Experimental testing for the influences of rotation and tip clearance on the labyrinth seal in a compressor stator well

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Experimental testing for the influences of rotation and tip clearance on the labyrinth seal in a compressor stator well

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School of Power and Energy, Northwestern Polytechnical University, 127 West Youyi Road, Xi’an, 710072, PR China

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Xiaozhi Kong, Gaowen Liu, Yuxin Liu, Longxi Zheng

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Article history: Received 7 December 2016 Received in revised form 18 September 2017 Accepted 2 October 2017 Available online xxxx Keywords: Compressor stator well Labyrinth seal Rotating cavity Leakage behavior Windage heating Swirl flow Rotation Tip clearance

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The design of the inter-stage seal in an axial compressor is an important topic because the leakage flow across the stator well would lead to aerodynamic mixing losses with the main flow, which will consequently impact the efficiency of the compressor. In this region, the leakage flow is normally controlled by a labyrinth seal with upstream and downstream rotating cavities. In addition, the long rotating wall results in substantial temperature rise and swirl flow development. In particular, the swirl flow in the compressor stator well has a great influence on the leakage behavior of the labyrinth seal. Therefore, it is essential to understand the leakage characteristic, windage heating characteristic and swirl flow characteristic of the stator well. A test rig capable of running at rotational speed 8100 rpm and pressure ratio 1.3 was built according to the simplified model of the labyrinth seal in a compressor stator well (one stage). Labyrinth rings with different rotor tip radii were manufactured to investigate the effect of tip clearance. Leakage flow rate, windage heating and swirl ratios in the outlet cavity were measured at different rotating speeds and different labyrinth rings. As the working tip clearance was very important for the analysis of the leakage behavior, the set up tip clearance was measured with plug gauges, while the radial displacements of rotating disc and stator casing were measured separately with two laser distance sensors. Since the tip clearance was varying with rotating speed and airflow temperature, the data interpolation method was used to find the pure influences of rotation and tip clearance. Numerical simulations were performed to analyze the flow characteristic, variation of total temperature and development of swirl flow in the stator well. Besides, CFD results could provide more detailed insight into the flow mechanisms that are responsible for the influences of rotation and tip clearance. © 2017 Elsevier Masson SAS. All rights reserved.

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1. Introduction

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Gaps between stationary and rotating parts are unavoidable in turbomachinery. Large gaps can lead to flow instability and decreasing efficiency while very small gaps can result in rotor–stator collision. The sealing system in turbomachinery is very important because it has many benefits such as increasing the output power and efficiency and improving the life [1]. Labyrinth seals are noncontacting, rotating and widely used throughout the modern engines. Since aero-engines are characterized by high temperatures, pressures and rotational speeds, they are the most available technology that allows the current standards in terms of reliability and durability to be met. In a labyrinth seal, flow occurs between two relatively moving components, namely, teeth and a seal land. When the air flows through the constriction between the tooth tip and land, a part of pressure energy is converted into kinetic energy.

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E-mail address: [email protected] (X. Kong). https://doi.org/10.1016/j.ast.2017.10.003 1270-9638/© 2017 Elsevier Masson SAS. All rights reserved.

Cavities are formed between adjacent teeth such that the kinetic energy is dissipated through uncontrolled expansion, turbulence and viscous before entering the next tooth tip restriction. Therefore, this increases the resistance of flow and controls the leakage flow rate [2]. Another characteristic of labyrinth seals is that there are many performance-influencing parameters, e.g. pressure ratio, rotational speed, tip clearance and tooth shape. The leakage behavior of labyrinth seals has often been the subject of investigations in the past through numerical and experimental methods. However, much less attention had been paid to the windage heating and swirl development. The stator well in a compressor is the space between the rotor and stator inside the mainstream annulus flow (see Fig. 1). As the mainstream pressure rises, it is necessary to establish the labyrinth seals in a compressor stator well in order to prevent too much leakage flow through the clearance. Compared to normal labyrinth seals, there are rotor–stator cavities at the upstream and downstream of labyrinth seals. Due to the long rotating wall, the windage heating and the swirl development are remarkable in this

