JOURNAL OF AIRCRAFT Vol.45.No.1.January-February 2008 Simultaneous Airframe and Propulsion Cycle Optimization for Supersonic Aircraft Design Sriram K.Rallabhandi*and Dimitri N.Mavris Georgia Institute of Technology,Atlanta,Georgia 30332 D0L:10.2514/1.33183 Supersonic aircraft design includes several tradeoffs,each with advantages and disadvantages.The selection of aircraft shape to meet the prescribed requirements is a nontrivial exercise in the case of commercial supersonic configurations with multiple stringent constraints.The number of discrete shape options,along with the detailed aircraft shaping,presents a difficult choice to the configuration designer.Most often,the aircraft shape is frozen based on experience.In the case of revolutionary shapes or designs,such a choice would be suboptimal.Furthermore, unlike the subsonic designs,the propulsion cycle plays a much more important role than in the earlier stages of design in the case of supersonic configurations.This paper presents an approach for the simultaneous inclusion of airframe and propulsion system parameters in the aircraft design process.The proposed approach parameterizes the geometry in terms of several shape variables and the propulsion system in terms of representative cycle variables Advanced genetic algorithms are developed and employed to obtain aircraft configurations and propulsion cycle parameters that simultaneously optimize several critical performance metrics including range,sonic boom loudness, and jet velocity.Results from the optimization are presented and design tradeoffs are discussed. Nomenclature design methods are integrated to perform tradeoffs and analyze the 阳 goal value associated with the mth objective results.The choice of the optimizer rested on the requirements of the number of objectives supersonic aircraft design problem.As a result of an extensive nm normalization value associated with the mth literature search,the significant needs identified for potential objective supersonic design optimization methods are an 1)ability to handle T41 turbine rotor inlet temperature design spaces that have multiple local optima,2)ability to handle T4IMAX maximum turbine rotor inlet temperature mixed continuous/discrete spaces,and 3)adaptability to multi- T41SLS sea-level static turbine rotor inlet temperature objective optimization.Genetic algorithms (GAs)are the most 心e weight associated with the mth objective suitable methods to tackle all these issues simultaneously.The next section briefly presents the background for this work,and the sections after that describe the constituent elements of the design I.Introduction environment developed in this study.Finally,the optimization C UPERSONIC aircraft design has received renewed impetus in results are presented and discussed. the recent past due to advances in aircraft shaping and other technologies.Various market studies [1.2]have concluded that there exists a significant market for a commercial supersonic business jet. Ⅱ.Background Such an aircraft,if successful,would significantly reduce the trip The positive market analyses for commercial supersonic transport time and pave the way for larger supersonic transports in the future. have reignited the passion of many companies and research units to However,several bottlenecks,including regulatory ones,have to be overcome the significant technical challenges associated with the overcome before such a design becomes reality.Because of stringent design of such an aircraft.From the high-speed civil transport noise and performance requirements,commercial supersonic aircraft (HSCT)sonic boom propagation and acceptability studies [6,7], design is a challenging task.Several organizations and entities [3-5] people have realized that a small airframe such as a business jet is a have proposed potential designs that could meet the requirements to stepping stone to demonstrate the technological advances necessary various degrees.These designs are obtained after several manual to meet the stringent operational requirements.The recent success of iterations.Because of the revolutionary nature of these designs,the the Shaped Sonic Boom Demonstrator [8]for sonic boom reduction design methods that rely on historical data cannot be used. has provided renewed hope for a viable supersonic transport.In Accordingly,new advanced design methods and techniques are response to the Defense Advanced Research Projects Agency's needed that allow engineers to leverage physics-based analysis tools Quiet Supersonic Platform program [9],various airframe companies to complement their experience in making conceptual decisions in an have attempted to design small supersonic transports.This has appropriate and systematic manner. resulted in a slew of patents [3-5]filed by various aircraft This research effort aims at developing a comprehensive manufacturers.Some of these designs are given in Fig.1.As can be multidisciplinary design optimization method to perform physics- seen from this figure,the proposed designs vary significantly from based conceptual design of supersonic configurations.Several each other.No definite trend in the shape of the aircraft can be observed.Each design seems to have been based on experience, Received I July 2007:revision received 19 September 2007:accepted for iteration,and redesign of a selected baseline configuration,which is publication 13 October 2007.Copyright 2007 by Sriram K.Rallabhandi different in each case.The configurations range from double-delta and Dimitri N.Mavris.Published by the American Institute of Aeronautics wing,swing wing,or continuously changing sweep-wing planforms and Astronautics.Inc.,with permission.Copies of this paper may be made for to canard or inverted T-tail configurations.There is no unique personal or internal use,on condition that the copier pay the $10.00 per-copy solution to meet the design requirements.This raises the important fee to the Copyright Clearance Center,Inc..222 Rosewood Drive,Danvers. MA 01923:include the code 0021-8669/08 $10.00 in correspondence with question of how these configurations compare against each other the CCC. with respect to performance and design tradeoffs.To answer this *Research Engineer,Aerospace Systems Design Lab.Member AIAA. question and investigate a larger concept space,a matrix of possible Director and Boeing Professor of Advanced Aerospace Systems Analysis. alternatives for the placement and topology of components,as Aerospace Systems Design Lab.Associate Fellow AlAA. described in Table 1.is established.Apart from the discrete choices 38
Simultaneous Airframe and Propulsion Cycle Optimization for Supersonic Aircraft Design Sriram K. Rallabhandi∗ and Dimitri N. Mavris† Georgia Institute of Technology, Atlanta, Georgia 30332 DOI: 10.2514/1.33183 Supersonic aircraft design includes several tradeoffs, each with advantages and disadvantages. The selection of aircraft shape to meet the prescribed requirements is a nontrivial exercise in the case of commercial supersonic configurations with multiple stringent constraints. The number of discrete shape options, along with the detailed aircraft shaping, presents a difficult choice to the configuration designer. Most often, the aircraft shape is frozen, based on experience. In the case of revolutionary shapes or designs, such a choice would be suboptimal. Furthermore, unlike the subsonic designs, the propulsion cycle plays a much more important role than in the earlier stages of design in the case of supersonic configurations. This paper presents an approach for the simultaneous inclusion of airframe and propulsion system parameters in the aircraft design process. The proposed approach parameterizes the geometry in terms of several shape variables and the propulsion system in terms of representative cycle variables. Advanced genetic algorithms are developed and employed to obtain aircraft configurations and propulsion cycle parameters that simultaneously optimize several critical performance metrics including range, sonic boom loudness, and jet velocity. Results from the optimization are presented and design tradeoffs are discussed. Nomenclature gm = goal value associated with the mth objective M = number of objectives nm = normalization value associated with the mth objective T41 = turbine rotor inlet temperature T41MAX = maximum turbine rotor inlet temperature T41SLS = sea-level static turbine rotor inlet temperature wm = weight associated with the mth objective I. Introduction S UPERSONIC aircraft design has received renewed impetus in the recent past due to advances in aircraft shaping and other technologies. Various market studies [1,2] have concluded that there exists a significant market for a commercial supersonic business jet. Such an aircraft, if successful, would significantly reduce the trip time and pave the way for larger supersonic transports in the future. However, several bottlenecks, including regulatory ones, have to be overcome before such a design becomes reality. Because of stringent noise and performance requirements, commercial supersonic aircraft design is a challenging task. Several organizations and entities [3–5] have proposed potential designs that could meet the requirements to various degrees. These designs are obtained after several manual iterations. Because of the revolutionary nature of these designs, the design methods that rely on historical data cannot be used. Accordingly, new advanced design methods and techniques are needed that allow engineers to leverage physics-based analysis tools to complement their experience in making conceptual decisions in an appropriate and systematic manner. This research effort aims at developing a comprehensive multidisciplinary design optimization method to perform physicsbased conceptual design of supersonic configurations. Several design methods are integrated to perform tradeoffs and analyze the results. The choice of the optimizer rested on the requirements of the supersonic aircraft design problem. As a result of an extensive literature search, the significant needs identified for potential supersonic design optimization methods are an 1) ability to handle design spaces that have multiple local optima, 2) ability to handle mixed continuous/discrete spaces, and 3) adaptability to multiobjective optimization. Genetic algorithms (GAs) are the most suitable methods to tackle all these issues simultaneously. The next section briefly presents the background for this work, and the sections after that describe the constituent elements of the design environment developed in this study. Finally, the optimization results are presented and discussed. II. Background The positive market analyses for commercial supersonic transport have reignited the passion of many companies and research units to overcome the significant technical challenges associated with the design of such an aircraft. From the high-speed civil transport (HSCT) sonic boom propagation and acceptability studies [6,7], people have realized that a small airframe such as a business jet is a stepping stone to demonstrate the technological advances necessary to meet the stringent operational requirements. The recent success of the Shaped Sonic Boom Demonstrator [8] for sonic boom reduction has provided renewed hope for a viable supersonic transport. In response to the Defense Advanced Research Projects Agency’s Quiet Supersonic Platform program [9], various airframe companies have attempted to design small supersonic transports. This has resulted in a slew of patents [3–5] filed by various aircraft manufacturers. Some of these designs are given in Fig. 1. As can be seen from this figure, the proposed designs vary significantly from each other. No definite trend in the shape of the aircraft can be observed. Each design seems to have been based on experience, iteration, and redesign of a selected baseline configuration, which is different in each case. The configurations range from double-delta wing, swing wing, or continuously changing sweep-wing planforms to canard or inverted T-tail configurations. There is no unique solution to meet the design requirements. This raises the important question of how these configurations compare against each other with respect to performance and design tradeoffs. To answer this question and investigate a larger concept space, a matrix of possible alternatives for the placement and topology of components, as described in Table 1, is established. Apart from the discrete choices Received 1 July 2007; revision received 19 September 2007; accepted for publication 13 October 2007. Copyright © 2007 by Sriram K. Rallabhandi and Dimitri N. Mavris. