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College of Energy and Power Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing 210016，P.R.China

Abstract: The cascade model was tested using transient liquid crystal temperature measurement technology. The effects of main flow Reynolds number，blowing ratio and tip clearance height on the convective heat transfer coefficient of the turbine outer ring were studied. Two feature lines were marked on the turbine outer ring corresponding to the position of the blade. The conclusions are as follows：The tip clearance leakage flow has a great influence on the convective heat transfer coefficient of the turbine outer ring. When the clearance height and the blowing ratio are kept constant，gradually increasing the main flow Reynolds number will result in an increase in the convective heat transfer coefficient of the turbine outer ring. When the clearance height and the main flow Reynolds number are kept constant and the blowing ratio is gradually increased，the convective heat transfer coefficient of the turbine outer ring is almost constant. The heat transfer coefficient of the turbine outer ring surface is little affected by the blowing ratio；The clearance height has great influence on the heat transfer characteristics of the turbine outer ring.Under the typical working condition in this paper，when the tip clearance height ratio is 1.6%，the convective heat transfer coefficient of the outer surface of the turbine is the highest.

Key words：tip leakage flow；film cooling；liquid crystal temperature measurement；heat transfer characteristics

0 Introduction

In the working state of an aeroengine，due to the presence of tip clearance，the high temperature gas is driven by the pressure difference and passes through the clearance. This results in a complex leakage flow，which directly affects the air flow and heat transfer characteristics of the turbine outer ring.Factors such as the tip clearance height，the Reyn?olds number of the main flow and the blowing ratio of the blade can all affect the leakage flow of the tip.Predecessors have conducted considerable research via numerical simulation and experimental methods.For instance，Kou et al.［1］exhibited the influence of blade rotation，blowing ratio and film cooling hole arrangement on the cooling of the high pressure tur?bine outer ring by numerical simulation. And he in?creased the blowing ratio to strengthen the Gourd shaped air film under the action of the tip leakage vortex. Zhang［2］investigated the effects of blowing ratio and number of film cooling holes on the turbine outer ring at the blade rotation speed of 1 500 r/min.Wang［3］numerically studied the effect of the periodic conditions of turbine blades on the turbine outer ring outlet on the cooling efficiency of the film. Tang et al.［4］studied the distribution of surface temperature of the turbine outer ring at different impact distances via 3-D numerical simulation，and presented an opti?mal impact distance. Using the liquid crystal ther?mography，Tamunobere et al.［5-7］reported the heat transfer behavior of the shroud and the effectiveness of the shroud cooling of a single stage turbine at a low rotation speed. In addition，an experiment of film cooling on a gas turbine outer ring with a blade speed of 1 200 r/ min was conducted，and the ef?fects of the forward，backward and lateral injection on the shroud heat transfer and cooling behavior were investigated. Amerie et al.［8］investigated the heat transfer characteristics of the GE-E3 high-pres?sure turbine casing and the characteristics when the turbine casing was specially processed. The influ?ence of the slotting operation on the heat transfer characteristics of the turbine casing was analyzed un?der different clearance height conditions.The conclu?sion indicated that the convective heat transfer coeffi?cient of the upper surface of the turbine casing was slightly reduced due to the slotting of the turbine cas?ing. Kwak et al.［9］studied the GE-E3 high-pressure turbine cascade，and the model is a two-dimensional flow channel composed of five blades. The paper fo?cused on the influence of different tip clearance heights on the surface heat transfer coefficient of the casing. It was found that there was a high convective heat transfer zone near the blade pressure surface，which was caused by the impact of the tip clearance leakage flow on the casing. As the tip clearance height increased，the convective heat transfer coeffi?cient on the casing decreased slightly. Chana et al.［10］obtained a certain heat transfer law of the blade and the surface of the casing via the MTI turbine test，and found that the corresponding position of the blade pressure surface was precisely the maximum convective heat transfer coefficient zone on turbine casing. Rhee et al.［11］studied the influence of the tip clearance height and inlet turbulence on the heat transfer characteristics of the casing in the flat blade tip. The study found that the convective heat trans?fer characteristics on the casing with tip clearance leakage flow were obviously different from those without tip clearance flow. The maximum convec?tive heat transfer coefficient on the casing appeared at the corresponding position of the blade pressure side，and the maximum convective heat transfer co?efficient increased as the gap height increased.

