Transonic Centrifugal Compressor Research Articles

Pressure Characteristic Rollover of a Transonic Centrifugal Impeller

Abstract This paper presents a detailed numerical investigation of a transonic centrifugal compressor to understand the mechanism causing its pressure rise characteristic rollover, which fundamentally impacts compressor stability. Distinct characteristic rollover behaviors at different compressor speeds are predicted and studied. It is found that the impeller characteristic rollover occurs at high blade tip Mach number (>1) conditions. It is the result of a combination of the inducer and exducer performance. The inducer is found to stall early, while the exducer is mostly a stable part maintaining the overall impeller stability. The overall impeller characteristic rolls over when the exducer’s performance deteriorates significantly, which happens at higher flow conditions toward high speed. This is due to the flow compressibility effect (density change). It shows that the flow density across the impeller increases with the blade tip Mach number. The increased density leads to a reduced exducer exit flow coefficient with higher workload and aerodynamic losses. Detailed analysis is carried out to understand the 1D and 3D flow mechanisms governing the inducer and exducer, hence the impeller characteristic.

Quantitative analysis on influence of secondary flow for centrifugal impeller internal flow

A comprehensive quantitative analysis of a high-loading transonic centrifugal compressor is performed under the design point. The reason for secondary flow within the impeller is examined under the approximation of boundary layer theory. Comparing the amplitudes of different terms of the Navier–Stokes (N–S) equations reveals that the acceleration that creates secondary flow within the shear layer is caused primarily by the Coriolis force difference, which has often been neglected in previous research. Migration flow on the wall surface further leads to the formation of three-dimensional secondary flow structures that occupy the entire blade passage. The vortex structure inside the impeller is visualized, and the contribution of the different vortices to the wake is clarified. The wake is ultimately composed of high-loss fluid that includes migration flow from the hub to the tip on the blade suction surface, leakage flow, and recirculating flow at the impeller outlet. By decomposing the N–S equations, it is clarified that the pressure distribution in the blade passage is mostly determined by the acceleration caused by the three-dimensional secondary flow structure, especially the momentum convection term. Therefore, the relationship between the secondary flow and the impeller loading is established. Furthermore, the natural frequency of the unsteady fluctuation of the secondary flow inside the impeller is discovered by unsteady numerical simulation, revealing the evolution of vortex structures.

Mechanism Underlying the Effect of Self-Circulating Casings with Different Circumferential Coverage Ratios on the Aerodynamic Performance of a Transonic Centrifugal Compressor

The aim of this research was to explore the mechanisms underlying the effect of self-circulating casing treatment with different circumferential coverage ratios on the aerodynamic performance of a transonic centrifugal compressor. A three-dimensional unsteady numerical simulation was carried out on a Krain impeller. The circumferential coverage ratios of the self-circulating casings were set to 36%, 54%, 72% and 90%, respectively. The numerical results showed that the Stall Margin Improvement (SMI) increased with the increase in circumferential coverage ratios. The self-circulating casing with a 90% circumferential coverage ratio exhibited the highest SMI at 20.22%. Internal flow field analysis showed that the self-circulating casing treatment improved the compressor stability by sucking the low-speed flow in the blade tip passage and restraining the leakage vortexes breaking, which caused flow blockage. The compressor performance was improved at most of the operating points, and the improvement increased with increase in circumferential coverage ratio. The improvement in compressor performance was mainly attributed to reduction in the area of the high relative total pressure loss in the blade tip passage and significant decrease in the flow loss by the self-circulating casings.

Collaborative Robust Design Optimization of Blade Geometry and Manufacturing Tolerance for a Transonic Centrifugal Impeller

