Rahul A. Bidkar1

General Electric Global Research,

Niskayuna, NY 12309

e-mail: bidkar@ge.com

Edip SevincerGeneral Electric Global Research,

Niskayuna, NY 12309

Jifeng WangGeneral Electric Global Research,

Niskayuna, NY 12309

Azam M. ThatteGeneral Electric Global Research,

Niskayuna, NY 12309

Andrew MannGeneral Electric Global Research,

Niskayuna, NY 12309

Maxwell PeterGeneral Electric Global Research,

Niskayuna, NY 12309

Grant MusgroveSouthwest Research Institute,

San Antonio, TX 78238

Timothy AllisonSouthwest Research Institute,

San Antonio, TX 78238

Jeffrey MooreSouthwest Research Institute,

San Antonio, TX 78238

Low-Leakage Shaft-End Sealsfor Utility-Scale SupercriticalCO2 TurboexpandersSupercritical carbon dioxide (sCO2) power cycles could be a more efficient alternative tosteam Rankine cycles for power generation from coal. Using existing labyrinth seal tech-nology, shaft-end-seal leakage can result in a 0.55–0.65% points efficiency loss for anominally 500 MWe sCO2 power cycle plant. Low-leakage hydrodynamic face seals arecapable of reducing this leakage loss and are considered a key enabling component tech-nology for achieving 50–52% thermodynamic cycle efficiencies with indirect coal-firedsCO2 power cycles. In this paper, a hydrodynamic face seal concept is presented forutility-scale sCO2 turbines. A 3D computational fluid dynamics (CFD) model with realgas CO2 properties is developed for studying the thin-film physics. These CFD results arealso compared with the predictions of a Reynolds-equation-based solver. The 3D CFDmodel results show large viscous shear and the associated windage heating challenge insCO2 face seals. Following the CFD model, an axisymmetric finite-element analysis(FEA) model is developed for parametric optimization of the face seal cross section withthe goal of minimizing the coning of the stationary ring. A preliminary thermal analysisof the seal is also presented. The fluid, structural, and thermal results show that large-diameter (about 24 in.) face seals with small coning (of the order of 0.0005 in.) are possi-ble. The fluid, structural, and thermal results are used to highlight the design challengesin developing face seals for utility-scale sCO2 turbines. [DOI: 10.1115/1.4034258]

1 Introduction

Closed-loop recompression Brayton cycles using supercriticalcarbon-dioxide (sCO2) as a working fluid have been proposed toreplace steam for power generation from pulverized coal [1]. Theprimary benefit of using sCO2 as a working fluid in such a cycle isthat it can achieve a higher thermal cycle efficiency (up to 5 points[1]) at the equivalent turbine inlet conditions of state-of-the-artultrasupercritical steam plants. Additional benefits includereduced water consumption, reduced power block size (smallerturbomachinery and condenser due to the higher working fluiddensity), and better thermodynamic integration with postcombus-tion CO2 capture and compression equipment as shown byLeMoullec [1]. Due to these potential benefits, sCO2 power cyclesand associated turbomachinery components have been the focusof recent research efforts [2–6]. Turbomachinery components likeseals [7,8] and gas bearings [9,10] have a direct impact on thepower cycle efficiencies and are critical for enabling sCO2 powercycles. In this paper, the importance of shaft-end seals for largelength-scale (utility-scale) turbines with sCO2 as the working fluidis discussed. Furthermore, fluid/structural/thermal analyses of alarge length-scale (about 24-in. diameter) and high-pressure

(higher than 1000 psia) sCO2 face seal are presented, and sealdesign challenges at such length scales and operating pressuresare highlighted.

Turbomachinery development for large-scale sCO2 recompres-sion cycles is still in its infancy. The majority of the recent workin this field has been for small-scale turbines [2,4,6] that are typi-cally rated for 0.3–10 MW power. Such small turbines either donot need end seals (in cases where the turbine is coupled with ahermetically sealed generator cavity with internal gas-foil bear-ings) or need small-sized end seals (typically hydrodynamic faceseals 4–6 in. diameter) that are commercially available [11]. Forutility-scale turbines (>100 MW), internal gas-foil bearings arenot possible due to load-bearing capacity limitations, therebydriving the need for hydrodynamic oil or hydrostatic bearings asdiscussed in Sienicki et al. [12]. Such hydrodynamic or hydro-static bearings need to operate at ambient temperatures outside theturbine, and inturn drive the need for shaft-end seals that can iso-late these bearings from the high-temperature shaft-end leakage.Recently, Bidkar et al. [13,14] presented a turbomachinery layoutfor a utility-scale sCO2 turbine (450 MWe), where turbine-endseals are used to isolate the bearings from the high-temperatureturbine exhaust. However, if the existing sealing technology (i.e.,labyrinth seals) is used for turbine-end seals on such a 450 MWe

sCO2 turbine, it can result in a loss of about 0.55% points to0.65% points thermodynamic cycle efficiency on a 51.9% efficientpower cycle. This huge efficiency loss is a result of the uniquecharacteristics of sCO2 as a working fluid not seen in conventionalgas or steam turbines. In this paper, the unique nature of sCO2

