Figure 3 presents original experiment image samples of the flow channel in boiling conditions. Its characteristics include: 1) The gas phase occupies a large proportion of the flow channel, and on occasion the bubbles can fill the cross section of the flow channel; 2) The flow pattern is mostly slug flow or churn flow, and the boundary between gas and liquid phase is blurred at high flow velocity; 3) The void fraction changes drastically and the sizes of bubbles/slugs in different working conditions and different time are quite different. The above characteristics, which mean the unevenness of the gas phase distribution in space and time, are mainly caused by the narrow channel structure and heating conditions. As a result, it is difficult for most traditional recognition methods based on single scales or features (such as edges, pixel thresholds and morphological structures) to obtain stable and efficient results. In order to solve these problems, this paper proposes a new image segmentation algorithm of FCN method based on deep learning technology. It can extract information from pixel level to abstract semantic concepts through multi-layer convolution operations. It also uses up-sampling layers and multi-scale fusion technology to further optimize the results and achieve higher segmentation accuracy. At the same time, we enhance the adaptability of the FCN algorithm by automatically learning various features from a large amount of data at different times, which makes it suitable for identifying complex gas-liquid images in narrow channels.

In this paper, FCN algorithm is utilized to extract the gas phase part in Figure 3, and realize the segmentation of gas and liquid. The flow channel part of the original captured image (the input of the FCN network) can be defined as C : C W × H = { C ( 1 ) , C ( 2 ) , C ( 3 ) , ⋯ , C ( i ) } , i = K (1) Where K is the number of the experimental image set, and C ( i ) is the i th single-frame image (RGB) of size W × H . The output pixel-level segmentation results are defined as G G G W × H = { G ( 1 ) , G ( 2 ) , G ( 3 ) , … , G ( i ) } , i = K (2) The output of the FCN are binary images of the same size  W × H , in which pixels value of one mean to gas phase and value of 0 mean to liquid phase. Then the results are applied for calculating the void fraction of the narrow channel. The flowchart of the image-processing algorithm is shown in Figure 4.

Figure 5 is an overall schematic diagram of the structure of FCN model established in this paper. As shown in the figure, the FCN model is mainly composed of two parts. The left part in the box is called convolution (downsampling) part, which is mainly composed of convolutional layers and pooling layers to extract various features of the input image. The right box is called deconvolution (upsampling) part, which is mainly composed of deconvolution layers and a classification layer. It is used to restore the original image size from the high-dimensional feature map and identify each pixel. The methods used in these two parts are introduced below.

In this paper, the neural network training adopts the traditional back propagation algorithm, and its core idea is to obtain the partial derivative of the loss function of the samples, so as to adjust the weight and bias of the network operation layers (convolutional and upsampling layers in FCN model) along the gradient descent direction to minimize the loss function.

Loss function. Since it is a binary classification problem (gas and water), the cross entropy formula is used for the loss function: L ( R , G ) = − 1 N ∑ i = 1 N [ g i   ·     log ( g i ¯ ) + ( 1 − g i ) · log ( 1 − g i ¯ ]   (6) where R and G are respectively the training input samples and labels (ideal segmentation results), N is the total number of input pixels, g i and g i ¯ are the label result values and their occurrence probabilities (calculated by the network layers).

Training optimizer. In training process, the FCN model applies the VGG-16 network pre-training value as the initial value, and optimizing the network by the Stochastic Gradient Descent (SGD) optimizer with momentum. SGD optimizer can quickly find the direction of gradient descent and converge to the global minimum through multiple iterations. Momentum can make convergence faster to avoid staying in the local extreme value area for a long time, and suppress the oscillation to increase the calculation stability. Calculation formula can be written as: v t = γ   ·   v t − 1 + ∇ f ( w t ) ,   w t + 1 = w t − α v t   (7) where w is the network’s weight of layers, ∇ f ( w ) is the gradient of the loss function, v represents first order momentum, α is the learning rate (lr) which affects the rate of convergence, γ is the momentum factor to control the influence of the momentum which the t − 1 moment has on t moment.