Abstract Turbomachinery components are inevitably subjected to various sources of manufacturing errors. The resultant variations in blade geometry eventually lead to performance degradation. This is especially true for transonic centrifugal compressor impellers where the complex interaction between the geometric variations and shock waves may amplify such degradation. However, relevant studies on uncertainty quantification or robust design optimization of centrifugal impellers are quite rare. The mechanisms of how the realistic manufacturing errors influence the impeller aerodynamic performance are not clear. In addition, most existing studies have considered a fixed level of manufacturing tolerance applied to the impeller blade surface, which neglects the combined effect of blade geometry and manufacturing tolerance on impeller performance. In this study, a collaborative robust design optimization was performed for a transonic centrifugal impeller considering realistic manufacturing errors. The realistic manufacturing error field was first modeled based on the measurements of 92 centrifugal impellers. With a combination of computational fluid dynamics simulation and the non-intrusive polynomial chaos method, the influence of manufacturing errors on impeller performance and flow field variations was quantified. To save computational costs for the uncertainty quantification, a dual dimensionality reduction method was proposed to reduce the dimensionality of uncertainties. Finally, blade angles and the manufacturing tolerance of the impeller were collaboratively optimized to enhance the impeller performance robustness against manufacturing errors. The results show that the impeller aerodynamic performance exhibited a downward trend in the presence of manufacturing errors. The flow mechanisms responsible for this trend were mainly associated with increased intensity of the shock waves near the inducer blade tip. Such shock waves were significantly alleviated by reducing impeller inlet blade angles without the loss of pressure rise capability. Consequently, the impeller performance robustness against manufacturing errors was enhanced with the standard deviation of polytropic efficiency being reduced by 35% at a lower anticipated manufacturing cost due to increased tolerance allowance.

Mechanism Affecting the Performance and Stability of a Centrifugal Impeller by Changing Bleeding Positions of Self-Recirculating Casing Treatment

This study aimed to investigate the influence of the bleeding position of a self-circulating casing on the aerodynamic performance of a transonic centrifugal compressor. Three types of self-circulating structures with the bleeding positions of 11% Ca (the axial chord length of the blade tip), 14% Ca and 20% Ca from the leading edge of the blade were studied by using the numerical simulation method, with the Krain impeller taken as the research object. It was found that all three types of self-recirculating casing treatments can expand the stable operating range of the impeller, and that at medium and small flow rates, the total pressure ratio and efficiency of the impeller increase gradually with the backward movement of the bleeding position. The self-circulating casing treatment can restrain the development of tip leakage vortex, reduce the blockage area, and improve the stability of the impeller by sucking low-energy fluid. The farther back the bleeding position is, the greater the bleeding mass flow rate of the self-circulating casing for the low-energy fluid in the blade-tip passage becomes. Additionally, a greater inhibition effect on the tip leakage vortex, and a better effect of improving the performance and stability of the impeller, can be obtained. The best air bleeding position is 20% Ca, but it is not directly above the blade-tip blockage center of the solid wall casing passage. Instead, it is downstream of the blockage area.

Performance Improvement of a Highly Loaded Transonic Centrifugal Compressor with Tandem Impeller and Freeform Blade Configuration

A highly loaded transonic centrifugal compressor is aerodynamically designed and numerically investigated. The objectives are to improve the compressor efficiency by using tandem impeller configuration and 3D free-formed blade design concepts. This approach has the potential to control both the transonic and distorted flows within impeller passages. The results suggest that employing the tandem impeller configuration can significantly improve the compressor efficiency by 1.4%. The efficiency gain is mainly contributed by the improved uniformity of the impeller discharge flow achieved when the newly generated inducer-shed vortices rearrange the secondary flow pattern. In addition, the location of the impeller passage shock moves downstream due to the potential effect within the tandem impeller and locally changes the back pressure of the inducer. These factors mitigate flow losses in the impeller and diffuser. Furthermore, the 3D design concepts of forward blade sweep and negative lean are employed in the tandem impeller configuration. The forward sweep design of the inducer weakens flow acceleration before the passage shock, and the negative lean design optimizes the secondary flow pattern, which yield an additional compressor efficiency improvement of 0.7%. The study conducted in this paper provides a valuable reference for future advanced transonic centrifugal compressor designs.

Investigation of Surge in a Transonic Centrifugal Compressor With Vaned Diffuser—Part I: Surge Signature

Abstract The identification of stall inception mechanisms and stability-limiting components in a centrifugal compressor is required for the development of effective surge suppression approaches. Part I of this two-part paper investigates the surge signature of a centrifugal compressor at subsonic, transonic, and supersonic inlet tip conditions, and Part II considers the relationship of the surge signature with the compressor static pressure characteristics, as well as the impeller leading edge relative tip Mach number. Experiments were performed in the single stage centrifugal compressor (SSCC) facility at Purdue University with both steady performance and dynamic pressure data recorded. Results show the presence of both mild and deep surges on the compressor map. Deep surge occurs at subsonic and supersonic impeller tip relative Mach numbers while the mild surge is observed as the tip relative Mach number nears unity. Long length-scale modal oscillations can be detected only at the transonic operating condition while spike disturbances are identified as the precursor to instability at subsonic and supersonic tips relative Mach numbers. Finally, the impeller is determined to be the origin of instability throughout most of the compressor map. The observation of impeller-induced instability refreshes the conventional understanding that the diffuser is typically the stability-limiting component for centrifugal compressors with vaned diffusers and suggests various surge suppression approaches may be necessary to achieve range extension throughout a compressor map.

