Analysis of a Stretched Derivative Aircraft with Open Rotor Propulsion

nd 22 International Symposium on Airbreathing Engines ISABE2015 - 22081 25 - 30 October 2015, Phoenix, Arizona

Analysis of a Stretched Derivative Aircraft

with Open Rotor Propulsion

Jeffrey J. Berton, Eric S. Hendricks and William J. Haller NASA Glenn Research Center, Cleveland, Ohio 44135 and Mark D. Guynn NASA Langley Research Center, Hampton, Virginia 23681 Research into advanced, high-speed civil turboprops received significant attention during the 1970s and 1980s when fuel efficiency was the driving focus of U.S. aeronautical research. But when fuel prices declined sharply there was no longer sufficient motivation to continue maturing the technology. Recent volatility in fuel prices and increasing concern for aviation’s environmental impact, however, have renewed interest in unducted, open rotor propulsion and revived research by NASA and a number of engine manufacturers. Recently, NASA and General Electric have teamed to conduct several investigations into the performance and noise of an advanced, single-aisle transport with open rotor propulsion. The results of these initial studies indicate open rotor engines have the potential to provide significant reduction in fuel consumption compared to aircraft using turbofan engines with equivalent core technology. In addition, noise analysis of the concept indicates that an open rotor aircraft in the single-aisle transport class would be able to meet current noise regulations with margin. The behavior of derivative open rotor transports is of interest. Heavier, “stretched” derivative aircraft tend to be noisier than their lighter relatives. Of particular importance to the business case for the concept is how the noise margin changes relative to regulatory limits within a family of similar open rotor aircraft. The subject of this report is a performance and noise assessment of a notional, heavier, stretched derivative airplane equipped with throttle-push variants of NASA’s initial open rotor engine design.

single-aisle airplane jointly-studied by NASA and I. Introduction General Electric is currently projected to enjoy a Chapter 4 cumulative margin of nearly 17EPNdB (Refs.

luctuating fuel prices and concerns over carbon 1, 2). Moreover, the open rotor transport is predicted to

emissions are spurring research into advanced, F

burn 36% less block fuel than a 1998 technology energy-efficient propulsion concepts for transport reference vehicle equipped with turbofans (Ref. 1 ).

aircraft. As a result, rekindled attention is being given to Although this is an exciting and promising result, open rotor propulsion systems. Once hailed as an these noise margin predictions require further study. Of innovative response to the sharp increases in aviation particular importance is the behavior of community fuel cost beginning in 1973, interest in open rotors noise within a family of similar aircraft. Certification waned in the face of falling oil prices starting in 1986.

noise levels tend to increase when a propulsion system Current energy concerns are reviving development undergoes a “throttle push” thrust increase and is efforts into open rotor propulsors (alternately known as coupled with a heavier derivative aircraft in the same advanced turboprops, propfans, or unducted fans).

family. If heavier, derivative open rotor transports do Counter-rotating open rotor propulsion systems – not have similarly comfortable noise margins, it may with highly-swept, contoured, wide-chord rotor blades – become difficult to develop a compelling economic combine the fuel efficiency of traditional turboprops argument for the concept.

with the high cruising airspeed of turbofan engines.

The subject of this report is a performance and noise Without inlet and bypass exhaust ducts, however, a examination of a throttle-pushed open rotor engine disadvantage of the open rotor relative to ducted variant coupled with a heavier derivative aircraft turbofans appears to be higher levels of community carrying additional payload. This assessment builds on noise. Despite this handicap, a notional open rotor earlier NASA open rotor transport studies documented analytically flown along a trajectory and propagated to in References 1 , 3, 4, and 5. noise certification monitors on the ground using NASA’s Aircra ft Noise Prediction Program (ANOPP, Refs. 9, 10).