Performance evaluation. In performance evaluation of the FCN model, we use pixel accuracy (PA) and mean intersection of union (MIoU) of foreground to measure segmentation accuracy. PA means the proportion of correctly marked pixels to total pixels. MIoU calculates the mean ratio of intersection between segmentation result and ground truth mask to the union of them. In the binary classification problem in this article, PA and MIoU can be calculated with the following formula: PA = G 1,1 G = G 1,1 G 0,0 + G 0,1 + G 1,1 + G 1,0 MIoU = 1 2 ( G 1,1 G 0,1 + G 1,1 + G 1,0 + G 0,0 G 0,1 + G 0,0 + G 1,0   )   (8) where G i , j means the number of pixels that belong to class i and are predicted to be class j . Class 0 refers to liquid phase (background) and class 1 refers to gas phase. As defined, the values of PA and MIoU are between 0 and 1. The closer the value is up to one means the recognition effect is closer to the ground truth, and the accuracy of the model is higher. Establishment of training set. The training set used in the training network mainly adopts the method of Pan et al. (2018), which is based on the traditional image method of two-step morphology to process the experimental images of narrow channels, and then manually selects 1,500 binarized images with clear bubble morphology and high accuracy as training samples. We partition the samples into training set (85%) and test set (15%). Considering the training cost and accuracy, the images are cut and the flow channel part are selected. To avoid overfitting and increase the stability of the model, further strategy like data augmentation is used in the training, images receive both horizontal and vertical flip and added to the training set.

Training environment and configuration. This paper employs the deep learning framework Pytorch for network construction and training. The experimental hardware environment is AMD 4800H CPU, 16 GB memory, NVIDIA RTX2060 graphics card for GPU acceleration.

The data set used in the experiment in this paper comes from the images collected by the visual narrow channel flow boiling experiment system of Tsinghua University. Each working condition point records 13,800 pictures (1,000 frames per second and the acquisition time is 13.8 s). Three typical conditions are chosen and the operating parameters are shown in Table 2.

Figure 8 shows the train loss of the network and MIoU of the test set under different learning rates and momentum factors. From the picture, we can see the learning rate less affects the training process, while higher momentum can effectively improve computing stability. By comparing the results, we choose learning rate = 0.01 and momentum factor = 0.9. After 33,500 iterations, the train loss basically converges, and the average PA and MIoU of the test set reach 0.991 (99.1%) and 0.982 (98.2%) respectively, which can meet the requirements for convergence speed and training accuracy, and reduce computational oscillation. Then the FCN model established in this paper is applied for the experimental data set and part of the processing results are shown in Figure 9, achieving recognition of the gas phase in the image under the conditions of different void fraction and different flow patterns. It can be seen that the method has basically identified the gas phase’s morphology, especially in the slug flow (Figure 9 a1 and a2) and churn flow (Figure 9 a3 and a4) of high void fraction. This verifies the portability and reliability of this method for different working conditions and flow patterns in boiling experiments.

As shown in Figure 10, the method in this paper is compared the traditional edge detection/filling algorithm and the two-step morphological method of Pan et al. (2018). It can be seen that in working condition A of low void fraction, the results of FCN method and the traditional algorithm are not much different, and both can identify bubbles with clear boundaries and regular shapes. The FCN method has a relatively better recognition effect on small bubbles. In working condition B and C where the void fraction is high, the traditional algorithm will overfill the gap between the bubble and the vapor slug, resulting in the unrecognizable gas phase areas and may detect an excessively high void fraction value. The designed morphological method can better extract the characteristics of local irregular bubbles, but it requires manual setting of parameters. When the pixel value of the picture changes greatly and the threshold parameters cannot be matched, a large block of recognition defects may occur like Figure 10C. The method in this paper also has some local recognition defects inside and between the bubbles, but it basically realizes the recognition of bubble shape. It also has better applicability for different flow patterns to improve the overall recognition accuracy, and does not require manual adjustment of parameters, which saves design costs.

