Numerical Investigations on Leakage Performance of the Rotating Labyrinth Honeycomb Seal

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Jun LiInstitute of Turbomachinery,

Xi’an Jiaotong University,Xi’an 71049, P.R.C.;

Department of Mechanical Engineering,Keio University,

Yokohama 223-8522, Japane-mail: [email protected]

Shengru Kong

Xin Yan

Institute of Turbomachinery,Xi’an Jiaotong University,

Xi’an 71049, P.R.C.

Shinnosuke ObiDepartment of Mechanical Engineering,

Keio University,Yokohama 223-8522, Japan

Zhengping FengInstitute of Turbomachinery,

Xi’an Jiaotong University,Xi’an 71049, P.R.C.

Numerical Investigations onLeakage Performance of theRotating Labyrinth HoneycombSealThree-dimensional Reynolds-averaged Navier–Stokes (RANS) solutions from CFX wereutilized to investigate the leakage flow characteristics in the labyrinth honeycomb seal ofsteam turbines. At first, the accuracy and reliability of the utilized RANS approach wasdemonstrated using the published experimental data of the honeycomb seal. It showedthat the utilized numerical method has sufficient precision to predict the leakage perfor-mance in seals. Then a range of sealing clearances, cell diameters, cell depths, rotationspeeds, and pressure ratios were investigated to determine how these factors affect theleakage flow rate of the labyrinth honeycomb seal. The computed leakage flow rateincreased with increasing sealing clearance and pressure ratios. Furthermore, the resultsshow that the studied labyrinth honeycomb seal has the optimum sealing performance inthe case of honeycomb cell diameter equals labyrinth step width, and the ratio of thehoneycomb cell depth to honeycomb cell diameter is 0.93 under the designed condition.The flow pattern of each case is also illustrated to describe the leakage flow character-istics in labyrinth honeycomb seals. �DOI: 10.1115/1.4000091�

Keywords: labyrinth honeycomb seal, leakage flow, numerical simulation

IntroductionThe increasing demand for aggressive power output, efficiency,

nd operational life for turbines requires us to pay more attentiono the leakage flow between stationary and rotating components.eakage flow has many disadvantages for a turbine. Leakage flow

s one of the main sources of loss in the through flow of a turbine.he leakage flow interacts with the main flow and reduces turbinefficiency �1�. In addition, leakage flows may induce flow excita-ion and result in rotordynamic instability �2�. Controlling leakageow, and the corresponding clearance technique, is one of theritical aspects of turbine design and manufacture process. Laby-inth seals, a noncontact dynamic sealing technology, are the keylements to control the amount of leakage flow for through flow inturbine. Despite advanced sealing technologies, including brush

eals, leaf seals, finger seals, and so on, for turbine leakage flowontrol �1,3�, labyrinth seals still play an important role in leakageow control. Thus, improved design tools are a necessity for aore efficient and reliable turbine �4�. To overcome the leakageow excitation of labyrinth seals for the recently developed largeower output steam turbine, gas turbine, labyrinth honeycombeals were developed and applied �5�. Figure 1 shows the struc-ural configuration of a labyrinth honeycomb seal. Labyrinth hon-ycomb seal technology requires that the honeycomb lands in-talled at the stator component and the rotating components areonsistent with the conventional labyrinth seals. To increase laby-inth honeycomb seal utilization for turbines, it is crucial to studyhe discharge behavior of this kind of sealing technology.

The sealing performance, including the discharge coefficient ofabyrinth honeycomb seals, is the subject of the current seal re-earch. There are many factors that can affect leakage flow of theabyrinth honeycomb seal. One of these factors is the sealing

Manuscript received March 3, 2009; final manuscript received June 17, 2009;
ublished online March 16, 2010. Editor: Dilip R. Ballal.
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clearance. At the same sealing clearance size, the leakage flowrate of the honeycomb seal is higher than that of the labyrinth sealat the same flow condition and axial distance �6�. Another factor isthe honeycomb cell size �7�. Empirical results, as well as theoret-ical analysis, have shown that other factors such as the pressureratio and rotational speed may impact the discharge characteristicsof the labyrinth honeycomb seal �8�. A few simple correctionequations based on the experimental data were derived and usedto predict the experimental results. Therefore, it is difficult todecide the factors for every new design. At present, the progressof computer and CFD technologies makes it possible to utilize anumerical simulation to predict the performance of rotating seals.Furthermore, it is also convenient to obtain the correction factorsdirectly if the validity of the numerical method has been demon-strated.

