Study on Rain Absorption Performance and Flow Field of Transonic Compressor under Different Working Conditions

Abstract

Taking a four-stage transonic compressor as the research object, the Lagrange particle tracking method was used to simulate the multiphase flow by considering the particle fragmentation, collision and evaporation models, and the influence of different inlet conditions (raindrop diameter, velocity, temperature and flow rate) on the compressor’s performance and stable working range was studied. The results show that inlet rain absorption can weaken the clearance leakage vortex make the shock wave move downstream, thus increasing the inlet flow rate, resulting in a decrease in stability margin and the highest efficiency point moving in the direction of flow increase. With the decrease in raindrop diameter, the pressure ratio and wet compression efficiency increase, and the stability margin decreases. With the increase in inlet raindrop velocity, the degree of pneumatic breakage increases and the raindrop diameter becomes smaller, which leads to the decrease in pressure ratio and efficiency. The influence of the mass flow rate of imported raindrops on the stable working range is significant. When the mass flow rate of imported raindrops accounts for 5% of the design flow, the stable working range can be reduced by more than half. Rain absorption increases the reaction force of the compressor and increases the load of the rotor blade.

1. Introduction

On 24 June 1975, an Eastern Airlines Boeing 727 crashed at John F. Kennedy International Airport [1]. The cause of the accident is that the plane encountered thunderstorms when landing, and the change in flight resistance caused by rain and wind shear is the direct cause of the accident. In May 1988, a Boeing 737 aircraft flew into a storm area during its descent, causing the engine of the aircraft to stall, and finally the plane was forced to land on the runway turf [2]. In order to ensure the safety and stability of flight, certain requirements have been put forward for the airworthiness of aeroengines at home and abroad. Now, a rain absorption test has become a necessary test item before the engine is delivered [3].

On the other hand, in order to increase the output power of the gas turbine, people have thought of the method of spraying water inside the compressor. Since the concept of wet compression was proposed by Kleinschmidt in the 1940s, wet compression technology has been widely used in actual industrial production with the deepening of research and the improvement of technical level [4]. In 1995, Siemens imported the W501 gas turbine and added an intake water jet device, which increased the output power by 20% [5]. In 2003, Alstom added a sprinkler system to the experimental unit GT26, which increased the output power of the gas turbine by 1.2% [6]. The practice shows that reasonable use of wet compression technology can effectively improve the pressure ratio and efficiency of compressors. In addition, wet compression in the steam compression cycle can be used to improve the performance factor of the compressor by injecting the steam refrigerant into it [7,8,9].

Murthy et al. [10,11] established a prediction model for the steady-state performance of compressors under water inlet and compared it with the test results. The results show that the influence of compressor water intake can be summarized by two factors: the distortion of compressor outlet fluid state and the change in compressor surge and clogging conditions. Mathioudakis [12] proposed a method to estimate the deviation of combustion chamber water injection performance parameters. Murthy et al. [13] established a prediction model for transient water injection performance. Ludorf [14] extended the model to include humidity and droplet evaporation in the analysis program of one-dimensional fractional compressor stability and studied the stage interaction of compressors under different working environments, while Loebig [15] extended the research scope to three-dimensional.

With the rapid development of CFD technology, numerical simulation has become an important means to study the wet compressed flow field. Khan [16] used FLUENT 2021 software to analyze the droplet trajectory by taking a rotor-stator stage of bivia-tone flow as a model. Sequeira et al. [17] took a single-stage subsonic axial compressor as a model and introduced the evaporation model with CFX 2021 software. Taking a turbofan engine as a model, Roumeliotis et al. [18] took into account the influence of the spoon effect and the fan effect at the engine inlet, as well as the presence of water in the operation and performance of the compressor and combustion chamber. The results showed that evaporation would lead to stage rematching, reduce the surge line at high speed, and move the working point to a higher mass flow rate. At the same time, the exhaust pressure increases significantly.

In the existing studies, there has been no research on the effects of rain absorption on the performance and flow mechanism of multi-condition multistage transonic compressor. In this paper, aiming at a four-stage transonic axial compressor model, a multiphase flow model based on Euler-Lagrange is adopted to analyze the total pressure ratio, total temperature ratio, efficiency and stable working range under different rain absorption conditions, considering the crushing, collision and evaporation processes of raindrop particles. The mechanism of rain absorption affecting compressor performance is discussed.