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Nomenclature

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A AR b

Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m Surface area of the seal . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2 Axial clearance between rotor and stator in the cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m B Tooth pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m CD Discharge coefficient CM Seal moment coefficient cp Specific heat capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . J/kg K c Working tip clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m c0 Set up tip clearance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m c 1 The radial displacement of labyrinth ring . . . . . . . . . . . m c 2 The radial displacement of stator casing . . . . . . . . . . . . m H Tooth height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m m Mass flow rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/s N Teeth number p∗ Total pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N/m2 p Static pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N/m2 Q Rotor power loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . W R Rotor radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m R0 Initial rotor radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m Rg Specific gas constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . J/kg K Re = m/π R μ Axial Reynolds number t Tooth tip thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m T∗ Total temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K T Windage heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K  Ta =

2c ×U

ν

c R

Taylor number

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U x V

α β

γ κ π ρ μ ν θ

ω Θ

Linear velocity of rotor . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s Axial coordinate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m Velocity of fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m/s Tooth front inclined angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . ◦ Swirl ratio The angle between V and V a . . . . . . . . . . . . . . . . . . . . . . . . ◦ Ratio of specific heats Pressure ratio Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/m3 Dynamic viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . kg/m s Kinematic viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . m2 /s Tooth rear inclined angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ◦ Rotational speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rpm Windage heating coefficient

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Fig. 1. A straight-through labyrinth seal in a compressor stator well [3].

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ideal labyrinth SYS ave a

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Ideal Labyrinth seal segment System parameter Average value Axial direction ϕ Circumferential direction r Radial direction 0 Initial value 1, 2..., 6 Measurement station

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region, which can have a great influence on the leakage characteristic. This inter-stage leakage flow is expected to further impact the aerodynamic performance of mainstream. In addition, the windage heating and swirl flow can affect the structural strength and vibration of rotor roots, as well as the accuracy of thermal analysis. In the earlier analytic and experimental attempts, very few researchers considered the rotational effects of labyrinth seals. Moreover, the centrifugal growth and the thermal expansion were not measured in most cases. Therefore, it is not suprising that some of the results are not in good agreement. For example, the leakage increased by 13% in Morrison’s and Chi’s [4] stepped seal but decreased by 9% in Stockers [5] seal toward higher rotational speeds. Then, an experimental study was presented by Waschka et al. [6], where the leakage rate was measured on a high speed straight-

through labyrinth seal. The rotation reduced the leakage flow rate beyond a certain Ta/Re ration of 0.2. Paolillo et al. [7] conducted the experiments for various stepped labyrinth seal designs and focused in particular on the effect of rotational speeds on the discharge characteristic. Leakage reduction was characterized in terms of C D /C D ,0 (the ratio of leakage rate with rotation over leakage rate without rotation) as a function of circumferential flow velocity to axial velocity. For large velocity ratios of V ϕ / V a > 5, leakage reductions of more than 20% were observed. As a rotating component, the labyrinth seal would cause the windage heating and swirl velocity of flow, which become more and more important for an optimized engine design. For example, the total temperature and swirl development after the labyrinth seal in pre-swirl chamber directly influence the blade cooling air temperature. McGreehan et al. [8] published the experimental results of windage heating for different labyrinth seal geometries and a tooth to tooth calculation algorithm was derived from shroudeddisk correlations. Millward et al. [9] provided a simple correlation to calculate seal moment coefficient based on McGreehan’s data in order to get the windage heating characteristic of the rotating labyrinth seal. In the current study, the measurement data of total temperature increase would be compared to the correlation developed by Millward. Denecke et al. [10] investigated the total temperature and swirl development across stepped labyrinth seals experimentally and numerically. The influences of inlet swirl ratio, circumferential Mach number and honeycomb on the windage heating were considered. In addition, Scherer et al. [11] found that the discharge behavior also affected the windage heating and swirl flow with CFD. Only few publications deal with the rotating labyrinth seal in a compressor stator well. An experimental study was presented by Wellborn [12], where the velocity and pressure parameters within the stator well at low speeds were investigated. Bayley and Childs [13] used previously published correlations for rotor disc moment coefficients to predict the windage heating, but this

