Numerical analysis of erosion of the rotorlabyrinth seal in a geothermal turbine

Zdzislaw Mazura,*, Gustavo Urquizaa,Fernando Sierrab, Rafael Camposa

aInstituto de Investigaciones Electricas, Av. Reforma 113, Col. Palmira, 62490, Temixco, Morelos, MexicobCentro de Investigacion en Energıa-UNAM, Ap. Postal 34, Col. Centro, 62580 Temixco, Morelos, Mexico

Received 20 August 2001; accepted 20 March 2002

Abstract

Excessive erosion of the labyrinth seal of a 110 MW geothermal turbine has been investi-gated. This study used computational fluid dynamics (CFD) and aims to identify one cause oferosion and a possible solution for substantially reducing it. The predictions were based upon

a numerical calculation using a CFD model of the labyrinth seal with a water/steam flowcontaining hard solid particles and solved with a commercial CFD code: Fluent V5.0. Theresults confirmed the existence of flow conditions that play a major role in the rotor labyrinth

seal erosion. Afterwards, the flow path was simulated with changes of rotor labyrinth sealgeometry, which are indeed feasible of being implemented. The results confirmed that it ispossible to reduce the erosion process by approximately 80% by incorporating a steam flow

deflector in the fourth stage diaphragm, which changes the steam flow direction in the inletzone to the rotor labyrinth seal channel, resulting in a reduction in steam volumetric massflow and hard particle velocity by about 44%. # 2002 CNR. Published by Elsevier ScienceLtd. All rights reserved.

Keywords: Erosion; Labyrinth seal; Geothermal turbine; Numerical simulation

1. Introduction

Steam contamination is a typical problem in geothermal steam turbines. This isdue to the contents of hard particles of silicon, sulphur, phosphor and other ele-ments that directly impact on steam path components (Mazur and Kubiak, 1996). Ingeneral, the nozzles, the cover bands and rivets formed on the tenon head of the

Geothermics 31 (2002) 563–577

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0375-6505/02/$20.00 # 2002 CNR. Published by Elsevier Science Ltd. All rights reserved.

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* Corresponding author. Tel./fax: +52-73-182598.

E-mail address: mazur@iie.org.mx (Z. Mazur).

moving blades, the fixed blade vanes, the rotor labyrinth seals, radial spill-strips,rotor discs, control valves and turbine casings are frequently affected by impactdamage (Mazur et al., 1995). The degradation of rotor labyrinth seals commonlyresults in considerable reduction of performance of the power plant. The internalefficiency decline in turbines typically reaches about 2–4% or more (Leyzerovich,1997). It also leads to a decrease in the time lapse between overhauls. The highnumber of repair periods also reduces the total energy production.One of the most influential factors affecting turbine efficiency is the increase in

axial and radial clearances in the turbine gland seals caused by rubbing and solidparticle erosion. This involves all of the steam path seals, including end seals and over-shroud seals. The undershroud seals of reaction-type turbines and the root and dia-phragm seals of impulse-type turbines are also affected.The problem of the erosion of solid surfaces has been widely studied and the

mechanisms through which it develops are attributed to the small solid particles orwater droplets that hit the surface of the steam path elements continuously.

Nomenclature

Aface surface areaCD drag coefficientd particle diameterf að Þ impact angle functionFx virtual mass forcem massm.

mass flow rate~RR ratioRe Reynolds numbert time

Greek symbols

� impact angle of the particleb logarithmic particle Reynolds number� molecular viscosity� density� velocity! angular velocity

