Design of a Wide-Range Centrifugal Compressor Stage for Supercritical CO₂ Power Cycles

A supercritical carbon dioxide (sCO₂) power cycle, based on recuperated Brayton cycle with recompression, has been developed for a 10 MWe application. The cycle utilizes a multistage main compressor, with compressor suction conditions near the critical point to reduce the compression work. Therefore, the first-stage main compressor must be designed to manage potential variations in the inlet state of the gas associated with operation near the critical point. Near the critical point, slight changes in either the temperature or pressure of the gas have large effects on the aerodynamic performance of the compressor. For example, in the case of a compressor inlet operating at 37 °C and 85 barA, a ±2 °C variation in inlet temperature is associated with a 45% change in inlet density. Therefore, to maintain a constant mass flow in the cycle, the compressor has to maintain the required head rise across a wide range of flow coefficients.

Supercritical carbon dioxide power cycles demand high off-design efficiency from the compressor in addition to the design point. Variations in compressor aerodynamic performance may adversely affect the cycle performance and make the turbine difficult to control. Even in cases where the design suction conditions are above the saturation line, there is still a risk for large gradients in fluid properties within the stage. In particular, as the flow accelerates though the aerodynamic throat in the inducer, the static pressure and temperature will drop. Care must also be taken to ensure that the flow does not transition below the saturation line and increase the potential for condensate formation.

Therefore, developing a first-stage main compressor that can stably operate over a wide range helps ensure a robust operating system. Expanding the stable operating range of a compressor has been a goal of many classes of turbomachinery and in many industries including axial and radial compressors, turbochargers, and aero-engines. Numerous technologies have been proposed to widen operating range between surge and choke for different types of applications. In this paper, a novel design is developed for a high pressure sCO₂ compressor.

One advantage of many sCO₂ power generation cycles is that the compressor or pump inlet condition can be operated near the critical point, resulting in low compression work. Although this approach does improve the cycle efficiency, it also increases the operability risk since small changes in temperature or pressure will have large effects on the inlet density and volume flow rate.

A detailed cycle optimization study for an sCO₂ recompression cycle was performed for concentrating solar power applications. The study, which is described more fully in Refs. [1] and [2], was performed iteratively with turbomachinery aerodynamic design calculations, resulting in a four-stage reheated expander, two-stage main compressor, and two-stage recompressor. The turbomachinery was incorporated into a single integrally geared machine with a main compressor first-stage design point inlet condition of 37 °C and 85 barA. The integrally geared core is coupled to a fixed speed generator. Based on this configuration, an off-design cycle optimization study was performed that incorporated turbomachinery performance maps and off-design heat exchanger performance calculations in order to determine the best combination of cycle controls that would optimize cycle efficiency over a range of compressor inlet temperatures relevant to daily and annual temperature variations. The off-design optimization included a combination of inventory (mass flow) control, variation in flow split between the main compressor and recompressor, incorporation of variable inlet guide vanes (IGVs) at the compressor inlet, changes in cycle pressures, and variations in cooling and heating duty required to achieve heat balance for compressor inlet temperatures ranging from 32 °C to 55 °C.

The optimal off-design control scheme results in changing the compressor operating point for each stage as indicated in Fig. 1, assuming constant shaft speed. These results indicate that the required flow range for steady off-design operation of the main compressor stages is approximately 20%, assuming variable IGVs on the first-stage and conventional-stage designs (see baseline). The various line styles and shades of gray in the stage 1 chart correspond to different IGV positions, ranging from 0 deg (solid black line) to 65 deg (solid light gray line), and different compressor operating points that may be encountered during normal plant operation are marked with a thick gray “x.” Although these results indicate that only moderate range is required to accomplish off-design operation, stages with wider a high-efficiency operating range would improve off-design compressor and cycle efficiency.

The off-design results shown in Fig. 1 assume steady off-design operation, but the effect of transients must also be considered to determine compressor range requirements. It is estimated that in a production application, there may be ±2 °C variation in the compressor inlet temperature potentially due to solar transients, control system response rates, etc. In the case of a compressor operating near the critical point at 37 °C and 85 barA, ±2 °C change in inlet temperature is associated with a 45% change in inlet density, Fig. 2. This is much greater than the density variation for compressor operating in an air Brayton cycle with an inlet near 1 bar, where a ±2 °C variation in inlet temperature will only have a 1.4% change in density.