II. Method of Analysis For brevity, the reader is referred to our earlier A. Engine design and operating considerations reports for more detailed information. Our most recent An engine must deliver sufficient thrust to satisfy an results using General Electric’s “Generation 2” rotor airplane’s performance requirements throughout its design can be found in Ref. 1 . Details regarding the flight envelope. It is sometimes feasible to design an engine thermodynamic cycle analysis, aeromechanical eng ine cycle that precisely matches the airplane’s thrust design, flowpath and weight analysis of the open rotor demand at altitude, at sea level, and at other flight powerplant, as well as the vehicle and noise analyses, conditions in between. Turbomachinery design can be found in Ref. 3 . Briefly, however, the propulsion variables, operating temperatures, pressures and system is modeled at NASA using the Numerical airflows may be selected so that the engine delivers Propulsion System Simulation code (Refs. 6, 7). NPSS required thrust levels at multiple design points.

is an engine cycle analysis tool developed jointly by NASA and U.S. industry. It is currently the accepted, Fore & aft state-of-the-art software for airbreathing engine cycle rotors performance analysis for U.S. aerospace industry, Nozzle academia, and NASA. Rotor performance is represented in the NPSS model via thrust coefficient and power coefficient propeller maps. These maps are based on Power turbine wind tunnel performance tests (conducted in NASA Glenn’s 9- by 15-ft and 8- by 6-ft wind tunnels) of Low - & high - General Electric’s advanced, Generation 2 open rotor pressure test articles (Ref. 8).

compressors Aeromechanical design, flowpath, and engine weight analyses are performed using additional elements coded within NPSS. NPSS provides a Low- & high- complete modeling capability of gas turbine engines. A pressure summary of NASA’s open rotor engine characteristics turbines is shown in Table 1 . A solid model of the open rotor propulsion system is shown in Figure 1 .

Figure 1. Solid model of NASA ’s notional open rotor propulsion system.

Table 1. NASA open rotor engine summary (reproduced from Ref. 1 ).

Front rotor diameter , ft 13.5 Thrust (Sea level, static, ISA+27 ° F) , lb 27810 Specific fuel consumption (M0.78/35kft/ISA), lb/hr/lb 0.415 Overall pressure ratio (M0.78/35kft/ISA) 42 Maximum combustor exit temperature, °R 3460 Total engine pod weight, lb 9365 NASA’s notional, advanced single-aisle transport airframe model accommodates 162 passengers in mixed-class seating. It is equipped with open rotor engines mounted on the rear of the fuselage. Vehicle sizing and mission performance are assessed using the methods described in Refs. 1 and 3 . A solid model of the airplane is shown in Figure 2 .

Certification noise predictions are made using noise measurements of the Generation 2 open rotor test articles collected in the NASA 9- by 15-ft Low Speed Wind Tunnel. A more detailed explanation of how these noise measurements are processed, scaled to full size, Figure 2. NASA’s notional, advanced single-aisle and projected to flight conditions is described in our transport equipped with fuselage-mounted open earlier reports. The open rotor noise sources (as well as rotor engines.

other propulsion and airframe noise sources) are 2 of 8 2015 International Symposium on Airbreathing Engines But often, practical considerations make this push options emerge, and each is investigated in this approach impossible. An attempt was made to design study: NASA’s open rotor propulsion system (Ref. 1 ) to B. Throttle push option 1 exactly match the airplane’s thrust demand at the end of In this scenario, the open rotor engine is required to its takeoff ground roll and at the top of its climb path.

overspeed at altitude. The maximum low-pressure spool The turbine temperatures at altitude required to match speed limit is allowed to increase by five percent. The these targets were discovered to be excessively hot.

engine is not overtemped near sea level. This results in Indeed, for engines with very low specific thrust (such more thrust at altitude, but the thrust near sea level is as an open rotor or a turboprop engine), it is possible for unchanged. Since the derivative airplane is heavier, the turbine temperatures at altitude to be uncomfortably most important consequences of this approach are close to the maximum temperatures used at takeoff. The longer takeoff field lengths and climbout rates. But field burner temperature in the final design was reduced over lengths for open rotor-powered transports are already concerns for hot section life. The result of this decision shorter than comparable turbofan-powered transports, so is an engine that satisfies airplane climb requirements, an increase in field length may be acceptable. Further, if but has more than enough thrust available for takeoff.

overtemping the open rotor cycle is unnecessary, its hot- Thus, unlike most turbofan airplanes, an open rotor section life characteristics would not worsen.

airplane would likely be constrained by performance requirements at top-of-climb, not by field length or by C. Throttle push option 2 other takeoff or landing considerations near sea level.