Investigation of Surge in a Transonic Centrifugal Compressor With Vaned Diffuser: Part II—Correlation With Subcomponent Characteristics

AbstractIn the first part of the paper, surge signatures and the underlying mechanisms thereof for a high-speed centrifugal compressor were investigated using signals from fast-response transducers installed along the flow path. The compressor surge signature is observed to vary as the impeller inlet tip flow transitions from subsonic to supersonic conditions. Spike-type deep surge is observed at subsonic and supersonic impeller inlet tip conditions while modal-type mild surge occurs at 90% speed with transonic inlet tip conditions. In Part II of the paper, a detailed analysis of the static pressure rise characteristics at the stage, component, and subcomponent levels is conducted. Additionally, the influence of the impeller inlet conditions on the instability is also considered. A connection between the surge mechanism and component static pressure rise characteristics is shown which exhibits the potential for prediction of the stall inception mechanism including identification of the destabilizing component. Furthermore, the transition from subsonic to transonic impeller inlet conditions is shown to be the cause of the unique mild surge instability at 90% speed. Lastly, both experimental and computational results are utilized to investigate the development of a shock wave at the impeller leading edge. The shock is considered to be critical to stage stability at speeds where the compressor experiences transonic inlet conditions.

Investigation on flow mechanism of an advanced transonic centrifugal compressor with free-form impeller at design and off-design speeds

A transonic centrifugal compressor with a ruled-impeller (that is, impeller blades are generated by a set of points swept by a moving straight line) was used as the baseline, and the impeller blades were redesigned using non-ruled surfaces (referred to as the ‘free-form impeller’) in this study to reveal the potential of this design approach to improve the performance of high-pressure-ratio centrifugal compressors. By using the method of Computational Fluid Dynamics (CFD) simulation, the performance characteristic and the flow field inside the impeller and diffuser of the baseline compressor and the free-form one were comparatively analyzed in detail. The results show that the free-form impeller design can improve the performance of the compressor in many aspects no matter at design or off-design speeds. The barreled-sweep inducer can reduce the losses from the shock wave at design speed and extend the compressor stable operating range at off-design speeds. The positive compound-lean impeller blades can suppress the reverse flow at impeller outlet. The flow downstream of the free-form impeller was also improved due to a more uniform outlet flow field provided by it at. This study aims to provide a valuable reference for applying free-form design methods to future advanced centrifugal compressors.

Stability improvement without efficiency penalty of a transonic centrifugal compressor by casing treatment and impeller/diffuser coupling optimization

Self-recirculation casing treatment (SRCT) is usually used to improve the flow stability of centrifugal compressors, while extra aerodynamic losses are often introduced. It is challenging to remove the efficiency penalty for the design of SRCT. In this study, a coupling optimization is implemented to redesign a transonic centrifugal compressor with an SRCT. Firstly, the physical design space is expanded to include the design parameters of both the SRCT and the impeller/diffuser. Secondly, data-mining techniques are used to explore and refine the expanded design space. Consequently, seven critical design parameters are quantitatively identified, and they generally present non-linear and trade-off correlations with the compressor performances. Then, the global optimization is carried out for the refined design space. As a result, significant improvements of the aerodynamic performances of the compressor are obtained. The efficiency penalty introduced by the SRCT is eliminated, and the stable flow range is maintained simultaneously. This is infeasible for the single redesign of the SRCT or the impeller/diffuser. The flow mechanisms of the coupling optimization are as follows. The recirculation flow rate of the SRCT is increased, and more low-energy fluid near the shroud is removed. The incidence angle and the leading-edge blade loading at high spanwise region of the impeller are reduced. The interaction between the tip leakage vortex and the inducer shock wave is delayed and weakened. The inlet mixing loss and the inlet radial distortion of the impeller are decreased. The friction loss is reduced and the flow separation is suppressed in the vaned diffuser.

