Design of Stress Constrained SiC/SiC Ceramic Matrix Composite Turbine Blades

This paper investigates issues associated with using SiC/SiC ceramic matrix composites (CMCs) to form rotor blades for the high pressure turbine (HPT). Results are given for aerodynamic and structural analyses for shrouded and unshrouded SiC/SiC CMC HPT rotor blades. SiC/SiC CMC materials have higher temperature capability compared to superalloys currently used for HPT vanes and blades. The density of SiC/SiC CMCs is only about 1/3 that of superalloys. The lower density of SiC/SiC CMCs is beneficial for rotor blade applications, where stresses from centrifugal loads are significant. SiC/SiC CMC materials have different strength versus temperature characteristics compared to superalloys currently used for vanes and blades. Typically superalloys rapidly gain strength as their temperature is reduced below their maximum use temperature. SiC/SiC CMCs gain some strength as temperature is reduced. But, the ratio of room temperature strength to the strength at maximum temperature is less for SiC/SiC CMCs than for superalloys. Shrouded first stage HPT blades are analyzed because the span of the first stage blade is typically shorter than the span of the second stage blade in a two stage HPT. A shorter span results in lower centrifugal loads.

The results presented in this paper are for the HPT of a NASA reference cycle given by Jones [1]. The cycle is for a single aisle aircraft engine to be available in the N + 3, (beyond 2030), time frame. The HPT has two stages. Typically, the second stage annulus area is greater than the first stage annulus area. This provides good aerodynamic efficiency for both stages. Since both rotor blades are on the same shaft, centrifugal stresses are higher for second stage blades. Additional second stage superalloy blade cooling can provide the necessary strength. For SiC/SiC blades, additional cooling is unlikely to provide the necessary strength without an excessive fuel burn penalty. Shrouding the first stage blade may be desirable because the through flow velocity in the first stage is much lower than in the second stage. Rotor blade aspect ratios are low for SiC/SiC CMC blades, and the efficiency benefit from shrouding the first stage blade can be significant.

Applying the same stress constraint, for example, 100 MPa (14.5 ksi), to both first and second stage rotor blades, may allow shrouding the first stage blade. The added weight of a low density SiC/SiC CMC shroud may result in acceptable stresses and improved aerodynamic efficiency. The aerodynamic benefits and increased stresses from shrouding the first stage blade will be examined.

The work presented here is a continuation of work reported in Refs. [2–4]. These references examined cases where the High Pressure Spool rotation rate was reduced from the value specified in a system analysis to keep stresses to acceptable levels. The aerothermal and structural analyses were concerned with the performance of the HPT. They did not examine in detail the effects of an rpm reduction on the overall engine performance. Reference [4] estimated the engine weight increase due to an rpm reduction. The engine weight increase was substantial when the rpm was reduced to give acceptable stresses. This work aims to quantify stresses and rotor blade aerodynamic efficiency where the high pressure shaft rpm is maintained at the value specified at the system level. Maintaining the rpm results in no adverse impact on the High Pressure Compressor or other engine components.

As mentioned in the introduction, the motivation for this work is the difference in strength characteristics between superalloys and SiC/SiC materials. Figure 1 compares the 1000 h strength versus temperatures from several sources (Refs. 5–11). Results are given for three current superalloys, an earlier generation superalloy, and SiC/SiC CMC materials. At a strength of 100 MPa (14.5 ksi), the SiC/SiC materials have a temperature capability $180 °C(324 °F)$ higher than the current superalloys. The room temperature 1000 h strength of the SiC/SiC CMC N24A is only about triple that of its strength at $1316 °C(2400 °F)$⁠. However, the room temperature strength of some superalloys can be an order of magnitude greater than their strength at their maximum use temperature. Cooling a superalloy below its maximum use temperature is an effective way of increasing strength. Cooling SiC/SiC CMCs is less effective in increasing strength. Thermal analysis is not part of this investigation. However, cooling of SiC/SiC blades is feasible and is required for the first stage rotor blade. The higher temperature capability of SiC/SiC CMCs results in less required cooling for SiC/SiC CMCs than for superalloys.

Figure 1 shows that the temperature capability of superalloys has increased over time. A similar increase in temperature capability is expected for SiC/SiC CMCs. Bhatt [11] showed that SiC/SiC CMCs under development are likely to have a $167 °C(300 °F)$ temperature capability at the same strength compared to N24A. Dunn [12] showed that increasing the fiber fraction increases the strength of a SiC/SiC CMC. In a creep test at $1315 °C(2400 °F)$⁠, he showed that increasing the fiber volume fraction from 0.26 to 0.33 increased the time to rupture from 74 to 479 h at a tensile stress of 166 MPa (24 ksi). The tests were conducted for nonwoven 12 ply SiC/SiC CMC composite coupons.