Subscripts

f fluidp particle0 initial condition1 final condition

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Wear due to solid particle erosion (abrasion) primarily depends on the surfacematerial exposed to the fluid and on the properties of the particles carried with thefluid. The abrasive process on a surface is determined by the relative velocity andimpact angle of the particles as well as the particles/steam flow ratio (Keck et al.,1997). The particle motion is governed by the local flow patterns. As flow patternschange significantly within a turbine, there is no possibility to predict abrasive wearwithout knowledge of the local flow patterns.One economic way of solving the problem of erosion (abrasive wear) is through

the analysis of flow patterns within the turbine under a variety of conditions, usingthe computational fluid dynamics (CFD) technique as a tool. CFD can be used forredesigning internal parts (Patancar, 1980; Sierra et al., 1999). In this paper theproblem of erosion on the rotor labyrinth seal of a 110 MW double-flow geothermalturbine is analyzed. Based on the use of CFD, this investigation aims to identify thecauses of erosion and possible means of reducing it substantially, and to assess thepotential of an RNG (Renormalization Group) k–e model for turbulence (Mack etal., 1999) to solve this problem. The predictions were based on a CFD model of thelabyrinth seal channel with a water-steam flow containing hard solid particles andsolved with a code: Fluent V5.0.One set of numerical results obtained this way suggests that a vapour jet is one of

the main causes of erosion by direct incidence. The jet constantly impinges on thesurface of the rotor labyrinth seal at velocities predicted around 52 m/s. High levelsof turbulence may also contribute to the problem.The predictions reported in this paper contain another set of numerical results,

where the entry to the labyrinth seal in the zone of the fourth rotor stage has beenredesigned. The objective was to modify the present flow patterns in such a way asto reduce their impact on the rotor labyrinth seal surface. The proposed designincorporates a steam flow deflector in the fourth stage diaphragm. The numericalpredictions indicate that this increases the steam flow path, which reduces steamflow through the seal. The result is a reduction in steam flow and hard particlevelocity by about 44%. As a consequence solid particle erosion is also reduced byapproximately 80%.The design proposed in this work allows for flow patterns of lower velocity

impinging on the rotor labyrinth seal surface than occur with the current design. Allsimulations were conducted in 2-dimensional models referring to the fourth-stagegovernor-side rotor labyrinth seal.

2. Background

The continuous operation of four geothermal 110 MW turbines for periods of 15–18 years is the focus of our attention. The turbines contain two identical rotorsarranged in seven stages: three initial stages followed by four double-flow stages.Geothermal steam flow, typically contaminated with small solid particles and waterdroplets, has been thought to produce erosion by steam-washing on the fourth-stagerotor labyrinth seal surface governor side, as is shown in Fig. 1. In this figure we can

Z. Mazur et al. / Geothermics 31 (2002) 563–577 565

also observe the severe damage to the rotor fourth-stage disc transition radius sur-face, but this problem will be the objective of another study.As can be seen from Fig. 1, the rotor labyrinth seal surface is subject to gradual

disintegration, loss of seal teeth, increased steam flow leakage and a consequentdeterioration in turbine efficiency. Being a costly process, any repairs made representpassive action because erosion still continues, along with the degradation of theturbine steam path. A substantial modification to the diaphragm labyrinth arrange-ment has been envisaged as a possible means of producing better flow patterns,reducing their impact on the rotor labyrinth seal.In Fig. 2 the present geometry of the diaphragm/rotor labyrinth seal of the fourth-

stage governor side of the 110 MW geothermal turbine is shown. This configurationsuggests that most of the steam flow containing small solid particles that enters thefourth-stage diaphragm, because of the open area of the flow channel, runs in anaxial direction, directly impacting at high velocity on the surface of the labyrinthteeth.The main parameters that influence erosion rate are known to be particle flow

velocity and impingement angle (Keck et al., 1997). From this knowledge it isargued that the physical arrangement facilitates erosion of the rotor labyrinth seal(Kubiak and Perez, 1989). The labyrinth seal entry is an open area with a high-volume steam flow that contains hard solid particles flowing towards the seal channel.

Fig. 1. Damage by erosion to fourth-stage rotor labyrinth seal surface.

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Counteracting this situation, the proposed geometry incorporates a steam flowdeflector in the fourth-stage diaphragm in the labyrinth seal entry, as shown in Fig. 3.

