Supercritical carbon dioxide (sCO_{2}) power cycles could be a more efficient alternative to steam Rankine cycles for power generation from coal. Using existing labyrinth seal technology, shaft-end-seal leakage can result in a 0.55–0.65% points efficiency loss for a nominally 500 MW_{e} sCO_{2} power cycle plant. Low-leakage hydrodynamic face seals are capable of reducing this leakage loss and are considered a key enabling component technology for achieving 50–52% thermodynamic cycle efficiencies with indirect coal-fired sCO_{2} power cycles. In this paper, a hydrodynamic face seal concept is presented for utility-scale sCO_{2} turbines. A 3D computational fluid dynamics (CFD) model with real gas CO_{2} properties is developed for studying the thin-film physics. These CFD results are also compared with the predictions of a Reynolds-equation-based solver. The 3D CFD model results show large viscous shear and the associated windage heating challenge in sCO_{2} face seals. Following the CFD model, an axisymmetric finite-element analysis (FEA) model is developed for parametric optimization of the face seal cross section with the goal of minimizing the coning of the stationary ring. A preliminary thermal analysis of 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 possible. The fluid, structural, and thermal results are used to highlight the design challenges in developing face seals for utility-scale sCO_{2} turbines.

## Introduction

Closed-loop recompression Brayton cycles using supercritical carbon-dioxide (sCO_{2}) as a working fluid have been proposed to replace steam for power generation from pulverized coal [1]. The primary benefit of using sCO_{2} as a working fluid in such a cycle is that it can achieve a higher thermal cycle efficiency (up to 5 points [1]) at the equivalent turbine inlet conditions of state-of-the-art ultrasupercritical steam plants. Additional benefits include reduced water consumption, reduced power block size (smaller turbomachinery and condenser due to the higher working fluid density), and better thermodynamic integration with postcombustion CO_{2} capture and compression equipment as shown by LeMoullec [1]. Due to these potential benefits, sCO_{2} power cycles and associated turbomachinery components have been the focus of recent research efforts [2–6]. Turbomachinery components like seals [7,8] and gas bearings [9,10] have a direct impact on the power cycle efficiencies and are critical for enabling sCO_{2} power cycles. In this paper, the importance of shaft-end seals for large length-scale (utility-scale) turbines with sCO_{2} as the working fluid is discussed. Furthermore, fluid/structural/thermal analyses of a large length-scale (about 24-in. diameter) and high-pressure (higher than 1000 psia) sCO_{2} face seal are presented, and seal design challenges at such length scales and operating pressures are highlighted.

Turbomachinery development for large-scale sCO_{2} recompression cycles is still in its infancy. The majority of the recent work in this field has been for small-scale turbines [2,4,6] that are typically rated for 0.3–10 MW power. Such small turbines either do not need end seals (in cases where the turbine is coupled with a hermetically sealed generator cavity with internal gas-foil bearings) or need small-sized end seals (typically hydrodynamic face seals 4–6 in. diameter) that are commercially available [11]. For utility-scale turbines (>100 MW), internal gas-foil bearings are not possible due to load-bearing capacity limitations, thereby driving the need for hydrodynamic oil or hydrostatic bearings as discussed in Sienicki et al. [12]. Such hydrodynamic or hydrostatic bearings need to operate at ambient temperatures outside the turbine, and inturn drive the need for shaft-end seals that can isolate these bearings from the high-temperature shaft-end leakage. Recently, Bidkar et al. [13,14] presented a turbomachinery layout for a utility-scale sCO_{2} turbine (450 MW_{e}), where turbine-end seals are used to isolate the bearings from the high-temperature turbine exhaust. However, if the existing sealing technology (i.e., labyrinth seals) is used for turbine-end seals on such a 450 MW_{e} sCO_{2} turbine, it can result in a loss of about 0.55% points to 0.65% points thermodynamic cycle efficiency on a 51.9% efficient power cycle. This huge efficiency loss is a result of the unique characteristics of sCO_{2} as a working fluid not seen in conventional gas or steam turbines. In this paper, the unique nature of sCO_{2} power cycles that lead to this high seal leakage penalty are discussed.