Control of Inner Flow Field Inside A Transonic Centrifugal Compressor with Splitter Through Chordwise Sweep

The strategy of sweep design should be based on the inner flow field of the compressor. In this paper, a transonic centrifugal compressor within the splitter is discussed in detail, and both forward sweep and backward sweep are studied with numerical simulation for optimization. Splitter introduces extra leakage and it’s worth noting that the high-entropy region is shifted from the suction side of the main blade to the suction side of the splitter. Different from the transonic axial rotor, the leakage of the main blade mainly occurs after the passage shock and will be mixed with the leakage of the splitter in the suction side of the splitter. Therefore, the flow control on the middle and rare part of the compressor is more essential for the performance of the stage. In this regard, the backward sweep of the main blade exhibits a good effect by reducing the mixing loss of secondary leakage. Due to the redistribution of the airflow, the mainstream velocity in the tip area is accelerated in the forepart and reduced in the rare part, the aerodynamic loss in the high-entropy zone is then improved, and the flow capacity of the compressor is also increased. The best performance is achieved by an 8° backward sweep for the centrifugal compressor in this work, the pressure ratio is increased by 2.84% and isentropic efficiency is increased by 1.40%, compared to the prototype.

Impact of the inducer meridional length on the tandem impeller performance within a transonic centrifugal compressor

Tandem impeller configuration has the potential to improve the performance of highly loaded transonic centrifugal compressors, while the related research is still in the early stages and general design guidelines, such as the selection of inducer meridional length, are limited so far. In this paper, a highly loaded transonic centrifugal compressor with various tandem impeller configurations is numerically investigated. The objective is to evaluate the impact of inducer meridional length [Formula: see text] on the tandem impeller flow structure and performance, and further to look into the underlying flow mechanisms and design principles of the tandem impeller. The results indicate that the inducer meridional length [Formula: see text] has significant effect on the tandem impeller and compressor stage performance. There exits an optimized tandem impeller [Formula: see text] value of Appr. 38% that achieves a compressor stage pressure ratio and efficiency gain (at the P.E. points) of 2.6% and 1.8%, respectively, and deviating from the optimized [Formula: see text] value will lead to deteriorated compressor performance. In terms of the impeller performance, the inducer trailing edge determined by the inducer meridional length [Formula: see text] should be located downstream of the passage shock to reduce the shock and inducer wake losses. However, the inducer blade should also be placed in the impeller axial part to avoid the exudcer incidence angle deviation. In terms of the diffuser performance which is partly determined by the impeller discharge flow uniformity, the inducer meridional length [Formula: see text] directly affects the tandem impeller discharge flow uniformity by rearranging and controlling the secondary flow patterns, and the flow uniformity is prone to be insensitive to the [Formula: see text] variation when the [Formula: see text] value is large enough (i.e. ≥30%). Additionally, the [Formula: see text] value should be large enough (i.e. ≥20%) to generate intense inducer shedding vortexes, which can suppress the development of Coriolis vortex and finally improve the impeller flow uniformity.

Effect of blade squealer tips on aerodynamic performance and stall margin in a transonic centrifugal compressor with vaned diffuser

In order to enhance the aerodynamic performance of a centrifugal compressor with a vaned diffuser while also improving its stall margin, squealer tip cavities were applied to the tips of the impeller blades. Computational analysis was carried out by solving the compressible three-dimensional Reynolds-averaged Navier-Stokes equations. The numerical approach was validated by comparing the results from the flat tip reference case with experimental measurements. Various squealer tips with different cavity depths were applied to both the main and splitter blades and were numerically tested to investigate the influence of cavity depth on the performance and stall margin of the compressor. The results show that squealer tips with a proper cavity depth were effective in enhancing compressor efficiency by 0.32% at the design point, in addition, they were able to improve the stall margin by 1.02%. It was found that the squealer tips reduce tip leakage flow and circumferential velocity near the impeller shroud compared to using flat tips due to the generation of vortical structure within the cavity, which blocks leakage flow in a similar way to labyrinth seals. However, it was observed that by increasing the cavity depth, the size of this vortex becomes larger and the entropy production is increased inside the cavity. Moreover, it was found that the proper cavity depth decreases the mixing tip loss by about 4% compared to flat tips, this plays an important role in the stall margin improvement.