To investigate how these factors, such as the sealing clearance,honeycomb cell sizes, pressure ratio, and rotation speed, affect thedischarge behavior, numerical investigations were performed inthe present study to calculate the leakage flow in the shaft laby-rinth honeycomb seal. First of all, the computed leakage flow rateand detailed velocity profiles within the seal chamber were com-pared with the obtained experimental data for the labyrinth sealwith smooth and honeycomb lands. After the accuracy and reli-ability of the utilized numerical approach have been demon-strated, the influence of sealing clearance, honeycomb cell sizes,pressure ratio, and rotation speeds on the leakage flow character-istics in the shaft labyrinth honeycomb seal were investigated indetail.

2 Literature ReviewLabyrinth seals are widely used in steam turbines, gas turbines,

and other applications where transient rubbing contact is likely.The labyrinth seal is a noncontacting dynamic seal, and the majoradvantages of this seal are its simplicity, reliability, and tolerance
to large thermal and pressure variations �2�. Labyrinth seals work
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n the principle that fluid pressure energy is converted at eachooth tip clearance into kinetic energy that is either dissipated intoeat by turbulence, or enters the subsequent tooth clearance byinetic energy carryover �9–11�.

The honeycomb seal, whose inner bore consists of many hex-gonal or honeycomb pockets, was originally introduced in the960s as a replacement for aluminum labyrinth seals, which wereeing eroded by processing fluids �10�. Stocker et al. �11� com-rehensively presented experimental results on the leakage perfor-ance of labyrinth seals with honeycomb lands. He used both

wo-dimensional planar and three-dimensional rotating seal testigs to measure the air leakage through labyrinths with honey-omb, abradable or solid stator walls. He concluded that the leak-ge flow rate of the honeycomb land was greatly increased, inomparison with that of the smooth land at a small tooth clearancef a straight-through labyrinth seal with four teeth. The honey-omb seal withstands severe operating conditions in terms of highemperatures and high rotational speeds while allowing limitedubbing of the stator fins at the rotor without the danger of sealailure. Therefore, a significantly tighter seal clearance, which rep-esents a leakage-reducing factor, can be realized �5�.

Research on the leakage flow characteristics in labyrinth seals,ncluding honeycomb seals, had initially been based on experi-

ental tests and numerical simulations. Advanced experimentalechniques, together with numerical methods, have been appliedo obtain detailed information of the complex leakage flow inabyrinth seals, and to identify the relevant parameters influencinghe labyrinth leakage flow characteristics. Regarding the effect ofub grooves formed into an abradable surface, Rhode and Allen12,13� obtained flow visualization digital images for large-scaletepped labyrinths that explain the measured effects on leakage.

ittig et al. �14� investigated the effects of the pressure ratio andeynolds number on straight-through labyrinth seals by measur-

ng the leakage rates of geometrically similar, two-dimensionallane models. Plots of the nondimensional discharge coefficientsgainst the overall pressure ratio for different scales were pre-ented.

ig. 2 Geometrical parameters of the labyrinth seal with hon-

ig. 1 Structural configuration of the labyrinth honeycombeal

ycomb lands †6‡

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Recently, Schramm et al. �6� obtained CFD results from a com-mercial code showing the leakage flow entering the honeycombcells. They also found agreement with laser doppler velocimeter�LDV� measurements regarding the presence of a three-dimensional velocity field near the tooth tips. Choi and Rhode�15� introduced a new approach for employing a two-dimensionalCFD model to approximately compute a three-dimensional flowfield in a honeycomb labyrinth seal. A numerical study for wornand unworn labyrinth seals with honeycomb land at different ra-dial clearances using the commercial CFD code, CFX, was pre-sented �16�. Yan et al. �17� applied three-dimensional commer-cially available CFD software, CFX, to predict the leakageperformance and windage effects of the labyrinth seal with differ-ent sizes of honeycomb lands. They presented results confirmingthe conclusions of Denecke and co-workers �7,8�.