2. Physical Models and Grids

Taking a four-stage transonic axial flow compressor as the research object, the meridian view is shown in Figure 1. The equal-diameter design is adopted with a wavy hub, and the flow channel gradually shrinks.

The numerical simulation adopts single-channel computing domain, and the AutoGrid5 software of NUMECA 14.1 is used to generate grids. The flow channel grid adopts an O4H topology structure, and the blade tip clearance area adopts an O-H type grid. The grid model is shown in Figure 2. Five grid schemes with 1.22 million, 1.44 million, 1.99 million, 2.23 million and 2.48 million grid numbers are used for calculation. The k-$\mathsf{\epsilon }$ model [19,20] was selected for the turbulence model.

Figure 3 shows the change in design point efficiency with the number of grids. When the total number of grids increases from 1.99 million to 2.33 million, the change in isentropic efficiency is 1.2%; therefore, the grid of 1.99 million is selected.

In this paper, the Euler–Lagrange particle tracking method is used to calculate the gas–liquid two-phase flow in a four-stage compressor. The mixture of air and water vapor is treated as a continuous phase, while raindrops are treated as discrete phases. The raindrop breaking model is the CAB (Cascade Atomization and drop Breakup) model [21], which determines the change in diameter and velocity of the raindrop after breaking by the size of the Weber number.

Antoine equation [22] is used to determine the saturated vapor pressure of water vapor, as shown in Equation (1).

(1)${\log }_{10}{\mathrm{p}}_{\mathrm{s}\mathrm{a}\mathrm{t}}=\mathrm{A}-{\displaystyle \frac{\mathrm{B}}{\mathrm{T}+\mathrm{C}-273.15\mathrm{K}}}$

where ${\mathrm{p}}_{\mathrm{s}\mathrm{a}\mathrm{t}}$ is saturated vapor pressure, $\mathrm{T}$ is saturation temperature. The constant terms take the valus A = $5.11564$, B = $1687.537$ and C = $230.17$, respectively.

The wall impact coefficient is used to describe the momentum loss after raindrop impact on the wall. The horizontal rebound recovery coefficient and vertical rebound recovery coefficient are both 0.5, and the wall rebound coefficient is shown in Figure 4.

In order to evaluate the compression efficiency of water and air, the concept of wet compression efficiency [23] is introduced, as shown in Equation (2). The efficiencies discussed later in this paper are all wet compression efficiencies.

(2)${\mathsf{\eta }}_{\mathrm{w}}={\displaystyle \frac{{\mathrm{W}}_{\mathrm{w}\mathrm{i}}}{{\mathrm{W}}_{\mathrm{w}}}}$

where ${\mathrm{W}}_{\mathrm{w}\mathrm{i}}$ is ideal compression work, ${\mathrm{W}}_{\mathrm{w}}$ is actual compression work. ${\mathrm{W}}_{\mathrm{w}\mathrm{i}}$ and ${\mathrm{W}}_{\mathrm{w}}$ is defined by Equations (3) and (4).

(3)${\mathrm{W}}_{\mathrm{w}\mathrm{i}}=\left({\mathrm{W}}_{\mathrm{a}}+\mathrm{f}{\mathrm{W}}_{\mathrm{v}}\right)/\left(1+\mathrm{f}\right)$

(4)${\mathrm{W}}_{\mathrm{w}}=\mathsf{\omega }{\mathrm{M}}_{\mathrm{t}}/{\mathrm{m}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$

where ${\mathrm{W}}_{\mathrm{a}}$ is ideal compression work of air, ${\mathrm{W}}_{\mathrm{v}}$ is ideal compression work of water vapor, $\mathrm{f}$ is mass fraction of water vapor, $\mathsf{\omega }$ is rotational angular velocity, ${\mathrm{m}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$ is outlet mass flow rate.