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0021-8669/08 $10.00 in correspondence with the CCC. ∗Research Engineer, Aerospace Systems Design Lab. Member AIAA. † Director and Boeing Professor of Advanced Aerospace Systems Analysis, Aerospace Systems Design Lab. Associate Fellow AIAA. JOURNAL OF AIRCRAFT Vol. 45, No. 1, January–February 2008 38
RALLABHANDI AND MAVRIS 西 Raytheon Gulfstream Aerion Fig.1 Industry designs for commercial supersonic flight. available to the designer,the design space is also defined by a large creates a geometry-centric approach to aircraft design.The following number of continuous parameters,some of which are explicitly is a brief description of the different analysis modules used within the defined in the Appendix,governing vehicle geometry and other integrated simulation environment. variables.Some,such as cruise Mach number and vehicle gross weight,are common to all possible configurations.whereas other parameters,such as wing planform and kink locations.are A. Geometry Modeling and Parameterization component-and configuration-specific.Each configuration has a Efficient geometry representation is an important consideration in different number of variables defining the complete geometry. aircraft design.In this study,Vehicle Sketch Pad(VSP),an enhanced To obtain an overall optimal design,the engine and airframe are version of conceptual rapid geometry modeler [13].is used.Using optimized simultaneously.A GA has been developed that incorpor- VSP,the designer can quickly create various aircraft geometries by ates several operator enhancements,including two of NASA's tools: assigning or changing engineering parameters,thus facilitating a flight optimization system(FLOPS)[10]and numerical propulsion more thorough search of the vehicle concept space.VSP has many system simulation(NPSS)[11],and integrates several physics-based features that make it ideal for use in conceptual design.These include analysis tools to solve a multi-objective problem.The objectives quick creation of geometry models,a batch processing ability,the considered in this study are range,sonic boom shock pressure rise,jet ability to create watertight geometries,the ability to perform Mach velocity at takeoff,approach speed,sonic boom perceived-loudness slicing,and the ability to run any geometry-based external analysis level,cruise Mach number,gross weight,stability penalty,aircraft application. length,and fuselage diameter.Some of these objectives are included to obtain practical configurations and others represent the B.Propulsion System Modeling performance metrics.Figure 2 shows the integration of the individual analyses into aircraft sizing and performance calculation Engine-airframe integration is an extremely important aspect that is routinely ignored in conceptual studies.For every mission an (FLOPS).The developed environment also has the ability to allow aircraft might fly.there are certain configurations that would prove to expert input to evaluate the designs for difficult-to-quantify better suit the different situations that the aircraft will encounter objectives such as aesthetics and difficult-to-compute objectives Similar to the concept of the swing wing in the airframe,variable- such as aeroelasticity.However,these are not discussed in the current document for the sake of brevity.After the geometry is generated cycle engines (VCE)can be developed to actually change the thermodynamic cycle,giving the effect of swapping engines in using a combination of continuous and discrete parameters [12],the midflight.This enables each cycle to be optimized to its intended drag polars are generated using the aerodynamic tools and the engine flight condition,theoretically giving a better-performing engine for deck is generated using cycle parameters and NPSS models;both of these are discussed later.These are then fed to the sizing analysis to the multistaged mission.Although adding this capability is beneficial.it has several penalties associated with it.such as size. run the aircraft configuration through the mission to obtain other weight,complexity,stability,technological risk,and overall system objectives and responses. cost.Previous studies conducted by NASA [14]explored some of these effects to discover if the benefits outweigh the costs,and the findings led to the fixed-cycle mixed-flow turbo fan (MFTF)still IⅡ.Design Methods being the best choice.The present study reinvestigates this topic by During the past several years,researchers have developed various varying the aircraft and engine parameters simultaneously to tools capable of analyzing vehicle performance.However determine which airframe/propulsion combination is optimal.There multidisciplinary analysis has been a problem because there is no are three different engine configurations used in this study:MFTF standard format for inputs and outputs required for analysis (fixed-cycle),core-driven-fan stage (CDFS)VCE,and fan-on-blade integration.Considerable effort has been devoted in this study to (FLADE)VCE. assemble all the relevant disciplinary analysis tools into a single The MFTF has eight main components,as shown in Fig.3:inlet, environment capable of predicting vehicle performance and fan,bypass duct,high-pressure compressor (HPC),combustor,high- environmental impact with only one input representation.This pressure turbine (HPT),low-pressure turbine (LPT),mixer,and a Table 1 Matrix of configuration alternatives Planform type Double-delta Ogee Swing Blended Wing location Low Mid High Pitch control Horizontal tail Canard T-tail Tailless Engine cycle Mixed-flow turbo fan CDFS VCE FLADE VCE Power plant installation Under wing Fuselage-mounted Tail-mounted
available to the designer, the design space is also defined by a large number of continuous parameters, some of which are explicitly defined in the Appendix, governing vehicle geometry and other variables. Some, such as cruise Mach number and vehicle gross weight, are common to all possible configurations, whereas other parameters, such as wing planform and kink locations, are component- and configuration-specific. Each configuration has a different number of variables defining the complete geometry. To obtain an overall optimal design, the engine and airframe are optimized simultaneously. A GA has been developed that incorporates several operator enhancements, including two of NASA’s tools: flight optimization system (FLOPS) [10] and numerical propulsion system simulation (NPSS) [11], and integrates several physics-based analysis tools to solve a multi-objective problem. The objectives considered in this study are range, sonic boom shock pressure rise, jet velocity at takeoff, approach speed, sonic boom perceived-loudness level, cruise Mach number, gross weight, stability penalty, aircraft length, and fuselage diameter. Some of these objectives are included to obtain practical configurations and others represent the performance metrics. Figure 2 shows the integration of the individual analyses into aircraft sizing and performance calculation (FLOPS). The developed environment also has the ability to allow expert input to evaluate the designs for difficult-to-quantify objectives such as aesthetics and difficult-to-compute objectives such as aeroelasticity. However, these are not discussed in the current document for the sake of brevity. After the geometry is generated using a combination of continuous and discrete parameters [12], the drag polars are generated using the aerodynamic tools and the engine deck is generated using cycle parameters and NPSS models; both of these are discussed later. These are then fed to the sizing analysis to run the aircraft configuration through the mission to obtain other objectives and responses. III. Design Methods During the past several years, researchers have developed various tools capable of analyzing vehicle performance. However, multidisciplinary analysis has been a problem because there is no standard format for inputs and outputs required for analysis integration. Considerable effort has been devoted in this study to assemble all the relevant disciplinary analysis tools into a single environment capable of predicting vehicle performance and environmental impact with only one input representation. This creates a geometry-centric approach to aircraft design. The following is a brief description of the different analysis modules used within the integrated simulation environment. A. Geometry Modeling and Parameterization Efficient geometry representation is an important consideration in aircraft design. In this study, Vehicle Sketch Pad (VSP), an enhanced version of conceptual rapid geometry modeler [13], is used. Using VSP, the designer can quickly create various aircraft geometries by assigning or changing engineering parameters, thus facilitating a more thorough search of the vehicle concept space. VSP has many features that make it ideal for use in conceptual design. These include quick creation of geometry models, a batch processing ability, the ability to create watertight geometries, the ability to perform Mach slicing, and the ability to run any geometry-based external analysis application. B. Propulsion System Modeling Engine-airframe integration is an extremely important aspect that is routinely ignored in conceptual studies. For every mission an aircraft might fly, there are certain configurations that would prove to better suit the different situations that the aircraft will encounter. Similar to the concept of the swing wing in the airframe, variablecycle engines (VCE) can be developed to actually change the thermodynamic cycle, giving the effect of swapping engines in midflight. This enables each cycle to be optimized to its intended flight condition, theoretically giving a better-performing engine for the multistaged mission. Although adding this capability is beneficial, it has several penalties associated with it, such as size, weight, complexity, stability, technological risk, and overall system cost. Previous studies conducted by NASA [14] explored some of these effects to discover if the benefits outweigh the costs, and the findings led to the fixed-cycle mixed-flow turbo fan (MFTF) still being the best choice. The present study reinvestigates this topic by varying the aircraft and engine parameters simultaneously to determine which airframe/propulsion combination is optimal. There are three different engine configurations used in this study: MFTF (fixed-cycle), core-driven-fan stage (CDFS) VCE, and fan-on-blade (FLADE) VCE. The MFTF has eight main components, as shown in Fig. 3: inlet, fan, bypass duct, high-pressure compressor (HPC), combustor, highpressure turbine (HPT), low-pressure turbine (LPT), mixer, and a Fig. 1 Industry designs for commercial supersonic flight. Table 1 Matrix of configuration alternatives Planform type Double-delta Ogee Swing Blended Wing location Low Mid High Pitch control Horizontal tail Canard T-tail Tailless Engine cycle Mixed-flow turbo fan CDFS VCE FLADE VCE Power plant installation Under wing Fuselage-mounted Tail-mounted RALLABHANDI AND MAVRIS 39
