Study on droplet behaviour in the gas–liquid coupled fan flow field

: The motion mechanism of the single droplet during wing cleaning of aeroengine is studied, and the force acting on the droplet entering the fan at low speed is analysed, and the motion model of a single droplet in swirl field is established. The influence of the main parameters such as droplet diameter, incident velocity and incidence angle on the droplet trajectory is analysed. The mechanism of droplet movement in the fan is described qualitatively.


Introduction
In the actual operation of aeroengine, due to the influence of many external factors, the appearances of failure modes such as fouling, wear, corrosion, fatigue and external impact cause the serious attenuation of engine performance; what is more, which have a direct impact on the reliability and economy of the engine. Engine cleaning is recognised as the most economical and effective performance maintenance method by the industry. Taken the use of foreign aeroengines into consideration, engine maintenance regulations basically stipulate the requirements of regular and irregular cleaning of engines [1].
In aeroengine cleaning, the speed and direction of fan droplets determine the quality of engine cleaning. On the basis of the results of the research of the aeroengine in wing cleaning system (Fig. 1), the scheme of a certain engine cleaning system is preliminarily designed, and the design parameters of the cleaning system scheme are optimised by using the flow field simulation technology. The results can be used to guide the design of the nozzle, the pipeline design of the nozzle support and the research of the compressor cleaning mechanism.
A great deal of research has been done on the wing cleaning system of the engine during several tens of years. Becker and Bohn [2] designed a cleaning system with two low jet nozzles to spray into the inlet on one side of the rotor suction surface. This method was considered to be the most effective design of cleaning system in the early stage, and they pointed out that the small droplets have smaller impact force in this paper, can avoid erosion of the blade and can follow the airflow better. However, larger droplets can go further into the compressor to clean the lower-stage blades. Patterson and Spring [3] begin to quantify droplet size in practise, using 125-200 μm in diameter and 80-200 μm in cleaning the engine. Tsuchiya and Murthy [4] at a water injection rate of up to 15%, using liquid droplets of 90 and 600 μm to clean six stage axial flow compressor. Syverud and Bakken [5] in the wing wash test of GE J85-13 engine: The experiments were carried out with 25 and 200 μm droplets. It was found that 75 μm droplets could better restore the engine performance and 25 μm droplets could be redeposited at the back of the compressor, resulting in the deterioration of the performance of the sixth-order compressor. The problem of blade erosion and structural damage should be considered in 200 μm droplets.
Mund and Pilidis [6] pointed out that the size, speed and inlet pressure of atomised particles in water or cleaning fluid are the main factors that affect the cleaning effect of the engine in his paper. Asplund [7] for different pressure levels: different blades should be cleaned with droplets of different sizes. It is suggested that the liquid droplets should be kept at 120 and 250 μm. Measured by Lambert, the input pressure is smaller when 2-4 and 7-10 MPa are produced, and the drop follows better [8].
Owing to the complexity of droplet motion in the fan flow field, most of the numerical simulations of droplet motion only consider the influence of drag force and gravity but ignore other factors. In this paper, a theoretical description and simulation of droplet motion in the flow of engine fan are carried out, and a single droplet dynamics model is used to study the droplet force and trajectory in the flow field of engine fan.

Single droplet model
In this paper, the aeroengine working conditions are as follows: the input pressure of the cleaning system is 5 MPa, the diameter of the droplet is 50-500 μm, the engine cold rotation speed is about 1000 r/min, the cleaning liquid is 68°C pure water and the water density is 978.8 kg/m 3 . In actual working conditions, there are many factors affecting the droplet trajectory. The basic assumptions of the droplet dynamics model are that (i) the droplet is an ideal sphere with uniform density under the cold rotation of aeroengine. The droplet is small, invariant and non-rotating. (ii) It is considered that the droplet phase in the fan flow field of the engine is a sparse phase, so the influence of droplets on the flow field parameters of the fan is ignored. (iii) The droplet itself has no turbulent diffusion. (iv) The droplet group is not regarded as a continuous medium and is grouped according to the initial size and initial velocity. (v) Ignoring the impact of droplet collision on each other. (vi) The mechanism of droplet trajectory in the fan flow field is studied only, and the process of information of droplet is not considered. (vii) There is no heat and mass transfer phenomenon in the droplet formation process. According to the above assumptions, the influence of the main factors is discussed.
The liquid droplet motion is described by Lagrange. Considering the coupling between the droplet and the gas phase, the single droplet motion equation is written by Newton's second law For the droplets in the fan flow field, the additional mass force, the buoyancy Basset force, Maguns force and the Saffman force can be neglected. In ΣF, only the drag force of the fluid and droplet phase F D , the centrifugal force F r and the Coriolis force F G are considered. Thus, the motion equation of a single droplet can be expressed as The air drag to which droplets are subjected is In the formula, μ g is the air velocity, μ d is the droplet velocity and C D indicating the Stokes resistance coefficient of the particles, as defined below [9]: The Reynolds Re g number is defined as μ g is the saturated aerodynamic viscosity; μ d is droplet velocity and d is the droplet diameter.