The suction rainfall is expressed as a percentage of the mass flow rate of the imported water and the design air flow rate, and the size of the stable working range is expressed by the flow difference between the near blocking point and the near stall point. The total temperature of the inlet is 349.4 K, the total pressure of the inlet is 180,014 Pa, the velocity direction of the air is axial intake, the speed of the raindrop is 20 m/s, 50 m/s and 100 m/s, the rainfall absorption size is 1%, 3% and 5%, the diameter of the raindrop is 1 mm, 3 mm and 5 mm, the temperature of the raindrop is 300 K, 330 K and 360 K. The k-$\mathsf{\epsilon }$ model was selected for the turbulence model, and the Scalable Wall Function was used to handle the near-wall surface. The heat transfer model of the mixture of water vapor and air was selected as Total Energy. In order to calculate the mass fraction of each component in the mixture, in the component model, the air component was selected as the Constraint option, the water vapor component was selected as the Transport Equation option, and the motion diffusion coefficient was 2.5 × 10⁻⁵ m²/s. The particle coupling mode was selected as Fully Coupled. The surface tension coefficient of raindrop particles and gas mixture was set at 0.072 N/m, the Schiller Naumann model was selected for the drag force model, and the Ranz Marshall model was selected for the heat transfer model of continuous phase and discrete phase [24]. The characteristic curve was simulated by changing the outlet back pressure, and the calculation was carried out until convergence could not be achieved near the stall point.

The number of particles tracked is a very important parameter when using the Lagrange particle tracking method to track raindrops. Figure 5 shows the diameter distribution of raindrop particles on the pressure surface of the first-stage rotor blade when the diameter of the raindrop is 1 mm and the rainfall absorption is 5%. It can be seen from the figure that when the number of raindrop particles is 5000, the diameter distribution of raindrop particles on the pressure surface of the first-stage rotor tends to be stable, so the final number of raindrop particles is determined to be 5000.

3. Results and Analysis

3.1. Overall Performance Analysis

Figure 6 shows the total pressure ratio–flow curve, and the horizontal coordinate is the normalized flow rate divided by the design point flow rate, which is a dimensionless number. From the overall law, compared with dry compression, the compressor pressure ratio after rain absorption has an upward trend; the flow near the blocking point and the stall point increases, but the stable working range decreases.

As shown in Figure 6a, when the initial temperature of the raindrop is lower, the total pressure ratio of the compressor is higher, and the flow near the stall point and the block point is larger, but the stable working range does not change much. Based on the stable working range of the dry compression condition, the initial temperatures of 300 K, 330 K and 360 K raindrops reduce the stable working range of the compressor by 15%, 16.9% and 13.6%, respectively. The widest stable range is the raindrop condition of 360 K initial temperature. When the inlet flow rate of the compressor is the design flow rate, compared with the dry compression condition, the initial temperature of 300 K, 330 K and 360 K raindrops increase the total pressure ratio of the compressor by 7.4%, 4.8% and 4%, respectively.

As shown in Figure 6b, when the initial velocity of raindrop is lower, the flow rate near the stall point of the compressor is larger, but the flow rate near the blocking point is slightly different, and the stable working range decreases. This may be because the flow rate near the blocking point is larger, the inlet air speed is larger, and the raindrop can be accelerated faster, thus weakening the impact of different initial raindrop speeds. Raindrops with initial velocities of 20 m/s, 50 m/s, and 100 m/s reduce the compressor’s stable operating range by 15.1%, 15%, and 8.5%, respectively. The total pressure ratio of the compressor at the initial raindrop velocity of 20 m/s and 50 m/s does not change much, but it is higher than the total pressure ratio at the initial raindrop velocity of 100 m/s. When the flow point is designed, the initial velocity of 20 m/s, 50 m/s and 100 m/s raindrops increases the overall pressure ratio of the compressor by 7.9%, 7.5% and 6.3%, respectively, compared to the dry compression condition.

As shown in Figure 6c, the lower the suction rainfall of the compressor, the lower the total pressure ratio of the compressor, the smaller the flow rate near the stall point and near the blocking point, and the larger the stable working range. Compared with the dry compression condition, the stable working range of the compressor decreases by 15%, 67.4% and 75.2% due to the suction rainfall of 1%, 3% and 5%, respectively. The effect is significant. When the inlet flow of the compressor is the design flow, compared with the dry compression condition, the total pressure ratio of the compressor increases by 7.5%, 15% and 19.7%, respectively, due to the rain absorption of 1%, 3% and 5%.