1Corresponding author.Contributed by the Structures and Dynamics Committee of ASME for publication

in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript receivedJune 19, 2016; final manuscript received July 3, 2016; published online September13, 2016. Editor: David Wisler.

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power cycles that lead to this high seal leakage penalty arediscussed.

Turbomachinery seals [7,8] for dynamic rotor-stator gaps havegradually evolved from conventional labyrinth seals to advancedcontact seals (e.g., brush seals [15] and finger seals [16,17]), andadvanced noncontact seals including leaf seals [18], film-ridinghybrid seals [19,20], circumferential hydrodynamic seals [21,22],noncontacting finger seals [23], and hydrodynamic face seals[24–31]. Noncontact seals offer superior leakage performance inaddition to the increased life compared to the degrading contactseals. Turbine shaft-end seals on a utility-scale sCO2 turbine arerequired to withstand large differential pressures (higher thanabout 1000 psia [13,14]), and hydrodynamic face seals are rela-tively well suited for this application due to their higher differen-tial pressure capability compared to other film-riding seals listedabove. However, large length-scale hydrodynamic face seals (atleast 24-in. diameter) that can also withstand the high differentialpressures (higher than about 1000 psia) are not readily availabledue to design and manufacturing challenges. In this paper, fluid/structural/thermal analyses of a hydrodynamic face seal withsCO2 as the working fluid are presented to show design feasibilityof such seals at large length scales and high differential pressures.

Typically, a hydrodynamic face seal (see Fig. 1) comprises ofan axial-spring-loaded stationary ring, a rotating ring, and a sec-ondary seal. During operation, the spring and the seal differentialpressure bias the stationary ring toward the rotating ring. A verythin fluid film (typically 0.0002 in. to 0.0005 in. thickness)between the stationary and the rotating ring generates large fluid-film pressures (due to the presence of spiral grooves on the axialface of the stationary or the rotating ring) to balance the axialbiasing load. These film pressures avoid contact between the sta-tionary ring and the rotating ring leading to a noncontact, nonde-grading mode operation. The leakage through the thin film inaddition to the leakage past the secondary seal is very small com-pared to the conventional labyrinth seals, and these flow savingstranslate into increased power cycle efficiency as described later.The requirement of a small fluid-film thickness (typically 0.0002-in. to 0.0005-in. thickness) during seal operation presents itself asa significant design challenge for face seals with large diametersand high differential pressures. In this paper, these designchallenges are discussed in the context of a representative large-diameter sCO2 seal (about 24-in. diameter) and pressure differen-tial higher than about 1000 psia.

The remainder of this paper is arranged in the following fash-ion. In Sec. 2, the operating conditions expected for shaft-endseals on utility-scale sCO2 turbines are discussed along with theunique characteristics of sCO2 that lead to a large seal leakagepenalty. In Sec. 3, a representative hydrodynamic face seal

concept is presented for end sealing application in utility-scalesCO2 turbines. A computational fluid dynamics (CFD) analysis ofthe face seal film is presented along with a finite-element analysis(FEA) of the seal. In Sec. 4, thermal analysis of the seal is used todemonstrate feasibility of the seal concept. Finally, in Sec. 5, asummary of the work is presented.

2 Operating Conditions and Leakage Penalty Analysis

for sCO2 End Seals

In Fig. 2, the end-seal layout is shown for a typical sCO2 tur-bine. The schematic shows one end of a turbine that uses a combi-nation of a shaft-end seal and a buffer seal between the lastturbine stage and the bearing (which operates at atmospheric pres-sure conditions). Note that the leakage past the end seal is recom-pressed using a seals scavenge compressor. The CO2 loss from theclosed-loop cycle is the leakage past the buffer seal, which isexpected to be small due to the small differential pressure acrossthe buffer seal. The auxiliary load of the seals scavenge compres-sor is the primary mode of cycle efficiency loss caused by sealleakage. This is described next.