Turbomachinery seals [7,8] for dynamic rotor-stator gaps have gradually evolved from conventional labyrinth seals to advanced contact seals (e.g., brush seals [15] and finger seals [16,17]), and advanced noncontact seals including leaf seals [18], film-riding hybrid seals [19,20], circumferential hydrodynamic seals [21,22], noncontacting finger seals [23], and hydrodynamic face seals [24–31]. Noncontact seals offer superior leakage performance in addition to the increased life compared to the degrading contact seals. Turbine shaft-end seals on a utility-scale sCO_{2} turbine are required to withstand large differential pressures (higher than about 1000 psia [13,14]), and hydrodynamic face seals are relatively well suited for this application due to their higher differential pressure capability compared to other film-riding seals listed above. However, large length-scale hydrodynamic face seals (at least 24-in. diameter) that can also withstand the high differential pressures (higher than about 1000 psia) are not readily available due to design and manufacturing challenges. In this paper, fluid/structural/thermal analyses of a hydrodynamic face seal with sCO_{2} as the working fluid are presented to show design feasibility of such seals at large length scales and high differential pressures.

Typically, a hydrodynamic face seal (see Fig. 1) comprises of an axial-spring-loaded stationary ring, a rotating ring, and a secondary seal. During operation, the spring and the seal differential pressure bias the stationary ring toward the rotating ring. A very thin 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 axial face of the stationary or the rotating ring) to balance the axial biasing load. These film pressures avoid contact between the stationary ring and the rotating ring leading to a noncontact, nondegrading mode operation. The leakage through the thin film in addition to the leakage past the secondary seal is very small compared to the conventional labyrinth seals, and these flow savings translate 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 as a significant design challenge for face seals with large diameters and high differential pressures. In this paper, these design challenges are discussed in the context of a representative large-diameter sCO_{2} seal (about 24-in. diameter) and pressure differential higher than about 1000 psia.

The remainder of this paper is arranged in the following fashion. In Sec. 2, the operating conditions expected for shaft-end seals on utility-scale sCO_{2} turbines are discussed along with the unique characteristics of sCO_{2} that lead to a large seal leakage penalty. In Sec. 3, a representative hydrodynamic face seal concept is presented for end sealing application in utility-scale sCO_{2} turbines. A computational fluid dynamics (CFD) analysis of the 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 to demonstrate feasibility of the seal concept. Finally, in Sec. 5, a summary of the work is presented.

## Operating Conditions and Leakage Penalty Analysis for sCO_{2} End Seals

In Fig. 2, the end-seal layout is shown for a typical sCO_{2} turbine. The schematic shows one end of a turbine that uses a combination of a shaft-end seal and a buffer seal between the last turbine stage and the bearing (which operates at atmospheric pressure conditions). Note that the leakage past the end seal is recompressed using a seals scavenge compressor. The CO_{2} loss from the closed-loop cycle is the leakage past the buffer seal, which is expected to be small due to the small differential pressure across the buffer seal. The auxiliary load of the seals scavenge compressor is the primary mode of cycle efficiency loss caused by seal leakage. This is described next.

Based on the utility-scale (450 MW_{e}) sCO_{2} turbomachinery layout presented in the work of Bidkar et al. [13,14], a typical end seal for a 450 MW_{e} sCO_{2} turbine needs to be at least 24 in. in diameter, with seal inlet pressure higher than about 1000 psia and seal exhaust pressure of about 15 psia. The seal inlet temperature can range from about 205 °F to 1111 °F depending on whether a thermal management system is used. The lower temperature case corresponds to a cooler purge flow used at the seal inlet, whereas the higher temperature case corresponds to the seal subjected to the turbine exhaust. Using these operating conditions, the sCO_{2} leakage flow past a typical labyrinth seal is estimated. This calculation using a labyrinth seal (i.e., existing technology) forms the baseline for power cycle efficiency loss caused by seal leakage flow.

General Electric (GE) proprietary calculations were used to estimate the leakage flow past a typical labyrinth seal for the conditions described above. The labyrinth seal was assumed to have a 0.028-in. radial tooth clearance, and 50 teeth with intertooth spacing of 0.15 in. With this labyrinth seal geometry configuration, the leakage past two end seals (one on either end of the turbine) was estimated 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 the overall turbine flow is a representative number (with the correct order of magnitude) that is expected to change depending on the detailed geometrical optimization and packaging of the labyrinth seal. Next, the impact of this leakage flow on the power cycle efficiency is described.