As shown in Figure 6d, the smaller the initial diameter of the raindrop, the higher the total pressure ratio of the compressor, the smaller the flow near the stall point, the larger the flow near the blocking point, and the larger the stable working range. Compared with the dry compression condition, the stable working range of the compressor decreases by 15%, 29% and 32.2%, respectively, for raindrops with an initial diameter of 1 mm, 3 mm and 5 mm. The influence of the diameter change on the stable working range is also great. When the inlet flow rate of the compressor is the design flow rate, compared with the dry compression condition, the total pressure ratio of the compressor increases by 7.5%, 2.2% and 0.6% with the initial diameter of 1 mm, 3 mm and 5 mm, respectively, which indicates that when the initial diameter of the raindrop is too large, the effect of rain absorption on the pressure ratio of the compressor is not obvious. This is similar to the conclusion of Roumeliotis [18].

Figure 7 shows the efficiency–flow curve. As a whole, rain absorption can increase compressor efficiency, but the increase in efficiency near the stall point is smaller than that near the design flow point. As shown in Figure 7a, the lower the initial temperature of the raindrop, the higher the compressor efficiency. When the inlet flow rate of the compressor is the design flow rate, compared with the dry compression condition, the raindrop with the initial temperature of 300 K, 330 K and 360 K increases the compressor efficiency by 1.38%, 0.72% and 0.85%. The initial temperature change in raindrops does not affect the increase range of compressor efficiency. When the design flow point is near, the impact range of the initial temperature 330 K and 360 K raindrop on the compressor efficiency is small, and the difference is not large, and the impact of the initial temperature 300 K raindrop on the compressor efficiency is more obvious. As shown in Figure 7b, the change in the initial velocity of the raindrop has little effect on the increase in the compressor efficiency. Only when the design flow point is near, the efficiency of the raindrop with the initial velocity of 100 m/s will be significantly less than that of other initial velocity raindrops. When the flow point is designed, the initial velocity of 20 m/s, 50 m/s and 100 m/s raindrops increases the compressor efficiency by 1.24%, 1.38% and 1.07%, respectively, compared to the dry compression condition. As shown in Figure 7c, the influence of the suction rainfall of the compressor on the efficiency is very significant compared with other conditions.

It can be seen from the figure that when the suction rainfall increases, the compressor efficiency has a very obvious upward trend. Under conditions of 1%, 3% and 5% rainfall absorption, the compressor efficiency increases by 1.38%, 3.4% and 6.33%, respectively, and the efficiency gap between the latter two is larger than that of the former two, which indicates that increasing rainfall absorption is an important way to improve the compressor efficiency. However, considering the influence of rainfall absorption on the stable working range is also very significant, we need to balance the relationship between the two. As shown in Figure 7d, the smaller the initial raindrop diameter, the greater the improvement effect on compressor efficiency, and the improvement effect near the design flow point is better than near the stall point.

When designing flow points, compared with dry compression conditions, raindrops with an initial diameter of 1 mm, 3 mm and 5 mm increase the compressor efficiency by 1.38%, 0.71% and 0.21%, respectively. It can be seen that when the initial diameter of raindrops increases to 5 mm, the improvement effect of rain absorption on compressor efficiency is already very small. As the diameter of the raindrop continues to increase, it even affects the efficiency of the compressor in the opposite direction.