Based on the utility-scale (450 MWe) sCO2 turbomachinerylayout presented in the work of Bidkar et al. [13,14], a typical endseal for a 450 MWe sCO2 turbine needs to be at least 24 in. indiameter, with seal inlet pressure higher than about 1000 psia andseal exhaust pressure of about 15 psia. The seal inlet temperaturecan range from about 205 �F to 1111 �F depending on whether athermal management system is used. The lower temperature casecorresponds to a cooler purge flow used at the seal inlet, whereasthe higher temperature case corresponds to the seal subjected tothe turbine exhaust. Using these operating conditions, the sCO2

leakage flow past a typical labyrinth seal is estimated. This calcu-lation using a labyrinth seal (i.e., existing technology) forms thebaseline for power cycle efficiency loss caused by seal leakageflow.

General Electric (GE) proprietary calculations were used toestimate the leakage flow past a typical labyrinth seal for the con-ditions described above. The labyrinth seal was assumed to have a0.028-in. radial tooth clearance, and 50 teeth with intertooth spac-ing of 0.15 in. With this labyrinth seal geometry configuration, theleakage past two end seals (one on either end of the turbine) wasestimated to be about 0.3–0.45% of the overall turbine mass flow.Note that this estimate of end-seal leakage as a percentage of theoverall turbine flow is a representative number (with the correctorder of magnitude) that is expected to change depending on thedetailed geometrical optimization and packaging of the labyrinthseal. Next, the impact of this leakage flow on the power cycle effi-ciency is described.

Fig. 1 Schematic diagram of a typical hydrodynamic face sealFig. 2 Schematic of one end of a turbine with end seal, bufferseal, and bearing

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For utility-scale sCO2 power cycle applications, leakage pastthe turbine-end seals is especially expensive. This drives the needfor development of low-leakage turbine-end seals for sCO2 tur-bines. Such end-seal technology has not been required for gas tur-bines because they typically exhaust to near-ambient pressure andrun open-loop, whereas sCO2 power cycles run closed-loop likesteam Rankine cycles. Unlike closed-loop steam Rankine cycles,low-pressure CO2 (that has leaked past the turbine-end seal) can-not be condensed to liquid and recovered through a liquid feedpump because its pressure is below the triple point of CO2 (75.41psia). This is shown graphically in Figs. 3(a) and 3(b), where con-densation of the leaked CO2 will result in the formation of dry ice.Consequently, the CO2 that has leaked past the end seal (seeFig. 2) must be compressed as a vapor from near atmosphericpressure conditions to the compressor inlet pressure (typically1000 psia) of the closed-loop sCO2 power cycle [13,14].

Recompressing CO2 leakage is typically done with multistageintercooled compressors resulting in a large auxiliary compressionload. As mentioned earlier, this auxiliary compression load resultsin a cycle efficiency impact for the overall power cycle. Previoussystem-level studies [1] have either ignored the effect of end-sealleakage on the overall cycle efficiency or assumed that it was verysmall and could be either neglected or allowed to leak unrecov-ered to the environment. Here, a system-level study is performedin the form of a preliminary design of a seals scavenge compres-sor to show that the end-seal leakage cannot be neglected for autility-scale sCO2 turbine.

The goal of the seals scavenge compressor design is the accu-rate estimation of the auxiliary compression load. For the combi-nation of large leakage flow and a high-pressure ratio, centrifugalcompressor architecture was chosen over an axial compressor or areciprocating pump. The one-dimensional compressor designmethod from Balj�e [32] was adapted to perform the design of amultistage centrifugal compressor. The inputs to the compressordesign include the labyrinth seal leakage flow (calculated above),inlet pressure of about 15 psia and exhaust pressure of about 1000psia. A preliminary design resulted in an integrally geared six-stage configuration with intercooling after three stages. The per-formance specifications of this six-stage centrifugal seals-scavenge compressor were integrated with the ASPEN HYSYSsCO2 power cycle model from the work of Bidkar et al. [13]. Theeffects of the scavenge compressor auxiliary load on the overallpower cycle efficiency are shown in Fig. 4. Note that only theeffects of turbine-end seals are shown, keeping other seals (forexample, compressor seals) unchanged. It can be seen that0.3–0.45% seal leakage flow can result in cycle efficiency loss ofabout 0.55% points to 0.65% points. Note that higher temperaturelabyrinth seals result in a higher penalty due to loss of useful ther-mal power in addition to the scavenge compressor penalty. Com-pensating for this auxiliary loss by raising the overall cycle

efficiency through higher firing temperatures would require anincrease in turbine inlet temperature, which is a very costly pros-pect requiring lengthy materials development effort. Alterna-tively, developing low-leakage seals is a very cost-effectivemanner of ensuring high power cycle efficiencies. A face seal con-cept, which can significantly reduce this efficiency loss caused bylabyrinth seals, is shown in Sec. 3.