40 RALLABHANDI AND MAVRIS Environment Stability&Control PBOOM(modyPCBOOM VORLAX/WINGDES/in house Propulsion Manufacturing NPSS/WATE ser assessed/optional Sizing and Performance Weights FLOPS FLOPS/WATE RSEs Aeroelasticity Geometry Aerodynamics VORLANBDAP/AWAVE Vehicle Sketch Pad AERO2S/INGDES Fig.2 Analyses setup. Inlet Fan HPC Burner Bypass HPT LPT Mixer Nozzle Bypass Inlet Fan Splitter HPC Bleed Bumer HPT LPT Mixer Nozzle *Indicates a pressure loss between components Fuel Fig.3 Mixed-flow turbofan schematic and model. variable nozzle.The component that defines the engine as mixed- (VABD).These can be seen in Fig.4.The CDFS VCE engine is flow is the mixer,which injects the bypass duct stream into the core intended to run in either a high (or double)bypass mode or a low (or flow after the turbines.Figure 3 also shows how the flow paths for single)bypass mode.In high bypass mode,the CDFS IGV is closed, this engine are modeled.The asterisk represents pressure loss which forces the passive door to open,creating an overall higher BPR between components in the propulsion model.This is one of the most and a lower specific fuel consumption(SFC)and exhaust velocity.In common engine configurations for modern military aircraft,and it is low bypass mode,the CDFS IGV is open,creating a supercharged also used in some commercial aircraft.The design bypass ratio How into the bypass duct and forcing the front door closed.This (BPR)of the engine depends on its intended use:supersonic designs essentially creates an extra fan stage;therefore,the fan pressure ratio tend to have a bypass ratio of less than 1,and subsonic designs (FPR)is increased and the BPR is decreased.This gives the engine usually have bypass ratios greater than 1.The same inlet was used for the capability to produce more thrust,but the SFC and nozzle all of the models.Each engine was sized for the supersonic thrust velocity both increase.The complicated flow path of this engine is requirement and then throttled down at takeoff to meet a 7000-ft also illustrated in Fig.4.The engine is intended to seamlessly switch takeoff-field length requirement.As aresult,mechanical suppression from high bypass mode to low bypass mode in midflight when the techniques to lower the takeoff noise signatures,such as a mixer- aircraft needs more thrust as it starts its transonic and supersonic ejector nozzle,were not used.However,jet-velocity response is journeys.The role of the VABI is the same as the mixer in the MFTF, minimized by the multi-objective genetic algorithm.The strong but in this case,a variable area is required due to the extreme changes correlation between the jet velocity and the takeoff helps the in the bypass properties between the two modes of operation. optimized configurations to proceed toward designs that meet the Fan-on-blade turbofan design has a fan that extends into an outer stringent noise goals. duct,called the FLADE duct,and sends a stream of air (only The core-driven-fan stage CDFS VCE receives its name from the compressed by the fan)through this duct to be accelerated through a extra fan stage that is powered by the HPT shaft.The components separate exhaust nozzle.A FLADE can be designed on different that make it different from the MFTF,as well as creating its variable- cores such as a turbojet,an MFTF,or even another VCE.A typical cycle capability,are the CDFS,the CDFS inlet guide vane (IGV),a configuration of a FLADE on an MFTF core (same as in Fig.3)is passive door,a bypass mixer,and a variable-area bypass injector shown in Fig.5.What gives this engine its variable-cycle Inlet Fan Passive Doo Bypass Mixer Bypass Duct VABI Nozzle CDFS IGVY CDFS HPC Burer HPT LPT Inlct Fan Splitter ®wDod®pWA國-Bs Spliter CDFS EIPC-BleedBurnerHPTLPTVABI-Buma-Blco间片Noa Fucl Fucl Fig.4 Core-driven-fan stage schematic and model
variable nozzle. The component that defines the engine as mixed- flow is the mixer, which injects the bypass duct stream into the core flow after the turbines. Figure 3 also shows how the flow paths for this engine are modeled. The asterisk represents pressure loss between components in the propulsion model. This is one of the most common engine configurations for modern military aircraft, and it is also used in some commercial aircraft. The design bypass ratio (BPR) of the engine depends on its intended use: supersonic designs tend to have a bypass ratio of less than 1, and subsonic designs usually have bypass ratios greater than 1. The same inlet was used for all of the models. Each engine was sized for the supersonic thrust requirement and then throttled down at takeoff to meet a 7000-ft takeoff-field length requirement. As a result, mechanical suppression techniques to lower the takeoff noise signatures, such as a mixerejector nozzle, were not used. However, jet-velocity response is minimized by the multi-objective genetic algorithm. The strong correlation between the jet velocity and the takeoff helps the optimized configurations to proceed toward designs that meet the stringent noise goals. The core-driven-fan stage CDFS VCE receives its name from the extra fan stage that is powered by the HPT shaft. The components that make it different from the MFTF, as well as creating its variablecycle capability, are the CDFS, the CDFS inlet guide vane (IGV), a passive door, a bypass mixer, and a variable-area bypass injector (VABI). These can be seen in Fig. 4. The CDFS VCE engine is intended to run in either a high (or double) bypass mode or a low (or single) bypass mode. In high bypass mode, the CDFS IGV is closed, which forces the passive door to open, creating an overall higher BPR and a lower specific fuel consumption (SFC) and exhaust velocity. In low bypass mode, the CDFS IGV is open, creating a supercharged flow into the bypass duct and forcing the front door closed. This essentially creates an extra fan stage; therefore, the fan pressure ratio (FPR) is increased and the BPR is decreased. This gives the engine the capability to produce more thrust, but the SFC and nozzle velocity both increase. The complicated flow path of this engine is also illustrated in Fig. 4. The engine is intended to seamlessly switch from high bypass mode to low bypass mode in midflight when the aircraft needs more thrust as it starts its transonic and supersonic journeys. The role of the VABI is the same as the mixer in the MFTF, but in this case, a variable area is required due to the extreme changes in the bypass properties between the two modes of operation. Fan-on-blade turbofan design has a fan that extends into an outer duct, called the FLADE duct, and sends a stream of air (only compressed by the fan) through this duct to be accelerated through a separate exhaust nozzle. A FLADE can be designed on different cores such as a turbojet, an MFTF, or even another VCE. A typical configuration of a FLADE on an MFTF core (same as in Fig. 3) is shown in Fig. 5. What gives this engine its variable-cycle PBOOM(mod)/PCBOOM VORLAX/BDAP/AWAVE/ AERO2S/WINGDES Aerodynamics Weights FLOPS equations Propulsion NPSS/WATE Stability&Control VORLAX/in house Environment PBOOM(mod .)/FOOTPR Sizing and Performance FLOPS Weights FLOPS/ WATE RSEs Propulsion NPSS/WATE Stability&Control VORLAX/WINGDES/in house Manufacturing “user assessed/optional” “user assessed” Aeroelasticity “user assessed/optional” Environment PBOOM(mod)/PCBOOM Geometry Vehicle Sketch Pad Sizing and Performance FLOPS PBOOM(mod)/PCBOOM VORLAX/BDAP/AWAVE/ AERO2S/WINGDES Aerodynamics Weights FLOPS equations Propulsion NPSS/WATE Stability&Control VORLAX/in house Environment PBOOM(mod .)/FOOTPR Sizing and Performance FLOPS Weights FLOPS/ WATE RSEs Propulsion NPSS/WATE Stability&Control VORLAX/WINGDES/in house Manufacturing “user assessed/optional” “user assessed” Aeroelasticity “user assessed/optional” Environment PBOOM(mod)/PCBOOM Geometry Vehicle Sketch Pad Sizing and Performance FLOPS Fig. 2 Analyses setup. Fig. 3 Mixed-flow turbofan schematic and model. Fig. 4 Core-driven-fan stage schematic and model. 40 RALLABHANDI AND MAVRIS