3. Modelling methodology

Numerical 2-dimensional predictions have been carried out with the finite volumecode Fluent V5.0 using an RNG k–e model for turbulence (Mack et al., 1999; Fluent,1999; Launder and Spalding, 1972). The method used in this work is based on thecalculation of the path of several individual solid particles through the flow field, theso-called Lagrangian tracking method. Each particle represents a sample of particlesthat follow an identical path. The motion of the tracked particles is taken to describethe average behaviour of the dispersed phase.While setting up the Lagrangian tracking and the erosion model described below,

the following assumptions have been made:

� particle–particle interactions are neglected;� any change of the flow turbulence caused by the particles is not accountedfor;

� only spherical, non-reacting and non-fragmentating particles are considered;and

� the geometry modifications, caused by the removal of wall by the solid par-ticles, have been neglected.

Fig. 2. Present configuration of the geometry of the labyrinth seal of the fourth-stage governor side of the

110 MW geothermal turbine.

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3.1. Governing equations

Consider a discrete particle traveling in a continuous fluid medium where the for-ces acting on the particle that affect its acceleration take place due to the differencein velocity between the particle and the fluid and due to the displacement of fluid bythe particle. The equation of motion for this case was derived by Basset, Boussinesqand Oseen for a stationary reference frame (Hinze, 1975).

mpd�pdt

¼ 3��dCD �f � �p� �

þ�d3�f6

d�fdt

þ�d3�f12

d�fdt

�d�pdt

� �þ Fx

þ3

2d2

ffiffiffiffiffiffiffiffiffiffiffi��f�

pðt1t0

d�fdt 0

�d�pdt 0ffiffiffiffiffiffiffiffiffiffiffi

t� t 0p dt 0 �

�d3

6�p � �f� �

! ! ~RR� �

��d3�p3

! �p ð1Þ

where Fx is the virtual mass force and is given by:

Fx ¼1

2

�

�p

d

dt�� �p� �

The last two terms of Eq. (1) are the centripetal and Coriolis force, which arepresent only in rotating frames of reference. These two forces are not present underthe real operation conditions of the present case rotor labyrinth seal, so they are notincluded in the analysis. Since the steam flow in the labyrinth seal region is notrotating like the rotor does, centripetal and Coriolis forces are neglected. Centripetaland Coriolis forces may have an effect only in the perpendicular direction to the

Fig. 3. Proposed configuration of the geometry of the labyrinth seal of the fourth-stage governor side of

the 110 MW geothermal turbine. Units are in mm.

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plane considered in this work. These forces may act principally on the surface of theinner diameter of the diaphragm, but this is not a part of the present analysis, whichfocusses on the erosion rate of the teeth of the rotor labyrinth seal. Comparison ofthe steam/particle flow velocity in the axial and tangential (perpendicular) directionreveals that the latter is many times smaller than the axially directed component, sothat its influence on the erosion rate of the seal channel is not considered. A dragcoefficient, CD (Basset, 1888; Boussinesq, 1897; Oseen, 1910) is introduced toaccount for experimental results on the viscous drag of a solid sphere, whichdepends on the particle Reynolds number. Within the range 0.01<Rep<260, wehave the drag coefficient given by the relation:

CD ¼ 1þ 0:1315 Rep� �0:82�0:05

Rep < 20

CD ¼ 1þ 0:1935 Rep� �0:6305

Rep > 20

with ¼ log Rep� �

, where the particle Reynolds number is defined by:

Rep ¼�f �f � �p d

�ð2Þ

If all particle acceleration terms are on the left-hand side only, the equations areintegrated by a forward Euler integration method.In turbulent flows particle trajectories are not deterministic and two particles

injected from a single point at different times may follow separate trajectories due tothe random nature of instantaneous fluid velocity. As a consequence, the particlesdisperse because of the fluctuating component of the fluid velocity. To account forthe influence of turbulent fluid fluctuations on particle motion, the method origin-ally developed by Dukowicz (1980), Gosman and Ioannides (1983), and Faeth(1987) has been applied in the code.The data recorded during the Lagrangian particle tracking include:

� number of particles impinging on the surface;� impinging velocity;� direction relative to the surface.