3 Face Seal for Utility-Scale Turbines

In Fig. 5, a face seal cross section for a utility-scale sCO2 tur-bine is shown. The Y-axis is parallel to the cylindrical axis of theturbine, and the Z-axis is along the radial direction. The seal sta-tionary ring is supported by springs. The springs are mounted onthe seal stator, which is attached to the turbine casing. The station-ary ring slides against a secondary seal. The stationary ring axialface has spiral grooves for generating a separating force. In Fig. 5,the bearing face has unit length. “a” and “b” signify axial dimen-sions of the cross section, while “c” signifies the nominal axiallocation of the secondary seal. “d” signifies the height of station-ary ring radially outward of the bearing face, and “e” signifies theradial height of the cross section below the bearing face. The radi-ally innermost dimension of the seal is constrained to be larger

Fig. 3 Thermodynamic differences in recovery of turbine end-seal leakage for (a) sCO2 and (b) steam turbines

Fig. 4 Cycle efficiency impact of two labyrinth end seals for autility-scale sCO2 turbine

Fig. 5 Cross section of a utility-scale sCO2 turbine-face seal.Note that all the dimensions are normalized by the bearing faceradial height.

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than about 24 in. based on the 450 MWe sCO2 turbine from thework of Bidkar et al. [13,14].

The bearing face is subjected to a pressure distribution (i.e., anopening force in the negative Y-direction) caused by the spiralgrooves. All surfaces of the seal cross section shown in Fig. 5(except the bearing face) that are located radially outward of thesecondary seal are subjected to the high pressure (Phigh). Allsurfaces of the seal cross section that are located radially inwardof the secondary seal are subjected to the low pressure (Plow).For force-balance analysis, it is assumed that the pressurereduces across the secondary seal from Phigh to Plow. The balancediameter (i.e., the diametrical location of the secondary seal) ischosen such that the closing force (spring force and the pressureforce on all faces except the bearing face) is equal to the openingforce (pressure force on the bearing face). The relative magni-tudes of the friction force at the secondary seal and the inertialload are small compared to the remaining forces and can beneglected for a preliminary force balance. In Sec. 3.1, CFD isused to evaluate the pressure distribution on the bearing face andhighlight interesting aspects of fluid-film physics in large-scalesCO2 face seals. CFD results from different fluid models arecompared. Following that in Sec. 3.2, an axisymmetric FEAmodel is used to optimize the cross section of the stationary ringshown in Fig. 5.

3.1 CFD Model for a sCO2 Face Seal. The primary goal ofthe fluid flow analysis is to evaluate the pressure distribution andwindage heat generated by the fluid film between the stationaryring and the rotor, i.e., the bearing face in Fig. 5. The pressure dis-tribution can be used for computing the seal opening force.Depending on the operating conditions and the film geometry,fluid analysis can be performed with 3D Navier–Stokes equations[33] or with simplified 2D Reynolds equation models [34]. In thissection, these models are briefly described along with theirregimes of applicability. This is followed by a comparison of thepredictions based on these models.

Typically, fluid film CFD analysis for thin-film seals is per-formed using 2D Reynolds-equation-based solvers [34]. Forthin fluid films, the 3D Navier–Stokes fluid momentum equa-tions and the continuity equation can be simplified usingassumptions of laminar flow, isothermal conditions, and idealgas behavior. The resulting Reynolds equation in polar coordi-nates is

@

@rr

ph3

l@p

@r

!þ 1

r

@

@hph3

l@p

@h

!¼ 6xr

@

@hphð Þ (1)

where r and h represent the radial and tangential directions, p(r, h)is the pressure distribution in the film, h(r, h) is the film thickness(separation between the rotor and the seal stationary ring), l is thedynamic viscosity of the fluid, and x is the angular speed of therotor. The partial differential equation shown in Eq. (1) can benumerically solved using a finite-difference scheme [34] to obtainthe unknown pressure distribution p(r, h) for a specified film thick-ness distribution h(r, h) and specified boundary conditions. Forcases involving high differential pressures and large film thick-ness, there is a possibility of approaching sonic conditions orsonic transition in the fluid film. The face seal experiences rapidlychanging pressures in the dam section near its low-pressureboundary, and the Reynolds equation (see Eq. (1)) is inadequatefor modeling this effect. For such cases, an analytical 1D model[35] can be used for studying the pressure and Mach number vari-ation. The 1D model is based on the assumptions of compressibleideal gas flowing between the parallel plates separated by a dis-tance equal to the film thickness. The fluid flow equations are