Experimental and Numerical Investigation of Clearance Effects in a Transonic Centrifugal Compressor

Extensive research studying tip clearance effects on compressor performance has been conducted during the past few decades with significant progress achieved. However, most of the previous investigations focus on stage-level analysis at the design condition, with very limited studies at the component level or part speed conditions. To fill this gap, this paper investigates the effects of impeller tip clearance on the performance of a high-speed centrifugal compressor, at both stage and component levels, covering a variety of operating speeds resulting in subsonic to transonic inlet conditions. Experiments were conducted on the Single Stage Centrifugal Compressor facility at two different running tip clearances. With increased clearance, the stage and impeller pressure ratio, isentropic efficiency, and work factor drop, but the static pressure recovery coefficient in the diffuser increases. As the compressor transitions from subsonic to transonic operation from 60 to 85% corrected speed, the sensitivities of stage and impeller pressure ratio and efficiency reach their peak values. Lastly, numerical simulations at design speed showed that the computational fluid dynamics (CFD) model sufficiently predicts the sensitivities due to tip clearance for most of the parameters at the stage and component levels, indicating the potential of using CFD to investigate the flow physics.

Redesign of casing treatment for a transonic centrifugal compressor based on a hybrid global optimization method

As a typical black-box problem, recirculating casing treatment (RCT) optimization of compressor stages is computationally intensive and time consuming, even though surrogate models are usually employed. In order to improve efficiency and robustness of the optimization, an expected-improvement (EI) based hybrid global optimization (EHGO) algorithm is developed by coupling an EI-based surrogate model with a hybrid optimization algorithm. Highly nonlinear and multiple modality mathematical tests show that the EHGO algorithm is able to create a high-fidelity surrogate model near targeted regions with less evaluated samples, and to obtain the global optimal solution simultaneously. The RCT of a compressor stage is optimized based on this algorithm. The number of CFD simulations required for obtaining an optimum solution is greatly reduced, as compared to similar studies using conventional methods. The optimization results show that the aerodynamic performance is improved over the whole speed line and the flow range is also extended. The dominant factors for the performance improvements and the enhanced stall margin are addressed by analyzing the local flow characteristics before and after optimization. It is found that those factors include: removing a larger amount of low-momentum fluid, achieving a more uniform flow of impeller passage in circumferential direction, and reducing the radial distortion of impeller inlet flow. The proposed algorithm has the potential to considerably speed up the optimization process and make the optimization much more accessible. It can be generalized to deal with other computationally intensive black-box problems, for example, turbomachinery optimization.

Numerical investigation of the diffuser throat length effect on a transonic centrifugal compressor

Vaned diffuser inlet flow uniform is challenging when the impeller is throttled to stall. In this study, we extend the stable operating range of the compressor by improving the uniform flow of the diffuser inlet. First, a numerical investigation of a transonic centrifugal compressor with a vaned diffuser is presented and compared against test data. Then, a new diffuser parameterization method is pro- posed, and the throat feature of a pipe diffuser is successfully applied to parameterized vane diffusers. The influence of the throat length and divergence angle of the diffuser on the performance of the centrifugal compressor is studied via steady and non-linear harmonic simulations. Throat length delays the time of fluid pressurization and accommodates large flow instabilities from upstream—this widens the stall margin but increases mixing loss. Divergence angle affects compressor performance. Stage peak efficiency increases by about 0.58% as the divergence angle increases from 3.79° to 5.79° but drops to about 2.46% as the divergence angle further increases from 5.79° to 11.79°. This is because the boundary layers in the diffuser channel thicken with increasing divergence angle; additionally, the fluid near the hub-pressure side first becomes unstable, then flow separation occurs along the flow direction, which results in a large flow loss. Detailed performance maps of centrifugal compressors with different throat lengths and divergence angles are given to provide a reference for designing transonic centrifugal compressors.