Figure 1 also shows the benefit of the lower density of SiC/SiC CMC compared to superalloys. SiC/SiC CMCs are only 1/3 the density of superalloys. Replacing a superalloy blade with a SiC/SiC CMC blade reduces centrifugal stress by a factor of three. At high temperatures, a superalloy blade has to be cooled nearly $345 °C(621 °F)$ more than a SiC/SiC CMC blade to accommodate the higher centrifugal stress.

The system parameters for the reference case were specified by Jones [1]. This case is a NASA specified engine for a single aisle aircraft to be available in the N + 3, (beyond 2030), time frame. Table 1 gives some of the parameters of this engine at the rolling takeoff condition. This condition results in higher stresses than at the cruise condition. The HPT has two stages and an overall pressure ratio of four. Each stage was assumed to have a pressure ratio of two. The combustor outlet temperature, T₄₀, of $1616 °C(3400 °R)$ is relatively low. This low value minimizes NOx production. Increasing T₄₀ was considered because it would ease satisfying stress constraints by decreasing the core mass flow. Decreasing T₄₀ was rejected because doing so was likely to adversely affect the compressor performance.

One benefit of a low T₄₀ is that heat transfer considerations are minimal even for the first stage rotor of the HPT. For the reference case, the total temperature at the first stage stator exit, T₄₁, was specified as $1560 °C(2840 °F)$⁠. The driving temperature for rotor heat transfer is the rotor inlet relative total temperature, which is approximately $100 °C(180 °F)$ lower than T₄₁. The Environmental Barrier Coating for use with SiC/SiC CMCs has a maximum use temperature of $1483 °C(2700 °F)$ (Lee et al. [13]). The maximum Environmental Barrier Coating temperature is slightly higher than the first stage rotor inlet relative total temperature. Some cooling is still required to account for hot day conditions and other factors such as combustor outlet hot spots.

$σCENT$ is the centrifugal stress; ρ is the material density; ω is the rotation rate; $AANN$ is the annulus area; $ATIP$ is the cross-sectional area at the tip; and $AHUB$ is the cross-sectional area at the hub.

Blade profiles were determined in an iterative fashion. Even though heat transfer was not explicitly included in the analysis, heat transfer considerations were part of the analysis. The inlet relative flow angle was close to axial to minimize the inlet velocity. Reducing the inlet velocity reduces the stagnation region heat transfer, and the stagnation heat transfer coefficient is often the highest rotor blade heat transfer coefficient. Increasing the leading edge diameter also reduces the stagnation region heat transfer. However, increasing the leading edge diameter increases blockage at constant blade count. Increasing blockage increases stagnation region heat transfer by increasing the upstream velocity. The annulus area for a SiC/SiC CMC blade is smaller than it would be for a highly cooled superalloy blade. The smaller inlet area leads to a higher inlet Mach number for the same flow rate. For inlet Mach numbers above 0.3, compressibility effects decrease the minimum pressure near the leading edge. This can lead to separated flow over a large region of the pressure surface and adversely affect aerodynamic efficiency. To reduce the likelihood of decreased efficiency from blockage and Mach number effects, leading edge sweep was incorporated into the rotor blade design.

While blade profiles were determined for both the first and second stage rotor blades, this paper has results for only the first stage blade. Results for both shrouded and unshrouded blades are discussed. Table 2 gives shroud dimensions. The relatively thin shroud has three finger seals to provide structural rigidity and clearance flow path redundancy. Figure 2 shows hub and tip blade coordinates and a meridional view of the blade. The blade count of 35 was chosen to keep blockage at a reasonable level. SiC/SiC CMC blade sections have relatively thick trailing edges, 1.4 mm (0.054 in). The blade profiles shown in Fig. 2 were chosen after examining many blade geometries. Hub and tip sections were used as input to a quasi-3D stream function analysis program. Reference [15] showed that this analysis can be expected to give a reasonably accurate efficiency estimate for unshrouded blades. This program was used to define blade coordinates and was not used to determine any efficiencies discussed in this paper.

