An experimental method for squealer tip flow field considering relative casing motion

Fei ZENG, Jinlin DU, Lin HUANG, Liming XUAN, Qiang ZHAO,Zhengping ZOU,*

a National Key Laboratory of Science and Technology on Aero-Engine Aero-thermodynamics, School of Energy & Power Engineering, Beihang University, Beijing 100083, China

b Collaborative Innovation Center for Advanced Aero-Engine, School of Energy & Power Engineering, Beihang University, Beijing 100083, China

KEYWORDS Blade tip/casing gap measurement;Particle Image Velocimetry(PIV);Relative casing motion;Similarity transformation;Turbine;Wide range of variable incidence angles

Abstract Squealer tip is widely used in turbines to reduce tip leakage loss.In typical turbine environment, the squealer tip leakage flow is affected by multiple factors such as the relative casing motion and the wide range of variable incidence angles.The development of experimental methods which can accurately model the real turbine environment and influencing factors is of great significance to study the squealer tip leakage flow mechanism. In the present paper, a low-speed turbine cascade test facility which can model the relative casing motion and wide range of variable incidence angles (-25° to 55°) is built. Based on the similarity criteria, a high-low speed similarity transformation method of the turbine cascade is established by considering the thickness of the turbine blade.A combined testing method of Particle Image Velocimetry(PIV)and local pressure measurement is proposed to obtain the complex flow structures within the tip cavity.The results show that the experimental method can successfully model the relative casing motion and the wide range of variable incidence angles. The low-speed cascade obtained by the similarity transformation can model the high-speed flow accurately. The measurement technique developed can obtain the complex flow field and successfully capture the scraping vortex within the squealer tip.

1. Introduction

Tip Leakage Loss(TLL)is a major source of the turbine aerodynamic loss,which accounts for about 1/3 of the total loss in rotor passage1,2. The Squealer Tip (ST), one of the effective passive control techniques,has obvious advantages in reducing the TLL3,4, and is being widely used in modern aero-engines.Recently, many researchers have found that there are kinds of vortices in the cavity, which could affect the flow state of the Tip Leakage Flow (TLF) and thus reduce the TLL5-12.Particularly,the Scraping Vortex(SCV),identified as the dominant flow structure in the cavity,could enhance the energy dissipation of the leakage flow within the cavity and reduce the discharge coefficient13. TLF and SCV are affected by multiple factors and the relative casing motion is a major factor. For ST,the relative motion of the casing has a significant influence on the TLF and the size and scope of the SCV13,14.In addition,the leakage vortex would approach to the blade suction surface due to the relative casing motion, causing the ‘‘leakage vortex blockage” effect and thereby decreasing the driving force of the TLF15,16. Therefore, the relative casing motion plays an important role in the flow mechanism within the tip cavity,and researches without considering the casing motion would lead to misunderstanding or even incorrect conclusions. In order to model the TLF in ST in the real turbine environment accurately, an experimental method considering the relative casing motion needs to be developed.

Recently,many researchers have studied the TLF structure by experimental method17-21. Most of these experiments are carried out in linear turbine cascade wind tunnels. The lowspeed cascade facilities built by Heyes17and Yaras18et al.could model the relative casing motion, but studies on the effect of incidence variation could not be carried out on these platforms. However, the incidence variation has great impact on the tip leakage vector, blade loading distribution and tip leakage vortex22,23. For modern aero-engines, the turbine operates at large incidence variation. Particularly, for Variable-Speed Power Turbine (VSPT), the range of the incidence angle is extended from -60° to 20°24. Therefore, to study the tip leakage flow experimentally, it is necessary to take the effect of large incidence variation into consideration.

