Figure
1.
Laser hologram optical beam diagram
| Citation: |
YU B Y，LYU H Q，ZHOU Y，et al. Predictive analysis of flow control in high-speed complex flow field based on machine learning[J]. Journal of Experiments in Fluid Mechanics, 2022，36（3）：44-54.. DOI: 10.11729/syltlx20210168
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The processes of fuel atomization, evaporation, mixing and combustion are critical to the performance of aeroengine combustor. In addition, the combustor performance directly affects the overall performances of aeroengine. Hence, investigation of the fuel atomization processes is essential for revealing the spray combustion mechanism of the aeroengine combustor under high temperature, high pressure and strong swirling conditions.
At present, the processes of spray atomization in combustor were studied mainly by experimental and numerical methods. M. Y. Leong et al[1], firstly studied the atomization in a gas turbine model combustor. They have studied the sprays structures under different flow conditions and obtained the jet trajectory equation. Cai[2] has studied the influence of nozzle structure on spray fields, and measured dispersed properties such as particle size distribution, velocity distribution by using a two-component Phase Doppler Particle Analyzer (PDPA) system. Based on high-speed photography, Particle Image Velocimetry (PIV) and phase Doppler technologies, Z. Feras[3] obtained the droplet velocity and particle diameter distributions of sprays generated by an airblast atomizer, which is widely used in aeroengine combustors, and the characterization of the sprays was investigated. Meanwhile, the influences of ambient pressure, airflow rate and liquid flow rate on droplets velocity and droplets particle size distribution were also studied. Based on PIV technology, Zhang Z.[4], Xu R.[5] and Deng Y.H.[6] have measured and studied the flow fields and spray characteristics in aeroengine combustors, and their works are fundamental to design and optimization of aeroengine combustor. Adopting the Euler-Euler method and the Euler-Lagrangian method, F. Jaegle[7] has studied the atomization and evaporation processes of spray in a model combustor, respectively. Hideki Moriai[8] has studied the processes of spray combustion in the aeroengine combustor using the methods of Large Eddy Simulation(LES) combined with Lagrangian method. A set of Single Swirler Lean Direct Injection experiments has been simulated by C. Anthony using National Combustion Code(NCC)[9], the comparisons between simulation data and experimental data indicate that simulation of the primary atomization process can more truly simulate the realistic combustion process. Cai W.X.[10] has carried out a numerical simulation of the two-phase combustion flow field of an annular combustor, and developed a visual calculation program of the three-dimensional two-phase chemical reaction flow field in arbitrary curvilinear coordinate system. Good results are obtained in comparison with the experimental results. Yan Y.W.[11] has also studied the spray combustion flow field in a baffled combustor. The Euler-Lagrangian method was used to simulate the gas-liquid two-phase spray combustion process, and the PSIC algorithm was used to solve the two-way coupling between two phases.
By now, very few researches have investigated whatever experimentally or numerically the processes of fuel atomization in combustor due to the complexity of combustor configuration and the restriction on experimental conditions. In this paper, cooperated with the Northwest Institute of Nuclear Technology, the spray field was measured using the particle field pulsed laser holography imaging technique. Meanwhile, the experiment was simulated numerically based on the LISA atomization model, and the simulation results were compared with experimental results.
In this paper, the particle field pulsed laser holography imaging technology is used to diagnose the spray fields in an aeroengine combustor. The method of the particle field pulsed laser holography imaging technology includes 3 steps, which are recording, reappearing and data processing. The laser ho-lographic setup (recording system) diagram is shown in Fig. 1. As shown in the figure, a pulsed laser beam emits from a Nd:YAG laser, and it is split into two beams. One passes through the beam splitter, and illuminates the spray field. The other beam reaches the recording platform directly after passing through fields but not scattered. Based on the two beams, the scattered light is interfered with the non-scattered direct light to form interference fringes on the platform. And the fringes are recorded by the holographic plate to form a hologram of the particle field.
The basic principle of the particle field holography are indicated here. As shown in Fig. 2, a beam passing through particles has an amplitude of B and a wavelength of λ, and it is irradiated onto a particle with a radius of a, and then the light field distribution on the particle surface is described.
The scattered light passing through the particles is interfered with the direct light (passing through the particle field but not scattered) to form an interference fringe. The fringe images are recorded by the recording medium. It is worthy to indicate that the distance from the medium to the particle is Z (Z satisfies the far field condition Z≫4πa2/λ), and thus a coaxial Fraunhofer hologram of the particle field is formed.
In this experiment, in order to prevent the holographic plate from being damaged by high-speed moving particles, the beams need to be handled carefully.
The optical beam firstly passes through the 4F imaging system, and the particle field is recorded at the appropriate position. Another beam as the reference beam passes through the optical splitter and is enlarged and collimated when passes through the collimated beam expander. The hologram is projected onto the developed hologram, and then the reconstructed image of the particle field is obtained on the observation surface in front of the hologram due to the diffraction effects. As described above, the hologram has been made through one of the light channels and can be reconstructed through another light channels as shown in Fig. 2(b). The particle size and location are extracted through analyzing the digital data and images. Through the image analysis, the spatial distribution and droplet diameter distribution of the spray during injection are obtained.