RALLABHANDI AND MAVRIS Flade Flade Duct Flade Nozzle(Separate) Core MFTF Flade Flade Nozzle Bypass Splitter HPC Blecd Bumer HPT LPT Mixer Nozzle .Indicates a pressure loss between components Fucl Fig.5 FLADE engine schematic and model. characteristics is its ability to shut off the outer bypass (FLADE) for the mission.This would be especially beneficial in the case of the duct.This would typically be accomplished using a stator that is only VCEs,so that both modes of operation would have their geometry in front of the FLADE duct (and separate from the fan inlet guide (nacelle lengths,diameter,and capture areas)optimized for their vane)to block air from entering the duct.Figure 5 also shows how the designed ambient conditions.However,due to the complexity flow is split between the core and the FLADE duct via the splitter. involved,only one design point (sea-level static)was used to model Theoretically,the FLADE duct could vary from completely open to the engines in this study.In the case of the MFTF,this is an completely closed.When the FLADE duct is closed,the engine appropriate way to get an engine deck;however,it should be noted behaves similarly to the MFTF engine [15].However,when the duct that for the VCEs.NPSS has a difficult time converging when the off- is open,the engine is in a higher bypass configuration,which is design-point engine geometry varies too much from the design point. intended to produce lower SFC and lower noise characteristics. The main problem for the VCE architectures was how to get the Another benefit of the FLADE design is the noise reduction bypass door to open at a relatively high power without causing attributed to the use of the FLADE duct flow at takeoff to create an model-convergence problems.This was accomplished by placing a acoustic shield.The ground noise signature can be lowered even lower limit on the pressure ratio,the limiting value being chosen to more by ducting the bypass stream to the bottom of the engine. reduce the number of failed cases.Additional assumptions for each creating a thick layer of acoustic shielding [16].The FLADE has VCE are briefly listed in the following paragraph.MFTF engine was more components than the MFTF,inherently making it more modeled first,due to its simplicity compared with the other cycle complex and heavier.Therefore,the possible performance gains architectures.MFTF design served as a good basis in the design of have to outweigh those deficits for it to survive in the optimization CDFS and FLADE. environment. For off-design operation,the engine power management is defined For each engine architecture,the cycle design variables to be for both maximum-power and part-power operation.For maximum varied by the GA to determine an optimal configuration are specified power [also called intermediate-rated power (IRP)],the engine in Table Al in the Appendix.There are four design variables maintains its design-point corrected fan speed (100%)until this is common to all three engines,and the FLADE and the CDFS VCE overridden by the maximum T41(T41MAX)limit.Additionally,the each has a variable unique to its architecture.A range for each of exhaust nozzle area is allowed to vary to maintain the design-point these variables was determined to create a realistic and fan stall margin.At part power,the engine throttle (fuel flow)is comprehensive design space exploration.The fan pressure ratio allowed to vary to match a thrust target,whereas the exhaust nozzle range was chosen to allow for both a single-stage and a two-stage fan area is held fixed at the IRP value.The thrust target is defined as a to be considered and to make the MFTF FPR more comparable with percentage of the maximum thrust [i.e.,maximum thrust multiplied that of the CDFS VCE.These fan pressure ratios are reasonable for a by percentage power represented by a power code (PC)].Thrust is two-stage fan.Even though transonic two-stage fans are known to assumed to vary linearly with power code between two extremes:a have pressure ratios in the range 2.4-4.3,the upper limit of 3.26 was maximum-power mode and an idle-flight mode.The top-of-climb chosen in this study for expediency;higher pressure ratios cause a point is run off-design to determine the inlet capture area match to the significant number of CDFS cases to fail during convergence.The engine airflow demand.This ensures that the inlet spillage drag is overall pressure ratio (OPR)values were estimated by comparing minimized during the supersonic cruise leg.This point is run at a with values of modern fighter engines.The extraction ratio(EXTR) nominal supersonic cruise condition (cruise Mach at 55,000 ft)at is the ratio of the bypass stream pressure to the core stream pressure at 90%power.An optimizer is used to find the capture area that the mixing plane.The throttle ratio (THR)is the ratio of the minimizes SFC at this condition.Thus,the effects of both inlet ram maximum-allowable turbine rotor inlet temperature (T41MAX)to recovery and inlet spillage drag are minimized. the static sea-level design point (T41SLS).The maximum T41 was Once the engine model is built,the flight envelope is run to create fixed to the same value for each engine.For the FLADE,the bypass the FLOPS engine deck.The flight envelope is an array of Mach ratio was chosen as the extra variable because of the effect it has on numbers and altitudes.Mach numbers are varied from 0 to 1.8,and the engine performance.The range was selected based on previous altitudes are varied from 0 to 65,000 ft.At each Mach number and NASA studies [14].For the CDFS VCE,the extra design variable altitude a throttle hook is run from maximum power to idle flight was chosen to be the CDFS pressure ratio.Its range was based on a using the appropriate power management.All of the engine decks are rational limit for a single compressor stage. created in this same fashion;however,due to the VCEs having The GA chooses the engine architecture and the values for the multiple modes of operation,there were some differences in the way corresponding cycle design variables for each case in the population. the power management was handled.For the FLADE at the design For each case,NPSS builds the model of the engine and generates the point,the IGV is opened,allowing NPSS to properly size the bypass engine deck (i.e.,the table of thrust and fuel flow data required by duct.At off-design conditions,the maximum-power definition has FLOPS).The NPSS build process requires two steps:1)a design two differences:first.the FLADE is intended to hold a constant point run at sea-level static conditions to size the engine corrected mass flow rate,and second,when the flight Mach number is thermodynamically and 2)an off-design run at the top of the climb to greater than 0.92,the IGV is closed.This closes off the FLADE duct match the inlet to the engine airflow demand.It would be optimal to for the higher-thrust mode needed for supersonic cruise conditions. design each of these engines using multiple design points,preferably The part-power function is identical to that of the MFTF,except that the supersonic cruise condition,the subsonic cruise condition,and again the FLADE duct is closed when the flight Mach number is the sea-level static takeoff condition,to create the best overall engine greater than 0.92.The CDFS power management was handled
characteristics is its ability to shut off the outer bypass (FLADE) duct. This would typically be accomplished using a stator that is only in front of the FLADE duct (and separate from the fan inlet guide vane) to block air from entering the duct. Figure 5 also shows how the flow is split between the core and the FLADE duct via the splitter. Theoretically, the FLADE duct could vary from completely open to completely closed. When the FLADE duct is closed, the engine behaves similarly to the MFTF engine [15]. However, when the duct is open, the engine is in a higher bypass configuration, which is intended to produce lower SFC and lower noise characteristics. Another benefit of the FLADE design is the noise reduction attributed to the use of the FLADE duct flow at takeoff to create an acoustic shield. The ground noise signature can be lowered even more by ducting the bypass stream to the bottom of the engine, creating a thick layer of acoustic shielding [16]. The FLADE has more components than the MFTF, inherently making it more complex and heavier. Therefore, the possible performance gains have to outweigh those deficits for it to survive in the optimization environment. For each engine architecture, the cycle design variables to be varied by the GA to determine an optimal configuration are specified in Table A1 in the Appendix. There are four design variables common to all three engines, and the FLADE and the CDFS VCE each has a variable unique to its architecture. A range for each of these variables was determined to create a realistic and comprehensive design space exploration. The fan pressure ratio range was chosen to allow for both a single-stage and a two-stage fan to be considered and to make the MFTF FPR more comparable with that of the CDFS VCE. These fan pressure ratios are reasonable for a two-stage fan. Even though transonic two-stage fans are known to have pressure ratios in the range 2.4–4.3, the upper limit of 3.26 was chosen in this study for expediency; higher pressure ratios cause a significant number of CDFS cases to fail during convergence. The overall pressure ratio (OPR) values were estimated by comparing with values of modern fighter engines. The extraction ratio (EXTR) is the ratio of the bypass stream pressure to the core stream pressure at the mixing plane. The throttle ratio (THR) is the ratio of the maximum-allowable turbine rotor inlet temperature (T41MAX) to the static sea-level design point (T41SLS). The maximum T41 was fixed to the same value for each engine. For the FLADE, the bypass ratio was chosen as the extra variable because of the effect it has on the engine performance. The range was selected based on previous NASA studies [14]. For the CDFS VCE, the extra design variable was chosen to be the CDFS pressure ratio. Its range was based on a rational limit for a single compressor stage. The GA chooses the engine architecture and the values for the corresponding cycle design variables for each case in the population. For each case, NPSS builds the model of the engine and generates the engine deck (i.e., the table of thrust and fuel flow data required by FLOPS). The NPSS build process requires two steps: 1) a design point run at sea-level static conditions to size the engine thermodynamically and 2) an off-design run at the top of the climb to match the inlet to the engine airflow demand. It would be optimal to design each of these engines using multiple design points, preferably the supersonic cruise condition, the subsonic cruise condition, and the sea-level static takeoff condition, to create the best overall engine for the mission. This would be especially beneficial in the case of the VCEs, so that both modes of operation would have their geometry (nacelle lengths, diameter, and capture areas) optimized for their designed ambient conditions. However, due to the complexity involved, only one design point (sea-level static) was used to model the engines in this study. In the case of the MFTF, this is an appropriate way to get an engine deck; however, it should be noted that for the VCEs, NPSS has a difficult time converging when the offdesign-point engine geometry varies too much from the design point. The main problem for the VCE architectures was how to get the bypass door to open at a relatively high power without causing model-convergence problems. This was accomplished by placing a lower limit on the pressure ratio, the limiting value being chosen to reduce the number of failed cases. Additional assumptions for each VCE are briefly listed in the following paragraph. MFTF engine was modeled first, due to its simplicity compared with the other cycle architectures. MFTF design served as a good basis in the design of CDFS and FLADE. For off-design operation, the engine power management is defined for both maximum-power and part-power operation. For maximum power [also called intermediate-rated power (IRP)], the engine maintains its design-point corrected fan speed (100%) until this is overridden by the maximum T41 (T41MAX) limit. Additionally, the exhaust nozzle area is allowed to vary to maintain the design-point fan stall margin. At part power, the engine throttle (fuel flow) is allowed to vary to match a thrust target, whereas the exhaust nozzle area is held fixed at the IRP value. The thrust target is defined as a percentage of the maximum thrust [i.e., maximum thrust multiplied by percentage power represented by a power code (PC)]. Thrust