Consequently, to permit stable operation of sCO₂ machinery during such transients, a range of approximately 65% is desired. This accounts for variations in gas density plus 10% choke and surge margins.

A meanline compressor sizing and initial performance estimates were developed to match the cycle specification. The meanline sizing and nondimensional performance of the first-stage main compressor are shown in Table 1. The head and flow coefficients were set at 0.98 and 0.061, respectively. A higher flow coefficient stage would typically be used in an integrally geared machine, but was not achievable in this case due to mechanical limitations of the gears and bearings associated with the high power density in an integrally geared machine.

A preliminary three-dimensional (3D) flowpath was then generated to match the meanline design. A shrouded impeller is applied since the tight tip clearances required for an efficient open impeller could not be maintained at these stage pressures. The stage design included an axial inlet, backswept blades, and a vaned diffuser, Fig. 3.

Several iterations of the design were made, based on computational fluid dynamics (CFD) assessment, to refine the flowpath, in order to maximize efficiency and range. The CFD analyses were performed using the commercial CFD solver Fine/Turbo¹. A fully structured, single passage, hexahedral mesh with matching periodic boundaries was created as the computational domain. The total mesh size of the main passage and the casing treatment was approximately 2.8 × 10⁶. The one-equation turbulence model, Spalart–Allmaras, with wall functions was applied for the computations. The boundary layer was resolved to an average y⁺ value less than 200 for the analysis. Wall functions were used to avoid solving a much finer mesh, which would be required to resolve the boundary layer. The inlet boundary condition was defined by total pressure and temperature with a given velocity direction. At the outlet boundary condition, a fixed static pressure was applied at high flow, and the mass flow rate was specified at low flow. Nonslip and adiabatic wall boundary conditions were applied as well. The computation was considered converged when the root-mean-square residual value was less than 10⁻⁶, or the oscillation of inlet and outlet mass flow rate was less than 0.1%.

Steady-state CFD was conducted for this evaluation since is it is economical to run, which enables a wide range of designs to be considered in detail. Accurately identifying the stall limit is challenging with a simple steady-state CFD analysis. Although the exact stall point may be difficult to model, steady CFD can be used to assess the relative improvement in the range of one design relative to another. In this paper, the stall flow rate identified in the CFD analysis is defined as the flow rate when either the static pressure no longer increases with lower mass flow rate or a stable solution could not be achieved. Fluid properties used in the analysis were based on real gas properties calculated using NIST REFPROP.

For the baseline design, the range was calculated to be 43% and an efficiency of 87% was estimated following the procedure detailed above. Figure 4 shows predicted streamlines in the impeller at the lowest flow point where a steady CFD solution would converge. The CFD solution shows clearly that stall develops at the inducer shroud. Therefore, the most effective range extension techniques for this case should address inducer stall.

A broad spectra of range extension concepts were considered for this application, including variable IGVs, variable diffusers, splitters, partially shrouded impellers, and casing treatments. Variable IGVs are used to change the amount of flow that a stage can accept through the addition of preswirl at the inlet [1]. By incorporating a variable IGV geometry, the amount of preswirl can be optimized for each operating condition and thus the compressor operating range is widened significantly as shown by Rodgers [3]. While the literature consists of extensive work, an example of a more recent study is that of Mohseni et al. [4] who show the potential to improve efficiency with various IGV profiles through reducing loss coefficients by 50% at high setting angles.

In general, vaneless diffusers offer a wider operating range than vaned diffusers [5], but have lower stage efficiency. Many authors have investigated these effects on compressor range with changes in vaneless diffuser design including parallel walls, curved walls, nonparallel walls, and the use of hub and/or shroud pinch. Features like pinch [6] or optimizing solidity can help stabilize the flow through the diffuser and improve range.

Variable diffusers vanes are another application of variable geometry that can extend the operating range. Similar to variable IGVs, variable diffusers allow for high compressor efficiency over a wider range of operation. It has also been shown [7] that several diffuser variables influence the onset of stall. These factors highlight the potential utility of variable diffuser geometry to extend range and improve stage efficiency [8]. The major disadvantages to employing a variable geometry design are the complications associated with an active system both from a stand point of controls and sealing, especially for process gas applications at high pressures and temperatures.