The holographic recorded light field intensity distribution is:
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(1) |
where m0 is the magnification of the recording system, r2=x2+y2, under the condition of parallel light incidence; J1 is a first-order Bessel function, and the distribution of the recorded light field intensity I(x, y) is represented by a sine or cosine osci-llation interference stripe modulated by a Bessel function. The first term represents a uniform background light, and the second term contains all the information of the particles, such as size, coordinates, etc., consisting of a high-frequency sine function and a low-frequency sine function, and representing the interference between the reference light and the scattered light. The third term is negligible compared to the striped information item, indicating the radiation distribution given by the diffuse diffraction. In the holographic recording process, theoretically, the number of lobes of the Bessel function should be recorded as much as possible. However, in the actual process, the maximum area of the center of the interference field must be recorded to record the particle size.
The intensity distribution of the reconstructed particle field is:
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(2) |
where circ is the uniformly distributed function, Γ=KB2/B′(B′ is amplitude of reconstructed light field, K is constant), and N=λZ/(2a)2 is the far field number.
The processing mainly includes 2 steps. Firstly, in order to get spray information on the X-Y plane, the holographic plate moves on the X-Y plane, and the Z-direction information of the spray is obtained by moving the CCD camera. So the entire particle field is obtained. Then, the last step is to analyse the digital data and obtain the particle coordinates and diameter.
LISA model is mainly based on the analysis of the stability of liquid membrane, and P.K. Senecal et al.[12-13] carried on the thorough research to this. At the formation stage of the liquid film, as shown in Fig. 3, the liquid film is wrapped around the air core from the nozzle outlet, and the mass flow rate and the axial velocity of the liquid phase determine the initial thickness of the liquid film together:
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(3) |
where m is the mass flow rate, the axial velocity component is u=Ucosθ, in which θ is the injection angle; h0 is the initial thickness of the liquid film; ρl is the liquid density and d0 is the nozzle diameter.
The magnitude of the velocity is related to the differential pressure through the nozzle:
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(4) |
where the velocity coefficient is Kv, expressed as a function of the nozzle form and the nozzle pressure, A.K. Lichtarowicz et al.[14] take Kv for 0.7. Taking into account the energy conservation and ensuring that there is sufficient mass flow, Kv is confined to less than 1.
For short waves, it is considered that the liquid ligament is formed by a liquid film within one wavelength, and for a long wave, the liquid ligament is formed within 2 wavelengths of the liquid film. The diameter of droplets formed from the liquid film is:
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(5) |
correspondingly, χ=1 is for short wave, and χ=2 is for long wave.
As the liquid ligament is perpendicular to the flow direction of the liquid film, we believe that the surrounding gas has little effect on its collapse, but the surface tension plays a major role in the breakup of the liquid ligament. It is assumed that the breakup occurs when the radius of the most unstable wave equals to the radius of the ligament, and then the unit wavelength would form a droplet. According to the quality balance, the diameter of the droplets is:
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(6) |
where 
The droplets formed by the primary atomization are suffered from aerodynamic force in the airflow, overcoming the surface tension force and the liquid viscosity force and are broken up into smaller droplets, which is called secondary atomization. The KH-RT secondary atomization model was developed by Reitz and Diwakar[15] and further improved by Reitz[16]. The KH-RT model considers that droplets formed by jet spray or liquid film breakage are affected by two kinds of unstable waves in the air flow, one of which is Kelvin-Helmhotz wave and the other one is Rayleigh-Taylor wave.
The smaller droplets diameter and breakup time generated by the KH breakup are:
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(7) |
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(8) |
where ΩKH and ΛKH are the maximum growth rate of the surface wave and the corresponding wavelength; B0 is constant, taken to be 0.61[17]; B0ΛKH > a indicates that the jet diameter is less than the breakup wavelength. Assuming that droplet is broken by the jet core, the diameter of the droplet is greater than the diameter. The constant B1 is related to the upstream nozzle, nozzle internal turbulence and cavitation, and so on. It is usually taken to be 1.73~ 60[17], and is taken to be 15 in this paper.
The breakup time and droplet diameter generated by the RT breakup are described as follows:
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(9) |
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(10) |
where ΩRT is the maximum growth rate of the surface wave; KRT is the wave number, CRT is the breakup time constant, and Cτ is taken to be constant 1.
In this paper, the research object is a single rectangular test head of combustor of aeroengine. Swirler is a two stage with discrete jets and radial-swirler, and there are primary jet holes, dilution jet holes and cooling film on the wall of the flame tube. Fig. 4 shows the calculation grid, and computational domain includes the expansion section and the entire case; the number of grid cells is about 6.21 million, and the grids of 228 cooling film holes are given. The time step is 1.0×10-6 s, 24 cores are used for parallel computation, and the total simulation time is about 300 hours. Flow field is simulated by a numerical software developed by ourselves, using URANS method, and the standard k-ε model is used as the turbulence model. The LISA model and KH-RT model are used as the primary and secondary atomization model respectively, and standard evaporation model is used to model the evaporation process. The boundary condition is shown in Fig. 5, and the inlet air flow rate is 0.44kg/s, the air temperature is 860K, the flow pressure is 0.55MPa, the kerosene is injected into the combustor by a mass flow of 11.4g/s, and the nozzle pressure is 0.94MPa. In this study, X axis is defined to downward, the origin of the coordinate is set at the center of the nozzle exit, and the distance between nozzle exit and the origin of the coordinate is 37mm, as shown in Fig. 5.