is assumed to vary linearly with power code between two extremes: a maximum-power mode and an idle-flight mode. The top-of-climb point is run off-design to determine the inlet capture area match to the engine airflow demand. This ensures that the inlet spillage drag is minimized during the supersonic cruise leg. This point is run at a nominal supersonic cruise condition (cruise Mach at 55,000 ft) at 90% power. An optimizer is used to find the capture area that minimizes SFC at this condition. Thus, the effects of both inlet ram recovery and inlet spillage drag are minimized. Once the engine model is built, the flight envelope is run to create the FLOPS engine deck. The flight envelope is an array of Mach numbers and altitudes. Mach numbers are varied from 0 to 1.8, and altitudes are varied from 0 to 65,000 ft. At each Mach number and altitude a throttle hook is run from maximum power to idle flight using the appropriate power management. All of the engine decks are created in this same fashion; however, due to the VCEs having multiple modes of operation, there were some differences in the way the power management was handled. For the FLADE at the design point, the IGV is opened, allowing NPSS to properly size the bypass duct. At off-design conditions, the maximum-power definition has two differences: first, the FLADE is intended to hold a constant corrected mass flow rate, and second, when the flight Mach number is greater than 0.92, the IGV is closed. This closes off the FLADE duct for the higher-thrust mode needed for supersonic cruise conditions. The part-power function is identical to that of the MFTF, except that again the FLADE duct is closed when the flight Mach number is greater than 0.92. The CDFS power management was handled Fig. 5 FLADE engine schematic and model. RALLABHANDI AND MAVRIS 41
42 RALLABHANDI AND MAVRIS differently from the FLADE.Instead of changing the mode of The code uses semi-empirical methods augmented by analytical operation at a specific Mach number,it is controlled by the power calculations for specific component elements setting.At full power,the blocker door is set to closed,and the CDFS To reduce environment run time and complexity,surrogate IGV is kept open.Once the power setting drops below about 90%, models of WATE are generated.To create the regressions,the MFTF chosen according to a cutoff pressure ratio that allows solver engine-cycle design variables FPR,OPR,THR,and EXTR were convergence,the blocker door is then open and the CDFS IGV is varied and engine weight normalized by baseline thrust was closed,creating the high bypass mode. recorded.Specifically,a four-level full factorial design of experiments was run with the ranges shown in Table Al.These C.Other Analyses regressions provide engine weight over baseline thrust.nacelle diameter over baseline thrust,and nacelle length.The first two are 1.Aerodynamics functions of FPR.OPR.EXTR.and THR,and the nacelle length has A number of conceptual aerodynamic tools based upon linearized an additional variable in cruise Mach number.The engine weight methods are used to calculate properties such as supersonic wave obtained from the regressions includes the nozzle and accessories drag (AWAVE)[17],induced drag(WINGDES)[18],skin-friction weight.but not the inlet weight.To account for the inlet weight,an drag (BDAP)[19],and low-speed aerodynamics (AERO2S)[18]. additional 2024.0 lb is added to the weight obtained from the Several secondary sources of drag,such as form drag and transonic regressions.Weight normalized by thrust was used so that the wave drag,are not accounted for by these programs,and they are regressions would not be entirely dependent on the mass flow rate calculated using handbook methods from Raymer [20].Once the chosen in the NPSS engine model.For moderate variation in mass geometry is generated and the aerodynamic quantities are calculated fow rate and nominal values of the engine-cycle variables,the using the preceding methods,the relevant data are written into a normalized weight remains relatively constant over a range of mass FLOPS file.The geometry includes not only airframe but also fow from 700 to 1000 Ib/s.In this study,all engine models in NPSS propulsion data,such as the longitudinal and lateral locations of the were modeled with a mass flow rate of 1000 Ib/s.The thrust and engines,nacelle diameter,and the overall nacelle length.The weight values were then scaled down later in the environment by locations are obtained by the optimizer from the limits imposed on FLOPS to reflect more realistic values of mass flow rate.Scaling the relevant design variables.The diameter and length are obtained thrust can lead to incorrect SFC and weight estimates.SFC may be from the engine-weight regressions discussed in a subsequent incorrect because,beyond a certain point,losses do not scale.A section.The geometry data are then used during the sizing and similar argument may be applicable to the weight of structural mission analyses phase of the design,instead of the aerodynamics components.However,for this study.these effects are believed to be module included within FLOPS. small,because the original loss and weight estimates were made for airflows sized nearer to the true values of the baseline case. 2.Sonic Boom A surrogate model using first order,second order,and first-order interaction effects is obtained by eliminating the parameters that do Design of a commercial supersonic aircraft invariably involves not affect the response.These can be identified by examining the p- sonic boom analyses.In this study,PBOOM [21]and PCBOOM[22] value of each parameter,listed under the parameter estimates in are used.To simulate the atmospheric absorption,a rise time of 3 ms Fig.6a.Using a cutoff a level of 0.10,parameters with a p-value is assumed for a shock strength magnitude of 1 psf.This is based on greater than 0.1 were eliminated from the model.Using this criterion, an empirical model fit based on experimental data[23]to account for the number of parameters in the model was reduced from 19 to 9. atmospheric attenuation and molecular relaxation. excluding the intercept term.The R2 value remains the same(0.983) as obtained using all the parameters,but now the model is simpler. 3.Stability and Control The parameters in Fig.6a and their corresponding coefficients make Stability is an important consideration in aircraft design,even up the final regression used to predict the engine weight of the MFTF today,after the advent of fly-by-wire systems,because there can The graph shows the actual value versus the model-predicted value. often be severe performance penalties if the vehicle is not properly Four clumps of points can be seen in the figure.This is explained by balanced.In conceptual design,the exact location of each subsystem the nature of the simulation experiments.Recall that the experiment within the vehicle is not calculated,and so historical data are used to was a four-level full factorial,with each variable taking on four place them for the purposes of center-of-gravity (c.g.)calculations.It different evenly spaced values.If more random points were run,then is known that for static stability,the center of gravity must be ahead less clumping would be observed.Regardless,the points lie mostly of the neutral point of the aircraft.In this study,neutral points (center along the diagonal,indicating that actual values in the design space of lift)are calculated using AERO2S and WINGDES.The stability closely follow their corresponding predicted values.Additionally, penalty is calculated to be the area enclosed by the center-of-lift lines the distribution of residual of the model is examined in two different and the c.g.envelope The optimizer attempts to minimize this plots.The model fit error is calculated for all the 256 points used to response. create the model.Ideally,the error of a model should be normally distributed with a mean around zero.Figure 6b shows the details of the model-fit-error distribution.The mean 0.082%is very close to 4.Weights zero.The standard deviation is 3.85%,and no point is off by more Weight analysis is still a difficult task for conceptual designers than 8.68%.The model fit error alone does not explain the predictive Though several codes such as equivalent laminated-plate solution power of the model.To evaluate the predictive power of the model, (ELAPS)[24]have been developed for predicting structural weight the model representation error is considered.A model representation studies have not conclusively shown that the results of these codes error is calculated for new data points that were not used in fitting the are more accurate than the much simpler methods based upon data:80 new points were run through WATE and their responses historical data and simple beam theory such as those used in FLOPS. recorded.The details of the model representation error are shown in This fact led to the use of the FLOPS weight module for empty- Fig.6c.The distribution is not normal,but still resembles a normal weight prediction,though it is recognized that a more detailed distribution,excluding the center.Interestingly,the standard structural and weight analysis will need to be performed on the deviation actually improves to 3.385%.The mean moves slightly resulting concepts before proceeding to preliminary design. further away from 0 to 0.55%,but this is still certainly acceptable Apart from computing the weights associated with the airframe Also,the worst error is only 5.83%.From these data,it was the propulsion system weights are also required.This was done by concluded that the model has sufficient accuracy and predictive modeling an MFTF using weight analysis of turbine engines power. (WATE)[25].The code was originally developed by the Boeing After the MFTF engine weight is predicted,FLADE and CDFS Military Aircraft Company in 1979.Improvements to the code were VCE engine weights are predicted by multiplying the MFTF engine later added by NASA and McDonnell Douglas Corporation [26]. weight by a scaling factor.The scaling factor for the FLADE engine