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method was not further verified by the measurement data. Lewis [14] presented the temperature measurements from the HP compressor stator wells of full size development engine tests. The results were compared with the Millward’s correlation and the correction factor of 0.36 to the formula was used in an attempt to predict engine temperature measurements of inter-stage seals. Liu et al. [15,16] numerically discussed the influences of pressure ratio, Reynolds number, rotational speed and inlet swirl ratio on the sealing characteristic, windage heating characteristic, and swirl characteristic. The results showed that the discharge coefficient reduced with the increase of rotational speed. Moreover, the inlet and outlet rotating cavities were the important factors for studying the sealing characteristics in a compressor stator well. In a previous paper [17], we presented some experimental results of the rotating labyrinth seal in a compressor stator well. However, the working tip clearance changed in the process of rotational experiments and the influences of pure rotation and tip clearance were not obtained. In this paper, the structure of test rig was described and several labyrinth rings of different rotor tip radii were replaced in order to get different working tip clearances at a specific rotational speed. Working tip clearances, mass flow rates, windage heating and swirl ratios in the outlet cavity were measured at different rotating speeds (1500 rpm ∼ 8100 rpm) and different labyrinth rings. This paper is a continuation of the previous effort and focuses in particular on the effects of pure rotation and pure tip clearance on the discharge behavior, windage heating and swirl flow characteristic. Additionally, numerical simulations were performed to identify the flow mechanisms, variation of total temperature and swirl development. Meanwhile, numerical results of leakage flow rate and discharge coefficient were compared with the experimental data.

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Fig. 2. The simplified experimental model (mm).

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Fig. 3. Labyrinth seal geometry.

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2.1. Model and seal geometry

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The simplified model of the labyrinth seal in a compressor stator well (one stage) is shown in Fig. 2. The dash line represents the rotational wall and the solid line represents the stationary wall. There are rectangular rotor–stator cavities at the upstream and downstream of the labyrinth seal. The main geometric parameters of the investigated model are defined. Particularly, the initial rotor tip radius is defined as R 0 . Five labyrinth rings with different rotor tip radii were designed to get different set up tip clearances. In the current study, the initial rotor tip radii were R 0 = 249.05 mm, 248.85 mm, 248.65 mm, 248.45 mm and 248.25 mm respectively. The geometry of the straight-through labyrinth seal investigated in the present study is shown in Fig. 3. A three-tooth labyrinth with following parameters were chosen: tooth pitch B = 4.5 mm, tooth height H = 3.2 mm, tooth tip thickness t = 0.3 mm, tooth front and rear inclined angle α , θ = 10◦ . Most importantly, the tip clearance c changed with the varying of rotational speed and temperature in the process of experiments and would be measured dynamically. The test rig was designed according to the experimental model.

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2.2. Test facility and rig instrumentation

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2. Experimental approach

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Fig. 4 shows a schematic diagram of the test facilities. Airflow was provided to the test rig by a compressor with a maximum absolute pressure of 0.8 MPa and a continuous air mass flow rate of up to 0.5 kg/s. After passing the air tank, the airflow was supplied to the test section uniformly by a flow divider. The valves upstream of the flow divider in combination with the electric pressure control valve downstream of the test section allowed the adjustment of the pressure ratio (π = 1.05–1.30) across the test section. The

leakage flow was metered by four high-precision orifice meters of different diameters with a maximum uncertainty of ±1% of the current reading. They had been calibrated by critical flow venturi nozzles in Shaanxi Institute of Metrology Science. The lubrication and cooling system was designed to ensure safe and stable operation of the rotating bearings. The maximum rotational speed of the rotor which was directly driven by a high-speed electrical motor reached 10000 rpm. The flow for axial force control was from the cavity on the left side of the rotor disc and would not influence the leakage flow measurements. The designed test rig is indicated in Fig. 5. A cantilevered structure was used to entirely collect the leakage flow for an accurate measurement. The rotor disc consisted of the left disc and the right disc in order to allow the installation of labyrinth ring. With this structure, it was convenient to replace the labyrinth rings of different geometries and measure the set up tip clearances. In this paper, five labyrinth rings with the same tooth shape but different initial rotor tip radii were manufactured and replaced. The working tip clearances of different labyrinth rings were different at a specific rotational speed, so the influence of pure tip clearance on the inter-stage leakage flow could be gained. Besides, the influence of pure rotation effect was obtained based on the data interpolation for a specific tip clearance at different rotational speeds. In addition, the left disc, right disc and labyrinth ring were tightly pressed together. Furthermore, seals were placed between both side surfaces of labyrinth ring and disc to avoid extra leakage. The airflow entered into the supply chamber through eight circumferential supply tubes and then passed through the axial orifices uniformly distributed in circumferential direction to the central test section, after which the air discharged through the exhaust cavity. The left disc and right disc were made of carbon fiber composite, the labyrinth ring was manufactured with aluminum alloy and the stator casing was manufactured with resin (see Fig. 6). The heat conductivities of carbon fiber composite and resin are quite