This option is similar to how a conventional Much like a turboprop airplane, there is typically plenty turbofan manufacturer might approach the problem. The of thrust available at takeoff to meet any reasonable open rotor engine is allowed to overspeed at altitude and field length requirement. An open rotor engine would to overtemp near sea level. A five percent increase in perhaps be sized by the airplane’s potential rate of climb the maximum low-pressure spool speed and a 50°F at its service ceiling for a maximum gross weight increase in the maximum combustor exit temperature mission. In our assessments, our open rotor airplanes are are assumed. This option results in more thrust required to have a minimum potential climb rate of everywhere. With the increased temperature, there 300ft/min at the 35kft initial cruise altitude.

would be an impact on hot-section life and engine The open rotor propulsion system developed in maintenance. But this option may be necessary only if Ref. 1 is subjected to a “throttle push . ” A throttle push the airplane becomes too heavy and the takeoff field is a change made to an engine that provides the length grows too much.

additional thrust required for a heavier derivative airplane. In this study, the changes made to the engine III. Results and Discussion are operational only – there is no redesign of any engine The higher maximum spool speed limit used in both component relative to its original configuration. The throttle push options results in additional thrust at original engine cycle design is assumed to have altitude. This additional top-of-climb thrust may be sufficient margins built into it to accommodate any new exploited and used to design a heavier derivative operational changes.

transport with a useful increase in maximum gross The engine cycle operation is constrained by hot- weight and payload weight.

section temperature limits near sea level, and by spool A. Derivative airplane design speed limits at altitude. The active constraint changes from the former to the latter at some point during the There is no clear convention for designing a derivative aircraft type. Passenger airline operators have climb from takeoff to cruising altitude. An engine throttle push may be achieved by relaxing the maximum route structures requiring equipment capable of flying hot section temperature constraint (i.e., “ overtemping ”) variable payload weights, fuel loads, seats, and ranges.

near sea level and/or by relaxing the maximum As such, airframe manufacturers build derivative types to try to satisfy a variety of customer needs. Insight into rotational rates of the spools (i.e., “ overspeeding ”) at altitude. The former approach results in more thrust at derivative type design can be gained from examining evolutionary trends within the 737NG transport series.

takeoff, while the latter results in more thrust at altitude.

For a heavier derivative open rotor airplane, extra Maximum gross weight, maximum payload weight, thrust should always be necessary at altitude to maintain number of seats, fuel capacity and range vary across the service ceiling performance and the initial cruise 737-600, -700, -800 and -900 family. In most cases, the maximum payload weight increases as the number of altitude requirement. However, given the open rotor engine’s excellent low -speed thrust performance, extra seats increase. Also, the range capability at the design payload weight tends to decrease as the number of seats thrust may not be needed for takeoff unless the field length requirement grows too much. Thus, two throttle increases. Another observation is that the maximum fuel capacity does not change from model to model.

3 of 8 2015 International Symposium on Airbreathing Engines There are no definitive rules for designing a A comparison of the original transport and its stretched derivative, but our process must begin derivatives is shown in Table 2 . The derivatives, with somewhere. One prerequisite is to determine roughly 20 additional passengers, are more than ten thousand how many additional rows of seats can be added to the pounds (eight percent) heavier in maximum gross derivative open rotor transport given the increase in weight than the original type. By the measure of thrust at the top of climb condition. When additional available seat miles per unit fuel burned, the derivatives seat rows are added (with five seats abreast at 200lb per are approximately five percent more efficient than the passenger), the payload weight increases by 1000lb per original type at maximum gross weight and maximum row. The following steps are taken: 1) passengers are payload.

added one row (i.e., five passengers) at a time and the fuselage is analytically stretched; 2) the additional Derivative fuselage weight, system weights and drag are computed; and 3) the takeoff gross weight is estimated. For each Original row of passengers added, a new service ceiling thrust requirement is computed. The process is repeated – one row of passengers at a time – until the service ceiling thrust required exceeds the engine thrust available.

In the end, our notional derivative transport is Payload, 1000lb assigned an additional four rows with an increase in payload weight of 4000lb. The original interior provides for 162 passengers in mixed-class, 4/5 abreast seating 0 1000 2000 3000 4000 5000 (12 seats on 36-inch pitch, 14 seats on 32-inch pitch, Range, nm and 132 seats on 31-inch pitch). The derivative interior Figure 4. Payload-range diagrams of the original and provides for 182 passengers with 152 seats on 31-inch pitch. Sketches of the interior arrangements of the derivative transports.

original and the stretched derivative are shown in Figure Table 2. Original and derivative type comparison.