Up to now，most of the studies on the turbine outer ring have been accomplished via numerical simulation，and the test variables of the turbine out?er ring were also relatively simple in some experi?ments. In this paper，the transient liquid crystal tem?perature measurement technology is used in the ex?periment，which is conducted considering three as?pects：The main flow Reynolds number，the blow?ing ratio，and the tip clearance height. By analyzing the experimental results，the influence of the tip leak?age flow on the heat transfer characteristics of outer surface of the turbine is comprehensively studied.

Fig.1 Blade installation diagram

1 Experimental Devices

1.1 Experimental components

In this experiment，the first stage bucket of the GE-E3 high-pressure turbine is magnified three times and used as a simulation blade for the test.The specific parameters of the blade profile are the blade height of 122 mm，the axial chord length of 86.1 mm，the blade installation angle of 32.01°，and the outlet angle of 65.7°，as shown in Fig.1. The ex?perimental section has two air inlets for supplying compressed gas to the main flow and the secondary flow separately. The main air inlet is connected to the cascade channel，while the secondary air inlet is connected to the cold air chamber，which provides cooling air for the film cooling holes. The cascade channel has an inlet height of 10 mm，a length of 310.7 mm，and a width of 125.3 mm. There are 15film cooling holes with a diameter of 1.2 mm at 1.2 mm in front of the front line of the blade，and the distance between the holes is 15 mm. The highspeed camera is set above the cascade channel through a cold air chamber to capture the liquid crys?tal coloration results in the channel. The cooling gas entering the cold air chamber is provided by the com?pressor，and is discharged into the main flow pas?sage through the air film cooling hole and converged with the main flow. The cold air chamber is connect?ed to the cascade channel through the flange. The di?ameter of the inlet pipe of the cold air chamber is 40 mm，and the base area of the cold air chamber is 259.54 mm×1 258.78 mm with a height of 150 mm and a thickness of 5 mm，as shown in Fig.2.

Fig.2 Schematic of experimental components

To ensure the accuracy of the tip clearance height，three blade models with different heights are machined before the experiment. The heights of the three blade models are 133.0， 134.3 and 135.0 mm［12-14］.

Three holes with the same shape as the blade are machined on the lower surface of the cascade channel，and the lower plate is inserted into the cas?cade channel together with the fixed blades on the plate. The plate is fixed on the lower surface of the cascade channel，using bolted connections.

1.2 Experimental system

The experimental system is shown in Fig.3.The main air flow is supplied by the compressor of the wind tunnel. In order to ensure the drying of the compressed air，a drying device is necessarily used to remove moisture from the air. The main air flow is controlled by the valve，and the flow rate is mea?sured by a flowmeter. After being stabilized by the pressure stabilizing device，the main flow enters the cascade channel. The flow is then adjusted until the cross-flow Reynolds number reaches the setting val?ue. The gas source of the secondary air supply sys?tem is also provided by the air compressor. After the secondary air flows out from the air compressor，it enters the surge tank and passes through the cold air chamber after being stabilized by the pressure stabi?lizing chamber. The airflow then enters into the cas?cade channel through the cold air chamber and is dis?charged into the atmosphere after being mixed with the main flow［15-17］.

Fig.3 Schematic of experimental system

In the experiment，the inside of the electric heater for heating the main flow（Fig.4）is a resis?tance exothermic element inside，and the exother?mic element is a combination of six carbide rods，which are uniformly distributed in the circumferen?tial direction of the pipe. The carbon rod uses a 380 V three-phase power with a maximum power of 200 kW. The heating control cabinet is used to con?trol the heating power，and the digital temperature controller in the control cabinet maintains the tem?perature control accuracy at±1 °C.