Several investigators report on the high performance of laby-rinth honeycomb seals. Paolillo et al. �18� experimentally studiedthe rotational speed on the discharge characteristics of two kindsof labyrinth honeycomb seals. Soemarwoto et al. �19� numericallyinvestigated the leakage performance of three designs of labyrinthhoneycomb seals, and they discussed detailed flow patterns. Theobtained results showed that the canted-knife seal design withrespect to the straight-knife case has the lower performance.Chougule et al. �20� utilized the three-dimensional CFD numericalapproach to investigate the leakage performance of their new de-sign labyrinth honeycomb seal. A staggered honeycomb land andstraight teeth with a newly designed inclined notch showed a 17%reduction in seal leakage, compared with the initial design.

However, the influence of sealing clearance and honeycombcell size on the leakage performance of labyrinth honeycomb sealsis seldom presented. Thus, the main objective of the present workwas to utilize a 3D numerical method to investigate the dischargebehavior in the shaft labyrinth honeycomb seal. The effects of

Table 1 Conditions and numerical methods

Inlet total temperature 300 KOutlet static pressure 101325 PaDiscretization scheme High resolutionComputational method Time marching methodTurbulence model k−�, scalable log wall functionFluid Air �ideal gas�Wall properties Adiabatic, smooth surface

Fig. 3 Boundary condition definitions

Transactions of the ASME


Fig. 4 Velocity flow pattern in the labyrin

Fpresent CFD results and the experimental data

Fthe present CFD results and the experimental data

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many factors such as sealing clearance, honeycomb cell size, pres-sure ratio, and rotational speed on the leakage flow characteristicswere conducted and are discussed here.

3 Numerical Method

3.1 Validation Model. To demonstrate the accuracy and reli-ability of the numerical approach for predicting the discharge be-havior of the labyrinth honeycomb seal, the experimental laby-rinth seal with smooth and honeycomb lands was utilized. Thecomputational geometrical parameters of the experimental re-search were obtained from Schramm et al. �6�. The labyrinth sealswith smooth and honeycomb lands configurations are defined inFig. 2. It features three straight knives on the rotor.

th smooth seal „s1=1.204 mm, �=1.1…

Fig. 7 Configuration and geometrical parameters of the laby-

ig. 5 Comparison of the discharge coefficients between the

ig. 6 Comparison of the leakage increase parameter between
rinth honeycomb seal
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3.2 Numerical Approach. Since the flow in both the laby-inth smooth seal and labyrinth honeycomb seal is typically three-imensional �turbulence due to the structure and flow conditions,nd there exists a high relative rotation speed�, it is necessary to

Fig. 8 Boundary condition definitions and the local grid

Fig. 9 Flow fields in the labyrinth honeyco
condition „T=0.75 mm, L=4.58 mm, and D=4.2
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solve 3D Reynolds-averaged Navier–Stokes �RANS� equations toanalyze the flow patterns, and to predict the leakage flow rate ofthe seals.

A multiblock structured grid was generated for the computa-tional case. In order to study the leakage flow characteristics forthe labyrinth smooth seal and labyrinth honeycomb seal, the com-mercial finite element code, CFX5.7 �21�, was used. This softwaresolves the compressible time-averaged RANS equations. Addi-tionally, a second order high resolution discretization scheme wasused. The turbulence characteristics of the flow are modeled bythe standard k−� equations. The scalable logarithmic wall func-

seal at two sections at the designed flow

Fig. 10 Leakage flow rate with different sealing clearancesizes „D=4.26 mm…

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6 mm…


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Fig. 11 Static pressure contours and velocity distributions in the labyrinth honeycombseal with different sealing clearance sizes „L=4.58 mm, D=4.26 mm…: „a… T=0.75 mm, „b…T=0.05 mm, and „c… T=0.25 mm

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ion was used to describe the near wall velocity. The scalableogarithmic wall function is utilized when the y+ is greater than1.06, according to the CFX user guide. The maximum y+ in theresent honeycomb seal simulation is about 200. The y+ criterions met over almost the entire wall region. The boundary conditionsnd numerical methods are listed in Table 1. The ideal gas settingas used in this numerical model. Figure 3 shows the boundary

onditions defined for the labyrinth smooth seal and the labyrinthoneycomb seal. In addition, the local computational grid for theabyrinth honeycomb seal is given in Fig. 3�b�. In this simulation,periodic boundary condition was assumed in the circumferentialirection. In the flow direction, specifications at the flow inlet andxit boundaries were needed. The inlet boundary was placed at theeal entrance, and total pressure, total temperature, and turbulenceuantities were defined, while the averaged static pressure waspecified at the outlet of the seal. The stationary walls were de-ned to be adiabatic. The desired convergence target of eachimulation was that the root mean square �rms� residuals of theomentum and mass equations, energy equations, and turbulence

quations reached �or were even lower than� 10−6.