3 . The additional four rows of seats are colored in red.

Original Option 1 Option 2 Passengers 162 1 8 2 1 8 2 Max payload wt, lb 46,640 50,640 50,640 Sea level static thrust, lb 30,310 30,310 31,330 Operating empty wt, lb 91,260 97,460 97,460 Max gross wt, lb 161,080 171,300 171,300 Takeoff f ield length, ft 6200 7310 6800 Climb rate (35kft), ft/min 300 416 416 Figure 3. Sketches of original (top) and derivative For the derivative with throttle push option 1 (where (bottom) interior arrangements. the engines are not overtemped and the thrust near sea level is unchanged), the FAA Part 25 takeoff field With this information in hand, the following steps length (standard day plus 27°F at sea level) increases are used to more rigorously design the heavier from 6200ft to 7310ft. This 1110ft increase in takeoff derivative open rotor transport: field length is, however, smaller than penalties 1) The maximum payload weight and the design experienced by other stretched derivatives, such as the payload weight are increased by 4000lb.

2800ft takeoff field length increase for the 737-900ER 2) The maximum fuel capacity remains constant.

compared to the 737-800 (Ref. 11). Overtemping the 3) The maximum gross weight is determined by a engine (via throttle push option 2) mitigates the increase sizing process (Ref. 3 ) while ensuring at least a in field length. But given the open rotor engine’s 4000lb increase in the available payload weight excellent low-speed thrust performance, overtemping for the maximum fuel, maximum gross weight the engine may not always be necessary.

mission.

The open rotor engines for the original transport are The wing design is unchanged during this process.

sized by an initial cruise altitude capability for a mission Analysis tools and assumptions described in our earlier beginning at maximum gross weight. This is determined reports are used. The resulting payload-range diagrams requiring a service ceiling defined by a minimum of the original and derivative transports are shown in potential climb rate of 300ft/min at M=0.78 and 35kft.

Figure 4 . The result of this approach is that the For the derivative types using engine overspeed, the differences between the payload-range curves of the potential rates of climb are better than the original. This derivative and original transports are similar to changes in the curves within the 737NG family.

4 of 8 2015 International Symposium on Airbreathing Engines suggests that a throttle push using less spool 2.5 overspeeding may be possible.

Original B. Takeoff and approach analysis: 2.0 Derivative, Option 1 Airplane trajectories and engine operating Derivative, Option 2 conditions have an important influence on certification 1.5 noise. The two derivatives are heavier than the original airplane. And the overtemped engine (using throttle 1.0 push option 2) has additional thrust available near sea level. The result is that all three airplane types behave differently during takeoff and approach. The trajectories 0.5 Altitude, 1000 ft AFE and engine throttle setting histories for each airplane are evaluated using the assumptions and methods discussed 0.0 in Ref. 3 and abide by FAA Part 36 regulations.

-10 -5 0 5 10 15 20 25 Trajectory data evaluated for a sea level field at 77°F are shown in Figure 5 . Altitude above field elevation, true airspeed, and true thrust per engine are plotted against the distance from brake release. The trajectories are shown with takeoff and landing operations superimposed. For presentation purposes, the touchdown point on landing is coincident with the point of brake release on takeoff. The noise abatement engine power cutback is completed at approximately 17,000ft True Airspeed, ktas from brake release. On approach, a three-degree glide slope is followed, the maximum landing weight is assumed, and the flaps, leading edge slats and landing -10 -5 0 5 10 15 20 25 gear are deployed. The engine thrust is set to a level that maintains a stable three degree glide slope.

The triangular markers on each plot denote noise certification measurement locations. A sketch of the noise monitor arrangement relative to the takeoff and landing flight paths is shown in Figure 6 . The approach microphone markers are shown in the figures at 6562ft behind the runway threshold, and approximately 7518ft behind the instrument landing system touchdown zone on the runway centerline. The monitor is located under the point of the approach path where the airplane is Approach Lateral Flyover 394ft above ground level. The lateral microphone True Thrust per Engine, 1000 lb locations lie along a sideline parallel to the runway -10 -5 0 5 10 15 20 25 displaced 1476ft from the extended runway centerline.