Generally,aero-engine turbines operate at high speed,making it is difficult to perform experimental research under laboratory conditions. Currently, the low-speed model experiment is the most universal and accepted method.Notably,the key to the low-speed model experiment is the aerodynamic similarity between the high-speed real turbine and the low-speed model,and the similarity criterion should be concerned25. Numerous researchers had proposed several similarity methods for compressors. Woolard26developed the mathematical expression of the compressor cascade and applied the Prandtl-Glauert rule27to subsonic flow in compressor cascades.Based on Woolard’s research,Zhu et al.28discussed the existence and uniqueness of the flow field similarity criterion based on different orders of the potential equation.Starting from the linear small disturbance potential equation, a new similarity criterion for ensuring aerodynamic similarity of two compressor cascades was derived, and a complete set of similarity transformation theory and design method has been developed. Compressor cascade tests were designed to verify the validity of the similarity transformation criterion. However, the turbine blade is thicker than the compressor blade, and the disturbance generated by a turbine blade is larger than compressor, causing the linear small perturbation theory applied to the compressor cascade inapplicable for the turbine blade.Therefore,the previous similarity method cannot be directly applied to the turbine cascade and a high-low speed similarity method for turbine cascade needs to be developed.

In terms of measurement methods, Yamamoto22used fivehole probes to measure the TLF in the clearance of low-speed turbine,Xiao et al.29,30used rotating five-hole probes and laser Doppler velocimeter to observe the flow field in the clearance region in detail, while Sjolander31and Rao32et al. used paint dots and oil film to study the TLF in the tip clearance.In addition, the leakage flow in the tip region was also measured by PIV method21. PIV devices and Pressure probes could be set on stationary casing and it is straightforward to measure the flow field in tip cavity. However, due to the relative casing motion, it is very difficult to set the PIV devices and pressure probes into the narrow space within the cavity(maximum size of 7.5 mm×13 mm in the current study), leading to the limitations of the conventional measuring method used previously.Therefore,it is necessary to develop a test method for the narrow space to obtain complex flow field information in the cavity.

In this paper, an experimental method for the squealer tip complex flow considering the relative casing motion is proposed, including the implementation techniques of the relative casing motion and the wide range of variable incidence angles,the high-low speed similarity transformation method of the turbine cascade and the high-precision measurement method for complex flow field in the cavity.The structure of the paper is as follows. In Section 2, the low-speed turbine cascade test facility is built. The experimental platform consists of four parts: a low-speed linear turbine cascade wind tunnel, relative casing motion equipment, test platform with a wide range of variable incidence angles and low-speed turbine cascade. In Section 3, a high-low speed similarity method of turbine cascade considering turbine blade thickness is developed and numerically validated. In Section 4, a high-precision PIV and pressure measurement method of the complex flow field in the narrow space is proposed. In addition, some preliminary experimental results are presented.

2. Experimental setup

2.1. Low-speed linear turbine cascade wind tunnel

As shown in Fig.1,the wind tunnel used in the experiment is a low-speed open-loop wind tunnel.The wind tunnel consists of five parts: a gas source, the expansion section, the stable section, the contraction section and the test section.

The air source is a Roots blower,with gauze element before and after the expansion section, honeycomb between the expansion section and the stable section. This experimental facility can ensure that the boundary layer at the exit is less than 4 mm, the dynamic pressure instability is less than 0.5%, the inhomogeneity of velocity is less than 1% and the turbulence intensity is less than 0.5% under the condition of 10 m/s at exit. In addition, the velocity of the outlet flow field can be continuously adjusted as needed.

2.2. Relative casing motion equipment

The experimental platform can be used to model the relative motion between the casing and cascade. The relative motion between the end-wall and the blade is simulated by the casing wall motion at the top of the cascade.Fig.2 is the front view of the moving casing simulator. The belt is used to simulate the end-wall.By adjusting the mechanism,the parallelism between the belt and the blade tip can be guaranteed and the vibration amplitude can be controlled within 0.08 mm. Fig. 3 is the connection diagram between the moving end-wall simulator and the cascade test platform. The moving endwall simulator can cooperate through the test platform with variable incidence angles.

Fig. 1 Structural sketch of wind tunnel.

Fig. 2 Sketch of test section.