3.3 Discharge Coefficients. To compare the experimentalata, a dimensionless discharge coefficient CD was defined touantify the leakage behavior. Equations �1� and �2� is adoptedrom Ref. �6�, as follows:

CD = m/mideal �1�

here the leakage mass flow rate m is taken from the CFD analy-is, and mideal stands for a theoretical mass flow for isentropiconditions

mideal =p1A�T1

� 2k

R�k − 1�� 1

��2/k

− � 1

��k+1/k �2�

In this formula, � represents the ratio of the inlet to outletressure. The cross sectional area of the gap is calculated as AB ·sThe discharge coefficients of two cases at different pressure

atios are calculated using Eq. �1�. The leakage mass flow rate ms calculated through the sealing clearance by summing the dotroduct of the density times the velocity vector and the area pro-ections over the faces of the inlet or exit boundary. The specified

˙

ig. 12 Leakage flow rate with different honeycomb cell diam-ters „T=0.75 mm, D=4.26 mm…

ormulation of m is described by the following equation. CFX cal-

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culates the inflow and outflow mass flow using Eq. �3� in itspostprocessing

m = �v� · dS� = � �iv� i · S� i �3�

To compare the leakage performance between the labyrinthsmooth seal and labyrinth honeycomb seal, the leakage increaseparameter � was used, according to Schramm et al. �6�. The leak-age increase parameter was defined as follows:

� =CD,HC

CD,SMOOTH�4�

where CD,HC and CD,SMOOTH are the dimensionless discharge co-efficient of the labyrinth honeycomb seal and labyrinth smoothseal, respectively.

3.4 Numerical Method Validation. The geometrical param-eters of the labyrinth and honeycomb seal is adopted from Ref.�6�. Three sizes of clearance of the computational seal equals s1=1.204 mm, s2=1.988 mm, and s3=3.192 mm, respectively.Figure 4 shows the leakage flow pattern in the labyrinth smoothseal. The present numerical result is in good agreement with theexperimental data. As shown in Fig. 4, the fluid passes the laby-rinth gap, and impinges on the step. The jet is then deflected byalmost 90 deg, and directed towards the bottom of the labyrinthchamber beneath the step. Inside the cavity, the jet separates twocounter-rotating and equally sized recirculation zones. The com-parison of the leakage flow rate between the experimental dataand numerical results for labyrinth smooth seal is given in Fig. 5.The leakage increase parameter between the experimental dataand calculated results for the labyrinth honeycomb seal is shownin Fig. 6. The reliability and accuracy of the utilized numericalapproach is demonstrated in Figs. 5 and 6.

4 Results and DiscussionsOn the basis of the accuracy and reliability of the utilized nu-

merical approach, the effects of sealing clearance sizes, honey-comb cell sizes, rotational speed, and pressure ratios on the leak-age performance of the labyrinth honeycomb seal were calculatedand are discussed in detail.

4.1 Problem Description. Figure 7 shows the configurationof the shaft labyrinth honeycomb seal of steam turbines. The laby-rinth and honeycomb seal diameter is 907.78 mm. The sealingclearance size s between the labyrinth fins and the rotor surface is0.75 mm. The height and width of the labyrinth step is designed asH=4.78 mm and b=3.18 mm, respectively. The honeycomblands are installed at the stator component between neighboringlabyrinth fins of the labyrinth seal. To investigate the effect ofsealing clearance sizes on the leakage performance, the sealingclearance size between the honeycomb lands and labyrinth step ofthe rotor surface varied as T=0.75 mm, T=0.5 mm, and T=0.25 mm in this work. At the fixed sealing clearance T=0.75 mm and the honeycomb cell depth D=4.26 mm, sevensizes of honeycomb cell diameters are utilized to study the celldiameter effects on the flow fields. In addition, at the sealingclearance T=0.75 mm and the honeycomb cell diameter L=4.58 mm, five sizes of honeycomb cell depths were used tostudy the leakage flow fields. Moreover, the effects of the rotationspeed and pressure ratios on the leakage performance of the laby-rinth honeycomb seal were also investigated at the constant seal-ing clearance and honeycomb cell sizes, respectively.