For utility-scale sCO_{2} power cycle applications, leakage past the turbine-end seals is especially expensive. This drives the need for development of low-leakage turbine-end seals for sCO_{2} turbines. Such end-seal technology has not been required for gas turbines because they typically exhaust to near-ambient pressure and run open-loop, whereas sCO_{2} power cycles run closed-loop like steam Rankine cycles. Unlike closed-loop steam Rankine cycles, low-pressure CO_{2} (that has leaked past the turbine-end seal) cannot be condensed to liquid and recovered through a liquid feed pump because its pressure is below the triple point of CO_{2} (75.41 psia). This is shown graphically in Figs. 3(a) and 3(b), where condensation of the leaked CO_{2} will result in the formation of dry ice. Consequently, the CO_{2} that has leaked past the end seal (see Fig. 2) must be compressed as a vapor from near atmospheric pressure conditions to the compressor inlet pressure (typically 1000 psia) of the closed-loop sCO_{2} power cycle [13,14].

Recompressing CO_{2} leakage is typically done with multistage intercooled compressors resulting in a large auxiliary compression load. As mentioned earlier, this auxiliary compression load results in a cycle efficiency impact for the overall power cycle. Previous system-level studies [1] have either ignored the effect of end-seal leakage on the overall cycle efficiency or assumed that it was very small and could be either neglected or allowed to leak unrecovered to the environment. Here, a system-level study is performed in the form of a preliminary design of a seals scavenge compressor to show that the end-seal leakage cannot be neglected for a utility-scale sCO_{2} turbine.

The goal of the seals scavenge compressor design is the accurate estimation of the auxiliary compression load. For the combination of large leakage flow and a high-pressure ratio, centrifugal compressor architecture was chosen over an axial compressor or a reciprocating pump. The one-dimensional compressor design method from Baljé [32] was adapted to perform the design of a multistage centrifugal compressor. The inputs to the compressor design include the labyrinth seal leakage flow (calculated above), inlet pressure of about 15 psia and exhaust pressure of about 1000 psia. A preliminary design resulted in an integrally geared six-stage configuration with intercooling after three stages. The performance specifications of this six-stage centrifugal seals-scavenge compressor were integrated with the ASPEN HYSYS sCO_{2} power cycle model from the work of Bidkar et al. [13]. The effects of the scavenge compressor auxiliary load on the overall power cycle efficiency are shown in Fig. 4. Note that only the effects of turbine-end seals are shown, keeping other seals (for example, compressor seals) unchanged. It can be seen that 0.3–0.45% seal leakage flow can result in cycle efficiency loss of about 0.55% points to 0.65% points. Note that higher temperature labyrinth seals result in a higher penalty due to loss of useful thermal power in addition to the scavenge compressor penalty. Compensating for this auxiliary loss by raising the overall cycle efficiency through higher firing temperatures would require an increase in turbine inlet temperature, which is a very costly prospect requiring lengthy materials development effort. Alternatively, developing low-leakage seals is a very cost-effective manner of ensuring high power cycle efficiencies. A face seal concept, which can significantly reduce this efficiency loss caused by labyrinth seals, is shown in Sec. 3.

## Face Seal for Utility-Scale Turbines

In Fig. 5, a face seal cross section for a utility-scale sCO_{2} turbine is shown. The *Y*-axis is parallel to the cylindrical axis of the turbine, and the *Z*-axis is along the radial direction. The seal stationary ring is supported by springs. The springs are mounted on the seal stator, which is attached to the turbine casing. The stationary ring slides against a secondary seal. The stationary ring axial face has spiral grooves for generating a separating force. In Fig. 5, the bearing face has unit length. “*a*” and “*b*” signify axial dimensions of the cross section, while “*c*” signifies the nominal axial location of the secondary seal. “*d*” signifies the height of stationary ring radially outward of the bearing face, and “*e*” signifies the radial height of the cross section below the bearing face. The radially innermost dimension of the seal is constrained to be larger than about 24 in. based on the 450 MW_{e} sCO_{2} turbine from the work of Bidkar et al. [13,14].