The removal of wall material is calculated using the Finnie model (Finnie, 1960)developed for ductile materials.We assume:

� no thermophoretic force;� no Brownian motion;� no Saffman hit force;� no radiation heat transfer.

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We do consider:

� change of the continuous trajectory due to the effect of the discrete phasetrajectories on the continuum (this is a condition for monitoring erosion).

We need to specify:

� starting positions, velocity for each particle stream (relative velocities ifmoving frames are used);

� diameter of the particle;� mass flow rate of the particle stream that will follow the trajectory of theindividual particle/droplet, m� p (required only for coupled calculations);

� injection refers to a stream of particles:

single — one particle stream

group — more than one stream (initial conditions)

� surface injection—release particles from a surface previously defined at theentry of the steam stream. In this case a particle stream will be released fromeach facet of the surface. In order to avoid the use of too many particles,sample points in plane surface are used.

Particle erosion and accretion rates are monitored at wall boundaries. The erosionrate is defined as (Fluent, 1999):

Rerosion ¼XNparticles

p¼1

m:pxf að Þ

Afaceð3Þ

where � is the impact angle of the particle path with the wall face, and f(�) is theimpact angle function, and Aface is wall face surface area. The accretion rate isdefined as (Fluent, 1999):

Raccretion ¼XNparticles

p¼1

m:p

Afaceð4Þ

Fig. 4. Computational mesh for the present configuration of the rotor labyrinth channel (not to scale).

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The computational domain that contains the details of both the present and theproposed geometry of the rotor labyrinth seal channel are represented by two grids,which were used to conduct the investigation. These are shown in Figs. 4 and 5.

3.2. Boundary conditions

For the present simulation particle diameter has been set at 80 mm in agreementwith steam chemical analyses (Kubiak and Perez, 1989). The steam flow velocity setas an entry boundary condition was obtained from running a turbine analysis pro-gram (Blaszko and Lidke, 1989) that resolves the turbine flow thermodynamicallysuch that a profile of the axial velocity can be obtained for any steam path.An average axial velocity of 52 m/s was obtained at the inlet to the labyrinth seal

channel of the present design from the calculated profile. A mass-flow inlet bound-ary was used for the incoming flow of steam water with a mass flow rate of 0.4004kg/s and a pressure of 2.99105 Pa (Fig. 6). The pressure inlet-boundary was used as

Fig. 5. Computational mesh with modified geometry of the flow channel (not to scale).

Fig. 6. Boundary conditions for rotor labyrinth seal channel.

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outlet boundary with the value just above 1 atm as calculated with the sameprogram, TUR88.

4. Results

4.1. Modeling results

A series of results is presented, which includes the simulations carried out with thecurrent labyrinth seal and the proposed configuration (with flow deflector). A com-parison of these results highlights the benefit obtained from incorporating a steamflow deflector (Fig. 3) in the fourth-stage diaphragm; this solution increases thesteam flow path around the deflector, reducing steam flow through the seal. It pro-duces a drop in the velocity of the steam flow that impinges on the teeth of the rotorlabyrinth seal. This drop in velocity of the steam (solid particles) means that a reduc-tion in erosion of the rotor seals can be expected with the configuration proposed.Fig. 7 shows the numerical solution for the present configuration in the form of a

field of velocity vectors in the labyrinth seal cavity in the zone of the first seal tooth,while Fig. 8 shows the numerical solution for the proposed configuration. The sizeand density of vectors for the present design (Fig. 7) indicate that the flow enters theregion of the first seal tooth with a higher velocity of impingement than with themodified geometry shown in Fig. 8. Significant recirculating flow can be observedafter the flow passed the first seal strip. The reduced size and density of the vectors

Fig. 7. Flow velocity with present geometry of the flow channel.