The boundary condition definition and local computational gridis shown in Fig. 8. A multiblock structural grid was generated inthe labyrinth honeycomb seal for numerical computation. The av-eraged mesh size for the honeycomb seal simulation is about
1,000,000. The mesh size is set up at about 800,000 for the small-


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Fig. 13 Static pressure contours and velocity distribution in the labyrinth honeycomb sealwith different cell diameters „T=0.75 mm, D=4.26 mm…: „a… L=4.58 mm „L /b=1.44…, „b… L
=3.178 mm „L /b=1.0…, and „c… L=1.37 mm „L /b=0.43…
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st clearance size, and 1,200,000 for the largest clearance size ofhe honeycomb seal. The same numerical approach delineatedbove was utilized. At the designed flow condition, a total pres-ure of 10.757 MPa, and a total temperature of 752.37 K, areiven at the inlet. The outlet static pressure is 2.8512 MPa. Theotation speed at the designed condition is set at 3000 rpm. Theoneycomb lands and labyrinth fins are defined as the static walloundary. In addition, the rotor surface is set to be the rotatingall boundary and equals 3000 rpm at the designed flow condi-

ion. Each case of the honeycomb seal is conducted on a personalomputer with CPU 2.40 GHz and 8G memory. It took about 48 hor each case computation in this work.

Figure 9 shows the computed flow field in the labyrinth honey-omb seal at two lateral positions, z1 and z2, under the designedow condition. The gap size was fixed at T=0.75 mm. The hon-ycomb cell diameter and depth were defined as L=4.58 mm and=4.26 mm, respectively. Inside each honeycomb cell cavities,

ecirculation zones occur that are driven by the viscous shear layert the opening honeycomb cell. The intensity and recirculationow pattern in each honeycomb cell is influenced by the clearanceize and cell geometrical parameters. Further discussion is to beiven in later computations. At the lateral position z1 where theection is centered at the computational region, the leakage jetmpinges into the bottom of the honeycomb cell, and forms atrong clockwise vortex inside the honeycomb cell where the hon-ycomb cell is located upon the labyrinth step. At the lateral po-ition z2 where the section is located at the periodic boundary ofhe computational region, a different leakage jet pattern is ob-erved, compared with position z1. A recirculation zone is ob-erved within each honeycomb cell, and the transfer of the kineticnergy of the leakage jet into heat energy also occurs here. The

ig. 14 Leakage flow rate with different honeycomb cellepths „L=4.58 mm, T=0.75 mm…

Fig. 15 Velocity distribution in the labyrinth honeycomb s

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pressure drop across the labyrinth honeycomb seal is due to thisflow pattern. Different honeycomb cell cavity sizes are observedat position z2. Thus, the detailed flow pattern in the computedlabyrinth honeycomb seals is to be discussed at position z2 foreach case.

4.2 Effects of Sealing Clearance. Three sizes of sealingclearance between the honeycomb cell and the labyrinth step werecalculated to investigate the effects on the leakage characteristics.The honeycomb cell depth was fixed at D=4.26 mm. Three hon-eycomb cell diameters with L=4.58 mm, L=3.67 mm, and L=2.75 mm were studied under three gap sizes. Comparison of theleakage flow rate among the three clearance sizes for the differenthoneycomb cell diameters is given in Fig. 10. A similar variationin the trend of the clearance size on the leakage flow rate of thelabyrinth honeycomb seal is observed. For the fixed honeycombcell diameter, the leakage flow rate increases with increasingclearance size. According to Fig. 10, the effect of the intensity ofthe gap size on the leakage flow rate at a small cell size �L=2.75 mm� is greater than that at a large cell size �L=4.58 mm�. For the fixed honeycomb cell diameter, the leakageflow rate increases with increasing clearance size.