Figure 8 shows the total temperature-flow curve. On the whole, near the stall point and the design flow point, the total temperature in the compressor can be reduced to a certain extent due to the evaporation and cooling process of raindrops in the compressor, while near the blocking point, the flow rate of the compressor near the blocking point increases due to rain absorption. As a result, the total temperature-flow line of dry compression intersects with the total temperature-flow line of the compressor after rain absorption, so that the dry compression temperature ratio is lower than the temperature ratio after rain absorption, but the influence of the overall rain absorption on the compressor still makes the total temperature-flow point move to the lower right. In addition, most of the total temperature-flow curves decrease with the increase in the flow rate. However, when the precipitation is 3% and 5% near the stall point, the total temperature-flow ratio shows a trend of first increasing and then decreasing. As shown in Figure 8a, the initial temperature of the raindrop has little difference near the stall point. However, when designing the flow point, when the initial temperature of the raindrop is 300 K, the total temperature ratio of the raindrop is less than 330 K and 360 K. Raindrops with initial temperatures of 300 K, 330 K and 360 K reduced the overall temperature ratio of the compressor by 1.04%, 0.42% and 0.39%, respectively. As shown in Figure 8b, the total temperature ratio of raindrops with an initial velocity of 20 m/s and 50 m/s near the stall point is not much different, but both are higher than that of raindrops with an initial velocity of 100 m/s. Near the designed flow point, raindrops with an initial velocity of 50 m/s have the best cooling effect on the compressor. This shows that the influence of the initial velocity of raindrop on the cooling effect of the compressor is related to the working position of the compressor. Compared with the dry compression condition, the total temperature ratio of the compressor decreases by 0.04%, 1.04% and 0.35%, respectively, when the initial velocity of the raindrop is 20 m/s, 50 m/s and 100 m/s.

As shown in Figure 8c, the influence of suction rainfall on the compressor’s total temperature ratio is the most significant. At the design flow point, compared with the dry compression condition, the suction rainfall of 1%, 3% and 5% reduces the compressor’s total temperature ratio by 1.04%, 3.77% and 7.18%, respectively. As shown in Figure 8d, when the initial diameter of raindrop is 3 mm, it has the best effect on reducing the total temperature inside the compressor, and the point with the initial diameter of 1 mm has the lowest cooling result on the compressor. When designing the flow point, compared with the dry compression condition, the total temperature ratio of the compressor decreased by 1.04%, 3.47% and 1.27%, respectively, with the initial diameter of 1 mm, 3 mm and 5 mm raindrops.

Figure 9 shows the temperature change in raindrop particles during their flow. There are two ways to change the temperature of raindrop particles: one is the convective heat transfer between the air, and the other is the latent heat of vaporization during the evaporation reaction, both of which will increase the temperature of the raindrop particles. As can be seen from the figure, the temperature of the raindrop particles does not change much in the front stage, because in the front stage, the temperature of the air is not very high, the temperature difference between the raindrop particles is small, the heat transfer by convection is relatively small, the evaporation reaction is not severe in the front stage, and the latent heat of vaporization is relatively small. At the latter stage, the raindrop absorbs enough heat, and the temperature rises enough for the evaporation reaction to occur. In addition, due to the radial pressure gradient, the pressure at the tip of the leaf is higher, resulting in a higher saturation temperature of the droplet during evaporation, so the temperature of the raindrop at the tip of the leaf is higher.

3.2. Flow Field Characteristic Analysis

The static pressure of the airflow will be increased when the airflow flows through the moving blade and the static blade. In order to measure the proportion of the increase in the pressure of the airflow in the moving blade and the static blade, the concept of inverse force is introduced. The inverse force is the ratio of the energy used for the pressure potential energy conversion in the moving blade to the pressure potential energy conversion in the whole stage. Figure 10 shows the distribution of reaction force along blade height. It can be seen from the figure that the inverse force in the direction of blade height presents a trend of higher blade tip and lower blade root, which indicates that the diffusing capacity of the tip region of the moving blade is stronger than that of the blade root. Rain absorption increases the reaction force on the whole, which indicates that rain absorption increases the load of the moving blade. This is consistent with Wang’s conclusion [25]. With the increase in rainfall absorption, the reverse force also increases, but the reverse force changes little when the rainfall absorption is 3% and 5%. Although raindrops converge in the overall upward casing region, the influence of rain absorption on the reaction force gradually extends from the blade root to the entire channel due to the gradual contraction of the flow channel shape of the compressor model.

Figure 11 shows the relative Mach number cloud image of the first stage rotor with different blade heights. It can be seen from the figure that when the back pressure is 785,000 Pa, rain absorption can move the compressor operating point from stall state to stable state. From the cloud image at the height of 99% of the blades, it can be seen that under dry compression, there is a wide range of low-speed areas in the compressor rotor channel, which can reach the lowest 0.3 Mach number in the blade channel. The low-speed area of the rotor trailing edge decreases with the increase in rainfall absorption. At 5% leaf height, it can also be seen that rain absorption reduces the low-speed region of the rotor suction surface, but compared with the cloud image at 99% leaf height, the influence of rain absorption on the velocity field at the position of the blade and the blade root is not obvious.