As design tools and manufacturing capabilities advance, the implementation of complex geometries into compressor designs has become more feasible. More intricate 3D stacking methods provide designs with greater means to control pressure gradients and the development of secondary flows and losses through a blade row. Early works [9] address the use of lean and sweep on impellers, while more recent works [10,11] have shown improvements of several points efficiency through the use of 3D stacking and combinations blade lean and sweep.

A thick-bladed impeller concept [12] recommends adding material to the trailing edge of the blade, thus filling the region that would otherwise experience excessively thick boundary layers, flow separation, and loss, and can reduce the surge mass flow rate by 70%. A more common alternative to achieving the same effect without increasing blade thickness (and rotating mass) is to reduce diffuser height. Since these approaches focus on improving exducer stability, it was not evaluated in further detail.

Splitters have long been used to facilitate range extension for open impellers through reducing blockage at the inducer and solidity near the trailing edge [13]. While the use of splitters is widely accepted and commonly utilized for open impellers, manufacturing capabilities have eliminated them from use in closed impellers. With more advanced manufacturing methods, such as 3D printing, the implementation of splitter blades has become an option for closed impellers. Other impeller range-extension concepts that could be realized through direct metal laser sintering (DMLS) are partially shrouded impellers [14].

Shroud designs can include features for flow control, both passive and active, used to improve compressor operating range, typically by delaying the onset of stall. Passive designs include various casing (or shroud) treatments and bleed cavities, and active control features that typically involve removing or injecting fluid in the end-wall boundary layer. Casing treatments have been studied as a means of delaying the onset of stall for many years in both axial and radial machines [15–17]. Casing treatments include lateral and skewed slots, radial grooves, pin holes, honeycomb, and circumferential grooves. In general, the increased range at low mass flow rates comes at the cost of reduced efficiency, although a few designs have shown negligible effects on efficiency. Shroud bleed is an effective passive mechanism used to extend the operating range of open centrifugal compressors. It is well documented that shroud bleed can help extend range by 30–50% [18].

This large improvement in operating range may sacrifice efficiency if not carefully matched to the stage. Some authors have shown that implementing vanes in the bleed slot can lessen this efficiency decrement by controlling the amount of swirl [19]. Boundary layer control is used extensively across various aerodynamic applications. The implementation in compressors requires increased manufacturing and system complexity. Several studies have shown potential range improvements through injection at the shroud [20] and hub end walls [21], but there is little work documenting the effects of this type of control on the blade or vane boundary layers.

The feasibility and impact of all of the concepts presented above were evaluated. Based on the preliminary compressor model analysis, each concept was ranked based on expected aerodynamic performance and mechanical feasibility, with 0 as the lowest to 10 for the highest as shown in Table 2. Several concepts were eliminated from consideration without a detailed analytical evaluation because of known mechanical challenges or minimal expected range improvements based on information reported in the open literature. These include variable diffusers, which are expected to produce excellent range, but will be difficult to incorporate mechanically. Based on a review of published work, casing grooves and flow injection are expected to give minimal range extension compared to a shroud bleed and were eliminated from consideration. Finally, the thick bladed impeller concept was eliminated since it did not offer any range enhancement for the current stage design.

Computational fluid dynamics results of the top concepts are shown in Fig. 5. Both the vaneless diffuser and splitter concepts offer improved range with minimal impact on efficiency—specifically in the higher flow region since low flow operation is limited by stall in the inducer. A vaneless diffuser was found to give both additional high and low flow margin compared to an airfoil cascade diffuser. A variable IGV was shown to effectively shift the operating point lower in flow. For the shroud bleed concept, a simple self-recirculating casing treatment was designed and incorporated in the CFD model. The analysis showed that incorporating a casing treatment extended the operating range significantly. After some refinement, an optimal design was identified that resulted in more than 70% range while the peak efficiency penalty was predicted to be less than 0.5% points lower than baseline case.