Figure 11 shows the static pressure contours and velocity dis-tribution under three different gaps in the local labyrinth honey-comb seal with a 4.58 mm cell diameter and a 4.26 mm cell depth.As to the smallest gap size, T=0.25 mm, the angel of the velocityvector toward and away from the honeycomb land �Fig. 11�c�� isgreater than that of the gap size T=0.75 mm �Fig. 11�a��. Thegreater angle of leakage velocity vector at the smallest gap leadsto a more distinct deflection of the leakage flow, and impinges onthe bottom of the labyrinth cavity directly downstream of the fintip. The clockwise recirculation zone is observed within each hon-eycomb cell. The recirculation inside two honeycomb cells lo-cated upon the labyrinth step is more obvious than that of otherneighboring cells. The leakage jet velocity increases with the in-creasing size of the gap between the honeycomb cell and thelabyrinth step. This results in an increase in the leakage flow rate.A similar flow pattern inside the honeycomb cell chamber is ob-served for the three gap sizes, according to Fig. 11.

4.3 Effects of Honeycomb Cell Diameter. To investigate theeffects of honeycomb cell diameter on the leakage performance,seven sizes of cell diameters were calculated for the fixed clear-ance size �T=0.75 mm� and cell depth �D=4.26 mm�. Seven di-mensionless honeycomb cell diameters L /b with 1.44, 1.15, 1.0,0.86, 0.72, 0.52, and 0.43 were calculated. The specified honey-comb cell diameter is determined to ensure integral numbers ofhoneycomb cells along the circumferential direction in the statorcomponent of the studied labyrinth seal.

Figure 12 shows the effect of the cell diameter on the leakageperformance of the labyrinth honeycomb seal. During the varia-tion of the cell diameter from 4.58 mm �L /b=1.44� to 3.178 mm�L /b=1.0�, the leakage flow rate decreased with the decrease in

eal with different cell depths „L=4.58 mm, T=0.75 mm…



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he cell diameter. However, the leakage flow rate increased withecreasing cell diameter in the range from 3.178 mm �L /b=1.0�o 1.37 mm �L /b=0.43�. That is to say, the leakage flow ratebtains the minimum value at the cell diameter equal to the laby-inth step �L /b=1� in seven point calculations. The reason for thiss interpreted using the flow pattern in each cell diameter of theabyrinth honeycomb seal.

The flow pattern in three typical cell diameter labyrinth seals ishown in Fig. 13. As shown in Fig. 13�a�, the leakage jet from theap between the labyrinth fin and the rotor surface forms a mainnticlockwise recirculation zone. The intensity of the recirculationone inside the cell downstream of the labyrinth fin becomes veryeak. In addition, the jet from the clearance between the honey-

omb land and the labyrinth step forms a clockwise recirculationone within the cell. The intensity of the vortex in the downstreamabyrinth step becomes weak, due to the interaction of the jet withhe vortex inside the large diameter cell cavity. When the celliameter equals the labyrinth step width, the flow pattern changedreatly, as shown in Fig. 13�b�. The jet forms two anticlockwiseecirculation regions and a clockwise recirculation zone down-tream of the labyrinth fin. Further, a strong anticlockwise recir-ulation region is generated in the chamber downstream of theabyrinth step, compared with that seen in Fig. 13�a�. The strongecirculation dissipated the kinetic energy of the leakage flow intoeat energy. Correspondingly, the leakage flow rate becamemaller than that of the 4.58 mm cell diameter case. The intensityf recirculation inside each cell and cavity becomes weak whenhe cell diameter decreases to 1.37 mm, as shown in Fig. 13�c�.herefore, the leakage flow rate is larger than that of the case with

he 3.178 mm cell diameter.

4.4 Effects of Honeycomb Cell Depth. Five sizes of cellepth were utilized to investigate its effects on the leakage perfor-ance of the labyrinth honeycomb seals with fixed cell diameter

ig. 16 Leakage flow rate at different rotation speeds „L4.58 mm, T=0.75 mm, D=4.26 mm…

Fig. 17 Velocity distribution in the labyrinth honeycomb s
=4.26 mm…
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and gap size. The specified honeycomb cell depth was set to be1.86, 1.4, 0.93, 0.74, and 0.47, divided by cell diameter L. Figure14 shows the dependence of the leakage flow rate upon the celldepth with a fixed cell diameter and clearance size. When the celldepth equals 4.26 mm �D /L=0.93�, the leakage flow rate obtainsa minimum value, according to Fig. 14. The velocity vector dis-tribution inside the honeycomb seal with three typical cell depthsis shown in Fig. 15. The leakage jet generates the clockwise re-circulation within each cell, and the corresponding kinetic energyis transferred into heat energy due to the recirculation flow in thecase of D /L=0.93. The recirculation pattern inside the cell isstrongly influenced by the cell depth, according to Fig. 15. Re-gardless of whether D /L is greater than 0.93 or less than 0.93, thekinetic energy of the jet is not sufficiently transferred into heatenergy because of recirculation patterns inside each cell. The leak-age flow rate is the smallest in the case of D /L=0.93 among thefive studied cases.