Distance from Brake Release, 1000 ft They are arranged along the sideline across from the locations where the airplanes reach an altitude of 1000ft Figure 5. Comparison of altitude, airspeed and above the field elevation (i.e., the point where ground thrust per engine during takeoff and approach.

attenuation effects diminish and where maximum lateral Table 3. Original and derivative trajectory noise is typically observed). The flyover microphone information at noise monitor locations.

markers are shown in the figures at 21,325ft from brake Original Option 1 Option 2 release on the extended runway centerline. Airspeed, Approach : altitude and thrust per engine for the three airplane types Airspeed, ktas 139 144 144 at each noise monitor are shown in Table 3 .

Altitude, ft 394 394 394 Thrust per engine, lb 5926 6359 6359 C. Noise analysis: Lateral : The following observations are made from the Airspeed, ktas 178 183 183 trajectory assessment above. Each effect is responsible Altitude, ft 1000 1000 1000 Thrust per engine, lb 18,940 18,720 19,600 for changes in noise relative to the original type: Flyover : 1) The heavier derivative airplanes do not reach Airspeed, ktas 181 185 185 altitude as quickly as the original type.

Altitude. f t 2030 1710 1860 Thrust per engine, lb 11,960 12,740 12,730 5 of 8 2015 International Symposium on Airbreathing Engines 2) The heavier derivatives require additional from concept to product) has some inherent, unknown airspeed before rotating. Since thrust lapses error. An analysis of this uncertainty is beyond the naturally with airspeed, the engine thrust for the scope of this report.

derivative with throttle push option 1 is less than Results indicate the derivative transport with engine the original type, despite having identical engine overtemping and overspeeding (option 2) has a higher performance in general near sea level. lateral EPNL than the original transport, given its higher 3) The derivative with overtemped engines (throttle maximum thrust. But the derivative with engine push option 2) has the highest maximum thrust. overspeeding only (option 1) has a higher flyover 4) The heavier derivatives cannot reduce engine EPNL, owing to its lower flyover altitude. These effects thrust as much as the original type during noise tend to be offsetting. Thus, certification noise levels on abatement cutbacks. This is a result of minimum a cumulative basis are nearly identical for both throttle climb gradients required by FAA Part 36 push options. There does not seem to be a preference for regulations. either engine throttle push strategy, at least in terms of 5) The derivatives, with heavier maximum landing the cumulative noise margin.

weights, require slightly more thrust and have The open rotor noise results are shown graphically higher airspeed on approach. in Figure 7 . Also plotted in the Figure are all 737NGs equipped with CFM56-7B27 series turbofans. As of Approach March 2014, 1044 of these types have been issued noise monitor certificates. These particular 737s are of interest since they are all derivative types with variable passenger Lateral counts and/or freight capabilities, maximum gross 6562ft reference weights and ranges, and they would compete in the same market as our open rotor transports. Further, they 1476ft are all equipped with the CFM56-7B27, which delivers 21325ft the same thrust performance to all of the derivative Lateral reference types. Thus, the trends of noise with maximum takeoff gross weight of these 737s should be well-suited to compare with our original open rotor transport and its Flyover monitor option 1 derivative. The option 2 derivative is not plotted since its thrust near sea level is higher than the Figure 6. Noise certification monitor arrangement original type and it would not be consistent with the 737 relative to takeoff and landing flight paths.

data shown.

Regression lines are shown for each transport Table 4. Original and derivative EPNLs with family. The cumulative noise levels for the subset of cumulative margins relative to Chapter 4 and 737 data are found to vary with a slope of 52 times the Chapter 14 limits (in EPNdB).

logarithm of the maximum takeoff gross weight. By Original Option 1 Option 2 way of comparison, ICAO has estimated the slope to be Approach 89.5 89.9 89.9 67, on average, across all aircraft and turbofan engine Lateral 90.1 89.9 90.9 families (Ref. 12).