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for the proposed design (Fig. 8) indicate smaller velocity and a changed direction ofimpingement. Smaller recirculating flow can also be observed after the flow passedthe first seal strip. The traces of several particles prior to the seal cavity in the zoneof the first seal tooth, for the present and proposed configuration, are shown inFigs. 9 and 10, respectively.In order to quantify the results one station for flow velocity monitoring was chosen,

as shown in Figs. 7 and 8. These profiles of velocity versus position in the vertical

Fig. 8. Flow velocity with modified geometry of the flow channel.

Fig. 9. Traces of particles prior to the seal cavity for the present geometry of the flow channel.

Z. Mazur et al. / Geothermics 31 (2002) 563–577 573

direction are shown in Fig. 11 for the actual and proposed configurations, respec-tively. By position we mean radial distance from the rotor outer diameter in thelabyrinth seal channel. By comparing these results we obtain a reduction in steam/particles velocity of 44% with the proposed configuration.An interpretation of these results follows. This flow velocity reduction is due to

the flow deflector action, which increases flow path length around the deflector, as

Fig. 10. Traces of particles prior to the seal cavity for the modified geometry of the flow channel.

Fig. 11. Comparison of axial velocity in the region of impact with the first seal tooth, emphasizing the

reduction obtained with the proposed deflector.

574 Z. Mazur et al. / Geothermics 31 (2002) 563–577

shown in Fig. 12, and reduces both the flow rate through the labyrinth seal channeland its velocity on the seal tooth surface. These results may be analyzed in terms oftheir effect on the erosion process as follows.

4.2. Solid particle erosion reduction

The numerical results presented in the previous section have been used to estimatethe erosion rate on the surface of the rotor seal teeth. The history of erosion pro-cesses in steam flow channel components has been described by Curran (1983). Amajor contribution to these studies was the plot of solid particles velocity versuserosion rate. The plot shows the trend of erosion on the metal surface as a functionof the velocity of impact of the stream impinging on the area of interest. Using thisplot, the erosion of the rotor labyrinth seal under the flow conditions of both theactual and the proposed configurations is compared as steady-state conditions. Thereduction in velocity by 44% between the actual and the proposed design leads to areduction in erosion of 80%, as estimated from the plot by Curran (1983).Figs. 13 and 14 show the numerically predicted erosion patterns caused by solid

particles for actual and modified labyrinth seal designs, based on calculations oferosion rate. As can be seen from Fig. 13, high-flow (steam + particles) velocity

Fig. 12. Flow velocity in the deflector.

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leads to severe erosion damage of the rotor labyrinth tooth for the present sealdesign, whereas in the modified design (Fig. 14) the predicted erosion damage isdefinitely less. This is in good agreement with the plot of the trend of erosion on themetal surface as a function of the velocity of solid particle impact described above.Based on these results, the time between rotor maintenance (repairs) may be exten-

ded more than 200% by implementing the proposed labyrinth seal configuration.

5. Concluding remarks

An axial symmetric fluid-flow simulation and the prediction of erosion based onLagrangian particle tracking have been presented for a geothermal turbine labyrinthseal. The erosion process is strongly dependent on particle velocity. The modifi-cation to the flow of steam/solid particles in the rotor fourth-stage labyrinth seal hasbeen analyzed. Two designs of steam flow through the rotor labyrinth seal channelwere investigated by numerical modelling. The results show that it is possible toreduce the erosion process up to 80% by incorporating a steam flow deflector in the

Fig. 14. Numerically predicted erosion pattern caused by solid particles for modified labyrinth seal

design.

Fig. 13. Numerically predicted erosion pattern caused by solid particles for current labyrinth seal design.

576 Z. Mazur et al. / Geothermics 31 (2002) 563–577

fourth-stage diaphragm. The flow path length around the deflector is longer, whichreduces steam flow through the seal and results in a reduction in steam flow andhard particle velocity of about 44%. The results show that numerical simulationreally can be used in a predictive manner. The simulation results can serve as inputin an early stage of the design procedure to identify regions in which special surfacetreatment or design modifications are needed to increase the life-time of the com-ponents. The proposed modifications to the rotor labyrinth seal can be made to theturbine during the next scheduled overhaul and its performance monitored.

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