differently from the FLADE. Instead of changing the mode of operation at a specific Mach number, it is controlled by the power setting. At full power, the blocker door is set to closed, and the CDFS IGV is kept open. Once the power setting drops below about 90%, chosen according to a cutoff pressure ratio that allows solver convergence, the blocker door is then open and the CDFS IGV is closed, creating the high bypass mode. C. Other Analyses 1. Aerodynamics A number of conceptual aerodynamic tools based upon linearized methods are used to calculate properties such as supersonic wave drag (AWAVE) [17], induced drag (WINGDES) [18], skin-friction drag (BDAP) [19], and low-speed aerodynamics (AERO2S) [18]. Several secondary sources of drag, such as form drag and transonic wave drag, are not accounted for by these programs, and they are calculated using handbook methods from Raymer [20]. Once the geometry is generated and the aerodynamic quantities are calculated using the preceding methods, the relevant data are written into a FLOPS file. The geometry includes not only airframe but also propulsion data, such as the longitudinal and lateral locations of the engines, nacelle diameter, and the overall nacelle length. The locations are obtained by the optimizer from the limits imposed on the relevant design variables. The diameter and length are obtained from the engine-weight regressions discussed in a subsequent section. The geometry data are then used during the sizing and mission analyses phase of the design, instead of the aerodynamics module included within FLOPS. 2. Sonic Boom Design of a commercial supersonic aircraft invariably involves sonic boom analyses. In this study, PBOOM [21] and PCBOOM [22] are used. To simulate the atmospheric absorption, a rise time of 3 ms is assumed for a shock strength magnitude of 1 psf. This is based on an empirical model fit based on experimental data [23] to account for atmospheric attenuation and molecular relaxation. 3. Stability and Control Stability is an important consideration in aircraft design, even today, after the advent of fly-by-wire systems, because there can often be severe performance penalties if the vehicle is not properly balanced. In conceptual design, the exact location of each subsystem within the vehicle is not calculated, and so historical data are used to place them for the purposes of center-of-gravity (c.g.) calculations. It is known that for static stability, the center of gravity must be ahead of the neutral point of the aircraft. In this study, neutral points (center of lift) are calculated using AERO2S and WINGDES. The stability penalty is calculated to be the area enclosed by the center-of-lift lines and the c.g. envelope The optimizer attempts to minimize this response. 4. Weights Weight analysis is still a difficult task for conceptual designers. Though several codes such as equivalent laminated-plate solution (ELAPS) [24] have been developed for predicting structural weight, studies have not conclusively shown that the results of these codes are more accurate than the much simpler methods based upon historical data and simple beam theory such as those used in FLOPS. This fact led to the use of the FLOPS weight module for emptyweight prediction, though it is recognized that a more detailed structural and weight analysis will need to be performed on the resulting concepts before proceeding to preliminary design. Apart from computing the weights associated with the airframe, the propulsion system weights are also required. This was done by modeling an MFTF using weight analysis of turbine engines (WATE) [25]. The code was originally developed by the Boeing Military Aircraft Company in 1979. Improvements to the code were later added by NASA and McDonnell Douglas Corporation [26]. The code uses semi-empirical methods augmented by analytical calculations for specific component elements. To reduce environment run time and complexity, surrogate models of WATE are generated. To create the regressions, the MFTF engine-cycle design variables FPR, OPR, THR, and EXTR were varied and engine weight normalized by baseline thrust was recorded. Specifically, a four-level full factorial design of experiments was run with the ranges shown in Table A1. These regressions provide engine weight over baseline thrust, nacelle diameter over baseline thrust, and nacelle length. The first two are functions of FPR, OPR, EXTR, and THR, and the nacelle length has an additional variable in cruise Mach number. The engine weight obtained from the regressions includes the nozzle and accessories weight, but not the inlet weight. To account for the inlet weight, an additional 2024.0 lb is added to the weight obtained from the regressions. Weight normalized by thrust was used so that the regressions would not be entirely dependent on the mass flow rate chosen in the NPSS engine model. For moderate variation in mass flow rate and nominal values of the engine-cycle variables, the normalized weight remains relatively constant over a range of mass flow from 700 to 1000 lb=s. In this study, all engine models in NPSS were modeled with a mass flow rate of 1000 lb=s. The thrust and weight values were then scaled down later in the environment by FLOPS to reflect more realistic values of mass flow rate. Scaling thrust can lead to incorrect SFC and weight estimates. SFC may be incorrect because, beyond a certain point, losses do not scale. A similar argument may be applicable to the weight of structural components. However, for this study, these effects are believed to be small, because the original loss and weight estimates were made for airflows sized nearer to the true values of the baseline case. A surrogate model using first order, second order, and first-order interaction effects is obtained by eliminating the parameters that do not affect the response. These can be identified by examining the pvalue of each parameter, listed under the parameter estimates in Fig. 6a. Using a cutoff level of 0.10, parameters with a p-value greater than 0.1 were eliminated from the model. Using this criterion, the number of parameters in the model was reduced from 19 to 9, excluding the intercept term. The R2 value remains the same (0.983) as obtained using all the parameters, but now the model is simpler. The parameters in Fig. 6a and their corresponding coefficients make up the final regression used to predict the engine weight of the MFTF. The graph shows the actual value versus the model-predicted value. Four clumps of points can be seen in the figure. This is explained by the nature of the simulation experiments. Recall that the experiment was a four-level full factorial, with each variable taking on four different evenly spaced values. If more random points were run, then less clumping would be observed. Regardless, the points lie mostly along the diagonal, indicating that actual values in the design space closely follow their corresponding predicted values. Additionally, the distribution of residual of the model is examined in two different plots. The model fit error is calculated for all the 256 points used to create the model. Ideally, the error of a model should be normally distributed with a mean around zero. Figure 6b shows the details of the model-fit-error distribution. The mean 0.082% is very close to zero. The standard deviation is 3.85%, and no point is off by more than 8.68%. The model fit error alone does not explain the predictive power of the model. To evaluate the predictive power of the model, the model representation error is considered. A model representation error is calculated for new data points that were not used in fitting the data; 80 new points were run through WATE and their responses recorded. The details of the model representation error are shown in Fig. 6c. The distribution is not normal, but still resembles a normal distribution, excluding the center. Interestingly, the standard deviation actually improves to 3.385%. The mean moves slightly further away from 0 to 0.55%, but this is still certainly acceptable. Also, the worst error is only 5.83%. From these data, it was concluded that the model has sufficient accuracy and predictive power. After the MFTF engine weight is predicted, FLADE and CDFS VCE engine weights are predicted by multiplying the MFTF engine weight by a scaling factor. The scaling factor for the FLADE engine 42 RALLABHANDI AND MAVRIS
RALLABHANDI AND MAVRIS 为 Actual by Predicted Plot Summary of Fit 04- RSquare 0983488 0982834 Root Meon Squore Error 0.006542 Mean of Response 023B486 Observations (or Sum Wgts) 256 03 Analysis of Variance Source DF Sum of Squares Mean Sausre F Ratio Model 9 10941814 0.1215761627999 Error 246 0.0183708 0100075p,hsF C.Total 255 1.1125522 .0001* Parameter Estimates Term Estimsle std Error t Ratio Prob=相 Intercept 0.3526925 0021633 16.300001 FPR 011324800009G .1141e0101* 0FFR-253)FPR-253 0.0861182 0.00228 37.760001* 2 OPR 0.00157650000145 10880001 WteyThrust Predicted FPR2.53THR.1.05) 0.18823430.026635 7.07<0001* P=0001RSg-0.98RMSE-0.00B6 EXTR 0.07178490.014492 4.95e0001 (FPR-253)(EXTR-1) -00m8167002665 -25600111 THR 0.02758760014492 19000581 (THR.105)'FPR-2.5310PR-30) 0.01330110.007147 18600639 (THR-1.05THR-105) -0.887741 0.486117 18300590 a)Model fit summary after removing inconsequential variables Quantiles Moments D 100 0%maximum 7409 Mean 00817948 95 7333 38450412 975% E3u slg日m6sn 02403151 -020 00% g042 aB5%Men05550495 760 a5 wer 95%Mean 039146 0.15 500 0.185 255 250 quortie 2642 0.10 100 .5232 5% .7559 005 8 0 b)Model fit error Quantiles Moments ◆ 100.0%mexmum 6,.866 05522769 995 686 Std Dev 975% B.49 Sld后t Mean 0.378478 025 900 4.771 upper 95%Mesn 13156185 020 750% qu 3.412 -02010 65 500% 1,381 250% 2.550 100% 3426 010 25% 5734 05% -5.826 005 00% mininun 5828 964202 c)Model representation error Fig.6 Engine-weight-regression model. weight used in this study is 1.2.For the one-stage-fan CDFS VCE a desired total range of 4000 n mile.The first 1500-n-mile segment of (i.e.,with FPR <1.8),the scaling factor is assumed to be 1.042,and the mission is the subsonic leg (including climb),with a cruise speed for the two-stage-fan CDFS VCE(i.e.,with FPR 1.8).the scaling of Mach 0.92.The remainder of the mission includes the supersonic factor is chosen as 1.3.These scaling factors had to be incorporated climb,a supersonic cruise at a Mach number in the range of 1.6-1.8. because WATE cannot model the VCE components.For example. and descent.This approximates the realistic missions for which a the bypass door must be modeled as a simple duct so that the weight supersonic business jet would be desirable for accelerated travel. of the moving parts is not captured.The same is the case with the Because of the Federal Aviation Administration(FAA)regulations variable-area bypass injector(VABD).The CDFS-stage weight is not on noise and supersonic travel over land,an aggressive supersonic computed properly,because associated frames,disks,bearings,etc. mission was not chosen;this will be studied in subsequent are not accounted for correctly.These factors have been treated efforts.With the desired total range for the mission being manually for a baseline engine,and the differences were combined 4000 n mile.approximately 2500 n mile is needed for the supersonic into a scale factor to be applied to an MFTF model that otherwise has cruise (including the descent).In this study,the takeoff gross the same cycle parameters of the VCE models.The authors realize weight (TOGW)is set by the GA for every run;therefore,the that these scale factors are somewhat subjective.But due to the lack aircraft flies a 1500-n-mile subsonic leg and then flies as far as it can of a proper tool to model complex VCE propulsion system weights, in the supersonic leg,sometimes exceeding the desired 4000-n-mile calibrated scale factors for baseline design were used in this study. threshold and sometimes falling short.Scaling of the engine,on the other hand,is performed through the use of the engine deck created by NPSS and the scaling laws imbedded in FLOPS. 5.Mission Analysis which scale the engine data to the thrust level that is necessary to FLOPS is used to perform mission analysis.The mission execute the mission performance module and takeoff and landing investigated in this study is a split subsonic/supersonic mission with module