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Fig. 6. Materials of the main parts.

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Fig. 5. Test rig of labyrinth seal in a compressor stator well.

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low thus ignoring the heat transfer from the test section to the environment.

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2.3. Measurement and data reduction

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In Fig. 7, the distribution of measurement stations is displayed. The stations 1, 2, 3 and 4 were defined as system inlet, labyrinth inlet, labyrinth outlet and system outlet respectively while the station 5 represented a specific radial position in the outlet cavity (R 5 = 263 mm). The static pressures and total temperatures of stations 1, 2, 3 and 4 were obtained in the experiments. In this paper, when calculating the pressure ratios, the static pressure at station 1 was regarded as the inlet total pressure because the flow velocity at system inlet was quite low. At station 5, the numerical results of radial velocity and circumferential velocity along axial direction in the outlet cavity are shown in Fig. 8. It should be noted that the radial velocity is negligibly small at the measurement station (dash line in Fig. 8) compared to the circumferential velocity. Therefore, at station 5, static pressure taps (diameter 1.0 mm) were used to determine the static

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Fig. 7. The distribution of measurement stations.

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pressure on the stator wall. Total pressure probes aligned with the circumferential direction were used to measure the circumferential total pressure, at x/b = 0.5 in the core region of swirl flow. The circumferential component of velocity in the core outside the

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Fig. 8. radial velocity and circumferential velocity along axial direction in the outlet cavity (ω = 8100 rpm,

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boundary layers was calculated from Bernouilli’s equation [18]. The pressure parameters were measured by a PSI9116 pressure scanner with modules of appropriate ranges and an accuracy of ±0.05% of full scale reading. Type K thermocouples were used for the measurement of these air temperatures with an accuracy of ±1 K. The analysis of the leakage behavior about a labyrinth seal is highly sensitive to tip clearance changes. Therefore, plug gauges with an accuracy of ±0.005 mm were used to measure the set up tip clearance c 0 at eight circumferential positions after installing the left disc, labyrinth ring and stator casing. Then the right disc and exhaust cavity were mounted. In the current study, the measured average set up tip clearances of different labyrinth rings were 0.721 mm, 0.988 mm, 1.191 mm, 1.233 mm, 1.586 mm respectively. In order to get the working tip clearance precisely, two laser distance sensors with an accuracy of ±0.01 mm were applied to measure the radial displacement of labyrinth ring c 1 and the radial displacement of stator casing c 2 (time averaged values) in the process of rotating. The windows for optical access were specially designed on the casing of exhaust cavity. The measurement positions of laser distance sensors are as indicated in Fig. 7. This type of laser distance sensor can be used to measure the relative displacements of rotor and stator. Therefore, at different rotating speeds, the working tip clearance and rotor tip radius were calculated by

c = c 0 − c 1 + c 2

(1)

R = R 0 + c 1

(2)

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The pressure ratio is defined as the ratio between the total pressure at system inlet and the static pressure at the system outlet (the ratio of the pressure at station 1 to the pressure at station 4) [19]:

π=

p ∗1

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p4

As a leakage flow parameter, the well-known discharge coefficient C D is used, which is defined as

CD =

m mideal

(4)

where mideal is calculated as follows [20]

   κ2  κ +κ 1

 ∗ p 1 A  2κ 1 1 mideal =  ∗ − κ − 1 π π T1 R g

inlet, R g is the specific gas constant and κ is the ratio of specific heats. The area available for the flow to pass the seal gap is calculated as