dp

p¼ cM2

1�M2

dA

A

� �� cM2 1þ c� 1ð ÞM2

� �2 1�M2ð Þ

4Cf dr

Dh

� �dqq¼ M2

1�M2

dA

A

� �� cM2

2 1�M2ð Þ4Cf dr

Dh

� �dM

M¼ � 1þ 0:5 c� 1ð ÞM2

� �1�M2

dA

A

� �

þ cM2 1þ 0:5 c� 1ð ÞM2� �

2 1�M2ð Þ4Cf dr

Dh

� �(2)

where c is the ratio of specific heats, M is the Mach number, Arepresents the cross-sectional area, Cf is the Fanning friction fac-tor, q is the fluid density, dr is the elemental length along theradial direction of flow, and Dh is the hydraulic diameter. Next,the domains of applicability of Eqs. (1) and (2) are discussed.

A typical fluid domain for a face seal is shown in Fig. 6. It con-sists of a periodic sector of the thin film between the stationaryring and the rotor. As shown, one axial face (perpendicular to theY-axis) of the domain represents the stationary ring with spiralgrooves on the axial face of the stationary ring. The definition ofthe spiral grooves is proprietary information and not discussed inthis paper. The second axial face of the domain represents therotor, where a tangential surface velocity is specified. Phigh andPlow are specified as the boundary conditions at the radially outerand radially inner plenums of the domain, respectively. Finally,periodic boundary conditions are imposed on the two radial edges.The Reynolds equation (Eq. (1)) is typically solved in region 1(see Fig. 6) and the 1D compressible flow model (Eq. (2)) issolved in region 2 (see Fig. 6) with pressures and mass flowsmatched at the boundary of region 1 and region 2.

Supercritical CO2 can exhibit nonideal gas behavior, especiallynear its critical point (1071 psia and 88 �F). Furthermore, the highdensity of supercritical CO2 can result in a high Reynolds number,where the laminar-flow results predicted by the Reynolds equation(Eq. (1)) become less accurate. Under these circumstances, itbecomes necessary to solve 3D Navier–Stokes equations in orderto accurately model the seal fluid-film physics.In this work, a 3Dfluid model was created using ANSYS CFX. The fluid model is shownin Fig. 6. Note that with ANSYS CFX, it is not necessary to split thefluid domain into region 1 and region 2. The 3D model is basedon the assumptions of turbulent flow and isothermal conditions. Itis also assumed that the stationary ring and the rotor are parallelto one another, i.e., there is no coning. The applicability and valid-ity of these assumptions are discussed later in this paper. SincesCO2 can exhibit nonideal gas behavior, real gas properties of

Fig. 6 CFD domain: A periodic sector of the fluid film betweenthe stationary ring and the rotor

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CO2 (REFPROP based tabular data) were used as input to theCFD model. Mesh convergence studies were performed to ensurea small y-plus value (average value less than 2) for the rotor andstationary ring surfaces. The results of the combined 2D–1Dmodel (i.e., Eqs. (1) and (2) solved together) and the 3D CFDmodel are discussed next.

The results of the combined 2D–1D model are based on solvingEq. (1) in region 1 and Eq. (2) in region 2, where the radial extentof region 2 was chosen to be 15% of the radial dimension of thebearing face. As mentioned earlier, the combined 2D–1D modelresults are obtained by matching pressures and mass flows at theboundary of the two regions. The overall opening force is com-puted by integrating the respective pressure distributions overregion 1 and region 2, and the average bearing pressure is com-puted by dividing the overall opening force by the total bearingface area. Finally, the average bearing pressure for the 3D fluidmodel is computed using postprocessing tools in ANSYS CFX.

In Fig. 7, the average bearing pressure (normalized by Phigh)predicted by both models is shown as a function of film thickness.It can be seen that both models agree well at very small film thick-ness (less than 0.0002 in.), but diverge at larger gaps. The agree-ment between the two models for the small film thicknessindicates that the underlying assumptions of ideal gas behaviorand laminar flow do not introduce a significant error (relative tothe 3D equations) at small film thickness. Specifically, for theoperating conditions analyzed in this work, the compressibilityfactor p/qRT of sCO2 is 0.9 or higher. This indicates that the flowcan be modeled using ideal gas law. In Fig. 8, the radial and tan-gential velocity profiles in the film as predicted by 3D CFD modelare shown for three different film thicknesses of 0.0001 in.,0.0003 in., and 0.0006 in. Interestingly, the tangential film veloc-ity profiles (Fig. 8(b)) show S-shape curves indicating a turbulentflow in the film. This validates the turbulence modeling assump-tion in the 3D CFD model. With increasing film thickness, theradial velocity profiles (Fig. 8(a)) show increased velocity gra-dients near the wall. The laminar-flow-based Reynolds equation(which assumes a parabolic radial velocity profile) cannot accu-rately model this turbulent flow. Consequently, for larger filmthickness (more than 0.0002 in.), the predicted bearing pressureand the seal leakages show disagreement between the combined2D–1D model and the 3D CFD model. For initial stages of design,the Reynolds-equation-based solver can provide relatively quickpredictions. On the other hand, for a detailed design, the 3D CFDmodel with real gas properties (needed for analysis near criticalpoint of CO2) and turbulent flow assumption is a better choice forhigh-density fluids like sCO2 that operate in the turbulent regime.