weight used in this study is 1.2. For the one-stage-fan CDFS VCE (i.e., with FPR <1:8), the scaling factor is assumed to be 1.042, and for the two-stage-fan CDFS VCE (i.e., with FPR 1:8), the scaling factor is chosen as 1.3. These scaling factors had to be incorporated because WATE cannot model the VCE components. For example, the bypass door must be modeled as a simple duct so that the weight of the moving parts is not captured. The same is the case with the variable-area bypass injector (VABI). The CDFS-stage weight is not computed properly, because associated frames, disks, bearings, etc., are not accounted for correctly. These factors have been treated manually for a baseline engine, and the differences were combined into a scale factor to be applied to an MFTF model that otherwise has the same cycle parameters of the VCE models. The authors realize that these scale factors are somewhat subjective. But due to the lack of a proper tool to model complex VCE propulsion system weights, calibrated scale factors for baseline design were used in this study. 5. Mission Analysis FLOPS is used to perform mission analysis. The mission investigated in this study is a split subsonic/supersonic mission with a desired total range of 4000 n mile. The first 1500-n-mile segment of the mission is the subsonic leg (including climb), with a cruise speed of Mach 0.92. The remainder of the mission includes the supersonic climb, a supersonic cruise at a Mach number in the range of 1.6–1.8, and descent. This approximates the realistic missions for which a supersonic business jet would be desirable for accelerated travel. Because of the Federal Aviation Administration (FAA) regulations on noise and supersonic travel over land, an aggressive supersonic mission was not chosen; this will be studied in subsequent efforts. With the desired total range for the mission being 4000 n mile, approximately 2500 n mile is needed for the supersonic cruise (including the descent). In this study, the takeoff gross weight (TOGW) is set by the GA for every run; therefore, the aircraft flies a 1500-n-mile subsonic leg and then flies as far as it can in the supersonic leg, sometimes exceeding the desired 4000-n-mile threshold and sometimes falling short. Scaling of the engine, on the other hand, is performed through the use of the engine deck created by NPSS and the scaling laws imbedded in FLOPS, which scale the engine data to the thrust level that is necessary to execute the mission performance module and takeoff and landing module. Fig. 6 Engine-weight-regression model. RALLABHANDI AND MAVRIS 43
44 RALLABHANDI AND MAVRIS D.Advanced Genetic Algorithms Table 2 Objective goals and weights In engineering design,there are almost always multiple criteria Objectives Goal value Normalization value that must be considered during the concept selection process. Objectives such as weight,cost,and speed must be balanced against Range,n mile 4200 1.0 each other to find the appropriate combination that will result in a Gross weight.lb×10O0 100 50.0 successful design.Traditionally,these problems are handled by Jet velocity for 7000-ft takeoff,ft/s 900 2.0 Cruise Mach number 1.7 0.0025 creating an aggregate objective function,the so-called overall Shock pressure rise,psf 0.35 0.002 evaluation criterion.However.this method cannot numerically Sonic boom,PL (dB) 88 0.01 quantify how important the objectives are in relation to each other Approach velocity.kt 140 0.1 resulting in designs that do not really best meet the designers goals. Length,ft 140 0.1 Multi-objective genetic algorithms attempt to solve this problem by Static stability penalty 100.0 10.0 using the concept of Pareto-optimality to find nondominated Cabin diameter.ft 69 0.001 solutions.A solution is said to be nondominated when there is no other solution in the space that is better with regard to all decision variables.The set of nondominated solutions,or Pareto front,makes up a hypersurface along which improvement in one objective is a vector of normalization constants.In the present study,all the requires a sacrifice in another.Once this front has been found,the objectives were equally weighted.The conceptual design process for engineer can use it to explore the relationship between the objectives the desired supersonic transport does not have a standard set of so that intelligent decisions can be made. requirements or goals,unlike many traditional subsonic design Several modifications to the conventional GA,such as the strength efforts.Certain well-accepted guidelines,as shown in Table 2,are Pareto evolutionary algorithm(SPEA)[27].have gained widespread used in this study as design goals.The normalization constants were acceptance for use in the multi-objective optimization problem.This determined by calculating the variance of each objective for a algorithm incorporates elitist and population-diversifying character- random population of individuals and then rounding that value to a istics to multi-obiective Pareto optimization.The SPEA2 algorithm convenient number.The normalization values allow for the width of balances the diversification of the population as well as exploits the distribution to be taken into account,thus including a convenient solutions from an archive ofelite designs.However,as the number of way to scale the objectives in an unbiased manner. objectives increases,the proportion of nondominated designs also increases.Recent research [28]has shown that although GA operators work well for two or three objective problems.their 2.Operator Enhancements effectiveness drops significantly when there are a large number of As has been mentioned earlier in this paper,one of the objectives conflicting objectives.The SPEA2 algorithm becomes ineffective of this work is to study the tradeoffs associated with component under these conditions.This is because the proportion of the placement.The GA not only attempts to optimize the component population that is nondominated grows exponentially as the number shapes,but also their placement,implying that the optimization of simultaneous objectives increase.In fact,Deb [29]found that as problem is a mixed discrete/continuous hierarchical problem.It is the number of objectives grows,nearly all solutions become found through experience that the conventional GA crossover nondominated and would therefore have equal fitness values. operators yield very poor performance for such a problem,due to Because of reliance on dominance-based fitness,most multi- excessive chromosome disruption.To overcome this.several objective algorithms have difficulties solving problems with more operator enhancements have been included in the GA.Conventional than two or three responses. GAs use binary encoding to discretize the computational domain According to the definition of nondominance,a solution is before searching for optimum locations.However,application of nondominated if no other solution in the set is better in any objective binary encoding to variables with discrete settings requires without being inferior in at least one other objective.This definition specification of several special cases,which can cause the procedure of dominance does not deal with magnitudes.A solution that trades a to become inefficient.To overcome this problem.real-valued genetic large amount of capability in one objective for an infinitesimal algorithms are used in this study amount of gain in another is not penalized by the fitness-assignment Although evolutionary algorithms have been applied to several schemes used by many of the common evolutionary algorithms in engineering design problems,not many studies have looked at literature. optimizing problems that have both the system architecture(discrete) and design (continuous)variables.One specific instance of 1.Multi-Objective Optimization combining discrete and continuous variables in evolutionary optimizers is described by Parmee [31].termed structured genetic In response to the poor performance of the multi-objective evolutionary algorithms available in literature,an advanced genetic algorithms.Unfortunately,the structured GA quickly focused on a single alternative,even for relatively small design hierarchies.The algorithm method has been developed.Rather than optimizing each of the M objectives,the problem is reformulated to solve for the tendency to quickly focus on a small portion of the design space may result in the algorithm overlooking potentially promising solutions. tradeoff between M biased aggregate functions that favor attainment This deficiency was addressed with a method called the hybrid of one particular objective but do not ignore performance of the other structured genetic algorithm [31],which introduced variable M-1 objectives.Goal programming [30]is used in the current study mutation probabilities to the discrete and continuous variables.This as the aggregation technique.In this method,three parameters per method used a bitwise mutation probability of 20%for discrete objective are specified:a goal or ideal value,a normalization value obtained using sampling.and a weighting value to specify variables and a much lower mutation probability of 2%for importance.The goal value corresponds to the minimum level of continuous variables.The large mutation probability applied to the performance in a given metric that would be considered acceptable. discrete variables effectively maintained genetic diversity,but may also prevent efficient convergence because of the mutation The problem is then recast as the minimization of the weighted operator's tendency to move away from good solutions. difference between the actual and goal values,as shown in Eq.(1) Goal programming may be understood to be analogous to a weighted The crossover operator is applied to a postreproduction population to cross genes between its members.The aim of this operator is to target-matching problem: attempt to create better designs by swapping genes (design variables);the idea is to insert a good gene from one design into fm(x)-8m 1) another design and increase its fitness value.Several choices exist for real-variable crossover,such as uniform linear,bilinear (BLX-a) [32],simulated binary (SBX)[33,34],or an enhanced version of where w is a vector of weights,g is a vector of goal values,and n simulated binary (VSBX)[35].Going into the details of each of the