2.3. Test platform with wide range of variable incidence angles

The test platform with variable incidence angles is shown in Fig.3.The bottom plate of the cascade is installed on the side,while the plate is installed on the variable incidence angles mechanism. The text cascade is a low-speed profile obtained by the similarity transformation in Section 3. The moving end-wall simulator is situated on the other side. The blade can be installed through the blade cavity on the bottom plate to adjust different clearance heights, and the different blade profiles can be studied by replacing the cascade bottom plate.A silt is located on the bottom plate at 0.5 axial chord length downstream of the blade exit.The cascade outlet flow field can be measured by five-hole probe through this silt. As shown in Fig.4,the baffle auxiliary mechanism is installed,which can be used to adjust the width of the incoming flow and weaken the boundary layer of incoming flow. In addition, the two baffles can adjust properly with the change of incidence angle. The design range of the variable incidence angles mechanism is-25° to 55°.

Fig. 3 Variable incidence angles mechanism platform.

2.4. Low-speed turbine cascade

Fig. 4 Sketch of bottom plate and auxiliary mechanism at different incidence angles.

Fig. 5 Low-speed turbine cascade.

The low-speed turbine cascade used in the experiment is obtained through high-low speed similarity transformation.Fig. 5 shows the low-speed turbine cascade applied in the experiment. The major aerodynamic geometric parameters and test conditions are shown in Table 1. When the loading distribution of the low-speed model is assured to be the same as the high-speed turbine, the high-low speed models satisfy the aerodynamic similarity conditions, and the aerodynamic performance of the high-speed turbine is basically consistent with the low-speed model. More details of the high-low speed similarity transformation are presented in Section 3.

2.5. Circumferential uniformity of exit

Fig.6 shows the total pressure coefficient distribution of three adjacent channels at the exit section of the cascade. In the figure, the leakage vortex and the wake can be clearly distinguished, and the total pressure coefficient distribution of the leakage vortex and the wake has a certain periodicity. Therefore, the circumferential uniformity of the outlet flow field could be satisfied.

The experimental platform built in this paper can simulate the relative motion of the casing, and can carry out a wide range of variable incidence angles research. In addition, it can also carry out the study of loading distribution, clearance size and tip geometry. The specific measurement schemes will be introduced in Section 4.

3. Similarity transformation

The similarity criterion proposed by Van Karman27based on the small perturbation equation requires that the blade is very thin and slightly cambered, and the disturbance generated is infinitesimal. However, the turbine blade does not conform to this condition, so the research results cannot be directly applied to the turbine blade. Based on the hypothesis of finite small disturbance, the similarity criterion of turbine cascade flow field under subsonic conditions is deduced, and its relationship with the similarity criterion of compressor cascade is elaborated.

3.1. Finite small perturbation hypothesis

As the thickness of a turbine blade is larger than that of a compressor blade, the disturbance produced by a turbine blade is larger than that produced by compressor blade. However,the disturbance can still be regarded as a small disturbance,which is called ‘‘finite small perturbation” in this paper.Assuming that the power of finite small perturbation is still higher order small quantity, the hypothesis of finite small perturbation is as follows.

Small perturbation hypothesis:

where u and v are velocity in x and y directions respectively and v∞is the inflow velocity.

According to the hypothesis of finite small perturbation,even if the Mach number is relatively small, the three terms(φxx,φxy,φyy)on the right side of the first order approximation of the velocity potential equation are no longer small relativeto the left side term, so they cannot be ignored. On the other hand, due to the existential requirement of similarity criterion under the conditions of unequal inlet Mach number,this paper ignores the cross-term. The impact of the cross-term is unknown, which needs to be verified by experiments.

Table 1 Cascade geometries and test conditions.

Fig. 6 Circumferential uniformity of exit.

The accurate two-dimensional velocity potential equation28is as follows:

where Ma0is the vector mean Mach number and k is the ratio of specific heat.

Under the ‘‘small perturbation hypothesis”,l=u/v∞=v/v∞＜1, （u/v∞）2and（v/v∞）2are the high order small quantity.When Ma0is small,the high order small quantity could be neglected:

3.2. Similarity criterion

The small perturbation equation is used to derive the similarity transformation relationship between two cascades with different Mach numbers.

From the affine transformation:

Fig. 7 Geometric sketch of turbine cascade.