The turbulence is attributed to the high Reynolds numbercaused by the high density (high pressure) of sCO2 and the largerotor velocity. The S-shape velocity profile (see Fig. 8(b)) alsoimplies that the shear stress and therefore the windage heat gener-ation are higher in sCO2 face seals compared to face seals with airas the working fluid. A direct comparison with air as the workingfluid shows that sCO2 seals generate about 1.5 times more heatthan air seals for the cases analyzed in this work. This increasedheat generation in sCO2 seals requires attention toward thermalmanagement of the seal, which will be discussed in Sec. 4.

The pressure distribution obtained using the 3D CFD model isused for the structural optimization of the stationary ringdescribed in Sec. 3.2. Finally, note that the fluid-film leakage(from the 3D CFD model) in addition to the secondary seal leak-age was predicted to be 1 to 2 orders of magnitude smaller thanthe labyrinth seal leakage (i.e., 0.3–0.45% of turbine flow). Basedon Fig. 4, this would imply that the seal leakage past two hydrody-namic face seals (one on either turbine end) would cause a negli-gible effect on the overall power cycle efficiency. In other words,hydrodynamic face seals (with a very small leakage penalty andthe associated small cycle efficiency loss) at turbine shaft endscan enable utility-scale sCO2 power cycles by allowing highefficiency operation that is otherwise at risk using the existingtechnology of labyrinth seals.

3.2 Structural Model. In this section, an axisymmetric FEAmodel of the seal stationary ring is developed. The primarypurpose of the FEA model is to study the coning sensitivity of thestationary ring (under applied pressure loads) to variation in sealcross section geometry. The seal geometry with various dimen-sions is shown in Fig. 5. As described earlier, Phigh and Plow pres-sures are applied on surfaces of the stationary ring that areradially outward and radially inward of the secondary seal, respec-tively. The pressure distribution computed from the 3D CFDmodel is applied on the bearing face. The FEA model assumesisothermal conditions and typical structural steel properties for theseal stationary ring. Switching to a different nickel-based alloywill improve the life of the component (creep-based life) but isnot expected to significantly change the coning deformationresults discussed in this paper. Thermal loads on the seal willcause deviation from the isothermal assumption, and the sealdeformations with thermal load are addressed in Sec. 4.

Fig. 7 Average bearing pressure (normalized by Phigh) as afunction of film thickness

Fig. 8 (a) Radial velocity profiles and (b) tangential velocityprofiles through the film thickness for different operating filmthickness of 0.0001 in., 0.0003 in., and 0.0006 in

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Coning is defined as the Y-displacement of the radially inneredge of the bearing face minus the Y-displacement of the radiallyouter edge of the bearing face. Thus, a positive coning valueimplies the outer edge is farther away from the rotor than the inneredge of the bearing face. In other words, a positive coning valueimplies a converging film shape moving radially inward fromPhigh to Plow. From a fluid-film stiffness perspective, it is alwaysdesirable to have a slightly converging film or a small positiveconing value when higher pressures are present at the outer edge.A diverging film or negative coning value results in very poorfluid-film characteristics and might result in seal failure in termsof rubs between the stationary ring and the rotor. In the followinganalysis, the effects of seal cross section dimensions a, b, c, d, ande are studied with regards to the pressure-induced coning of thestationary ring. Note that the overall coning and shape of the fluidfilm is a net result of the coning of the stationary ring as well asthe coning of the rotor surface. The analysis of this section focuseson just the stationary-ring coning, while the overall coning includ-ing the rotor deformation is discussed in Sec. 4.

To study the effects of geometrical parameters on the stationaryring coning, values of a¼ 4 and e¼ 1.21 were chosen (note alldimensions are nondimensionalized by the radial height of thebearing face). The pressure-induced coning of the stationary ringwas studied for two values of d¼ 0 and d¼ 2.54 for differentcombinations of ratio “b/a” and “c/(a-b).” The rationale here is tofind (for a fixed value of a, e, and d) the optimal dimension b andc such that the stationary ring has a small positive coning.