(6)

With the increase of rotational speed, rotor tip radius and tip clearance were changing. When processing the data, the actual values measured at each rotating speed were used in equation (6). As shown in the above equations, mideal depends on measured values of p ∗1 , p 4 , T 1∗ and A. Combining all measurement errors, the maximum error of the ideal mass flow rate at the minimum pressure ratio is ±3.78%. Then, the uncertainty (±1%) of mass flow measurements was considered and consequently the precision of the discharge coefficient is better than ±3.91%. Millward’s correlation to calculate the windage heating through labyrinth seals is shown as follows:

T =

Q 1 2

ρω

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Q



m

ρω

R 3ave



 T labyrinth = T 3∗ − T 2∗

(9) (10)

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In the following, the measured temperature rises of labyrinth seal segment were compared to the values calculated by Millward’s correlation. In addition, the windage heating coefficient can be used to describe the windage heating characteristic, which is defined as

Θ=

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In equation (7) and (8), C M is the seal moment coefficient, Q is the rotor power loss, ρ is the density, ω is the rotational speed, R ave is the average radius of rotor, A R is the surface area of the seal, N is the teeth number,  T is the total temperature rise and c p is the specific heat capacity. The windage heating of whole system and the windage heating of the labyrinth seal segment can be expressed as

 T SYS = T 4∗ − T 1∗

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mc p

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A = 2 × 3.1416 × R × c

CM =

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 T SYS

(11)

(ω R )2

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2c p

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(5)

In the above equations, m is the actual mass flow rate, mideal is the ideal mass flow rate, T 1∗ is the total temperature at system

Swirl ratio can be used to describe the swirl characteristic of outlet cavity in the stator well, which is defined as

β=

Vϕ U

=

Vϕ

ωR

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(12)

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Fig. 9. The comparisons between computational results and test data (π =1.10).

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where, V ϕ is the circumferential velocity of flow, U is the local linear velocity of disc and R is rotor radius. The measurement error of swirl ratio is ±3%.

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The geometry of axisymmetric computational domain was the same as the experimental model (see Fig. 2). The commercial software FLUENT (v.6.3.26) was used with the grid generator GAMBIT. In order to capture the flow physics well, triangular mesh elements and relatively high grid resolution were used around the teeth while structured grids were applied in the other domains. The grids were appropriately stretched towards the rotor and stator walls to sufficiently resolve the boundary layer by the value of y + of around unity. To obtain an appropriate accuracy for the numerical results, three grid sizes (100,000, 130,000 and 170,000) were used. Comparing the results of three grids showed that the grid consisting of 130,000 nodes was fine enough to ensure grid independency. Therefore, 130,000 nodes mesh was employed in the present numerical study. Two-dimensional, axisymmetric swirl flow numerical simulations were carried out and the SIMPLE pressure correction was used. The turbulence characteristics of the flow were modeled by the realizable k–ε equations with enhanced wall treatment to resolve the viscous sub-layer region. The given total pressure was imposed on the inlet boundary along with the total temperature, while the static pressure was imposed on the outlet boundary. The swirl at the inlet boundary was set to zero and a range of pressure ratios (π = 1.05–1.30) were considered in this study. An adiabatic wall and no-slip boundary condition were applied to all wall boundaries. Additionally, a rotational speed was imposed on the rotor wall (dash line in Fig. 2) and the stator wall was set to be stationary wall boundary (solid line in Fig. 2). In order to verify the numerical method, the computational results of leakage flow rate and discharge coefficient were compared to those obtained from test rig measurements in Fig. 9. Numerical simulations were performed at p 4 = 0.12 MPa, π = 1.10. Particularly, the tip clearance of numerical model at a specific rotating speed was set to be the same with the actual working clearance which was measured in the experiment. The inlet and outlet parameters corresponded with the experimental conditions also. Fig. 9 shows a good agreement between the CFD results and the test data. The maximum deviation of discharge coefficient is 3.2% at ω = 8100 rpm.

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Fig. 10. The streamline in the stator well.

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The objective of numerical simulations is to analyze the flow characteristic, variation of total temperature and swirl development in the stator well. Besides, CFD results can provide more detailed insight into the flow mechanisms that are responsible for the influences of rotation and tip clearance.

