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Optimization of an HP steam turbinestage for a wide flow coefficient rangeBY JURI BELLUCCI, FILIPPO RUBECHINI, ANDREA ARNONE / DEPARTMENT OFENERGY ENGINEERING UNIVERSITY OF FLORENCEVINCENZO DOSSENA / DEPARTMENT OF ENERGY POLITECNIC OF MILANLORENZO ARCANGELI, NICOLA MACELI / TURBOMACHINERY, GE OIL & GAS

Proceedings of ASME Turbo Expo 2012 GT2012 June 11-15, 2012, Copenhagen, Denmark

AbstractThe overall optimization strategy of a high pressure steam turbine stage relies on a neural network-based approach aimed at maximizing the stage efficiency, while at the same time, increasing thestage loading. The stage under investigation is composed of prismatic blades, usually employed in arepeating stage environment and in a wide range of operating conditions.

For this reason, two different optimizations are carried out at high and low flow coefficients. Theoptimized geometries are chosen taking into account aerodynamic constraints such as limitation ofthe pressure recovery in the uncovered part of the suction side as well as mechanical constraintssuch as root tensile stress and dynamic behavior. As a result, an optimum airfoil is selected and itsperformance is characterized over the whole range of operating conditions. Parallel to thenumerical activity, both optimized and original geometries were tested in a linear cascade, andexperimental results are available for comparison purposes in terms of loading distributions andloss coefficients. Comparisons between measurements and calculations are presented and

discussed for a number of incidence angles and expansion ratios.

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NomenclatureA Area

AR Aspect Ratio = H/C

c Absolute velocity

C Chord

DR Diffusion Rate =

h Enthalpy

H Blade height

J Principal moment of inertia

M Mach number

N Rotational speed

p Pressure

PR Pressure Ratio = p01/ps2

R Radius

RR Radius Ratio = Rtip/Rhub

S Curvilinear abscissa

u Blade speed

Greek:a Blade-to-blade flow angle

Dh Efficiency variation

h Stage total-to-total efficiency

f Flow coefficient = cax/u

y Work coefficient = Dh0/u2

z Enthalpy loss coefficient

Subscripts:0 Total

1 Inlet section

2 Outlet section

ax Axial direction

is Isentropic

max Maximum

min Minimum

s Static

TE Trailing edge

IntroductionSteam turbines are used in a wide range of applications, from mechanical drive applications, e.g., driving compressors andpumps, to power generation application, e.g., driving a generator for electric power production. The steam turbines used inthese segments must have high efficiency and reliability and, at the same time, their design must remain extremely flexible tomeet the operating conditions of the plant and customer requirements.

When looking for opportunities for efficiency improvement, it is important to consider that the efficiency of the overall steamturbine can be split into three main contributions: 20% is due to the control stage, 40% is due to the LP section and 40% is dueto the intermediate pressure stages.

The available literature covers a large number of topics, from blade redesign to leakage control (Havakechian and Greim [1]and Yoon et al. [2]). As far as blade redesign is concerned, efforts have focused in the past years on the development of newLP sections, where the height of the last stage bucket has increased over the years to up to 54 inches to reduce exhaust losses(J. D. Denton and A. Spurr [3], Yoshinori et al. [4]). Recently, renewed interest in intermediate pressure stages has resulted in aconsiderable number of activities. Different approaches have been followed to improve the efficiency: Maughan et al. [5]increased the degree of reaction, the aspect ratio, and reduced the stage load; Mindok et al. [6] and Segawa et al. [7]improved the profile robustness to incidence and also contoured the nozzle endwall.

In some cases, a performance improvement was obtained by just improving the airfoil shape of prismatic blades (Sakai et al.[8]), while in others, by replacing the prismatic blades with twisted blades and also applying bowing and leaning(Schaarschmidt et al. [9]).

As for the drum stages, in the large steam turbine market, great effort has been made to increase the efficiency of steamturbines, leading to variable reaction stages (Simon et al. [10]) and stages with a hybrid architecture (Littlewood et al. [11]). Inthe IPG segment, the efficiency of steam turbines can be maximized when the drum stage reaction is close to 50%, due to thelow volume flow range (Cotroneo et al. [12]).

Nowadays, many optimization techniques are applied to redesign the aerodynamic components of turbomachines. Industrialinterests push for continuous improvement of these tools towards automatic and effective procedures for aerodynamic andmechanical design. The emphasis is justified by the capability of optimization algorithms to exploit the great amount ofinformation provided by numerical simulations and correlate them to the geometrical parameters in order to find optimalcombinations.