A large number of liquid droplets are formed rapidly due to the atomization process under the action of the nozzle. Fig. 6 and Fig. 7 show the Sauter mean diameter distributions of the atomized particles along the X axis in the plane of Y=0 and Z=0, respectively. As shown in the figure, the Sauter mean diameter of liquid particles is distributed uniformly in the horizontal direction at high temperature and high pressure, and it is approximately equal to 12μm. But there is a slight fluctuation in the vertical direction of the jet, the Sauter mean diameter of liquid particles ranging from 12.6μm to 16.1μm. Obviously, the atomization uniformity in the vertical direction is inferior to the droplet diameter distribution in the horizontal direction. Fig. 8 and Fig. 9 show that the Sauter mean diameter of particles in the cross section of X=31.5mm vary along the Y direction and the Z direction, respectively. From the distribution trend in the figure, it can be seen that the diameter distribution of the ato-mized particles is uniform even in the Y direction or the Z direction, the average diameter of most droplet particles in different positions are between 10μm and 15μm, and the symmetry in the Y direction is somewhat worse than that in Z direction.
Fig. 10 shows the atomization structure of fuel sprays in the combustor. As shown in the figure, the fuel is injected from the swirl nozzle and expanded into a hollow cone with the form of liquid film. In the Lagrange model, liquid films are replaced by liquid particles in discrete phase, and the detailed description will be introduced later. The large droplets formed by the breakup of liquid film continue to break into small droplets under the action of air flow. As shown in Fig. 10, the small droplets are heated in the airflow, and most of the droplets have evaporated before they reach primary jet holes. In Fig. 11, the kerosene droplets are divided into 2 ca-tegories. As shown in the figure, kerosene droplets form a fuel torch under the action of swirling flow and move downstream through the primary jets. At the same time, due to the effect of the recirculation zone, a large number of droplets are sucked into the recirculation zone and then move upstream.
Fig. 12 and Fig. 13 show the comparisons between simulation results and experimental data of the Sauter mean diameter distributions of droplets in different positions along the X axis in the Y=0 plane and in the Z=0 plane respectively. Liquid film is formed after fuel leaving the nozzle, then the films are teared into liquid ligaments or large droplets, and then the large droplets are further subjected to secondary breakup under the action of a strong swirling flow. Because of the large number of droplets in the flow field, it is impossible to track each droplets during the simulation. So, a discrete element method is adopted, and the identical droplet particles are replaced with a certain amount of particle samples. Fig. 12 and Fig. 13 show that the liquid droplets diameter in the flow field are generally distributed exceeding 20μm. Fig. 12 shows the Sauter mean diameter of the droplets at Z=-1cm and Z=-2cm. Obviouly, the Sauter mean diameter of the droplets obtained from simulation is about 30μm and the corresponding diameter obtained from the experiment is approximately equal to 10μm. Fig. 13 shows the Sauter mean diameter of the droplets at Z=-0.48cm and Z=-0.96cm. The comparisons between the experiment and the simulation are the same as that shown in the Fig. 12. Compared with Fig. 12, the number of particles sample is less in Fig. 13, and the diameter in the plane is about 20μm. The atomization and evaporation processes of the fuel in high temperture and high pressure environment of the aeroengine combustor are extremely complicated. Up to now, because of the complexity of atomization mechanism and the environment of high temperature and pressure, the study of fuel atomization in aeroengine is extremely difficult, so the experimental measurement and numerical simulation of the fuel atomization of the real aeroengine combustor are rarely reported in the public literature. In this paper, the Sauter mean diameter of the fuel particles obtained by the simulation is between 20μm and 30μm, the diameter in the Y=0 plane is larger than that in the Z=0 plane obviously, and the experimental results is about 13μm. To a certain extent the simulation results are in good agreement with the experimental results, which shows the atomization model adopted in the paper can capture the spray characteristics under the conditions of high temperature, high pressure and strong swirl in aeroengine combustor.
The spray field in aeroengine combustor is measured with the particle field pulsed laser holo-graphy imaging technique, and the spray characteristics in combustor under the force of swirling gas are obtained. The Sauter mean diameter of liquid droplets was measured at the exit of the swirler, and the mean diameter is about 13μm. At the same time, the experiment was studied numerically using the developed atomization numerical model, and the spray structure in the combustor was simulated. Based on the simulation results, the Sauter mean diameter of droplets was calculated, and the mean diameter is between 20μm and 30μm. The comparison between the simulation results and the experiment results indicates that the atomization model developed in this work can capture the atomization process of the fuel in the combustor.
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