Coning analysis results for the cases of d¼ 0 and d¼ 2.54 areshown in Figs. 9 and 10, respectively. Both Figs. 9 and 10 showcontour plots of coning (reported in 1/1000 in.) for different com-binations of ratios b/a and c/(a-b). For the case of d¼ 0 (seeFig. 9), negative coning values are obtained for all combinationsof b/a and c/(a-b) reported here. For the case of d¼ 2.54 (see Fig.10), positive coning values are obtained for a range of combina-tions of b/a and c/(a-b). Comparing the two cases of d¼ 0 andd¼ 2.54, it can be seen that increased radial height of cross sec-tion allows the face seal to switch from negative coning values topositive coning values. Furthermore, high values of ratio c/(a� b)will tend to improve coning from a diverging film to a convergingfilm. Similarly, increasing b/a will cause film to switch from adiverging behavior to a converging behavior. The overall trendsfor d, c/(a-b), and b/a suggest that higher values for these threeparameters/ratios will result in positive coning. Physically, thiscorresponds to bulkier seal cross sections that might have otherseal design challenges including large seal inertial loads and seal

vibration modes interacting with the turbine rotor. This parametricFEA model shows that a seal cross section for a large face seal(about 24-in. diameter) with high differential pressures (higherthan about 1000 psia) is feasible with coning (or out-of-plane dis-placement) less than 0.0002 in. Furthermore, the FEA modelshows that the seal designer has several geometrical parametersthat can be used to control the pressure-induced coning and even-tually compensate for thermal-load-induced coning. We addressthe thermal coning issue and clarify some of the assumptionsstated earlier during the CFD and FEA studies in Sec. 4.

4 Thermal Analysis and Seal Design Challenges

The primary design challenge for large-scale sCO2 face seals issimultaneously controlling the pressure-induced and thermal-load-induced coning of the seal with the intention of operating theseal with a small converging film (a positive coning value). TheCFD results presented in this paper assume that the rotor and thestationary ring are parallel to each other (zero coning). This is agood assumption for early analysis to compute the opening force(Fig. 7). Multiple CFD simulations with different converging/diverging films (radially varying thickness) are desirable to mapthe entire space. These CFD analyses are not presented in thispaper. Similarly, the isothermal assumption used in the CFD stud-ies is a good starting assumption. In conjunction with the CFDand FEA models presented above, a thermal model is required forpredicting the structural temperatures and the fluid temperaturesaround the seal. The fluid temperatures predicted by the thermalmodel can be used as an input to the CFD model instead of assum-ing isothermal conditions with temperature known a priori. Athermal model will also allow computation of the temperatures onthe stationary ring and the rotor, which can be used to calculatethe thermal-load-induced coning. The overall coning is the netresultant of the pressure-induced and the thermal-load-inducedconing.

A preliminary axisymmetric, steady-state thermal analysis wasperformed for the seal and the accompanying rotor using an ANSYS

thermal solver. For the thermal analysis, the seal stationary ringcross section dimensions were chosen such that the pressure-induced coning (no thermal loads) resulted in a small positiveconing. Specifically, a stationary ring cross section with d¼ 2.54,a¼ 4, e¼ 1.21, b/a� 0.75, and c/(a-b)� 0.75 was chosen basedon the results from Fig. 10. Details of the seal cross sectionincluding the springs and the secondary seal were not included inthis preliminary thermal analysis. Heat transfer coefficients werecalculated for all surfaces of the stationary seal ring and the rotor

Fig. 9 Coning (1/1000 in.) for different combinations of b/a andc/(a-b) for a fixed value of d 5 0, a 5 4, and e 5 1.21. Note thatpositive coning indicates a radially converging film shape, anda small positive coning value is desirable.

Fig. 10 Coning (1/1000 in.) for different combinations of b/aand c/(a-b) for fixed value of d 5 2.54, a 5 4, and e 5 1.21. Notethat positive coning indicates a radially converging film shape,and a small positive coning value is desirable.

