Study of rivulet deflections and interactions on the surface of heated liquid film

. Study of rivulet deflections and interactions on the surface of vertical flowing heated liquid film at Reynolds number Re = 75 and initial temperature T 0 = 25 o C has been carried out. For recognition of rivulets and calculation maximal deflection amplitude neural network YOLOv5 was used. Distribution of rivulets’ interaction is presented. Obtained results are in good agreement with the data for Re = 33.


Introduction
Gravitational film flows are widely used in industrial devices.Understanding the processes occurring in the heated liquid films is very important for the design and implementation of such mechanisms.
During isothermal gravitational film flow 2dimensional waves decay to 3-dimentional ones.The wavelength of instability to transverse threedimensional perturbations decreases with increasing Reynolds number [1].Transition from 2D flow to 3D waves is accompanied by essential redistribution of liquid in the longitudinal direction.[2] Different shapes of 3D-structures are observed.The rivulet formation mechanism was described in [3]: when the 3D wave passes along the residual liquid film layer, there takes place a lateral suction (inleakage) of the liquid to under the wave crest and its discharge through a wake with an increased film thickness behind the wave.This wake behind the wave induces synchronization of the wave pattern: the waves align in chains thus making the liquid being sucked continuously to the same flow regions, which gives rise to rivulets.
When liquid films flow along heated surfaces, thermocapillary structures of different types are also formed.Structures of type A was firstly described in [4], where flow of 25% alcohol solution along small size heater of 6.5 x 13 mm at low Reynolds numbers was studied.At heat flux density higher than the threshold value, a horizontal roller was formed on the upper edge of the heater, and this led to liquid movement in the form of vertical rivulets and a thin film between them.In regime B, the rivulet flow formed gradually with increasing heat flux and distance from the upper edge of the heater.Such structures were described in [5], where flow of dielectric liquid FC-72 along the heater with size of 150х150 mm in the wide range of Reynolds numbers was explored.
In [6] film flows of water and water-ethanol solutions along an inclined electrically heated foil were studied.Heat transfer processes were discussed.Thermocapillary phenomena in flowing down heated liquid films were reviewed in [7].Interaction between the waves and thermocapillary structures results in formation of rivulets on the liquid film surface, their motion across the flow (deflection), and interaction with each other (Figure 1).As a characteristic of the rivulets deflection, the maximal amplitude was used.The maximal amplitude of deflection was defined as the distance between the extreme right and extreme left positions of the rivulet crest during thermal imaging (600 frames, 6 second) [8].In [9] 4 types of rivulet interactions were distinguished: absence of interactions (type 0), merging (type 1), bridge (type 2) and branching (type 3).The influence of instabilities and structures of different types on water film breakdown was investigated in [10].It was shown, that interaction threedimensional waves with thermocapillary structures and rivulet deflection leads to an increase of liquid film stability and critical heat flux corresponding to the film breakdown.

E3S Web of
The aim of the work is to detect rivulets on the surface of heated liquid film using a neural network and to study deflections and interactions of rivulets at Reynolds number Re = 75 and initial temperature T0 = 25 o C.

Experimental setup 2.1 Circulation circuit
The setup was a closed circulation circuit, including working section, thermostat with a pump, pipelines, rotameter and stop valve.
The working section consisted of a vertical textolite plate with film former, thermostabilizer and heater placed on this plate.A flat copper heat exchanger of 100 mm length and 150 mm width was used as the heater.Hot water was pumped through the rectangular channels inside this heat exchanger.The average heat flux was calculated by the water temperature difference at inlet and outlet of the heater and mass flow rate of water.
Distilled water with addition of dye (rhodamine 6Zh) was used as the working liquid.Water with dye was pumped to the film former, which included an accumulation chamber, dispenser, and nozzle with a calibrated flat slot.The working liquid flowed down along the plate and returned by gravity to the thermostat.