Based on this assessment, a final stage design was developed, which combines these best range extension concepts. The final stage design is a shrouded impeller and includes a vaneless diffuser, shroud bleed, variable inlet guide vanes, and splitters with a shrouded impeller. While these concepts have been individually applied successfully in other commercial applications, combining them into one stage is unique in the market. Integration of IGVs and a vaneless diffuser is straightforward, and needs no further explanation. The integration of a self-recirculation casing treatment and splitters to a shrouded impeller is more complex.

The main roadblock to applying these technologies to a shrouded impeller has been manufacturing limitations. A complex shrouded impeller design would be challenging to produce with traditionally manufacturing methods, but is relatively simple to produce by additive manufacturing. Single piece shrouded impeller manufacturing has been shown to be a viable method for rotating machinery. In particular, DMLS yields final parts with robust mechanical properties [22].

Figure 6 shows the final stage design incorporating the selected range extension concepts. For this application, a passive shroud bleed concept was modified to work with a shrouded impeller. The design utilizes a partially shrouded impeller. The axial inducer portion of the compressor is unshrouded and a bleed slot is created at the intersection of the open and shrouded portion of the blade. Straight guide vanes are included inside of the cavity to guide flow back to the inlet and to reduce swirl flow, and another slot is connected to the inlet where the flow can re-enter the main flow path. A cover is integrated to the remainder of the shroud.

The semishrouded feature creates a unique design where the inducer blade tip is unsupported in front of the flow extraction slot. A potential high stress was identified at the intersection of the blade tip to shroud interface. By carefully transitioning the blade surface to the shroud with generous filets, the stress was reduced to acceptable levels. The detailed geometry required to reduce the stresses in this region is possible by DMLS manufacturing. The final 3D impeller design is shown in Fig. 7. A stepped eye seal land on the cover is also visible, and was used due to the small size of the compressor.

Figure 8 shows streamline comparison between the baseline model and the casing treatment model at the same flow rate. The results of the CFD analysis clearly indicate how the self-recirculating casing treatment concept operates to extend the low flow stability. The casing treatment removes the recirculation along the shroud and captures it in the bleed cavity. The cavity recirculates the flow from the inducer back to the inlet through a vaned cavity as seen in the plot. Near the stall condition, the flow through the recirculation cavity is approximately 10% of the overall compressor flow.

The final CFD performance prediction of the wide range design is compared to the baseline design in Fig. 9. The stage is predicted to achieve a range of 74% and a peak efficiency of 86.2%, not accounting for windage or leakage losses. This represents an increase in range of 72% compared to the baseline, and a reduction in efficiency of 1.2 points. The efficiency loss, compared to the baseline, is due to two main contributors. The largest reduction in efficiency is due to switching from a vaned to a vaneless diffuser which accounts for 0.9 points. The remaining 0.3 point drop is due to losses associated with application of the casing treatment.

The final compressor stage design incorporated four range extension techniques to improve the stability of the stage under variable inlet conditions. The resulting design achieves a significant range improvement over a traditional stage design. The stage maintains the same ability of a traditional shrouded impeller to tolerate significant axial movement without compromising efficiency. Thus, the stage can be used in applications where tight axial clearances cannot be maintained, such as high pressure or temperature designs.

The largest range enhancement came from adapting a self-recirculating casing treatment to the stage impeller. A vaneless diffuser and splitters complement the casing treatment integration by maximizing the baseline range of the impeller and diffuser. The greatest efficiency penalty came from the application of a vaneless diffuser, with a minor penalty associated with the casing treatment. Relative to the baseline design, the new configuration will be able to maintain stable operation and deliver the required cycle mass flow rate up to ±5 °C inlet temperature (70% range) as compared to just ±2 °C (30% range) for the baseline design.

This material is based upon work supported by the Department of Energy and Office of Energy Efficiency and Renewable Energy (EERE).

• Office of Energy Efficiency and Renewable Energy (DE-0007114).

This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. 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 U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.

a₀₀ =

inlet sonic velocity

d₂ =

impeller diameter

h =

enthalpy

M_U2 =

U₂/a₀₀

Q =

volume flow rate

Range =

$(φchoke−φstall)/φchoke$

U₂ =

impeller tip speed

η =

$Δhisen/Δh$

φ =

$4Q/(πU2d22)$

ψ =

$2Δhisen/U22$