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4. Numerical results: the flow characteristics

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The numerical results of streamline, swirl flow development, static pressure and total temperature in the stator well with different rotating speeds and different tip clearances are presented as follows. The streamline in the stator well is shown in Fig. 10, where T 1∗ = 300 K, p 4 = 0.12 MPa, π = 1.10, c = 0.5 mm, ω = 0 rpm and ω = 8100 rpm. As shown in Fig. 10(a) and Fig. 10(b), there is a significant difference of the flow characteristic in the inlet cavity between ω = 0 rpm and ω = 8100 rpm. Air flows into the inlet cavity against the rotor wall (R) when the rotating speed is zero. However, when the rotor rotates, the flow is radially outward on the rotor (R) which forces the radial inflow close to the stator wall (S, in contrast to that on the rotor). This forms a large clockwise vortex in the inlet cavity. Note, that the rotating clockwise vortex will suppress the leakage through the stator well. In terms of outlet cavity, due to the rotational effect, a radial outflow on the rotor is visible and most of them move out of the cavity through the outlet slot. Meanwhile, part of flow is radially inward on the stator. This forms a large anticlockwise vortex which promotes the leakage through the stator well. In this paper, the phenomenon of radial outflow on the rotor is called pumping effect.

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Fig. 11. Swirl ratio contour in stator well (π = 1.10,

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Fig. 13. Static pressure contour in stator well ( P /Pa) (π = 1.10, c = 0.3 mm).

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Fig. 12. The influence of circumferential velocity on the effective area.

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Due to the rotation, fluid is forced to flow circumferentially and swirl velocities develop gradually in the stator well, which will have a significant influence on the leakage characteristic. Fig. 11 presents the swirl ratio contour in the stator well and the labels represent the local values, where T 1∗ = 300 K, p 4 = 0.12 MPa, π = 1.10, c = 0.5 mm, and ω = 8100 rpm. The swirl ratio jumps across the teeth are much larger. In the inlet cavity, the swirl ratio nearby the rotor decreases because the air flows centrifugally on the rotor. On the other hand, the swirl ratio nearby the stator increases due to the radially inward flow. In the outlet cavity, the area averaged swirl ratio gradually decreases where air flows centrifugally. It should be noted that the effective area available for the flow to pass through the tip clearance would reduce due to the circumferential velocity of the flow. In Fig. 12, lines of AC and BD are regarded as the flow passage at the seal tip. V a is the axial velocity, V ϕ is the circumferential velocity and V is the resultant velocity. Therefore, the effective flow area would reduce from AB to A B = AB cos γ due to the existence of V ϕ . By increasing the rotational speed, the circumferential velocity would increase before the labyrinth seal and the effective flow area would decrease and consequently the leakage mass flow rate would decline. Fig. 13 presents the static pressure contour in the stator well and the labels represent the local values, where T 1∗ = 300 K, p 4 = 0.12 MPa, π = 1.10, ω = 8100 rpm, and c = 0.3 mm. The swirl flow driven by the rotor causes the centrifugal forces which lead to the pressure gradients in the inlet and outlet cavities along radial direction called the effect of the centrifugal booster. The pressure gradient can be expressed as,

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(13)

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r

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Fig. 14. Total temperature contour in stator well (π = 1.10,

ω = 8100 rpm).

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through the stator well. It should be noted that with the increase of the tip clearance, the mass flow rate would increase, resulting in smaller swirl ratios as well as less effect of the centrifugal booster in the outlet cavity. In Fig. 14, total temperature variation across the stator well is shown and the labels represent the local values, where T 1∗ = 300 K, p 4 = 0.12 MPa, π = 1.10, c = 0.5 mm, and ω = 8100 rpm. The viscous work generated by the rotational wall induces an increase in total temperature of the fluid along the flow direction. The flow near the rotor has a higher total temperature. It is also clear that the average total temperature of flow increases significantly after passing the labyrinth seal segment. In the outlet cavity, due to the anticlockwise vortex, part of air on the rotor with high temperature flows to the stator, while the flow in the core vortex has low velocity and the temperature rise mainly depends on the heat conduction. Therefore, the core of the vortex shows a lower total temperature than outside.