Linear static stress analyses were done using ANSYS, Canonsburg, PA [16]. It was felt that, based on the 1000 h strength behavior shown in Fig. 1, configurations that had maximum stresses nearly the same as, or less than, the SiC/SiC CMC strengths would be appropriate for further analysis. Both Von Mises and radial stresses are given. Reference [4] showed that even with pressure and centrifugal loads radial stresses were the dominant blade stresses. Fillets were not used at the junction of the blade with the hub or shroud. Reference [4] also showed that fillets had only a small influence on the overall stress distribution. However, because of the smooth junctions with fillets, the maximum stresses were reduced.

The aerodynamic efficiency of shrouded and unshrouded rotor blades was determined using the star-ccm+ computer code, using the $k−ω$ SST turbulence model. Steady-state analyses were done for isolated blade rows. Stage efficiencies were calculated assuming a constant stator kinetic energy loss coefficient, $e¯$⁠, of 0.035. The geometries used in this analysis are significantly different from those used by Banks et al. [2,3]. But, the computational approach is similar.

Figure 3 shows the geometry analyzed along with the cell distribution. For both the shrouded and unshrouded cases, there were basic grids and refined grids with cells added in regions where high velocity gradients were expected. A typical grid for the unshrouded blade analysis had over 10 × 10⁶ cells, and a shrouded blade had 50% more cells.

Figures 4 and 5 show Von Mises and radial stresses due to centrifugal loads. Parts a and b of each figure show stresses on the suction and pressure surface of the blade. Part c shows stresses on the hub plane of the blade. The highest stresses are on the suction surface at the blade-to-hub junction. Part a of each figure shows large regions of the suction surface have stresses above 100 MPa (14.5 ksi). This was not expected since stress analysis for second stage blades showed that the one-dimensional stress equation agreed reasonably well with the three dimensional ANSYS stress analysis. High, but extremely localized stresses, are not likely to be accurate. These high stresses are often at junctions or regions of very high curvature. Excessive stresses over a significant area are believed to accurately show regions of excessive stress.

Part c of Figs. 4 and 5 show that hub blade stresses are not uniform. Figure 4(c) shows that most of the blade has Von Mises stresses between 100 and 250 MPa (14.5 and 36.3 ksi). The average stress for the hub was 149.8 MPa (21.7 ksi). This value was nearly twice the value calculated from the one-dimensional equation. The radial stresses shown in Fig. 5(c) also show a large region of the blade hub section with stresses above 100 MPa (14.5 ksi). Somewhat surprisingly, Fig. 5(c) shows that significant blade hub regions are in compression, with negative radial stresses.

Figures 6 and 7 show Von Mises and radial stresses for a shrouded blade. As expected, there is an increase in stresses when the shroud was added. Comparing Figs. 4 and 6 for Von Mises stresses shows that much of the blade stresses that were in the 50–100 MPa (7.3–14.5 ksi) range for the unshrouded blade are above 100 MPa (14.5 ksi) for the shrouded blade. On the other hand, Figs. 5 and 7 for radial stresses show that adding a shroud has only a minor effect on blade radial stresses. Adding a shroud causes increases in other component stresses. Stresses are calculated relative to a fixed frame of reference, so that shear stresses are present. Shear stresses are heavily weighted in the calculation of Von Mises stress. Comparing hub radial stresses in Figs. 5(c) and 7(c) show that the presence of the shroud serves to redistribute stresses, rather than dramatically increase the average stress. The region of compressive radial stress near the front of the blade is larger when the shroud is present.

Figures 8 and 9 show Von Mises and radial stresses when pressure loads are combined with centrifugal loads. The inlet absolute total pressure was 4.25 MPa (616 psi). The inlet relative total pressure near midspan was approximately 0.7 of this value. Since the stage pressure ratio was two, the maximum pressure differential across the blade was 1.5 MPa (218 psi). The shape of the differential pressure is triangular. The pressure differential is zero at the leading and trailing edges, and maximum near midchord. Comparing pairs of figures, (Figs. 8 and 4 and Figs. 9 and 5), show that, as expected, the effect of a pressure load on stresses is small. Comparing Figs. 8(c) and 4(c) shows that there is nearly a 10% decrease in the hub average Von Mises stress when pressure and centrifugal loads are combined. Comparing Figs. 9(c) and 5(c) show that adding a pressure load to centrifugal load had no effect on hub radial stresses The average weighted stress changed by less than 1%.