Measuring system
Synchronous measurements of temperature and thickness fields were carried out.Temperature distribution on the water film surface was measured by the infrared scanner Titanium 570M.
Thickness field was determined by the modified fluorescence method.To excite the fluorophore, a laser with diode pumping was applied.The digital camera registered light, reradiated by fluorophore.
The experimental setup is described in more details in [11].

Detection of rivulets using neural network 3.1 Neural network YOLOv5
For automatic detection of rivulets neural network YOLOv5 (https://github.com/ultralytics/yolov5)was used.YOLOv5 has an architecture of a One-Stage detector approach, which predicts coordinates of a certain amount of bounding boxes with the results of classification and probability of an object being there and further correcting their location.Bounding box is a rectangle that marks the boundaries of an object.Each such rectangle is a set of coordinates, which correspond upper, lower, left and right boundaries.
The net scales the original image into a few feature maps.Feature map is a processed image which is represented as a tensor and contains so-called "features" which are then used by a network to form correct result.Obtained feature maps are rescaled to a same resolution and concatenate.Then classes and bounding boxes are predicted for objects, after that the most probable bounding box is picked for every object.
In this work the network predicted bounding boxes with rivulets inside them.

Training process
Neural network training is a process in which incoming data is distributed between neurons of using synapses.The transmission is carried out until the data reaches the output layer, where it is transformed into a prediction.This operation is called "forward propagation".As soon as the prediction is received, the error is calculated, and backpropagation is performed in accordance with it.The purpose of this action is to bring the synaptic weights to optimal values when moving from the output layer to the input.In this work for training process, images from IR scanner were binarized (Figure 2).Then for every image a text file was created and coordinates of bounding box for each rivulet on the image were written in this file.
Dataset for training consisted of 600 binarized images and text files for them.This dataset was loaded to neural network.

Neural network image processing
Binarized images (like the one in the figure 2, but without text files) were loaded to neural network.Processed image is presented in the figure 3.Each rivulet is located inside bounding box defined by the network.
The bounding box is a set of coordinates.Left and right sides of the rectangle correspond to far left and far right points of the rivulet on the picture.Maximal amplitude of deflection was defined as a difference between extremely right and extremely left coordinates across all frames of thermal imaging.Note, that the neural network calculates difference not between positions of the rivulet crest, as it is described in [8].Therefore, it is necessary to make a correction due to rivulet width (4mm).

Results
Maximal amplitude of deflection (Ar) was calculated for distance X = 75 mm.from upper edge of the heater.For each heat flux, Ar was defined as the distance between the extreme right and extreme left positions of the rivulet crest during imaging by infrared scanner (12 second).In details method of calculation is described in [8].
Different types of rivulet interactions are presented in the figure 4. [9] Numbers of interactions of each type were counted for different heat fluxes.As the type 0 (absence of interactions) there were considered rivulet−surface waves passing the observed area without interactions with other rivulets.All 600 frames made by infrared scanner were reviewed, and all interactions were fixed.Then diagram of distribution by types was constructed.The counting method is described in details in [ ].

Conclusion
Comparison between dependences of Ar on heat flux density at two different Reynolds numbers is presented in the figure 6.Data from neural network is given after correction due to rivulet width.
In both cases (Re = 33 and Re = 75) threshold growth is observed at heat flux density values corresponding to formation of thermocapillary structures of type A. Also, it can be noted, that spread of maximal amplitude at heat fluxes, exceeding the threshold value, significantly more, than at low ones.
The same agreement is observed for the distribution of interactions.When heat flux density reaches values  Rivulet deflection and interaction prevents the formation of dry spots on the heater surface and the development of critical phenomena in the liquid film.
This work was carried out under state contract with IT SB RAS 122022800489-6.

Fig. 3 .
Fig. 3. Example of image processed by neural network.

Figure 5
Figure 5 shows dependence of the maximal amplitude of deflection on the heat flux and pie charts of interactions distribution by types for different values of heat flux.At the heat flux values corresponding to formation of thermocapillary structures of type A threshold growth of the maximal amplitude of deflection
structures A, part of type 0 decreases, parts of types 1, 2 and 3 increase.