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based on the geometry and local fluid properties. As shown in Eq.(3), the principle of conservation of energy was applied to a con-trol volume between the stationary ring and the rotor

_mleakhin þ _Qwindage ¼ _Qrotor þ _Qseal þ _mleakhout (3)

where _mleak is the leakage flow, hin is the specific enthalpy of thefluid prior to entering the thin film, hout is the specific enthalpy of

the fluid exiting the thin film, _Qwindage is the windage heat gener-

ated by viscous shearing in the thin fluid film, _Qseal and _Qrotor

represent the convection heat flow to the seal stationary ring andthe rotor, respectively. Note that the leakage flow and the windageheat generated in the fluid film are known from the 3D CFDmodel and the heat flow to the rotor and seal are iteratively eval-uated from the ANSYS thermal solver until Eq. (3) is satisfied. Fig-ure 11 shows a representative temperature contour for the sealstationary ring and the rotor as predicted by the thermal analysis.These thermal loads were combined with the pressure loads(described in Sec. 3) to predict the coning of the stationary ringand the rotor. The combined pressure-temperature loadingresulted in a stationary ring coning of about þ0.0003 in. and arotor coning of about þ0.0001 in., resulting in a net coning ofabout þ0.0004 in. Overall, these results show that a large-diameter sCO2 face seal design with coning of the order of 0.0005in. is possible for utility-scale sCO2 turbines.

The fluid, structural, and thermal analysis results presented inthis paper demonstrate a framework for preliminary sizing oflarge-length-scaled sCO2 face seals. For a detailed design, thesemodels might need further refinement including but not limited tocoupling of the fluid, structural, and thermal analyses. In thatsense, the analyses presented in this paper form a starting pointfor a coupled fluid–structure–thermal interaction model. Note thatsuch coupled fluid–structure–thermal analysis approaches havebeen used for traditional face seals [36], but with simplifyingassumptions of one-dimensional flow and ideal gas behavior thatgreatly reduce the computational cost and time. Traditional sim-plifying assumptions (for example, ideal gas behavior and thinfilm Reynolds equation solutions [34]) might have limited applic-ability with sCO2 and a 3D CFD model (such as the one presentedabove) may be required in many cases. The need to use 3D CFDfor the seal complicates the framework for a coupledfluid–structure–thermal analysis in terms of cost and computa-tional time. Developing a simple and quick, yet accurate frame-work for a coupled fluid–structure–thermal analysis is asignificant challenge for such large-scale sCO2 seals. Also, notethat since sCO2 is a relatively new fluid, there is limited experi-mental data that can be used for validating thermal models of

seals. High-fidelity thermal models for seals can be developedonly in conjunction with supporting experimental testing efforts.In summary, developing a simplified framework for a coupledfluid–structure–thermal analysis of seals and experimental valida-tion of the thermal model remain as challenges for seal design.Finally, note that the challenges discussed in this paper are in thecontext of seal design/analyses and a discussion on other chal-lenges in developing large-scale sCO2 seals (e.g., manufacturabil-ity/installation of large seals, etc.) is beyond the scope of thispaper.

5 Summary and Conclusions

Hydrodynamic face seals are a key enabling technology forutility-scale sCO2 turbines. Analysis shows that a nominally 500MWe power plant can lose up to 0.65% points in thermodynamiccycle efficiency if existing technology of labyrinth seals is used.

In this paper, a hydrodynamic face seal was presented as analternate to the existing technology of labyrinth seals. Hydrody-namic face seals technology is well known and commerciallyavailable, but needs further development when using this technol-ogy for large length scales (about 24-in. diameter) and high differ-ential pressures (higher than 1000 psia). In this paper, a 3D CFDmodel was developed to compute the bearing pressures. It wasseen that the flow in the sCO2 fluid film is turbulent and generateslarger viscous heat than traditional air seals. The bearing pressurescomputed in CFD were used as an input to an axisymmetric FEAmodel of the seal stationary ring. The FEA results show that it ispossible to design a large-scale sCO2 seal with high differentialpressures and there is flexibility in controlling the coning defor-mation of the seal. A preliminary thermal analysis of the sealshowed manageable coning deformations with thermal loads.Finally, the importance of a coupled fluid–structural–thermalanalysis was also highlighted.

Acknowledgment

This material was based upon the work supported by theDepartment of Energy under Award No. DE-FE0024007. Theauthors want to thank Dr. Seth Lawson at U.S. Department ofEnergy—National Energy Technology Laboratory for his supportand guidance during this program. We are thankful to XiaoqingZheng, Doug Hofer, Chris Wolfe, and Norm Turnquist of the Gen-eral Electric Company for discussions on seals and their system-level impact. This paper was prepared as an account of work spon-sored by an agency of the United States Government. Neither theUnited States Government nor any agency thereof, nor any oftheir employees, makes any warranty, express or implied, orassumes any legal liability or responsibility for the accuracy, com-pleteness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe pri-vately owned rights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark, manufac-turer, or otherwise does not necessarily constitute or imply itsendorsement, recommendation, or favoring by the United StatesGovernment or any agency thereof. The views and opinions ofauthors expressed herein do not necessarily state or reflect thoseof the United States Government or any agency thereof.

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