Model and grid
In this paper, the geometry model of the engine fan is established by using the full-three-dimensional numerical simulation method, taking the Trent 900 turbofan engine as the research object. The inner structure and flow of the fan are very complicated, so the Tgrid unstructured meshing method of tetrahedron mesh is adopted, and the impeller boundary is encrypted. To ensure the accuracy of the calculation, the number of meshes is verified independently. Owing to the existence of both moving and stationary areas in the computational region, in order to simulate the flow field and droplet traversing process of the fan, the whole computing area is divided into several small subdomains by using multiple reference model, each of which has its own motion mode. The rotation domain is rotated at 1000 r/min, and the stationary domain is stationary relative to the absolute coordinate system. Finally, the mesh division is obtained as shown in Fig. 2.

Turbulence simulation
The turbulence models commonly used in the numerical calculation are standard k-ɛ model, re-normalisation group k-ɛ model, realisable k-ɛ model, standard k-ω model and shear pressure transfer (SST) k-ω model. SST k-ɛ model combines the advantages of the k-ɛ model and k-ω model. K-ω model is used near the wall and k-ɛ model is used in the boundary layer and free shear layer, which can simulate both boundary layer turbulence and free shear turbulence. The gradual transformation from the k-ω model suitable for low Reynolds number to the k-ɛ model for high Reynolds number is completed by mixing function from the near wall to the external potential flow region. The transport variables of the model are turbulent kinetic energy k and specific dissipation rate ω, and the transport equation is as follows: Since the turbulent kinetic energy and energy dissipation rate of the near wall change very sharply, which requires high mesh size near the wall, so it is necessary to refine the near wall mesh and capture the influence of the near wall viscous layer as far as possible.
Ensure that the dimensionless distance y + is in the range of ≃20-30.

Boundary conditions
In this paper, the actual working conditions are simulated as far as possible, the input rotor rotation speed is in the state of slow train, the inlet condition is standard atmospheric pressure, the exit region is extended appropriately and the outlet condition under atmospheric pressure is as far as possible. The ideal gas is calculated at normal temperature and atmospheric pressure. The physical constant of the gas is assumed to be a parameter and does not change with time and space. The calculation parameters of boundary conditions are shown in Table 1.

Flow field calculation
The commercial CFD software Fluent 17.0 is used to simulate the steady flow field of the engine. The calculation is divided into two parts. First, the gas-phase turbulent flow field is solved, SST k-ɛ model and the enhanced wall function is used by the turbulence  model, the pressure and velocity coupling is based on the SIMPLE-Consistent algorithm and the discrete scheme of momentum equation is the first-order upwind scheme. The second-order upwind scheme is used by the discrete scheme of energy equation and turbulent dissipation equation; the fan region is rotated with a multi-reference system model, and the convergence residual is 10 −6 . After the calculation of gas-phase flow field converges, droplets are added, and then the governing equations of continuous and discrete phases are solved until both of them converge. CFD-POST post-processing software is used to analyse the data after the convergence of flow field calculation.

Individual droplet behaviour
In this paper, the operating conditions are as follows: the speed of the fan is 1000 r/min, the distance of the droplet is 300 mm, the initial velocity of the droplet is 50 m/s, the initial angle of incidence is 90°, the time interval is 0.002 s and the diameter of the droplet is calculated at 50, 100, 150, 200, 250 and 300 μm. The corresponding velocity and displacement of the droplet can be obtained, as shown in Fig. 3. The droplets moving in the fan flow field are affected by the drag force because the droplet velocity is lower than the gas velocity. Fig. 4 shows the axial velocity-time curve of droplets of different diameters. It can be seen that the velocity of the droplets increases rapidly after entering the fan flow field, and the effect of increasing speed is strongest when passing through the fan cascade channel. After 0.01-0.02 s, the droplet velocity reaches the terminal velocity, and then the small and medium droplets in the fan flow field move in a uniform straight line, while the large droplet velocity decreases gradually. The terminal velocity of 50 μm droplet is about 130 m/s, and the terminal velocity of 100 μm droplet can follow the air flow very well. The terminal velocity of 100 μm droplet is about 120 m/s, the terminal velocity of 200 μm droplets is about 110 m/s and the maximum velocity of 300 μm droplets reaches 90 m/s, and then decreases gradually. It can be seen that in the fan flow field, small droplets move at a speed similar to that of the air and follow the air to the compressor, while large droplets can hardly follow the air to the depth of the compressor in the fan flow field. This indicates that small droplets are 'following' and are more easily transported by air to the depths of the cleaning compressor. Consequently, large droplets may slow down quickly, and the larger the diameter, the faster the speed will decrease. Fig. 5 shows the variation of droplet radial velocity with time at 90° incident angle. Fig. 5 indicates that the larger the droplet diameter, the larger the radial velocity, the faster the radial velocity increases when the droplet enters the fan flow field, the smaller the droplet diameter is, the larger the acceleration is, and the more the droplet velocity is affected by the air drag force. After the droplet passes through the cascade channel, the radial velocity increases slowly, and the larger the droplet diameter, the greater the acceleration. At this time, the main factors affecting the droplet velocity are gravity and centrifugal force. Therefore, the larger the droplet diameter is, the higher the radial terminal velocity is, the easier it is to meet the outer wall of the engine, and the shorter the total moving time of the droplet is. The axial motion of the droplet is affected by air drag, the radial force by gravity, the centrifugal force and the drag force, so the velocity in the cascade channel increases more rapidly than the radial direction, and the axial motion determines the moving time of the droplet in the cascade.