The bearing face is subjected to a pressure distribution (i.e., an opening force in the negative *Y*-direction) caused by the spiral grooves. All surfaces of the seal cross section shown in Fig. 5 (except the bearing face) that are located radially outward of the secondary seal are subjected to the high pressure (*P*_{high}). All surfaces of the seal cross section that are located radially inward of the secondary seal are subjected to the low pressure (*P*_{low}). For force-balance analysis, it is assumed that the pressure reduces across the secondary seal from *P*_{high} to *P*_{low.} The balance diameter (i.e., the diametrical location of the secondary seal) is chosen such that the closing force (spring force and the pressure force on all faces except the bearing face) is equal to the opening force (pressure force on the bearing face). The relative magnitudes of the friction force at the secondary seal and the inertial load are small compared to the remaining forces and can be neglected for a preliminary force balance. In Sec. 3.1, CFD is used to evaluate the pressure distribution on the bearing face and highlight interesting aspects of fluid-film physics in large-scale sCO_{2} face seals. CFD results from different fluid models are compared. Following that in Sec. 3.2, an axisymmetric FEA model is used to optimize the cross section of the stationary ring shown in Fig. 5.

### CFD Model for a sCO_{2} Face Seal.

The primary goal of the fluid flow analysis is to evaluate the pressure distribution and windage heat generated by the fluid film between the stationary ring and the rotor, i.e., the bearing face in Fig. 5. The pressure distribution 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 this section, these models are briefly described along with their regimes of applicability. This is followed by a comparison of the predictions based on these models.

*r*and

*θ*represent the radial and tangential directions,

*p(r, θ)*is the pressure distribution in the film,

*h(r, θ)*is the film thickness (separation between the rotor and the seal stationary ring),

*μ*is the dynamic viscosity of the fluid, and

*ω*is the angular speed of the rotor. The partial differential equation shown in Eq. (1) can be numerically solved using a finite-difference scheme [34] to obtain the unknown pressure distribution

*p(r, θ)*for a specified film thickness distribution

*h(r, θ)*and specified boundary conditions. For cases involving high differential pressures and large film thickness, there is a possibility of approaching sonic conditions or sonic transition in the fluid film. The face seal experiences rapidly changing pressures in the dam section near its low-pressure boundary, and the Reynolds equation (see Eq. (1)) is inadequate for modeling this effect. For such cases, an analytical 1D model [35] can be used for studying the pressure and Mach number variation. The 1D model is based on the assumptions of compressible ideal gas flowing between the parallel plates separated by a distance equal to the film thickness. The fluid flow equations are

where *γ* is the ratio of specific heats, *M* is the Mach number, *A* represents the cross-sectional area, *C _{f}* is the Fanning friction factor,

*ρ*is the fluid density,

*dr*is the elemental length along the radial direction of flow, and

*D*is the hydraulic diameter. Next, the domains of applicability of Eqs. (1) and (2) are discussed.

_{h}A typical fluid domain for a face seal is shown in Fig. 6. It consists of a periodic sector of the thin film between the stationary ring and the rotor. As shown, one axial face (perpendicular to the *Y*-axis) of the domain represents the stationary ring with spiral grooves on the axial face of the stationary ring. The definition of the spiral grooves is proprietary information and not discussed in this paper. The second axial face of the domain represents the rotor, where a tangential surface velocity is specified. *P*_{high} and *P*_{low} are specified as the boundary conditions at the radially outer and 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)) is solved in region 2 (see Fig. 6) with pressures and mass flows matched at the boundary of region 1 and region 2.

Supercritical CO_{2} can exhibit nonideal gas behavior, especially near its critical point (1071 psia and 88 °F). Furthermore, the high density of supercritical CO_{2} 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, it becomes necessary to solve 3D Navier–Stokes equations in order to accurately model the seal fluid-film physics.In this work, a 3D fluid model was created using ANSYS CFX. The fluid model is shown in Fig. 6. Note that with ANSYS CFX, it is not necessary to split the fluid domain into region 1 and region 2. The 3D model is based on the assumptions of turbulent flow and isothermal conditions. It is also assumed that the stationary ring and the rotor are parallel to one another, i.e., there is no coning. The applicability and validity of these assumptions are discussed later in this paper. Since sCO_{2} can exhibit nonideal gas behavior, real gas properties of CO_{2} (REFPROP based tabular data) were used as input to the CFD model. Mesh convergence studies were performed to ensure a small *y*-plus value (average value less than 2) for the rotor and stationary ring surfaces. The results of the combined 2D–1D model (i.e., Eqs. (1) and (2) solved together) and the 3D CFD model are discussed next.