Flyover 82.2 84.4 83.7 Cumulative 261.8 264.2 264.5 Of particular interest is the slope of flyover noise Ch 4 cumulative margin 16.8 15.2 14.9 relative to gross weight. The flyover noise of open rotor Ch 14 cumulative margin 9.8 8.2 7.9 transports appears to increase with increasing weight more quickly than the noise of the selected 737s. Open Effective Perceived Noise Levels (EPNLs) are rotor engine thrust lapses more quickly with airspeed calculated using the methods and tools discussed in our than comparable turbofans. It may be that open rotor earlier reports. The trajectories and engine thrust levels transport families are not able to fly as high over, nor of the new derivative transports result in noise changes able to cut back thrust as deeply at the flyover noise relative to the original type. The results and cumulative monitor point as a comparable family of turbofan margins relative to current Chapter 4 and future Chapter transports. On a cumulative basis, the open rotor 14 limits are shown in Table 4 . Chapter 14 limits for transports are found to vary with a slope of 91. In a this aircraft size are expected to debut on December 31, comparison made by ICAO (Ref. 12 ), the slope of open 2017. Although these EPNLs are computed using the rotor transports was estimated to be 74, based on a study best available data and analytical methods, they should conducted by Airbus and using our own, earlier results.

be regarded with some skepticism. Projecting acoustic The slope of the regulatory limits with gross weight measurements from a subscale open rotor test article to has further implications. Chapter 3 noise limits are flight conditions at full-scale (and further projections plotted in the Figure for each of the three noise 6 of 8 2015 International Symposium on Airbreathing Engines measurement locations. The Chapter 4 cumulative limit maintenance requirements for throttle-pushed open rotor for twin-engine transports is plotted along with the systems could be similar to the original engine type.

cumulative noise data. The flyover, approach and Further, there appears to be no preference for either cumulative noise margins of open rotor transports of our throttle-push methods insofar as cumulative noise appear to erode more quickly with increasing gross margin is concerned. A derivative equipped with weight than comparable turbofan-powered transports. engines using option 1 results in higher flyover noise The slopes with respect to maximum gross weight of the than the original type, while a derivative with engines open rotor and 737 transports relative to the limits are using option 2 results in higher lateral noise. The labeled in the Figure. resulting cumulative noise margins for the derivatives are nearly identical.

Last, these calculations indicate that the noise IV. Conclusions margins of a family of open rotor transports may erode Two approaches for throttle-pushing a notional open more quickly with increasing takeoff gross weight than rotor engine are described. In one, the maximum takeoff margins of comparable families of turbofan transports.

combustor temperature is kept the same as the original The more aggressive Chapter 14 limit may constrain engine type (option 1), while in the other it is increased growth versions of open rotor transports, particularly if to provide additional thrust near sea level (option 2). In our open rotor noise levels are underpredicted or if very both, the maximum spool speed limit is increased to large derivatives are desired.

provide more thrust at altitude. The throttle-pushed engines are used to analytically design stretched- Acknowledgements derivative transports that are larger and heavier than the open rotor transport described in our earlier reports. T hanks to NASA’s Advanced Air Transport Overtemping the engine (via throttle push option 2) Technology Project for supporting this study.

mitigates increases in takeoff field length incurred by heavier transports. But given the open rotor engine’s excellent low-speed thrust performance, field lengths are nevertheless shorter than many comparably-heavy 737s. Overtemping an open rotor engine to obtain additional thrust for takeoff may not always be necessary. In that case, engine hot section life and 7 of 8 2015 International Symposium on Airbreathing Engines 94 100 737/CFM56-7B27 data 737/CFM56-7B27 data 92 Open rotor transport predictions Open rotor transport predictions Chapter 3 flyover limit, twins Chapter 3 lateral limit 13.3log MTOW 8.5log MTOW 10 10 86 94 - 11log MTOW 55log MTOW - 8log MTOW Lateral EPNL, EPNdB 85log MTOW Flyover EPNL, EPNdB 10 90 78 88 290 104 737/CFM56-7B27 data 737/CFM56-7B27 data Open rotor transport predictions Open rotor transport predictions 102 Chapter 3 approach limit Chapter 4 cumulative limit, twins 7.7log MTOW 29.5log MTOW 98 275 96 270 8log MTOW 91log MTOW 52log MTOW 15log MTOW Approach EPNL, EPNdB Cumulative EPNL, EPNdB 90 260 88 200 200 120 120 Maximum Takeoff Gross Weight, 1000lb Maximum Takeoff Gross Weight, 1000lb Figure 7. Dependency of noise on maximum gross weight: certification noise predictions of original open rotor transport and a derivative equipped with engines using throttle push option 1, compared with all 737NGs equipped with CFM56-7B27 series turbofans.

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