Moreover, an important characteristic of these tools is their versatility, which allows them to be used for differentturbomachinery applications. Bonaiuti et al. [13] used the design of experiments technique to optimize a transonic centrifugalcompressor and extract important information on the influence of some of the geometrical parameters on the globalperformance. Bonaiuti and Zangeneh [14] coupled an inverse design and evolutionary algorithms to redesign a centrifugaland an axial compressor stage, confirming the validity of such a design strategy for a three-dimensional optimization. Moseret al. [15] used an evolutionary algorithm to optimize a steam turbine control stage, studying the impact of flowpath profilingon pressure loss in a wide range of pressure ratios. Rubechini et al. [16] used a neural-network-based approach to redesign a17-stage steam turbine. This paper deals with the optimization of a high pressure (HP) steam turbine stage for small steamturbines. The stage investigated is composed of prismatic blades, usually employed in both high and medium pressure steamturbines. This type of blading is characterized by a high aspect ratio (AR) and low radius ratio (RR). It is designed to work in arepeating stage environment and in a wide range of operating conditions, using a single airfoil geometry for stator and rotorrows.

Acronyms:CFD Computational Fluid Dynamics

HP High Pressure

IPG Industrial Power Generation

LP Low Pressure

RBF Radial Basis Function network

The optimization strategy is aimed at maximizing the stage efficiency under stringent constraints of stage loading and bladecount in order to ensure manufacturability. The overall strategy relied on a well proven neural-network-based approach,using CFD RANS calculations, coupled with a mechanical integrity check to ensure the same mechanical capability for theoptimized geometry as for the original one.

Parallel to the numerical activity, an experimental campaign was conducted in which both the original and the optimizedblades were tested in linear cascade configurations.

In the following sections, a detailed description of the optimization procedure will be provided. Moreover, the characteristicsof the new geometries will be compared to the original ones and discussed in light of the experimental measurements.

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This paper was prepared for presentation at the ASME TURBO EXPO 2012 held in Copenhagen, Denmark, 11-15 June 2012

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Figure 1Camber line optimization parameters

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Numerical Tools

RANS solverThe CFD results shown in this paper were obtained using the multi-row, multi-block version of the TRAF code (Arnone [17, 18]). In this flow solver, the unsteady, three-dimensional, Reynolds averaged Navier-Stokes equations are written in conservative form in a curvilinear, body fitted coordinate system and solved for density, absolutemomentum components and total energy. The spatial discretization of the equations is based on a finite volume cell-centered scheme.

A blended second and fourth order artificial dissipation model (Jameson et al. [19], Swanson and Turkel [20]), together with eigenvalue scaling, is used in order to minimizethe amount of artificial diffusion inside the shear layers. The equations are advanced in time using an explicit four-stage Runge-Kutta scheme. In order to speed upconvergence to the steady state solution, implicit residual smoothing, local time stepping, multi-grid full approximation storage (FAS) and grid refinement are employed.Several turbulence closures are available, ranging from simple algebraic models to advanced multi-equation models [21, 22, 23, 24]. In the present work, a two equations k-w turbulence model was used throughout all optimization runs.

Optimization strategyIn the present work, an approach similar to that proposed by Pierret and Van den Braembussche [25] was adopted, which consists of coupling CFD analyses with a neuralnetwork-based method.

The first action consists of the geometrical parameterization. The blade geometry was described using a parameterization based on Bzier curves. The use of such aparametric curve to describe the airfoil and the spanwise distributions of all airfoil parameters makes the parameterization powerful and versatile. This is a key aspect forthe optimization process, because it allows any shape of interest to be reproduced with sufficient accuracy, and ensures good airfoil shapes when moving a limited numberof parameters.

The selection of the parameters subjected to optimization, together with their range of variation, defines the design space. Then, the design space is populated using a lowdiscrepancy sequence (e.g., Latin hypercube, Sobols sequence, hypersphere, etc.), and the corresponding geometries are calculated. In this way the design space is mostuniformly sampled with respect to a simple random sequence, thus ensuring better training of the networks.