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

In Fig. 7, the average bearing pressure (normalized by *P*_{high}) 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 thickness (less than 0.0002 in.), but diverge at larger gaps. The agreement between the two models for the small film thickness indicates that the underlying assumptions of ideal gas behavior and laminar flow do not introduce a significant error (relative to the 3D equations) at small film thickness. Specifically, for the operating conditions analyzed in this work, the compressibility factor *p/ρRT* of sCO_{2} is 0.9 or higher. This indicates that the flow can be modeled using ideal gas law. In Fig. 8, the radial and tangential velocity profiles in the film as predicted by 3D CFD model are shown for three different film thicknesses of 0.0001 in., 0.0003 in., and 0.0006 in. Interestingly, the tangential film velocity profiles (Fig. 8(b)) show S-shape curves indicating a turbulent flow in the film. This validates the turbulence modeling assumption in the 3D CFD model. With increasing film thickness, the radial velocity profiles (Fig. 8(a)) show increased velocity gradients near the wall. The laminar-flow-based Reynolds equation (which assumes a parabolic radial velocity profile) cannot accurately model this turbulent flow. Consequently, for larger film thickness (more than 0.0002 in.), the predicted bearing pressure and the seal leakages show disagreement between the combined 2D–1D model and the 3D CFD model. For initial stages of design, the Reynolds-equation-based solver can provide relatively quick predictions. On the other hand, for a detailed design, the 3D CFD model with real gas properties (needed for analysis near critical point of CO_{2}) and turbulent flow assumption is a better choice for high-density fluids like sCO_{2} that operate in the turbulent regime.

The turbulence is attributed to the high Reynolds number caused by the high density (high pressure) of sCO_{2} and the large rotor velocity. The S-shape velocity profile (see Fig. 8(b)) also implies that the shear stress and therefore the windage heat generation are higher in sCO_{2} face seals compared to face seals with air as the working fluid. A direct comparison with air as the working fluid shows that sCO_{2} seals generate about 1.5 times more heat than air seals for the cases analyzed in this work. This increased heat generation in sCO_{2} seals requires attention toward thermal management of the seal, which will be discussed in Sec. 4.

The pressure distribution obtained using the 3D CFD model is used for the structural optimization of the stationary ring described in Sec. 3.2. Finally, note that the fluid-film leakage (from the 3D CFD model) in addition to the secondary seal leakage was predicted to be 1 to 2 orders of magnitude smaller than the labyrinth seal leakage (i.e., 0.3–0.45% of turbine flow). Based on Fig. 4, this would imply that the seal leakage past two hydrodynamic face seals (one on either turbine end) would cause a negligible effect on the overall power cycle efficiency. In other words, hydrodynamic face seals (with a very small leakage penalty and the associated small cycle efficiency loss) at turbine shaft ends can enable utility-scale sCO_{2} power cycles by allowing high efficiency operation that is otherwise at risk using the existing technology of labyrinth seals.

### Structural Model.

In this section, an axisymmetric FEA model of the seal stationary ring is developed. The primary purpose of the FEA model is to study the coning sensitivity of the stationary ring (under applied pressure loads) to variation in seal cross section geometry. The seal geometry with various dimensions is shown in Fig. 5. As described earlier, *P*_{high} and *P*_{low} pressures are applied on surfaces of the stationary ring that are radially outward and radially inward of the secondary seal, respectively. The pressure distribution computed from the 3D CFD model is applied on the bearing face. The FEA model assumes isothermal conditions and typical structural steel properties for the seal stationary ring. Switching to a different nickel-based alloy will improve the life of the component (creep-based life) but is not expected to significantly change the coning deformation results discussed in this paper. Thermal loads on the seal will cause deviation from the isothermal assumption, and the seal deformations with thermal load are addressed in Sec. 4.