Fig.4 Electric heater

The main flow range of this experiment is cal?culated to be 0—0.6 kg/s，thus the range of vortex flow meter used for measurement is 320—2 000 /h.The flow rate of the secondary flow is measured with a float flow meter with a range of 0.25—2.5 m3/h. The pressure measurement points and the temperature measurement points are set before and after the flow meter intake，and the actual mass flow rate is obtained by the compensation calcula?tion.

During the experiment，it is necessary to mea?sure the static pressure before and after the blades and the static pressure after the flow meter.The stat?ic pressure measurement points of the blades are dis?tributed on the lower surface of the cascade channel，where there is a measurement hole with a diameter of 1 mm. A static pressure probe with a diameter of 0.8 mm is inserted into the hole to extract the gas and connected to the pressure sensor via a hose. The pressure sensor model number is CYG1601 with an accuracy rating of 0.25，as shown in Fig.5. At the same time，the static pressure after the flow meter is measured with a BP-801 pressure transmitter.

Fig.5 Pressure sensor diagram

The temperature is measured with a K-type thermocouple（±0.75%）with a range of -40 to+350 ℃，which is used together with the multichannel temperature tester JK-48U to measure the inlet temperature of the cascade channel and the temperature of the airflow after the flow meter. The liquid crystal temperature measurement technology is used in the experiment. The pitch of the liquid crystal changes with temperature. When a beam of light is irradiated onto the surface of the liquid crys?tal，only that with a wavelength equal to the molecu?lar rotation pitch can be reflected back，exhibiting different colors，and the temperature is measured due to this characteristic. A high speed camera is used to record the different colors that the liquid crystal layer displayed at different temperatures.The images captured by the camera are processed by a self programming program to obtain the temper?ature distribution of the turbine outer ring surface.

The temperature range of liquid crystal is 40 ℃to 60 ℃，and therefore the total temperature of the main flow in the experiment is set to 338 K. The main flow Reynolds number is calculated based on the main flow rate，and the calculation formula is Eq.（1）. The above determines all the main flow gas parameters.

wherem?1is the the main flow rate measured by the flowmeter，dthe equivalent diameter of the main flow cavity，μthe dynamic viscosity，andA1the ar?ea of the main flow cavity.

The temperature of the secondary flow provid?ed by the surge tank is 293 K，and the secondary flow rate is determined by the blowing ratio and the main flow.In the experiment，the main flow temper?ature and the main flow and secondary flow tempera?ture ratio are kept unchanged［18］. The definition of the blowing ratioMin the test is

wherem?2is the secondary flow andA2the outflow area of the secondary flow.

Table 1 Different experimental conditions

The test conditions are shown in Table 1. For the typical working condition，τ/H=1.6%（τis the blade tip clearance andHthe blade height），and to be specific，the tip clearance is 1.97 mm，the main flow Reynolds number is 80 000，and the blowing ratio is 1.5. The remaining control trials only change one type of the variables.

In the experiment，the maximum flow velocity is 11 m / s and the maximum Mach number is 0.03.

2 Photonic Arbitrary?Waveform Generation

2.1 Analysis of typical working conditions of turbine outer ring test

The typical working condition is taken as an ex?ample，of which a temperature contour is given in Fig.6 according to the experimental data processing results. In Fig.6，the heat transfer coefficient at the position of the turbine outer ring surface correspond?ing to the blade region is higher，and the heat trans?fer coefficient at the turbine outer ring surface out?side the blade region is lower. This indicates that the tip clearance leakage flow has a great influence on the heat transfer coefficient of the turbine outer ring surface. While the motion law of the tip clear?ance leakage flow is complicated，the tip clearance leakage flow continuously impacts the tip and tur?bine outer ring surfaces in the clearance，and then a heat transfer coefficient increase zone of the turbine outer ring surface is formed. In Fig.6，there is a rela?tively low heat transfer coefficient region at the lead?ing edge of the blade. This is because the blade is thicker at the leading edge and the pressure differ?ence is smaller，which makes the air movement slower，and as a result，the heat transfer coefficient is lower. Two feature lines are marked on the tem?perature contour corresponding to the position of the blade，as shown in Fig.7. By analyzing the change of heat transfer on the feature line，the influence law of several parameters on the surface heat transfer co?efficient of the turbine outer ring is found.