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5. Experimental results: the variation of the tip clearance

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In Fig. 15, for different labyrinth rings, the variations of working tip clearance with the rotational speed are plotted at π = 1.10 and π = 1.30. It demonstrates that by increasing rotational speed the working tip clearance would decrease sharply at a specific pressure ratio. With the increase of rotational speed the centrifugal force and wall temperature would increase, which leads to the expansion of labyrinth rings. Also, the temperature rise is responsible for the radial displacement of stator casing. It is essential to obtain the working tip clearance exactly in order to get a better understanding of the leakage characteristic in a compressor stator well.

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Fig. 15. Influence of rotation on working tip clearance.

Fig. 16. Influence of tip clearance on leakage characteristic.

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In order to investigate the effects of pure rotation and pure tip clearance, five labyrinth rings with the same tooth shape but different set up tip clearances were tested. For different labyrinth rings, the experiments were conducted at different rotating speeds (1500 rpm–8100 rpm). The working tip clearances of different labyrinth rings were different at a specific rotational speed, so the curves of pure tip clearance effect on the inter-stage leakage flow at different rotational speeds were obtained. The mathematical interpolation method was used for the curves and then, a specific tip clearance was given for these curves, after which the influence of pure rotation on the flow characteristics was gained.

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6. Experimental results: the influence of the tip clearance

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Fig. 16 presents the influence of tip clearance on the leakage characteristic at π = 1.10 and π = 1.30. Very small as well as very large tip clearances yield lower C D values than medium clearances with a maximum around c = 0.8 mm. There are many factors that can affect the leakage characteristic with the increase of tip clear-

ance. (1) The increase of tip clearance leads to decreasing restriction loss. (2) Increasing the tip clearance causes the leakage mass flow rate to raise at a specific rotational speed and pressure ratio. Therefore, the swirl velocity at seal tip would reduce and consequently the reduction of the effective flow area would be smaller. (3) Due to the increase of leakage flow rate, the swirl ratios in the outlet cavity would reduce. This contributes to less significant pumping and centrifugal booster effects. Based on the above discussion, with the increase of the tip clearance, these factors are opposite and result in this leakage behavior of the compressor stator well which is different from the leakage characteristic of normal straight-through labyrinth seals [21]. The influence of tip clearance on the windage heating characteristic of whole system is plotted in Fig. 17 at π = 1.10 and π = 1.30. It indicates that increasing the tip clearance leads to rising leakage flow rate and consequently decreasing windage heating coefficient. When the tip clearance increases from 0.536 mm to 1.056 mm, the windage heating coefficient decreases by about 22% at π = 1.10 and ω = 8100 rpm.

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Fig. 17. Influence of tip clearance on windage heating characteristic of whole system.

Fig. 18. Influence of rotation on leakage characteristic.

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7. Experimental results: the influence of the rotation

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Fig. 18 shows the influence of rotation on the leakage characteristic at π = 1.10 and π = 1.30. For a specific pressure ratio and tip clearance, increasing rotational speed causes discharge coefficient to reduce. For the higher speed, the reduction is more significant. By increasing the rotational speed, the swirl flow would be enhanced and this would affect the leakage characteristic in several aspects. (1) Stronger swirl flow in the stator well causes more axial flow losses and thus the reduction of leakage. (2) The effective flow area at seal tip would reduce, resulting in falling leakage flow rate and discharge coefficient. (3) Higher swirl flow would lead to greater pumping and centrifugal booster effects in the inlet cavity, which would suppress the leakage flow through the stator well. On the other hand, stronger pumping and centrifugal booster effects in the outlet cavity would promote the leakage flow. Compared to the stationary state, when ω = 8100 rpm, the reduction of discharge coefficient is 11.6% at π = 1.10 and c = 0.75 mm.