Coning is defined as the *Y*-displacement of the radially inner edge of the bearing face minus the *Y*-displacement of the radially outer edge of the bearing face. Thus, a positive coning value implies the outer edge is farther away from the rotor than the inner edge of the bearing face. In other words, a positive coning value implies a converging film shape moving radially inward from *P*_{high} to *P*_{low}. From a fluid-film stiffness perspective, it is always desirable to have a slightly converging film or a small positive coning value when higher pressures are present at the outer edge. A diverging film or negative coning value results in very poor fluid-film characteristics and might result in seal failure in terms of rubs between the stationary ring and the rotor. In the following analysis, the effects of seal cross section dimensions *a*, *b*, *c*, *d*, and *e* are studied with regards to the pressure-induced coning of the stationary ring. Note that the overall coning and shape of the fluid film is a net result of the coning of the stationary ring as well as the coning of the rotor surface. The analysis of this section focuses on just the stationary-ring coning, while the overall coning including the rotor deformation is discussed in Sec. 4.

To study the effects of geometrical parameters on the stationary ring coning, values of *a* = 4 and *e* = 1.21 were chosen (note all dimensions are nondimensionalized by the radial height of the bearing face). The pressure-induced coning of the stationary ring was studied for two values of *d* = 0 and *d* = 2.54 for different combinations of ratio “*b/a*” and “*c/(a-b)*.” The rationale here is to find (for a fixed value of *a*, *e*, and *d*) the optimal dimension *b* and *c* such that the stationary ring has a small positive coning.

Coning analysis results for the cases of *d* = 0 and *d* = 2.54 are shown in Figs. 9 and 10, respectively. Both Figs. 9 and 10 show contour plots of coning (reported in 1/1000 in.) for different combinations of ratios *b/a* and *c*/(*a-b*). For the case of *d* = 0 (see Fig. 9), negative coning values are obtained for all combinations of *b/a* and *c/(a-b)* reported here. For the case of *d* = 2.54 (see Fig. 10), positive coning values are obtained for a range of combinations of *b*/*a* and *c*/(*a-b*). Comparing the two cases of *d* = 0 and *d* = 2.54, it can be seen that increased radial height of cross section allows the face seal to switch from negative coning values to positive coning values. Furthermore, high values of ratio *c*/(*a* − *b*) will tend to improve coning from a diverging film to a converging film. Similarly, increasing *b/a* will cause film to switch from a diverging behavior to a converging behavior. The overall trends for *d*, *c/(a-b)*, and *b/a* suggest that higher values for these three parameters/ratios will result in positive coning. Physically, this corresponds to bulkier seal cross sections that might have other seal design challenges including large seal inertial loads and seal vibration modes interacting with the turbine rotor. This parametric FEA model shows that a seal cross section for a large face seal (about 24-in. diameter) with high differential pressures (higher than about 1000 psia) is feasible with coning (or out-of-plane displacement) less than 0.0002 in. Furthermore, the FEA model shows that the seal designer has several geometrical parameters that can be used to control the pressure-induced coning and eventually compensate for thermal-load-induced coning. We address the thermal coning issue and clarify some of the assumptions stated earlier during the CFD and FEA studies in Sec. 4.

## Thermal Analysis and Seal Design Challenges

The primary design challenge for large-scale sCO_{2} face seals is simultaneously controlling the pressure-induced and thermal-load-induced coning of the seal with the intention of operating the seal with a small converging film (a positive coning value). The CFD results presented in this paper assume that the rotor and the stationary ring are parallel to each other (zero coning). This is a good 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 map the entire space. These CFD analyses are not presented in this paper. Similarly, the isothermal assumption used in the CFD studies is a good starting assumption. In conjunction with the CFD and FEA models presented above, a thermal model is required for predicting the structural temperatures and the fluid temperatures around the seal. The fluid temperatures predicted by the thermal model can be used as an input to the CFD model instead of assuming isothermal conditions with temperature known a priori. A thermal model will also allow computation of the temperatures on the stationary ring and the rotor, which can be used to calculate the thermal-load-induced coning. The overall coning is the net resultant of the pressure-induced and the thermal-load-induced coning.