Numerical Investigation of Rotating Stall Characteristics in a Full-Annulus Transonic Centrifugal Compressor

The present paper numerically investigates the rotating stall mechanism in the NASA CC3 transonic centrifugal compressor with wedge-type vaned diffuser. The three-dimensional compressible, unsteady Navier–Stokes equations have been applied to a full-annulus high-speed centrifugal compressor comprising an inlet duct, impeller, and vaned diffuser. The scale-adaptive simulation model is selected as the turbulent closure model. The aim of this paper is to predict and capture the key features of rotating stall in a transonic high-pressure centrifugal compressor based on the scale-adaptive simulation approach. First, the steady numerical model was validated by the experiment for the aerodynamic compressor performance at different operating conditions from choke to surge. Then, unsteady simulations were conducted near the surge point to propose a detailed analysis of stall characteristics within the compressor diffuser passages. Comparison of the unsteady pressure signals with those of the measurement data revealed that the numerical results matched well with the experimental data to capture the rotating speed of the stall cells. Time/space analysis of transient entropy production distribution was performed within the diffuser passages to show the stall behavior and to confirm the existence and development of rotating stall cells during the impeller revolutions. Evaluation of the spectral analysis of the computed pressure fluctuation by the current numerical approach showed reasonable agreement with the experimental data for blade passing and rotating stall frequencies. The present paper demonstrates that the current numerical model is a beneficial engineering approach to provide accurate solutions compared to experimental data for prediction of the rotating stall as well as to resolve the unsteady turbulence structures.

Aerodynamic analysis of the small-scaled centrifugal compressor for micro-turbojet engine applications

This paper presents the results of an aerodynamic analysis of a small-scaled transonic centrifugal compressor for micro turbojet engine (TJE) applications. The analysis was conducted using a CFD model validated by experimental data collected for the gaged JetCat P200-RX micro-TJE. The loss coefficients of the impeller, vaned diffuser and deswirler were estimated for 4 design points corresponding to 70%, 80%, 90% and 100% rotation speeds to perform the loss balance diagram. The flow angle spanwise variation demonstrated an intensive flow separation zone at the top 25% of the vaned diffuser span due to the pressure shock appearance. It was shown that the main source of the losses in the investigated compressor is the deswirler due to non-optimal flow turning conditions. The diffuser loss coefficient was estimated as 0.18 at the compressor full load.

Transient Analysis of Flow Unsteadiness and Noise Characteristics in a Centrifugal Compressor with a Novel Vaned Diffuser

The demands to apply transonic centrifugal compressor have increased in the advanced gas turbine engines. Various techniques are used to increase the aerodynamic performance of the centrifugal compressor. The effects of the inclined leading edges in diffuser vanes of a transonic centrifugal compressor on the flow-field unsteadiness and noise generation are investigated by solving the compressible, three-dimensional, transient Navier–Stokes equations. Diffuser vanes with various inclination angles of the leading edge from shroud-to-hub and hub-to-shroud are numerically modeled. The results show that the hub-to-shroud inclined leading edge improves the compressor performance (2.6%), and the proper inclination angle is effective to increase the stall margin (3.88%). In addition, in this study, the transient pressure variations and radiated noise prediction at the design operating point of the compressor are emphasized. The influences of the inclined leading edges on the pressure waves were captured in time/space domain with different convective velocities. The pressure fluctuation spectra are calculated to investigate the tonal blade passing frequency (BPF) noise, and it is shown that the applied inclination angles in the diffuser blades are effective, not only to improve the aerodynamic performance and stall margin, but also to reduce the BPF noise (7.6 dB sound pressure level reduction). Moreover, it is found that the diffuser vanes with inclination angles could suppress the separation regions and eddy structures inside the passages of the diffuser, which results in reduction of the overall sound pressure level and the broadband noise radiated from the compressor.

Numerical study of the influence of high-transonic outlet blade angle of the Wedge diffuser with airfoil characteristics on the performance centrifugal compressor

In this paper, a transonic centrifugal compressor is investigated, and a design method of a wedge diffuser with airfoil characteristics is proposed. The effect of different outlet blade angles of the wedge diffuser with airfoil characteristics on the performance of the compressor was studied using a validated numerical calculation method. The results show that the use of a wedge diffuser with airfoil characteristics can more suitable for the transonic flow, which greatly reduces the flow loss of the diffuser pressure surface due to the inconsistent incidence. In addition, without changing the shape of the prototype compressor, the compressor performance is best when the outlet blade angle is 20 ~ 22 °. Compared with the prototype compressor, its peak efficiency increased by 0.93%, the pressure ratio increased by 0.517%, and the stable working margin increased by 4.2%.