For each objective function and constraint, a response surface is generated using a radial basis function network (RBF). This type of meta-model is a well-known approach tofit a wide class of functions (Mazzetti [26], Cichocki and Unbehauen [27]), and is suitable for optimization problems where the number of degrees of freedom is low. Itrepresents a good trade-off between gradient methods (e.g., steepest descent, conjugate gradient) and exploratory techniques (e.g., genetic algorithm, simulated annealing),because it is able to resolve problems where the design space is not convex and continuous, and the drawback of using an approximated function is balanced by the reducednumber of calculations required. The network used in this work is a feed-forward type. A moving-K-mean clustering algorithm was employed to train the RBFs centers whilethe second layer of weights was trained with a least-square algorithm (Bishop [28], Mashor [29]).

Finally, the optimum set suggested by the net is verified by CFD calculations and a solution is chosen by the designer. It is worth noting that the optimum geometries typicallydescribe a Pareto front when plotted against the different objective functions; hence, the choice of the final optimum solution is not unique and always implies somearbitrariness from the designer.

Airfoil optimizationThe present optimization is aimed at maximizing the turbines power output and efficiency, while meeting themanufacturability constraints for the number of stages and the blade count of each stage.

During the optimization process several constraints of a different nature were imposed in order to meet the presentdesign rules. First of all, the mass flow rate was held constant to obtain the required stage loading increase withoutchanging the operating point when replacing the original stage with the optimized one.

Moreover, for the blade loading distribution over the airfoil surface and especially on the rear part of the suction side,limitation of the diffusion rate was imposed to avoid boundary layer separation. As far as the mechanical integrityissues are concerned, both the static and the dynamic behaviors of each geometry were checked downstream of theCFD analysis.

Accounting for structural limitations is essential for final design purposes, since it may guide the designer in choosing agiven solution from several aerodynamic optima by eliminating those geometries that do not meet structuralrequirements. In the present optimization, the mechanical integrity checks relied on simplified design rules based onthe evaluation of the root tensile stress and minimum inertia moment-to-area ratio (Jmin/A), ensuring the samemechanical capability for the optimized geometry as the original one.

In the first optimization step, a realistic geometry of the meridional flowpath was chosen, representative of an embedded stage of an existing HP/IP package. Bearing inmind that the optimized airfoil should operate in a wide range of flow coefficients, as does the original one, two different optimizations were carried out, assuming boundaryconditions representative of low and high flow coefficient operating conditions. To do this, two design points were identified, characterized by different mass flow rates andexpansion ratios. Following this strategy, the whole range of operating conditions of interest was covered by two optimized airfoils: the first working in the low-to-mid flowcoefficient range and the second working in the mid-to-high range.

A single airfoil for stator and rotor rows was used, according to the original design strategy. Such an assumption, together with that of prismatic blades, limited theparameters subjected to optimization to those of a single airfoil section, thus dramatically reducing the number of degrees of freedom of the redesign problem. As aconsequence, the stage geometry was handled by varying only nine parameters in all, which control the camber line (Figure 1) and thickness distribution over the airfoil forboth stator and rotor rows simultaneously, and maintaining the trailing edge thickness constant.

Once the range of variation of the input parameters was specified, that is, once the design space was defined, the training data set for the RBFs was created by calculatingeach geometry by means of a 3D CFD stage run. In order to account for the repeating environment experienced by the stage within the actual turbine, suitable repeatingboundary conditions were adopted, aimed at obtaining prescribed pressure and temperature drops while ensuring the same spanwise profiles at the stage inlet and outlet.

Figure 2Example of an optimization cloud

Figure 3Experimental test section scheme and an example of acascade

An example of an optimization cloud is shown in Figure 2, where the stage efficiency is plotted against the mechanicalconstraints. The dashed lines represent the limiting values of these constraints, and therefore, the solutions in the bottomright part have a structural capability that meets the mechanical design rule.

The results of the optimizations, in terms of performance curves over a wide range of operating conditions, andcomparison with the experimental measurements will be presented and discussed later in this paper.

Experimental facilityThe experimental investigation was performed in the blowdown facility for linear cascades located at the LFM(Laboratorio di Fluidodinamica delle Macchine) in Milan. This is a transonic wind tunnel with a test section of 80x470mm, fed by 6000 kg of pressurized air stocked at 20 MPa (Dossena et al. [30, 31]), as depicted in Figure 3. For thepresent research, cascades were composed of 9 blades and the central passage was outfitted with 36 pressuretaps of 0.4 mm diameter, 20 located on the suction side and 16 on the pressure side. Flow field measurements wereperformed by traversing a miniaturized five-hole probe with a head diameter of 1.8 mm on a plane located 0.5 axialchords downstream from the trailing edge: the measurement plane is defined by a grid of 50 points (equally spacedapproximately every 2 mm along two blade pitches) repeated 10 times at different spanwise positions on one half ofthe blade height. The probe was calibrated in the range of 25 degrees and 16 degrees in yaw and pitch anglerespectively, and for Mach numbers ranging from 0.2 to 1.0.