4.5 Effects of Rotational Speed. Figure 16 shows the effectsof rotational speed on the leakage flow rate of the labyrinth hon-eycomb seal with a constant honeycomb cell and clearance size.The leakage flow rate remains approximately constant in the rangeof 0–3000 rpm. The leakage flow rate decreases with increasingrotation speed when the rotational speed is greater than 3000 rpm.The corresponding reason is illustrated according to the velocityvector distribution inside the seal, according to Fig. 17. A similarflow pattern is observed for the case of rotation speeds of 0 rpmand 3000 rpm. The intensity of recirculation inside the chamberdownstream of the labyrinth step in the case of 6000 rpm is stron-ger than that at 0 rpm and 3000 rpm. The larger viscous shearstress is generated to dissipate the jet kinetic energy efficientlydue to the large rotation speed. This results in a decrease in theleakage flow rate.

l at different rotation speeds „L=4.58 mm, T=0.75 mm, D

Fig. 18 Leakage flow rate at different pressure ratios „L=4.58 mm, T=0.75 mm, D=4.26 mm…

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4.6 Effects of Pressure Ratio. The dependence of the leakageow rate upon the pressure ratio of the labyrinth honeycomb seal

n the case of fixed cell and clearance size is shown in Fig. 18.he leakage flow rate increases approximately linearly as theressure ratio increases. The computed flow fields of the labyrinthoneycomb seal with two different pressure ratios are shown inig. 19. The pressure decreases along the chamber step by step.he low speed fluid is filled within the honeycomb cells in the

orms of vortices, which push the chamber flow to the seal bottomr back into the cells. According to Fig. 19, the influence of theressure ratio on the leakage flow pattern is omitted. The leakageow rate increases linearly with the increasing pressure ratio at

he fixed geometrical parameters of the labyrinth honeycomb seal.

ConclusionsBased on Schramm’s experimental data �6�, a three-dimensional

ANS solution with the commercial CFD software, CFX, was uti-ized to analyze the influence of clearance size, cell size, pressureatio, and rotation speed on leakage performance in the labyrinthoneycomb seal for steam turbines.

As for the clearance size factor, the computed leakage flow ratencreases with increasing sealing clearance for three kinds of celliameters in the designed condition.

As for the cell diameter factor, the computed leakage flow ratehows that the labyrinth honeycomb seal displays optimum leak-ge performance when the cell diameter equals the labyrinth stepidth. The leakage flow rate becomes large when either the celliameter is greater or smaller than the corresponding labyrinthtep width.

As for the cell depth factor, the investigated labyrinth honey-omb seal with the case of D /L=0.93 shows better sealing per-ormance than that of other cases. The strongest intensity of theormed vortex inside the cell was observed in the case of D /L0.93. The obtained results show that the studied labyrinth hon-ycomb seal displays optimum sealing performance in the case of/b=1 and D /L=0.93 under the designed condition.The leakage flow rate remains approximately constant with the

otational speed variation of 0–3000 rpm. The leakage flow rateecreases with the increasing rotation speed when the rotationalpeed is greater than 3000 rpm. The computed leakage flow ratencreases with increasing pressure ratio at the fixed geometricalarameter of the labyrinth honeycomb seal. The influence of theressure ratio on the leakage flow pattern is nearly negligible.

cknowledgmentJ.L. is grateful to the Program with Grant No. 50506023 sup-

orted by National Natural Science Foundation and New Century

Fig. 19 Static pressure contours and velocity distribution„L=4.58 mm, T=0.75 mm, D=4.26 mm…

xcellent Talents in University with Grant No. NCET-07-0669.