In Fig. 19, the leakage characteristics of the labyrinth seal in a compressor stator well at constant tip clearance and changing tip clearances with the increase of the rotational speed are illustrated. The dash lines represent the variations of the discharge coefficient and leakage flow rate with the rotational speed in the condition of constant tip clearance c = 0.988 mm. The solid lines are the variations of the discharge coefficient and leakage flow rate in the condition of changing tip clearances, where c 0 = 0.988 mm. For solid lines, the reduction of working tip clearance with the rotational speed is plotted in Fig. 15(a). As can be seen in Fig. 19, the leakage flow and discharge coefficient would decrease in both cases. The discharge coefficient for the condition of changing tip clearances is larger than that in the constant tip clearance case at the same rotational speed. In addition, the reduction of the leakage flow is much larger in changing tip clearance case with the increase of the rotational speed. Compared to the stationary state, when ω = 8100 rpm, the reduction in leakage flow finds to be 52.2%. The reduction caused by the rotation effect accounts for

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about 16.7%, while 35.5% of leakage reduction can be attributed to the variation of the working tip clearance. The influence of rotation on the windage heating characteristic of whole system is shown in Fig. 20 at π = 1.10 and π = 1.30. As can be seen, the increase in windage heating coefficient is almost linearly proportional to the rotational speed. This is mainly because by increasing the rotational speed, the viscous work generated by the rotor would increase and as a result, the windage heating would rise. Also, the reduction of mass flow rate leads to an increase in the temperature rise. The measured windage heating coefficient is around 0.79, when π = 1.10, c = 0.75 mm and ω = 8100 rpm. In Fig. 21, the experimental temperature rises of labyrinth seal segment (equation (10)) were compared to the correlation from Millward (equations (7) and (8)). It can be seen that the results from the correlation over predict the experimental values. This is caused by the unconsidered inlet swirl in the correlation. However, there is swirl at the inlet of the labyrinth seal (station 2) in the current study. Additionally, the heat transfer from the test section to the environment would lead to lower measured temperature rises in the experiments. The swirl ratios measured at R 5 = 263 mm in outlet cavity are illustrated in Fig. 22. It is obvious that by increasing the rotational speed, the swirl flow would be enhanced and consequently the swirl ratio at a specific radial location would increase. The swirl characteristic in the outlet cavity serves as an important role in studying the leakage and windage heating characteristics. Stronger swirl flow in outlet cavity causes greater pumping and centrifugal booster effects, which could have a great influence on the leakage flow. On the other hand, for higher swirl flow, the circumferential velocity difference between flow and rotor is smaller, resulting in less viscous work as well as less windage heating.

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8. Conclusions

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In the current study, numerical simulations were carried out to provide insight into the flow field details, swirl flow development, pressure distribution and total temperature variation in the stator well. In the experiments, several labyrinth rings of different rotor

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Fig. 20. Influence of rotation on windage heating characteristic of whole system.

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tip radii were tested in order to investigate the effects of pure rotation and pure tip clearance on the discharge behavior, windage heating and swirl flow characteristic. The following conclusions can be drawn. (1) Due to the existence of swirl flow, the reduction of the effective flow area, pumping and centrifugal booster effects in the inlet and outlet cavities play very important roles in the leakage characteristic of compressor stator well. (2) Increasing rotational speed causes discharge coefficient to reduce. Very small as well as very large tip clearances yield lower discharge coefficient values than medium clearances with a maximum around c = 0.8 mm. (3) The increase in windage heating coefficient is almost linearly proportional to the rotational speed and increasing the tip clearance leads to decreasing windage heating coefficient. When the tip clearance increases from 0.536 mm to 1.056 mm, the windage heating coefficient decreases by about 22% at π = 1.10 and ω = 8100.

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Acknowledgements

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The authors are thankful for the financial support of Shenyang Engine Design & Research Institute and AVIC Commercial Aircraft Engine Co. LTD and the permitting of this presentation.

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References

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Fig. 21. The comparisons between Millward’s correlation and experimental data.

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(4) By increasing the rotational speed, the swirl ratio at a specific radial location would increase. The largest measured swirl ratio is around 0.35 at low pressure ratio and high rotational speed. The flow characteristics of the compressor inter-stage seal are different from normal labyrinth seals due to the presence of rotating disc cavities. This study provides important data for the thermal analysis because the exact knowledge of swirl flow and total temperature is expected to be the accurate boundary conditions. In addition, it requires a better understanding of swirl velocities and windage heating characteristic in order to predict leakage flow through the stator well accurately.

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Conflict of interest statement

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None declared.

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