The estimated probe accuracy for static and total pressure is 0.3% of the dynamic pressure and 0.2 degrees for theflow angle measurement. A prismatic 3-hole probe was used for continuous monitoring of the inlet total pressure.In order to provide proper CFD inlet boundary conditions, a miniaturized, flattened total pressure probe wastraversed in the upstream boundary layer for all flow conditions considered. The inlet freestream turbulenceintensity was estimated as 1% by means of hot wire anemometer measurements.

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Figure 4Efficiency comparison: original and optimized geometricsperformance curve (CFD)

Figure 5Work coefficient comparison: original and optimizedgeometrics performance curve (CFD)

Figure 6Comparison between original and OPT performancecurve at different stagger angles (CFD)

Flow path 1 Flow path 2 Flow path 3

/ 1.00 1.50 2.15

N/N 1.00 2.33 1.00

AR/AR 1.00 0.55 1.10

RR/RR 1.00 1.22 1.10

Table 1Flow paths characteristics

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ResultsTwo different optimizations, performed at both high and low flow coefficient conditions, were carried out to achieve the optimization targets. As a result, two differentoptimum airfoils were identified. Each one of these airfoils, hereafter referred to as OPT-A (for low ) and OPT-B (for high ) respectively, were tested in off-designconditions by varying the stage pressure drop in order to draw a performance curve in the range of interest, thus providing two optimum curves at low and high flowcoefficient conditions. Two equivalent curves were obtained by setting the original airfoil at two different stagger angles in order to cover the same flow coefficient range. Inaddition, both optimized airfoils were re-staggered to cover the whole operating range: the OPT-A one was opened and tested at high flow coefficient, whereas the OPT-Bone was closed to fit the low region.

Figure 4 shows the comparison between the efficiency curves of the original airfoil and those of the optimized airfoils. The efficiency gain obtained from the optimizations, interms of peak-to-peak from the original geometry, is about 0.5% for the OPT-A airfoil (low ), and 1.25% for the OPT-B one (high ). The new geometries exhibit anoperating range similar to that of the original and maintain an elevated efficiency gain in off-design conditions. It is worth noting that the position of the peak efficiencyundergoes a shift towards the low flow coefficients for the optimized geometries.

This is due to a different position of the new airfoils in the chart, shown in Figure 5, associated with the blade loading increase required as the optimization target.

Figure 4 also shows how similar the OPT-A performance is to the re-staggered version of the OPT-B, closed to fit the same working line, and the same holds truewhen comparing the OPT-B geometry to the opened version of the OPT-A one. In both cases, the benefits of using the native optimized airfoil instead of the re-staggeredone seem quite small, with a peak-to-peak of about 0.03%. This important result, due to the fact that the mechanical constraints were independent of the operatingconditions, thus driving the two optimizations towards similar airfoil shapes with different stagger angles, suggested the possibility of using a single optimized airfoil.Besides a negligible decrease in performance, the overall design process also greatly benefits from the ease of managing a single airfoil. In light of these considerations andobserving that most of the existing stages are actually designed to work at low flow coefficients, the OPT-A was selected to cover, by re-staggering, the entire operatingrange. A complete characterization of such an airfoil (which hereafter will be referred to as the OPT airfoil) was carried out at different stagger angles, as shown in Figure 6.

Compared to the original design, the OPT geometry is thinner, has a higher nominal stagger angle (by about 8degrees) and a smaller radius of curvature in the rear part of the suction side (Figure 7). The large leading edgeexhibited by both airfoils ensures good mechanical capability and robustness with respect to incidence angle, asrequired to function over a wide operating range. The reduction of thickness, limited by structural constraints, hasplayed an important role in increasing the efficiency, in fact the optimization pushed towards the reduction of thethickness-to-chord ratio. The combination of the other two new features, higher stagger and smaller radius ofcurvature, was used to increase the stage loading. Moreover, the small radius of curvature allows the blade loadingto be moved towards the uncovered part of the suction surface, thus producing a more aft-loaded distribution(Figure 8) and increasing the diffusion rate (about 10%).

Figure 8 also shows the more uniform isentropic Mach distribution of the OPT airfoil. This is due to detailed controlof the pressure and suction surface curvature, and to the asymmetric thickness distribution in the leading edgeregion that produced a smooth acceleration on the pressure side.