3.3. Numerical verification of similarity transformation

A turbine cascade with slightly cambered surface is selected as a high-speed cascade.The inlet Mach number is Ma1=0.2384 and the vector mean Mach number is Ma0=0.6127.The similarity criterion derived in this paper is applied to the similarity transformation of the high-speed cascade. After the similarity transformation, the inlet Mach number of the low-speed cascade is Ma2=0.02941 and the vector mean Mach number is Ma′0=0.02941.

Fig. 8 Geometry of two-blade profile.

Fig. 9 Dimensionless isentropic Mach number distributions for two blades.

In Fig.8,the two blades before and after a similarity transformation are given.The inlet and exit blade angles of the lowspeed blade are larger than those of the high-speed blade when the chord length is basically unchanged by an affine transformation. In addition, the thickness and camber of the lowspeed blade are also significantly larger than those of the high-speed blade.

In order to verify the reliability of the similarity criterion,the numerical simulation of high- and low-speed cascades is carried out respectively. The results of numerical simulation are shown in Fig. 9, where Caxis the axial blade chord. The dimensionless isentropic Mach number (Mai) distributions for two blades are given.The results show that the loading distribution trends of the two blade surfaces are basically the same, which verifies that the similarity criterion is reasonable.

4. Experimental measurement and results

4.1. Pressure measurement schemes

Fig. 10 Pressure measurement scheme.

Pressure measurement mainly includes measurement of the velocity and pressure field at cascade outlet and pressure distribution on the blade tip surface. As shown in Fig. 10, when measuring the pressure distribution on the blade tip, the pressure hole connections relate to the Rosemount pressure differential transmitter and are finally transmitted to the acquisition computer through the terminal box and the resistance box.When measuring the velocity and pressure field at the wind tunnel outlet,the five-hole probe is used to probe into the cascade passage, and the high-precision displacement mechanism is controlled by programming to realize the automatic sweeping of the planar grid points.

The experimental blade profile is a low-speed profile obtained by the similarity transformation in Section 3. And the three tip geometries used to measure tip pressure distribution are shown in Fig.11.The three geometries are the flat tip,the normal ST and the inclined ST (incline to pressure side).The details of tip geometries are illustrated in Fig.12.The test results are shown in Fig. 13. It can be observed that the pressure measurement method proposed in this paper is feasible and accurate.It is worth noting that the pressure measurement error is 0.2% of the range, which is 0.4 Pa.

Fig. 11 Tip geometries used in experiment.

Fig. 12 Sketch of squealer tip with inclined pressure side squealer rim.

Fig. 13 Pressure distribution of blade tip.

4.2. PIV measurement scheme

The main difficulty of PIV measurement in the cavity is that the laser and camera are difficult to enter because of the small blade size.In order to measure the flow field under relative casing motion,the laser device and the camera device can only be located on the same side of the blade, and the device is prone to interference.Therefore,in order to capture the TLF and the SCV in the cavity, a PIV measurement scheme which can be used in the confined space of the cavity is designed in this section.

Fig. 14 PIV testing scheme.

Fig. 15 Arrangement of camera and laser device in PIV measurement.

The test scheme adopted in this paper and the blade used are shown in Fig.14.The outer part in Fig.14(a)is the hollow shell of the blade,and the inner part is the calibration block for the test. The calibration block is divided into two parts. After the block inserting into the blade shell,a channel is formed for the laser,as shown in Fig.14(b).The upper part of the calibration block is cut off and opened. There is a through-hole for easy insertion into the endoscope in the former part. A blade-shaped optical glass with a thickness of 1 mm is adhered to the top of the calibration block,which can ensure the depth and shape of the ST without affecting the light path.