From Figure 12, the cloud image of 99% leaf height, it can be seen that the position of the shock wave of the compressor moves downstream after the rain absorption, and the position of the shock wave is closer to the downstream with the increase in the rain absorption. Under the action of the leakage vortex, the shock wave bends. As shown, under the same back pressure, the top tip of the shock wave under wet compression tends to be flat compared with that under dry compression, and the position of the shock tip moves downstream, delaying the time for the tip leakage vortex to reach the shock wave.

Figure 13 and Figure 14 show the static entropy distribution of the first stage rotor outlet and 99% blade height of the first stage rotor. It can be seen from the figure that rain absorption reduces the entropy in at the shock wave, reduces the compressor loss, and reduces the entropy increase at the tip of the blade. With the increase in rain absorption, the greater the decrease in entropy increase, the lower the compressor loss.

Figure 15 shows the limit flow diagram of the suction surface of the first-stage blade of the compressor. Compared with the dry compression condition, the flow separation area of the rotor and stator suction surface of the compressor is significantly reduced after rain absorption, and the flow field of the compressor is improved, so that the compressor enters the stable condition from the stall condition. The larger the suction amount, the smaller the separation zone on the suction surface of the blade. When the absorption rate is 3%, the separation zone on the first stator has disappeared.

4. Conclusions

In this paper, the influence of rain absorption on the flow field of a small four-stage compressor is studied based on the Lagrange particle tracking method. The overall performance and flow field characteristics of the compressor are studied, respectively. The main conclusions are as follows:

• (1). After the compressor absorbs rain, it will increase the flow rate near the stall point and near the blocking point, reduce the stable working range, increase the total pressure ratio and efficiency of the compressor, and reduce the total temperature ratio of the compressor, which has the greatest impact on the performance of the factor of rainfall absorption when the design flow point is 1%, 3% and 5%. The overall pressure ratio of the compressor increased by 7.5%, 15% and 19.7%; the efficiency increased by 1.38%, 3.4% and 6.33%; the total temperature ratio decreased by 1.04%, 3.77% and 7.18%; and the stable working range decreased by 15%, 67.4% and 75.2%, respectively.

• (2). Rain absorption increases the compressor’s reaction force and increases the load on the moving blade, and the reaction force increases with the increase in rain absorption. The influence range of rain absorption on the reaction force gradually expands from the tip area of the blade to the whole blade height direction with the flow direction.

• (3). After the compressor absorbs rain, the shock wave position moves to the downstream of the compressor, and under the same back pressure, the compressor absorbs rain, which can change the working point from stall state to stable state. The influence of rain absorption on the compressor flow field is mainly in the tip area but has little effect on the velocity field and temperature field in the middle and root area. After the compressor absorbs rain, the static entropy of the blade tip region will decrease, and the loss will also decrease. Rain absorption can weaken the separation flow on the blade, thereby improving the flow field.

Author Contributions

Writing—original draft preparation, S.L. (Shamiao Luo); writing—review and editing, S.L. (Shaobin Li) and X.S. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data presented in this study are available on request from the corresponding author. The data are not publicly available due to confidentiality.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures

Figure 1. Meridian view of four-stage transonic axial compressor.

Figure 2. Four-stage compressor single-channel computing grid.

Figure 3. Grid independence verification.

Figure 4. Rebound diagram when the horizontal and vertical rebound coefficient is 0.5.

Figure 5. Particle independent verification.

Figure 6. Total pressure ratio—flow curve.

Figure 7. Efficiency–flow characteristic curve.

Figure 8. Total temperature–flow characteristic curve.

Figure 9. Raindrop temperature distribution.

Figure 10. Distribution of reaction force along leaf height.

Figure 10. Distribution of reaction force along leaf height.

Figure 11. First stage rotor channel with different blade heights relative to Mach number cloud image.

Figure 12. Local magnification of 99% blade height first stage rotor relative to Mach number.

Figure 13. Static entropy cloud image of 99% blade height first stage rotor channel.

Figure 14. First stage rotor outlet static entropy cloud image.

Figure 15. Limit flow diagram of the suction surface of the first stage blade.

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