In order to assess the benefits of the optimized airfoil in different machine layouts than the one used for theoptimization, three different stage configurations were extracted from existing turbines. These three cases arecharacterized by different meridional flow-path (AR, RR), rotational speed, expansion ratio, flow coefficient andblade count (see Table 1).

For each layout, the original and the OPT designs were investigated in design and off-design conditions by means ofCFD stage computations.

The results are shown in Figure 9, which reports the performance curves of the original and OPT geometries.

In all three cases, the optimized airfoil demonstrated an efficiency gain greater than 1%, depending on the case, andexhibited an off-design behavior comparable to the original one in terms of operating range extension.

Parallel to the numerical activity, an experimental campaign was conducted in which both the original and the OPTairfoils were tested in a linear cascade arrangement. The geometry of the airfoils were scaled up in order to obtainthe best compromise between Reynolds number (based on chord and exit velocity) and cascade aspect ratio (about AR

= 1:4). The experimental results are available in terms of surface loading distributions and enthalpy loss coefficients, defined by:

ref

ref

ref

ref

Figure 7Comparison of airfoil geometries

Figure 8Isentropic Mach number distribution at same operatingcondition: comparison of original and OPT (CFD)

Figure 9Performance curve for three different real machinelayouts: comparison of original and OPT (CFD)

Figure 10Experimental and computational enthalpy losscoefficient span distribution; original airfoil, M = 0.47and zero incidence case

Figure 11Experimental and computational blade-to-blade exitangle span distribution; original airfoil, M = 0.47 andzero incidence case

The aerodynamic measurements were performed at three different expansion ratios (PR) for Mach numbers ranging from 0.25 to 0.64. Due to the test rig layout, Reynoldsand Mach numbers cannot be controlled independently, so the corresponding Reynolds numbers range from 3.5x10 to 9.5x10 . For each pressure ratio, three differentincidence angles were also tested in the broad range from -30 to +20 degrees.

Although the experimental campaign was mainly focused on the characterization of the mid-span airfoil section, the measurements were performed at ten spanwisepositions over one half of the blade height. This allowed the comparison between measurements and CFD not only in terms of 2D results at mid-span (profile losses, velocitydistributions), but also in terms of spanwise distributions of flow angle and loss coefficient. To do this, CFD calculations were carried out over the 3D cascade geometry, byimposing the measured boundary conditions (inlet profiles, outlet static pressure profile) in order to reproduce as accurately as possible the experimental operatingconditions. Because of the low turbulence intensity and relatively low Reynolds numbers, transitional conditions are likely to be found within the test rig. For this reason,calculations were performed using a low-Reynolds formulation of the two-equation k- model.

The results of these computations, in terms of spanwisedistributions of loss coefficient and blade-to-blade exit flow angle,are shown in Figures 10 and 11. The comparison is quiteencouraging, showing a substantial agreement between the testrig environment and the computational one. This good agreementis confirmed by looking at the surface pressure distributions atmid-span reported in Figures 12 and 13 for both the original andthe optimized geometries.

The main goal of the experimental activity was to confirm theperformance increase of the new OPT airfoil over the original onein terms of profile loss. Figures 14 to 16 report the predicted andmeasured lapse rates, at cascade midspan, for three differentincidence angles at Mach numbers varying from 0.25 to 0.64 (andReynolds numbers from 3.5x10 to 9.5x10 ).

As a first comment, it can be noticed that the measurementsconfirm, for any pressure ratio and incidence angle, thesuperiority of the OPT airfoil. A general agreement is observedbetween the measurements and predictions in terms of the shape

of the loss curves, which follow the theoretical trend of loss reduction with increasing Reynolds number. Moreover, the loss level is also fairly well predicted, the maximumerror between computations and measurements being lower than 0.3%.

More specifically, some appreciable differences arise for the highest Mach (and hence, Reynolds) number cases, especially at off-design incidences. At any incidence, thecomputations predict the same loss-decreasing trend for both the original and the OPT airfoils, whereas the measurements highlight a different tendency between the twoairfoils. In particular, for the OPT airfoil, at M = 0.64, the measured profile loss remains almost constant for the -30 negative incidence case, and rises slightly for the +20positive case. This behavior, which is limited to the highest Reynolds number, off-design incidence cases, is likely to be related to transitional issues: the OPT airfoil mightundergo an earlier transition, thus increasing the profile loss with respect to the CFD-predicted value. It should be remarked that, although the calculations were carried outusing a transition-sensitive turbulence model, many factors could prevent the complete reproduction of the transitional behavior within the actual cascade for allinvestigated configurations. Just to cite a few of these factors, we may address the inherent sensitivity of CFD-predicted transitional behavior to the turbulence modeling,the uncertainty affecting inlet turbulence characteristics (intensity, length scale) and the impact of the actual surface roughness on the onset of transition.

