Experimental estimation of liquid phase concentration in aerosol jet

. Rapid-mixed models are a key tool in the numerical solution of aerosol flow evaporation problems. Despite the fact that these models are mainly based on analytical arguments, they have shown fairly good reproducibility in practice. However, with the advent of the DNS results, cases of discrepancies with the classical theory of droplet evaporation began to be discovered, which require an experimental study of the problem. The present paper shows an experimental method for estimating the concentration of the liquid phase in aerosol flows based on digital video processing.


Introduction
To understand the physics of turbulent aerosol jets, various theoretical and numerical studies have been carried out that complement traditional experimental studies. One of the first attempts to describe the evaporation process of spherical droplets entrained in a gas flow is based on the well-known d-square law [1][2][3]. The law states that the surface of a drop decreases linearly with time in quiescent media with uniform and fixed thermodynamic properties (temperature, vapor concentration, etc.). Using the d-squared law, [4,5] developed a rapid-mixed model. Later, [6] proposed an improved droplet evaporation model applicable to inhomogeneous and time-dependent environmental conditions. These models prove self-efficiency and reliable in reproducing the dynamics of liquid droplet evaporation in direct numerical simulation (DNS) and in large eddy simulation (LES) [8][9][10][11][12][13]. However, recent work [7] on direct numerical simulation of an aerosol jet at Reynolds number of 10,000 raised the question of the accuracy of the dsquare law. The authors found that at low Reynolds numbers, the use of this law based on environmental conditions leads to a significant overestimation of the droplet evaporation rate. Such theses appear due to a rather significant gap in the field of experimental methods for estimating the concentration of the liquid phase in high-speed aerosol flows. Although various numerical and experimental studies and theoretical developments have already been carried out, it is still premature to conclude that a satisfactory understanding of the dynamics of the turbulent flow of aerosol particles has been achieved. The capabilities of the existing analytical models involved in the reproduction of the phenomena are not fully confirmed experimentally, most of the numerical data sets obtained from the DNS results are limited by relatively low Reynolds numbers due to high computational requirements.
The present paper shows a method for estimating the concentration of the liquid phase in aerosol flows based on processing the high-speed digital video recording. Figure 1 shows an experimental setup. The experimental bench comprised the compressor to create a flow of a gaseous medium, liquid tank, liquid and gas flowmeters, nozzle, ultrasonic transducer for creating dispersed liquid droplets, camera, laser, and external jet blowing system.