The void fraction at the outlet of the flow channel is of significance to the calculation of the two-phase model and determining the flow pattern. After the gas-liquid recognition results are obtained by the method in this paper, the numerical matrix H ( i , j ) (size =   M × N ) near the outlet is extracted from the output binary image. The following formula is for calculating the void fraction of the outlet in narrow channels: α = ∑ i − 1 M ∑ j − 1 N H ( i , j ) M × N (9)

The time-dependent change of the void fraction (0–2.5 s) obtained by the method in this paper is shown in Figure 11. It can be seen that due to the small size of the narrow channel, the bubble develops more rapidly after its generation, which cause the outlet void fraction extremely fluctuates with time. In condition 1, the flow channel is mainly dominated by annular flow, a large section of gas column is accompanied by intermittent liquid film oscillation, and the proportion of outlet void fraction alternately changes with a period of about 0.2s. Operating condition two and three have lower heat flux density than condition 1, and are dominated mainly by slug flow and churn flow. So we can observe from Figure 11 that intermittent steam generation phenomenon occurs, resulting in a rapid and regular decrease and rise of the void fraction.., which is consistent with the high speed photography images at the corresponding time.

For further verifying the accuracy of the neural network recognition results, we use the theoretical method to calculate the time-averaged void fraction under experimental conditions and compare it with the average value obtained by the method in this paper. The formula of energy conservation method for calculating the mass quality of the gas at the outlet of the narrow channel is shown in the following: x = P ( 1 − k ) M − h l , out + h l , in h v , out − h l , out (10) where x is the mass quality of the gas, P is the heating power, k is the heat loss ratio, M is the mass flow rate, h is the enthalpy value, the subscript l indicates the liquid phase, v indicates the gas phase, the subscript i n means the inlet of the test section while the o u t means the outlet. In calculating the heat loss ratio k , the influence of the parameters is analyzed and it is found that the mass flow causes less change, indicating that the internal flow has little effect on the heat dissipation. In addition, it is natural convection in a limited space outside the test section, and the heat transfer conditions are basically constant. Therefore, the two-phase heat dissipation loss ratio can be derived by fitting the heat dissipation data of single-phase flow: l g k = ( − 0.03338 + 2 × 10 − 4   Δ   T − 3 × 10 − 6 G ) q − 6 × 10 − 4   Δ   T 2 − 0.00362   Δ   T − 5 × 10 − 5 G + 0.19232 (11) In this formula, Δ T is the degree of subcooling (°C),   G is the inlet mass flow rate (kg/s), and q is the heat flux density (kW/m²).

So far, numerous of empirical, semiempirical and analytical two-phase flow void fraction correlations have been developed, and according to many review literatures these formulas can be mainly divided into slip ratio model, Lockhart-Martinelli parameter based model, drift flux model, K α H model, etc. (Vijayan et al., 2000; Dalkilic et al., 2009) According to Huang et al. (2013), the slip ratio model which essentially specify an empirical equation for the slip ratio S is more suitable for narrow channels with relatively low outlet mass quality. Therefore, according to the survey, three commonly used calculation models of void fraction are selected as shown in Table 3.

The void fraction calculated by our FCN method is instantaneous and the data is time-averaged for comparing with the theoretical results: α ¯ = ∑ i = 1 K α i K (12) Where α ¯ is the time-averaged result of the FCN model, α i is the instantaneous void fraction of the corresponding images in experimental data set, and K is the number of the experimental image set. The comparison results are listed in Figure 12. It shows that the relative deviation between the method in this paper and various empirical models is within ±11%, which illustrates the accuracy of the FCN model proposed in this paper. In addition, the neural network method uses the tensor operation method based on the pre-training weights, and the processing speed has also been improved. After further optimizing the network, it can be applied to real-time monitoring and online void fraction identification.