*d*= 2.54,

*a*= 4,

*e*= 1.21,

*b/a*∼ 0.75, and

*c*/(

*a-b*) ∼ 0.75 was chosen based on the results from Fig. 10. Details of the seal cross section including the springs and the secondary seal were not included in this preliminary thermal analysis. Heat transfer coefficients were calculated for all surfaces of the stationary seal ring and the rotor based on the geometry and local fluid properties. As shown in Eq. (3), the principle of conservation of energy was applied to a control volume between the stationary ring and the rotor

where $m\u02d9leak$ is the leakage flow, $hin$ is the specific enthalpy of the fluid prior to entering the thin film, $hout$ is the specific enthalpy of the fluid exiting the thin film, $Q\u02d9windage$ is the windage heat generated by viscous shearing in the thin fluid film, $Q\u02d9seal$ and $Q\u02d9rotor$ represent the convection heat flow to the seal stationary ring and the rotor, respectively. Note that the leakage flow and the windage heat generated in the fluid film are known from the 3D CFD model and the heat flow to the rotor and seal are iteratively evaluated from the ANSYS thermal solver until Eq. (3) is satisfied. Figure 11 shows a representative temperature contour for the seal stationary 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 ring and the rotor. The combined pressure-temperature loading resulted in a stationary ring coning of about +0.0003 in. and a rotor coning of about +0.0001 in., resulting in a net coning of about +0.0004 in. Overall, these results show that a large-diameter sCO_{2} face seal design with coning of the order of 0.0005 in. is possible for utility-scale sCO_{2} turbines.

The fluid, structural, and thermal analysis results presented in this paper demonstrate a framework for preliminary sizing of large-length-scaled sCO_{2} face seals. For a detailed design, these models might need further refinement including but not limited to coupling of the fluid, structural, and thermal analyses. In that sense, the analyses presented in this paper form a starting point for a coupled fluid–structure–thermal interaction model. Note that such coupled fluid–structure–thermal analysis approaches have been used for traditional face seals [36], but with simplifying assumptions of one-dimensional flow and ideal gas behavior that greatly reduce the computational cost and time. Traditional simplifying assumptions (for example, ideal gas behavior and thin film Reynolds equation solutions [34]) might have limited applicability with sCO_{2} and a 3D CFD model (such as the one presented above) may be required in many cases. The need to use 3D CFD for the seal complicates the framework for a coupled fluid–structure–thermal analysis in terms of cost and computational time. Developing a simple and quick, yet accurate framework for a coupled fluid–structure–thermal analysis is a significant challenge for such large-scale sCO_{2} seals. Also, note that since sCO_{2} is a relatively new fluid, there is limited experimental data that can be used for validating thermal models of seals. High-fidelity thermal models for seals can be developed only in conjunction with supporting experimental testing efforts. In summary, developing a simplified framework for a coupled fluid–structure–thermal analysis of seals and experimental validation of the thermal model remain as challenges for seal design. Finally, note that the challenges discussed in this paper are in the context of seal design/analyses and a discussion on other challenges in developing large-scale sCO_{2} seals (e.g., manufacturability/installation of large seals, etc.) is beyond the scope of this paper.

## Summary and Conclusions

Hydrodynamic face seals are a key enabling technology for utility-scale sCO_{2} turbines. Analysis shows that a nominally 500 MW_{e} power plant can lose up to 0.65% points in thermodynamic cycle efficiency if existing technology of labyrinth seals is used.

In this paper, a hydrodynamic face seal was presented as an alternate to the existing technology of labyrinth seals. Hydrodynamic face seals technology is well known and commercially available, but needs further development when using this technology for large length scales (about 24-in. diameter) and high differential pressures (higher than 1000 psia). In this paper, a 3D CFD model was developed to compute the bearing pressures. It was seen that the flow in the sCO_{2} fluid film is turbulent and generates larger viscous heat than traditional air seals. The bearing pressures computed in CFD were used as an input to an axisymmetric FEA model of the seal stationary ring. The FEA results show that it is possible to design a large-scale sCO_{2} seal with high differential pressures and there is flexibility in controlling the coning deformation of the seal. A preliminary thermal analysis of the seal showed manageable coning deformations with thermal loads. Finally, the importance of a coupled fluid–structural–thermal analysis was also highlighted.

## Acknowledgment

This material was based upon the work supported by the Department of Energy under Award No. DE-FE0024007. The authors want to thank Dr. Seth Lawson at U.S. Department of Energy—National Energy Technology Laboratory for his support and guidance during this program. We are thankful to Xiaoqing Zheng, Doug Hofer, Chris Wolfe, and Norm Turnquist of the General Electric Company for discussions on seals and their system-level impact. This paper was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.