Fig.6 Physical photo of the test

Fig.7 Schematic diagram of typical working conditions

Fig.8 Influence of main flow Reynolds number on distribu?tion of heat transfer coefficient on feature Line 1

2.2 Influence of main flow Reynolds number on surface heat transfer characteristics of turbine outer ring

Fig.8 shows the relationship between the heat transfer coefficient on the feature Line 1 and the main flow Reynolds number，whereX/Caxialrepre?sents the relative position on the feature Line 1. The abscissa is the dimensionless axial distance and the ordinate is the turbine outer ring heat transfer coeffi?cient. As shown in Fig.8，when the main flow Reyn?olds numbers are different，the heat transfer coeffi?cient changes on Line 1 are almost the same，in?creasing first and then decreasing. It can be seen from the corresponding position of the blade on Line1 that the heat transfer coefficient on the feature line suddenly increases to a peak at the pressure side position of the blade，and then gradually decreases.When the feature Line 1 is in the tip clearance，the heat transfer coefficient fluctuates continuously along the feature line. As the leakage flow flows out from the tip clearance，the heat transfer coefficient of the feature line at the suction side of the blade de?creases rapidly. It can be clearly seen that as the main flow Reynolds number increases，the heat transfer coefficient on Line 1 also increases. This is because the larger the main flow Reynolds number is，the larger the inlet flow rate of the main passage is，and the more the flow leaking into the tip clear?ance becomes. When the main flow Reynolds num?ber is 60 000，the convective heat transfer coeffi?cient of the turbine outer ring surface is the smallest.When the main flow Reynolds number is 100 000，the convective heat transfer coefficient of the turbine outer ring surface reaches its maximum，which is 36% higher than the minimum value. And the in?creasing main flow Reynolds numbers increase the percentage of convective heat transfer coefficient on the feature line by 14%，12.8%，12.5%，and 8.6%.

Fig.9 shows the variation of the heat transfer coefficient on the feature Line 2 with the main flow Reynolds number，whereY/Caxialrepresents the rel?ative position on the feature Line 2. It can be seen that the heat transfer coefficient increases less before the airflow enters the gap. With the mixing of the main flow and the leakage flow，the leakage flow impacts back and forth between the turbine outer ring surface and the blade tip，thereby enhancing the convective heat transfer at the impact point. As the leakage flow flows out of the tip clearance，the fluc?tuation of the heat transfer coefficient on the Line 2 is relatively reduced. Furthermore，the heat transfer coefficient on the feature Line 2 is basically increas?ing when the main flow Reynolds number is increas?ing.

Fig.9 Influence of main flow Reynolds number on distribu?tion of heat transfer coefficient on feature Line 2

2.3 Influence of air blowing ratio on heat trans?fer characteristics of turbine outer ring sur?face

Fig.10 is a curve of the heat transfer coefficient on Line 1 as a function of the blowing ratioM. It can be seen from Fig.10 that when the blowing ra?tios are different，the heat transfer coefficient on Line 1 changes almost the same. It can also be found that when the blowing ratios are different，the heat transfer coefficient on Line 1 corresponding to the area before the airflow enters the clearance is ba?sically unchanged. After the leakage flow flows out of the tip clearance，the heat transfer coefficients are similar on the feature line when the blowing ratio is 1，1.5 and 2，and when the blowing ratio is in?creased to 4，the heat transfer coefficient on Line 1 is somewhat decreased compared with those under other blowing ratio conditions，by about 27%.