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NomenclatureA � areab � labyrinth step widthB � seal circumference

CD � discharge coefficientD � honeycomb cell depthh � fin height

HHC � honeycomb cell heightH � seal step heightk � ratio of specific heatsL � honeycomb cell diameterm � mass flow rate

mideal � ideal mass flow raten � rotation speed

p1 � upstream pressurep2 � downstream pressureR � specific gas constants � sealing clearance between fin and rotor surfacet � fin pitch

T � sealing clearance between honeycomb land andstep

� � the ratio of the inlet to outlet pressure p1 / p2� � leakage increase parameter

CD,honeycomb /CD,smooth� � fluid density

References�1� Lakshminarayana, B., 1996, Fluid Dynamics and Heat Transfer of Turboma-

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�6� Schramm, V., Willenborg, K., Kim, S., and Wittig, S., 2002, “Influence ofHoeycomb Facing on the Flow Through Stepped Labyrinth Seal,” ASME J.Eng. Gas Turbines Power, 124�1�, pp. 140–146.

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�8� Denecke, J., Färber, J., Dullenkopf, K., and Bauer, H.-J., 2008, “Interdepen-dence of Discharge Behavior, Swirl Development and Total Temperature In-crease in Rotating Labyrinth Seals,” ASME Paper No. GT2008-51429.

�9� Stoff, H., 1980, “Incompressible Flow in a Labyrinth Seal,” J. Fluid Mech.,100, pp. 817–829.

�10� Soto, E., and Childs, D., 1999, “Experimental Rotordynamic Coefficient Re-sults for a Labyrinth Seal With and Without Shunt Injection and a HoneycombSeal,” ASME J. Eng. Gas Turbines Power, 121, pp. 153–159.

the labyrinth honeycomb seal at different pressure ratios
in
�11� Stocker, H., Cox, D., Holle, G., 1977, “Aerodynamic Performance of Conven-



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tional and Advanced Design Labyrinth Seals With Solid-Smooth, Abradableand Honeycomb Lands,” NASA Technical Report No. NASA-CR-135307.

�12� Rhode, D. L., and Allen, B. F., 1998, “Visualization and Measurements ofRub-Groove Leakage Effects on Straight-Through Labyrinth Seals,” ASMEPaper No. 98-GT-506.

�13� Rhode, D. L., and Allen, B.F., 1999, “Measurement and Visualization of Leak-age Effects of Rounded Teeth Tips and Rub-Groove on Stepped LabyrinthSeals,” ASME Paper No. 99-GT-377.

�14� Wittig, S., Schelling, U., Jacobsen, K., and Kim, S., 1987, “Numerical Predic-tions and Measurements of Discharge Coefficients in Labyrinth Seals,” ASMEPaper No. 87-GT-188.

�15� Choi, D. C., and Rhode, D. L., 2004, “Development of a Two-DimensionalComputational Fluid Dynamics Approach for Computing Three-DimensionalHoneycomb Labyrinth Leakage,” ASME J. Eng. Gas Turbines Power, 126,pp. 794–802.

�16� Chougule, H. H., Ramerth, D., Ramchandran, D., and Kandala, R., 2006, “Nu-merical Investigation of Worn Labyrinth Seals,” ASME Paper No. GT2006-
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�17� Yan, X., Li, J., Song, L., and Feng, Z. P., 2008, “Investigations on the Dis-charge and Total Temperature Increase Characteristics of the Labyrinth SealsWith Honeycomb and Smooth Lands,” ASME J. Turbomach., 131�4�, p.041009.

�18� Paolillo, R., Moore, S., Cloud, D., and Glahn, J. A., 2007, “Impact of Rota-tional Speed on the Discharge Characteristics of Stepped Labyrinth Seals,”ASME Paper No. GT2007-28248.

�19� Soemarwoto, B. I., Kok, J. C., de Cock, K. M. J., Kloosterman, A. B., Kool, G.A., and Versluis, J. F. A., 2007, “Performance Evaluation of Gas TurbineLabyrinth Seals Using Computational Fluid Dynamics,” ASME Paper No.GT2007-27905.

�20� Chougule, H. H., Ramerth, D., and Ramchandran, D., , 2008, “Low LeakageDesigns for Rotor Teeth and Honeycomb Lands in Labyrinth Seals,” ASMEPaper No. GT2008-51024.

�21� AEA Technology GmbH, 2004, CFX-TASCflow User Documentation, AEATechnology, Software Ltd., Waterloo, ON, Canada.

JUNE 2010, Vol. 132 / 062501-11


Documents

Numerical Investigations on Leakage Performance of the Rotating Labyrinth Honeycomb Seal