Whatever the reason for the small discrepancy between the predictions and measurements for the highest Reynolds numbers, the measurements confirm, in all cases, thesuperiority of the OPT airfoil over the original one. Furthermore, considering that in a real machine these airfoils deal with higher Reynolds numbers and turbulenceintensities, and that the benefits of the OPT airfoil increase the closer they get to fully turbulent conditions, even greater benefits would be reasonably expected in realturbine applications.

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5 5

5 5

2

is is

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Figure 12Experimental and computational pressure coefficientdistribution: original airfoil, zero incidence case

Figure 13Experimental and computational pressure coefficientdistribution: optimized airfoil, zero incidence case

Figure 14Experimental and numerical enthalpy losscoefficient: midspan values, zero incidence case

Figure 15Experimental and numercial enthalpy losscoefficient: midspan values, incidence +20 degreescase

Figure 16Experimental and numercial enthalpy losscoefficient: midspan values, incidence -30 degreescase

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Summary and conclusionsThis paper describes the aerodynamic optimization of a high pressure steam turbine stage.

The overall optimization strategy relies on a well-proven neural-network-based approach, aimed at maximizing the turbines power output and efficiency, while meeting themanufacturability constraints for the number of stages and the blade count of each stage.

The optimization activity was undertaken using CFD RANS calculations, coupled with mechanical integrity checks in order to ensure the same mechanical capability for boththe optimized and the original geometries. In particular, both the static and dynamic behaviors of each candidate geometry were checked downstream of each CFD analysisby means of simplified design rules based on the evaluation of root tensile stress and minimum inertia moment-to-area ratio.

In order to account for the repeating environment experienced by the stage within the actual turbine, suitable repeating boundary conditions were adopted, aimed atobtaining the prescribed pressure and temperature drops while ensuring the same spanwise profiles at the stage inlet and outlet.

Two different optimizations, at high and low flow coefficients, were carried out to reach the optimization targets over the whole range of operating conditions where thesetypes of stages are employed. As a result of the two optimizations, two different optimum airfoils were identified. Both airfoils were tested in off-design conditions byvarying the stage pressure drop in order to draw a performance curve in the range of interest, thus providing two optimum curves at low and high flow coefficientconditions.

The new geometries exhibited an operating range similar to that of the original, and maintained a good efficiency gain in off-design conditions.

Furthermore, both optimized airfoils were re-staggered to cover the whole flow coefficient range. The benefit of using the native optimized airfoil instead of the re-staggered one was quite small, suggesting that mechanical constraints have driven the two optimizations towards similar airfoil shapes with different stagger angles. As aresult, a single airfoil was selected to cover, by re-staggering, the entire operating range.

In order to assess the benefits of the optimized airfoil in machine layouts different from the one used for the optimization, three different stage configurations wereextracted from existing turbines. For each layout, the original and the OPT designs were investigated at design and off-design conditions, and in all cases the optimizedairfoil demonstrated an efficiency gain greater than 1% (depending on the case) and exhibited an off-design behavior comparable to that of the original one in terms ofoperating range extension. Parallel to the numerical activity, an experimental campaign was conducted in which both the original and the OPT airfoils were tested in a linearcascade configuration. The aerodynamic measurements were performed at three different expansion ratios (PR), for Mach numbers ranging from 0.25 to 0.64 and Reynoldsnumbers from 3.5x105 to 9.5x105. For each pressure ratio, a broad range of incidence angle was also investigated.

A general agreement was found between the measurements and predictions in terms of shape of the loss coefficient curves. Moreover, the loss level was also fairly wellpredicted, since the maximum error between the computations and measurements was lower than 0.3%. Although some discrepancies were highlighted and discussed, themeasurements confirmed, in all cases, the superiority of the OPT airfoil over the original one.

Acknowledgments

The present research was carried out in the framework of a joint activity involving both industry and university members.

The authors would like to gratefully acknowledge the contributions of the many people who provided numerous and fruitful discussions. The authors also thank GE Oil & Gas forpermission to publish this work.

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