Effects of droplet velocity and diameter
The rotational speed of the droplet fan is calculated at 1000 r/min, the drop distance from the fan is 300 mm, the initial incidence angle is 90°, the droplet diameter is 300 mm and the initial velocities are 40, 50, 60 and 70 m/s. Fig. 6 shows the droplet trajectory at different velocities.
When the droplet moves in the fan flow field, it needs to pass through the high-speed rotating cascade. From Fig. 4, it can be seen that the droplet enters the cascade channel when the axial displacement is 2.323 m. The smaller the velocity is, the greater the axial displacement is, and when the axial displacement is about 1 m or so, The radial displacement increases with the increase of the initial velocity of the droplet. Moreover, the effect of droplet diameter is shown in Section 4.1. It can be seen that in the cascade channel the lower the initial velocity of the droplet the smaller the

Effect of drop incidence angle and position
The initial velocity of the droplet is 50 m/s, the speed of the fan is 1000 r/min, the distance between the droplet and the fan is 300 mm, the diameter of the droplet is 300 mm and the distance between the droplet and the fan is 300 mm. The initial incident angles are 50°, 70°, 90°, 110° and 130°. Fig. 7 shows the X-axis displacement and Y-axis displacement curves of liquid droplets at different incident angles.
The droplets moving in the fan flow field are not only affected by the drag force of the gas phase, centrifugal force but also by gravity. For the droplets with an initial incident angle of 110°, the potential energy of gravity can be effectively overcome and the Ydirection displacement can be reduced. It can be seen that the larger the incident angle of the droplet is, the smaller the axial displacement in the Y-direction of the droplet is, and the farther away from the wall, the easier the droplet is to be transported.

Effect of drop position
The initial velocity of the droplet is 50 m/s, the speed of the fan is 1000 r/min, the initial incident angle is 90°, the diameter of the droplet is 300 mm and the distances between the droplet and the fan are 150, 200, 250 and 400 mm. Fig. 8 shows the terminal velocity of the drop X-direction at different distances.
It can be seen that the closer the initial position of the droplet to the axial velocity, the higher the maximum velocity of the droplet from the fan blade 150 mm, and when the droplet is far away from the 400 mm, the maximum velocity of the droplet can reach 100 m/s. Since the droplet has been accelerated 400 mm and the velocity has reached 65 m/s when entering the cascade channel, the terminal velocity of the droplet has been improved. This indicates that the closer the droplet position is, the higher the terminal velocity is, and the easier it is to transport to the compressor interior when the droplet diameter, initial velocity and incident angle are the same.

Conclusion
Through the simulation of the droplet model under the fan flow field, the behaviour of the droplet passing through the cascade channel is quantitatively studied, and the droplet velocity increases rapidly to a certain value under the coupling action of the fan flow field. The droplets with small diameters can be stabilised at a certain value to reach the terminal velocity and follow the gasphase uniform velocity, while the larger droplet velocity increases to a certain value, and the velocity decreases gradually under the action of the gas-phase resistance. In the case of different droplet diameter, droplet velocity, initial incident angle and initial position, the characteristics of droplet motion in the fan flow field are analysed: droplet velocity, initial incident angle and initial position are the same, the smaller the diameter, the better the droplet follows; droplet diameter, initial incident angle and initial position are the same, the lower the droplet velocity is, the easier it is to enter the intension channel; the smaller the radial displacement is when the initial incident angle is properly increased, the smaller the droplet diameter, the droplet velocity, the same initial position, the lower the droplet diameter and the lower the droplet velocity. With the same initial incident angle, the higher the initial position is, the higher the speed of the fan blade terminal is, and the more favourable it is to enter the compressor interior.