. Close to 0 level gray, indicating that the image is dark; close to 255 level gray, indicating that the image is bright. Therefore, for an experimental image
I(
M,
N), its gray histogram can be expressed as [
21]:
where
rk is the
k level gray of the image
I(
M,
N),
nk is the number of pixels in image
I(
M,
N) with grayscale value
rk, and
L is the largest gray level of all images.
When comparing the gray distribution of different images, the image size will have a significant impact on the number of pixels which will reduce the accuracy of the gray histogram. In order to avoid the influence of the image size, we defined the normalized gray histogram as [
21]:
where
M and
N are the number of pixels in the row and column of the image, respectively. The components of P(
rk) are estimates of the frequency of gray levels occurring in an image.
In this paper, the gray histogram and normalized gray histogram of experimental images are obtained by Matlab software. At present, the research results on the gas-liquid flow in the mixing zone of the flow focusing/blurring nozzle using the gray distribution have not been reported. Therefore, the feasibility of using the gray distribution to study the gas-liquid flow in the mixing zone will be analyzed below.
3.2. Feasibility Analysis
For the flow focusing/blurring nozzle, when the flow parameters and the nozzle structure are different, the two-phase interaction in the mixing zone is different, so the flow pattern will be different. Different flow patterns will lead to different gray distribution of the experimental image. In this part, we will analyze the change of the gray distribution of the experimental image with time and study whether the gray distribution of one experimental image can represent the gray distribution of the experimental images under a certain working condition. Then, we will choose several cases. By comparing the difference of the gas-liquid flow images in mixing zone and the difference of the gray distribution of the experimental images in these cases, we can give the relationship between the gray distribution of the experimental images and the flow patterns (flow characteristics), and verify the feasibility of gray distribution analysis methods to study gas-liquid flow inside the nozzle, to a certain extent.
Figure 3 shows the gray distribution curves of the experimental images in a mixing zone at different times when the gas flow rate is 40 L/min, the liquid flow rate is 600 mL/min, the orifice diameter is 5 mm, and the tube hole distance is 1 mm.
It can be seen from
Figure 3 that the gray distribution of the experimental images of gas-liquid flow inside the nozzle has certain differences at different times. This difference may be caused by the high frequency instability of the turbulent flow. The effect of high frequency turbulence instability can be reduced to a certain extent by averaging the gray distribution of the experimental images at different times under the same condition, but it cannot be completely eliminated. The average value of the experimental image’s gray distribution curve is also affected by many parameters (such as the number of the experimental images). When we study the gas-liquid mixing in the nozzle through the gray distribution of the experimental images, we pay more attention to the overall trend of the gray distribution curve and we can see from
Figure 3 that the difference of the gray distribution curve caused by high-frequency turbulence instability has little effect on the overall trend of the gray distribution curve. Therefore, for one working condition, it is feasible to use the gray distribution of one experimental image to study the gas-liquid mixing in the nozzle.
Figure 3 also shows that the analysis results of the gray distribution analysis method for gas-liquid flow in the nozzle are statistically convergent.
Figure 4 shows the images and gray distribution of different flow patterns in the mixing zone obtained by the experiment. The gas-liquid flow images in the mixing zone of the nozzle are marked with a red dotted rectangular box, which is also the area to extract the gray distribution of the experimental image. In the experimental images of
Figure 5 and
Figure 6, the extracted area of the gray distribution curve is also labeled.
As can be seen from
Figure 4, for case 1, the gas-liquid two-phase fluids in the mixing zone do not mix; we can observe the liquid column in the mixing zone, and the boundary of the gas-liquid two-phase fluids is relatively clear, so the flow pattern in the mixing zone is flow focusing. At this time, the gas-liquid interaction in the mixing zone is weak, the light enters the SLR camera through transmission and the brightness of the pixel points is high and uniform, so the image has a high gray level and a good concentration. For case 3, the boundary of the gas-liquid two-phase fluids in the mixing zone is fuzzy, the gas-liquid flow in the mixing zone is close to fog and the gas-liquid mixing is good, so the flow pattern in the mixing zone is flow blurring. At this time, the liquid in the mixing zone is broken into tiny droplets by gas, and the light enters the SLR camera by scattering. The brightness of the pixels is low but still relatively uniform, which reduces the gray level of the image, but the concentration of gray distribution is still very good.