Very high Von Mises stresses were seen in the finger seal region of the shroud. High stresses were not confined to a very small finger seal area. The tops of the finger seals were rounded to determine if that would reduce the maximum finger seal Von Mises stress. Comparing Figs. 10 and 6(a) show that rounding the tops of the finger seals had only a small effect on the Von Mises stresses in the shroud.

Figure 2(a) shows that the hub section leading edge stagnation point is at an ordinate of 0.0. A stacking axis is where θ is zero. To investigate the effects of stacking, the entire blade was shifted in the positive tangential direction. For the restacked blade, the ordinate of the hub section leading edge stagnation point became 1.5 cm. The $Rθ=0$ location moved to near the centroid of the hub section. Figure 11 shows Von Mises stresses for the restacked blade. Comparing parts a and b of Figs. 4 and 11 shows very similar patterns. While the patterns are similar the restacked blade has a significantly higher maximum Von Mises stress. Comparing part c of these two figures shows that the hub plane the maximum Von Mises stress is lower for the restacked blade. For the restacked blade, Fig. 11(c), the area averaged Von Mises stress is 108.3 MPa (15.7 ksi) compared to an area averaged Von Mises stress of 149.8 MPa (21.7 ksi) for the original blade. This 28% reduction in area averaged stress shows that restacking the blade can be significant in achieving acceptable stresses.

Figures 12 and 5 show results for radial stress, and lead to a somewhat different conclusion. The maximum radial stress is reduced by 12% for the restacked blade. The minimum radial stress of −816 MPa (−118.3 ksi) for the restacked blade is a compressive stress. The magnitude of this maximum compressive stress is nearly 70% greater than the maximum compressive stress for the original blade. Restacking the blade changed the area averaged radial stress by only 1%.

The maximum stress value may not be relevant if stresses near this value are confined to a small region of the blade. The maximum stress may be a function of grid parameters, and a denser grid does not necessarily result in a more accurate maximum stress. An alternate approach is to average stresses over an area. Table 3 shows area averaged stresses at the hub of the blade. These are the Von Mises and radial stress. Also shown is the one-dimensional stress using the stress equation shown previously. The constant section blade was formed by extruding the hub section. The “coarse” grid results were obtained from a model with 154,268 nodes and 39,900 elements. The “refined” grid had 5.2 times as many nodes and 6.2 times as many elements. Results presented herein had grids similar to the “refined” grid. In addition to the cases discussed, comparisons were made for stress analysis of second stage blades.

The comparisons in Table 3 show that often the one-dimensional radial stress equation gives a useful approximation to stresses calculated from the three dimensional ANSYS analysis. For the second stage blade analysis the one-dimensional stress equation gives an accurate estimation of the stresses at the blade hub. The second stage blade hub and tip sections were more radially aligned than the base case first stage blade sections. Not unexpectedly, the one-dimensional equation agrees well with the three- dimensional analysis when the Von Mises stress nearly equals the radial stress.

Although developed decades ago a Smith chart, Smith [17] shows the effect of normalized axial velocity, $VX/U$ and stage output, $ΔH/U2$⁠, on efficiency. The chart indicates that at a given stage output there is an axial velocity corresponding to maximum efficiency. Because of the stress constraints a SiC/SiC CMC bladed rotor may have a normalized axial velocity greater than the velocity corresponding to maximum efficiency. Sufficiently cooled superalloy bladed rotors can have larger annulus areas, and thus lower axial velocities. But, additional cooling imposes a fuel burn penalty. For a two stage HPT turbine with SiC/SiC CMC rotor blades the second stage has the higher axial velocity. For a first stage pressure ratio of two, the second stage axial velocity is nearly double that of the first stage. It is feasible to reduce the first stage annulus area and shroud the blade so as to have similar stresses in the first and second stage blades. On the other hand reducing the annulus area increases the clearance-to-span ratio for the same physical clearance.

Figure 13 shows stage efficiency as a function of clearance for shrouded and unshrouded rotor blades. Data are shown at two axial gaps, h_G in Fig. 2. The effect of axial gap is clearly significant. It is useful to first compare the results for the larger axial gap of 2 mm (0.079in), which is 8.3% of span. This axial gap is consistent with what could be provided for to accommodate relative axial movement during different phases of a flight. The smaller axial gap was chosen primarily to show the effect of a significant variation in axial gap.