The arrangement of the camera and laser device in PIV measurement in the cavity is shown in Fig. 15. The highspeed camera equipped with endoscope is fixed on the photographic platform. It has three rotational degrees of freedom and can move along the direction of the blade height. It can ensure the location of the shooting position. The endoscope has lens rotation and focusing function,which ensure the clarity and accuracy of the shooting field of view.As the volume of the laser device is too big, the device will interfere with the high-speed camera. Therefore, the new scheme changes the optical path to solve this problem. The laser device is placed on the lifting platform. Firstly, the laser is transformed into sheet light through a cylindrical mirror. Secondly, the laser is reflected through a right triangular prism into the laser channel between the calibration blocks.Finally, the laser brightens the photographic area of the cavity. The laser wavelength is 532 nm.The right triangular prism is made of K9 optical glass and can realize total reflection of the laser in this band. The laser device is equipped with a focusing cylinder, which can realize laser focusing and ensure that the sheet light meets the experimental requirements. Cylindrical mirror and right triangular prism are fixed on the rotary table,which can ensure that the sheet light can enter the cavity parallel to the laser channel and prevent it from reflecting on the calibration block.In particular, the blade and casing wall surface is extinct.

Fig.16 shows the calibration board used for the ST and the measured results.It can be seen that after extinction treatment of the blade and casing wall,although the end-wall part reflects a little light,the cavity concerned has not been greatly affected,and the effective area of the photography still meets the experimental requirements. To extract the velocity from the PIV particle image, the particle image is divided into several interrogation regions and the displacement of the interrogation region is obtained by analyzing two exposed particle images utilizing the autocorrelation method. Then the velocity distribution of PIV results is obtained.

Fig. 16 Scanning schematic diagram of calibration board.

Fig. 17 Vortices structure in cavity.

The experimental results and numerical results are shown in Fig. 17. The distribution of vorticity of PIV results is illustrated. The experimental results are in good agreement with the numerical simulation results. The experimental results show that there is an obvious SCV structure in the cavity under the condition of relative casing motion.

The PIV results of six sections in the squealer tip region are illustrated. These sections perpendicular to the middle arc are set at 12.5%, 25%, 37.5%, 50%, 67.5% and 75% of streamwise position respectively. The distribution of vorticity and streamline of section is shown in Fig.18.The evolution of flow structures with stationary casing and moving casing is investigated.

Fig. 18 Evolution of flow structures in squealer tip region (left:stationary casing; right: moving casing).

The photographic device of the cascade outlet flow field is shown in Fig. 19. The bottom plate after the cascade outlet is replaced by a transparent Polymethyl Methacrylate(PMMA) plate in order to adjust the laser irradiation cross section. The numerical results and the final photographed exit flow field are shown in Fig.20.The Tip Leakage Vortex(TLV)can be clearly seen in the picture. The distribution of vorticity of PIV result is illustrated as well.

Fig. 19 Photographic device at outlet.

Fig. 20 Flow field at outlet.

5. Conclusions

In this paper,a low-speed turbine cascade test facility which can model the relative casing motion and wide range of variable incidence angles (-25° to 55°) is built. Under the hypothesis of finite small perturbation,the high-low speed similarity transformation method between the flow fields of turbine cascades at different Mach numbers under subsonic conditions is derived.Based on the previous measurement methods, a new PIV measurement scheme for the TLF is developed, which can measure the complex flow field in the cavity under the condition of relative casing motion. The conclusions are as follows:

(1) The experimental platform built in this paper can simulate the effect of the relative casing motion and the wide range of variable incidence angles(-25°to 55°)on TLF.In addition, other factors such as tip clearance size and tip geometry can also be considered.

(2) A similarity transformation method is proposed to simulate the performance of high-speed cascades with lowspeed cascades.CFD results show that the dimensionless Mach number distributions of the two cascades are almost the same. The results also indicate that the lowspeed cascade can accurately simulate the aerodynamic characteristics of the high-speed cascade,and prove that the transformation method is reliable.

(3) The experimental measurement scheme implemented in this paper can not only acquire the vortices structure in the tip region, but also observe the evolution of the TLF at the cascade outlet.The SCV structure can be seen clearly in the cavity under the condition of relative casing motion.The experimental results show that the PIV technology designed in this paper is feasible and provides a feasible experimental idea for the follow-up study.

Acknowledgement

This study was supported by the National Natural Science Foundation of China (No. 51676005).