Experimental setup
The mass flow rate (3.8 m 3 /h) of atmospheric air at room temperature (ρa=1.2 kg/m 3 , νa=1.51·10 -5 m 2 /s, Ta=293 K, Pa=101325 Pa) was realized using a centrifugal compressor 1. Air flow divided into two streams: to create an aerosol jet and external blowing of the jet. The air flow rate for the aerosol jet was adjusted by a ball valve 2 and measured by an LZM-15T gas flowmeter with an 4%-accuracy of flow rate measurement in the range from 1.6 to 16 m 3 /h. When carrying out test experiments, the air temperature in nozzle 7 was also measured. Based on the measurement results, it was confirmed that the air heated after the compressor moving along the path has time to cool down to the ambient room temperature. The air flow rate for the external jet blowing was also regulated by a ball valve and measured by an ultrasonic flowmeter. The external flow around the aerosol jet was implemented in a transparent cylindrical 0.2 m diameter and 2 m length channel. The ratio of the channel radius R to the radius of the nozzle exit section was R/r=20.4, which according to the results [7,14] is quite sufficient for the given boundary conditions (the area of jet propagation does not reach the boundary layer of the flow in the channel). The averaged bulk air velocity in channel 10 was 2.2 m/s, Reynolds number Re=29000. A turbulence generating grid with 5 mm cell size, 1.2 mm steel wire diameter, and 36% solidity was mounted to maintain a uniform cross-sectional velocity at the channel inlet.
Regulated by ball valve liquid (acetone CH3COCH3 ρl=791 kg/m 3 , νl=4.1·10 -7 m 2 /s, Tl=293K) flowed (flow rate 77 g/min) from 5-liter-volume storage tank 6 with a slight pressure in the air cushion, and was measured via 4 LZB-3 liquid rotameter with 4% accuracy in the range from 4 to 40 ml/min. After the rotameter, the liquid entered to the acoustic transducer 5, where under the action of mechanical vibration of the emitter membrane, it was crushed into drops with a size of 1 to 20 μm. Using the acoustic drop crushing method in the setup allow to obtain more uniform distribution of aerosol particle sizes before subsequent crushing of the remaining large drops in the nozzle 7.
Aerosol acetone b air flow with 0.26 mass flow ratio was mixed in the nozzle 7. The design of the nozzle (Figure 2) was identical to the nozzle [14]. In DNS [7], the outlet diameter was also 9.8 mm. The measurement area (Fig. 3) was illuminated by a continuous diode-pumped solidstate laser (DPSS-Laser) KLM-532/5000-h. The flow pattern in the jet symmetry plane was recorded with a monochrome high-speed camera Fastec HiSpec 9 with the frame resoltution of 665 × 110 pixels (scaling factor of 0.1961 mm/pixel), frame rate f=2530 1/s and recording time of 3.5 s. The camera was equipped with a Navitar 1''F/0.95 lens with manual focus control. 8225 digital video were refined by median filtering, which made it possible to reduce the level of white noise on the velocity oscillograms due to the exclusion of the reflections of dispersed particles from the frames and the general stabilization of the gray gradation in the images.
The image in Figure 4 is compared with the visualization of the macroscopic structures of a turbulent jet at the same Re number obtained from the DNS [7]. From this comparison, it can be seen that visually the DNS results are very similar to the experiment.

Results
In DNS, the average Euler mass fraction of the liquid phase Φ=ml/ma is defined as the ratio of the mass of the liquid phase ml to the mass of the carrier phase ma calculated in each cell. Having at our disposal a digital storyboard of the aerosol jet flow with dispersed particles illuminated by a laser, we can also use this formulation.
To estimate the eulerian mass fraction of liquid in each pixel of the image, a specially prepared algorithm based on the conversion of grayscale in a digital image into the concentration level of the liquid phase has been used. A similar algorithm is used in medicine to recognize the results of computed tomography. After the median filtering method used at the first stage of digital image processing, the black area on the digital frame was considered the area with no liquid phase, the gray area was considered the area with the presence of the liquid phase. The averaging algorithm consisted in determining the average level of grayscale at each of the 8225 video frames in each pixel and building a single field of average concentration based on these data. Figure 5 shows the result of averaging all frames of the video recording. The ratio between the grayscale level in the pixel and the concentration level was determined from the grayscale level outside the jet, where the concentration of the liquid phase in the gas flow was known Φ=0. Unfortunately, this approach does not give a numerical estimate of Φ; we can only see the nature of its distribution. Nevertheless, comparison with the DNS results for the field Φ/Φmax (where Φmax is the maximum established value) can be considered quite successful ( Figure 6). The measurement results also showed the presence of an extremum in the region of the y/R=11 and a further drop in concentration of dispersed phase along the jet length due to the evaporation of drops. The physical substantiation of this extremum is described in detail in [15] and is related to the inertia of the drops in the field of the damped carrier flow velocity.

Conclusions
Rapid-mixed models are a key tool in the numerical solution of aerosol flow evaporation problems. Despite the fact that these models are mainly based on analytical arguments, they have shown fairly good reproducibility in practice. However, with the advent of the DNS results, cases of discrepancies with the classical theory of droplet evaporation began to be discovered, which require an experimental study of the problem. The present paper shows an experimental method for estimating the concentration of the liquid phase in aerosol flows based on digital video processing. The experimental estimation of eulerian mass fraction of the liquid phase by the distribution of pixel color intensity in grayscale agree well with the distribution of the ratio of the liquid phase mass to the mass of the carrier phase calculated in each cell using DNS.