First comparing results for the larger axial gap shows that at a clearance of either 2 or 4% of span the difference in efficiency between shrouded and unshrouded blades is small. This was unexpected. The ordinate in Fig. 13 is the normalized efficiency, $ηCLE/ηCLE=0$⁠. The calculated zero clearance efficiency, $ηCLE=0$⁠, was 0.920. This measure minimizes the effects of parameters other than clearance on the results. For example, variations in the downstream location where efficiency is calculated or measured have little or no effect on the efficiency ratio, but do affect each efficiency almost equally.

One parameter that does affect the efficiency ratio is stage reaction. Hong and Groh [18], as quoted by Glassman [19] showed that for an unshrouded turbine the slope of normalized efficiency versus clearance depends on stage reaction. For a reaction of 0.7 the slope of efficiency versus clearance was almost double the slope at a reaction of zero. The data in Fig. 13 for the unshrouded rotor are for a reaction of 0.54. The slope of the normalized efficiency versus clearance for the unshrouded rotor shown in Fig. 13 is $0.0235ΔηNORM/%clearance$⁠. This value agrees well with the slope of the normalized efficiency curve give by Hong and Groh [18] of $0.025ΔηNORM/%clearance$ at the same reaction.

Most data show that at clearances above 1% shrouding improves stage efficiency. Figure 13 shows very little efficiency gain due to shrouding for an axial gap of 8.3% of span, even at a clearance-to-span ratio of 4%. However, at an axial gap of 2% of span there is a significant efficiency gain due to shrouding. Yoon et al. [20] showed that at a clearance less than 0.5% a shrouded blade is less efficiency than an unshrouded blade. At larger clearances shrouded blades are more efficient.

The efficiency gain for shrouding a rotor is more consistent with published results when the axial gap is small. The axial gap is as significant as the clearance in determining shrouded HPT blade efficiency. Banks [21] showed efficiency changes as the axial gap varied from the baseline of 3.3% of span.

Figure 14 shows clearance region flows for two axial gaps at a casing-to-finger seal clearance of 2% of span. Flow vectors are superimposed on loss values. Near the inlet the loss is negative because the absolute total pressure, $PIN!$⁠, is greater than the inlet relative total pressure, $PIN!!$⁠.

Figure 15 shows unshrouded blade relative Mach numbers at 50% and at 75% of span for clearances of zero, 2, and 4%. The clearance effect is mostly downstream of the blade. The aspect ratio is low. Zero clearance Mach numbers are similar at 50 and 75% of span. The maximum Mach number is just over sonic, so shock losses are absent. The ratio of maximum-to-exit Mach numbers is above 0.8, indicating moderate suction surface boundary layer growth. Zero clearance blade row efficiency is 0.935. Clearance flows penetrate to 75% of span. Pressure losses increase with clearance.

Figure 16 shows shrouded blade Mach numbers at 75% of span. At the larger axial gap for either clearance, Mach numbers for shrouded and unshrouded blades are similar. The smaller axial gap Mach numbers at 2 and 4% clearance are similar to unshrouded blade zero clearance Mach numbers. The ratio of mass flow over the tip to inlet mass flow is linear with clearance for either unshrouded or large axial gap shrouded blades, and was over 8% at 4% clearance. For the smaller axial gap the mass flow ratio was 3% for clearances of 2 and 4%.

SiC/SiC materials retain most of their low temperature strength to temperatures higher than the maximum usable temperatures of superalloys used in current HPTs. Cooling SiC/SiC CMC blades gives a more modest strength increase as temperature is reduced. Consequently, when SiC/SiC materials are used in highly stressed HPT components, such as rotor blades, simple substitution of metallic components by CMC components may not be feasible. This work showed that HPT SiC/SiC CMC blades can be designed to have acceptable stresses without reducing the rpm of a future notional engine. Stage efficiency is acceptable since neither excessive suction surface diffusion nor excessive Mach numbers were required.

The benefits of increased efficiency without excessive stresses due to shrouding the blade can be achieved if the axial gap can be held to a small fraction of span. The importance of the axial gap to the efficiency versus clearance gradient is independent of the blade material. Future HPT stages are likely to have smaller spans for the same thrust levels because of higher engine overall pressure ratios.

Under some, but not excessively constraining, circumstances a one-dimensional radial stress equation gave a reasonably accurate value for the hub area averaged Von Mises stress. This is significant because choosing a blade profile may involve determining results for a large number of parameters.

This work was supported by the NASA Phase II SBIR contract 80NSSC19C0062 Vikram Shyam is the technical monitor for this work.

• National Aeronautics and Space Administration (Grant No. 80NSSC19C0062; Funder ID: 10.13039/100000104).