In case 2, the boundary of the gas-liquid two-phase fluids in the mixing zone is also fuzzy. The gas-liquid fluids mixed, but it is obvious that the gas-liquid flow in the mixing zone is not uniform. The flow pattern in the mixing zone is in a transition state between flow focusing and flow blurring. At this time, there are both liquid drops and distorted two-phase interface in the mixing zone, which makes the light enter the SLR camera through transmission or scattering. Therefore, the pixel points of the image are either bright or dark, which is very nonuniform, resulting in a large range of gray distribution of the image and a smooth gray distribution curve.
Figure 4 and its analysis show that the gray distribution of the experimental image is different when the flow pattern of the mixing zone of the flow focusing/blurring nozzle is different, so it is completely feasible to use the gray distribution of the two-phase flow images to identify the flow pattern. In fact, there are many methods to distinguish the flow pattern in the mixing zone, and the two-phase flow in the mixing zone under the flow blurring is the real difficulty in the study of this nozzle. Generally, the mixing intensity and uniformity can be used to characterize the two-phase mixing in the mixing zone under the flow blurring, but there is no suitable instrument to measure these two parameters. The gray distribution of the experimental images can be used to analyze the gas-liquid mixing intensity and uniformity.
Figure 5 and
Figure 6 show the experimental images with different mixing intensity or uniformity and their gray distribution curves, respectively.
Figure 5a,b show the two-phase flow images in the mixing zone with different mixing intensity. Compared with case 1, the gas-liquid flow in the mixing zone is closer to fog in case 2, and the boundary of the gas-liquid fluid is more fuzzy, which indicates that the gas-liquid mixing intensity in case 2 is stronger. By comparing the gray distribution of case 1 and case 2, it can be found that the average gray scale level of the images is lower when the mixing intensity of two-phase is larger. This is because, when the gas-liquid mixing intensity is relatively high the number of broken droplets is large and the size of the droplets is small, which makes the scattering effect stronger. Therefore, the light entering the image acquisition equipment is weakened and the average gray level of the image is relatively low.
Figure 6a,b show the two-phase flow images in the mixing zone with different mixing uniformity. Compared with case 2, the gray scale level of the gas-liquid flow images at different positions in the mixing zone in case 1 is significantly different, which indicates that the uniformity of the gas-liquid fluid mixing in the mixing zone in case 1 is low. The gray distribution of the images indicates that the frequency value of the maximum frequency gray scale level is larger when the gas-liquid mixing is uniform and the gray distribution curve of the image is more concentrated. When the two-phase mixing is nonuniform, the size of the liquid drops at different positions in the mixing zone is different, and the scattering effect is different, resulting in different gray levels of the pixels. When the two-phase mixing is uniform, the scattering effect of the liquid drops at different positions in the mixing zone is the same, and the gray scale level of the pixels is almost the same. Therefore, when the two-phase mixing is uniform, the gray distribution curve of the two-phase flow image is more concentrated.
The above research shows that the difference of the flow pattern, the gas-liquid mixing intensity and mixing uniformity in the mixing zone can be described by the gray distribution of the image. Therefore, the influence of flow parameters and nozzle structure on the flow pattern, the gas-liquid mixing intensity and uniformity can be studied by gray distribution of the images. However, factors such as the position, number and illumination intensity of the experimental light source, as well as the preliminary processing of the experimental images will affect the gray distribution of the experimental images, so that the accuracy of using the gray distribution of the images to study the two-phase mixing is greatly reduced. Therefore, during the experiment in this paper, the relative arrangement of the light source and the image acquisition equipment is always maintained and the illumination intensity is constant. In addition, when using Matlab software to extract the gray distribution of the experimental images, we adopted the same parameters to ensure that the influence of image processing on the research results was minimized. On the whole, it is feasible to use gray distribution of the images to study two-phase mixing inside the nozzle. The control of the experimental method and the conditions can ensure the accuracy of the research results.