Fig.10 Influence of blowing ratio M on heat transfer coeffi?cient on feature Line 1

Fig.11 shows the curve of the heat transfer co?efficient on Line 2 as a function of the blowing ratioM. As can be seen from Fig.11，multiple peaks of the heat transfer coefficient appear in the tip clear?ance because the leakage flow continuously impacts the turbine outer ring surface. In addition， in Fig.11，after changing the blowing ratio，the heat transfer coefficient on the feature line is less affect?ed. Based on a comprehensive analysis of Figs.10，11，the blowing ratio has little effect on the convec?tive heat transfer coefficient of the turbine outer ring.

Fig.11 Influence of blowing ratio M on heat transfer coeffi?cient on feature Line 2

2.4 Influence of tip clearance height on heat transfer characteristics of turbine outer ring

Fig.12 is a curve of the heat transfer coefficient on Line 1 as a function of the tip clearance height.Under different clearance heights，the heat transfer coefficient of the turbine outer ring along Line1 ex?hibits the same change law，first increasing and then decreasing. The maximum of the heat transfer coef?ficient occurs at the position where the leakage flow flows into the tip clearance，and the minimum ap?pears to be at the position where the leakage flow flows out of the tip clearance. It can also be seen from Fig.12 that the relatively suitable clearance size isτ/H= 1.6% under this typical working con?dition，and the turbine outer ring surface heat trans?fer coefficient is increased by about 53% compared with that whenτ/H= 2.7%. The reason is that when the clearance height is large，the influence of the entrance effect and the fluid acceleration is weak?ened，and the leakage flow rapidly flows out of the tip clearance. Hence，the influence of the heat trans?fer coefficient on the turbine outer ring surface is weak；and when the clearance height is reduced，the tip clearance leakage flow decreases. Therefore，the convective heat transfer coefficient on the sur?face of the turbine outer ring also decreases.

Fig.13 shows the influence of the tip clearance height on the distribution of the heat transfer coeffi?cient on Line 2. When the feature line passes through the corresponding tip clearance position，the change of the heat transfer coefficient on the fea?ture line is complicated，and a significant difference appears with different clearance heights. The heat transfer coefficient corresponding to the tip clear?ance region on the feature line fluctuates greatly，and there is a plurality of points with a high heat transfer coefficient. The reason is that the leakage flow and the main flow are mixed in the tip clear?ance，and the turbine outer ring surface is subjected to multiple impacts，thus resulting in an increase in the heat transfer coefficient at the impact point. It can also be seen from Fig.13 that when the tip clear?ance height ratioτ/H= 1.6%，the heat transfer ef?fect is optimal，and the maximum heat transfer coef?ficient in the leakage clearance is about twice that of the other states.

Fig.12 Influence curves of tip clearance height on heat transfer coefficient on feature Line 1

Fig.13 Influence of tip clearance height on heat transfer co?efficient on feature Line 2

3 Conclusions

The following conclusions can be drawn from the experiment.

The heat transfer effect of the outer surface of the turbine is greatly affected by the tip clearance leakage flow. Increasing the main flow Reynolds number as well as maintaining the same gap height and blowing ratio will result in more leakage flowing into the tip clearance. At the main flow Reynolds number of 100 000，the convective heat transfer co?efficient is increased by 36%，compared with that when the main flow Reynolds number is 60 000.

Under the condition of keeping the gap height and the main flow Reynolds number unchanged，by the way of comparing and analyzing the leakage amount entering the tip clearance when several sets of different blowing ratios are obtained，it is found that the tip clearance leakage is less affected by the blowing ratio. Therefore，the blowing ratio has little effect on the convective heat transfer coefficient of the turbine outer ring.

Changing different gap heights，the heat trans?fer coefficient of the outer ring surface of the turbine at the tip clearance changes complicatedly. Too much or too little leakage flow will result in a de?crease in the heat transfer coefficient of the outer sur?face of the turbine. Under typical conditions with a clearance height ratio ofτ/H= 1.6%，the maxi?mum heat transfer coefficient can be twice that un?der other height ratio conditions，meanwhile the overall heat transfer effect is optimal.