D. Advanced Genetic Algorithms In engineering design, there are almost always multiple criteria that must be considered during the concept selection process. Objectives such as weight, cost, and speed must be balanced against each other to find the appropriate combination that will result in a successful design. Traditionally, these problems are handled by creating an aggregate objective function, the so-called overall evaluation criterion. However, this method cannot numerically quantify how important the objectives are in relation to each other, resulting in designs that do not really best meet the designers goals. Multi-objective genetic algorithms attempt to solve this problem by using the concept of Pareto-optimality to find nondominated solutions. A solution is said to be nondominated when there is no other solution in the space that is better with regard to all decision variables. The set of nondominated solutions, or Pareto front, makes up a hypersurface along which improvement in one objective requires a sacrifice in another. Once this front has been found, the engineer can use it to explore the relationship between the objectives so that intelligent decisions can be made. Several modifications to the conventional GA, such as the strength Pareto evolutionary algorithm (SPEA) [27], have gained widespread acceptance for use in the multi-objective optimization problem. This algorithm incorporates elitist and population-diversifying characteristics to multi-objective Pareto optimization. The SPEA2 algorithm balances the diversification of the population as well as exploits solutions from an archive of elite designs. However, as the number of objectives increases, the proportion of nondominated designs also increases. Recent research [28] has shown that although GA operators work well for two or three objective problems, their effectiveness drops significantly when there are a large number of conflicting objectives. The SPEA2 algorithm becomes ineffective under these conditions. This is because the proportion of the population that is nondominated grows exponentially as the number of simultaneous objectives increase. In fact, Deb [29] found that as the number of objectives grows, nearly all solutions become nondominated and would therefore have equal fitness values. Because of reliance on dominance-based fitness, most multiobjective algorithms have difficulties solving problems with more than two or three responses. According to the definition of nondominance, a solution is nondominated if no other solution in the set is better in any objective without being inferior in at least one other objective. This definition of dominance does not deal with magnitudes. A solution that trades a large amount of capability in one objective for an infinitesimal amount of gain in another is not penalized by the fitness-assignment schemes used by many of the common evolutionary algorithms in literature. 1. Multi-Objective Optimization In response to the poor performance of the multi-objective evolutionary algorithms available in literature, an advanced genetic algorithm method has been developed. Rather than optimizing each of the M objectives, the problem is reformulated to solve for the tradeoff between M biased aggregate functions that favor attainment of one particular objective but do not ignore performance of the other M-1 objectives. Goal programming [30] is used in the current study as the aggregation technique. In this method, three parameters per objective are specified: a goal or ideal value, a normalization value obtained using sampling, and a weighting value to specify importance. The goal value corresponds to the minimum level of performance in a given metric that would be considered acceptable. The problem is then recast as the minimization of the weighted difference between the actual and goal values, as shown in Eq. (1). Goal programming may be understood to be analogous to a weighted target-matching problem: Vix XM m1 wm fmx gm nm p1=p (1) where wm is a vector of weights, gm is a vector of goal values, and nm is a vector of normalization constants. In the present study, all the objectives were equally weighted. The conceptual design process for the desired supersonic transport does not have a standard set of requirements or goals, unlike many traditional subsonic design efforts. Certain well-accepted guidelines, as shown in Table 2, are used in this study as design goals. The normalization constants were determined by calculating the variance of each objective for a random population of individuals and then rounding that value to a convenient number. The normalization values allow for the width of the distribution to be taken into account, thus including a convenient way to scale the objectives in an unbiased manner. 2. Operator Enhancements As has been mentioned earlier in this paper, one of the objectives of this work is to study the tradeoffs associated with component placement. The GA not only attempts to optimize the component shapes, but also their placement, implying that the optimization problem is a mixed discrete/continuous hierarchical problem. It is found through experience that the conventional GA crossover operators yield very poor performance for such a problem, due to excessive chromosome disruption. To overcome this, several operator enhancements have been included in the GA. Conventional GAs use binary encoding to discretize the computational domain before searching for optimum locations. However, application of binary encoding to variables with discrete settings requires specification of several special cases, which can cause the procedure to become inefficient. To overcome this problem, real-valued genetic algorithms are used in this study. Although evolutionary algorithms have been applied to several engineering design problems, not many studies have looked at optimizing problems that have both the system architecture (discrete) and design (continuous) variables. One specific instance of combining discrete and continuous variables in evolutionary optimizers is described by Parmee [31], termed structured genetic algorithms. Unfortunately, the structured GA quickly focused on a single alternative, even for relatively small design hierarchies. The tendency to quickly focus on a small portion of the design space may result in the algorithm overlooking potentially promising solutions. This deficiency was addressed with a method called the hybrid structured genetic algorithm [31], which introduced variable mutation probabilities to the discrete and continuous variables. This method used a bitwise mutation probability of 20% for discrete variables and a much lower mutation probability of 2% for continuous variables. The large mutation probability applied to the discrete variables effectively maintained genetic diversity, but may also prevent efficient convergence because of the mutation operator’s tendency to move away from good solutions. The crossover operator is applied to a postreproduction population to cross genes between its members. The aim of this operator is to attempt to create better designs by swapping genes (design variables); the idea is to insert a good gene from one design into another design and increase its fitness value. Several choices exist for real-variable crossover, such as uniform linear, bilinear (BLX-) [32], simulated binary (SBX) [33,34], or an enhanced version of simulated binary (vSBX) [35]. Going into the details of each of the Table 2 Objective goals and weights Objectives Goal value Normalization value Range, n mile 4200 1.0 Gross weight, lb 1000 100 50.0 Jet velocity for 7000-ft takeoff, ft/s 900 2.0 Cruise Mach number 1.7 0.0025 Shock pressure rise, psf 0.35 0.002 Sonic boom, PL (dB) 88 0.01 Approach velocity, kt 140 0.1 Length, ft 140 0.1 Static stability penalty 100.0 10.0 Cabin diameter, ft 6.9 0.001 44 RALLABHANDI AND MAVRIS
RALLABHANDI AND MAVRIS 45 crossover schemes is beyond the scope of the present study;complete operator has the desired characteristics of both design space details are presented in the cited references.In this study,the exploration and clustering near the parent designs. enhanced version of the simulated binary crossover scheme (vSBX) Simple crossover types do not guarantee a good design space is used.The justification for this is provided in Fig.7.Four different exploration for hierarchical problems.This prompted the develop- crossover schemes are compared by starting with two parents,(5.0 ment of a new type of hierarchical crossover [36]in which the vSBX 5.0)and (10.0,10.0),and allowing repeated crossover operations crossover is implemented over components of the same category The resulting offspring are depicted as small dots.It is seen that type(for example,if both aircraft have variable geometry wings),but uniform linear operator explores the domain without preference the components are swapped with 50%probability if dissimilar(one given to the location of parents and the BLX-a operator does the parent has a canard and one has a T-tail).Figure 8 depicts an example same,except it explores a slightly larger domain.The SBX operator in which two parents of dissimilar topologies undergo hierarchical produces offspring that are concentrated more around the parents: crossover to produce two offspring.Results have shown that this however.it fails to explore the design space thoroughly.leaving out method allowed useful genetic information transfer with minimal the top left and bottom right quadrants of the design space.The vSBX gene disruption. 15 15 BLX-a Uniform Linear 10 10 义 义 0 10 15 10 15 SBX 15 15 SBX 10 10 15 0 15 Fig.7 Comparison of design exploration ability of crossover schemes Parent 1 Parent 2 Parent Mission Fuselage der-Wing Engine Parent 2 Fuselage Oguu Wing T.Tail Af-Mounted Engines Child 1 Child 2 Fig.8 Hierarchical crossover scheme [36]
crossover schemes is beyond the scope of the present study; complete details are presented in the cited references. In this study, the enhanced version of the simulated binary crossover scheme (vSBX) is used. The justification for this is provided in Fig. 7. Four different crossover schemes are compared by starting with two parents, (5.0, 5.0) and (10.0, 10.0), and allowing repeated crossover operations. The resulting offspring are depicted as small dots. It is seen that uniform linear operator explores the domain without preference given to the location of parents and the BLX- operator does the same, except it explores a slightly larger domain. The SBX operator produces offspring that are concentrated more around the parents; however, it fails to explore the design space thoroughly, leaving out the top left and bottom right quadrants of the design space. The vSBX operator has the desired characteristics of both design space exploration and clustering near the parent designs. Simple crossover types do not guarantee a good design space exploration for hierarchical problems. This prompted the development of a new type of hierarchical crossover [36] in which the vSBX crossover is implemented over components of the same category type (for example, if both aircraft have variable geometry wings), but the components are swapped with 50% probability if dissimilar (one parent has a canard and one has a T-tail). Figure 8 depicts an example in which two parents of dissimilar topologies undergo hierarchical crossover to produce two offspring. Results have shown that this method allowed useful genetic information transfer with minimal gene disruption. 0 5 10 15 0 5 10 15 x1 x2 0 5 10 15 0 5 10 15 x1 x2 0 5 10 15 0 5 10 15 x1 x2 0 5 10 15 0 5 10 15 x1 x2 SBX Uniform Linear v−SBX BLX−α Fig. 7 Comparison of design exploration ability of crossover schemes. Fig. 8 Hierarchical crossover scheme [36]. RALLABHANDI AND MAVRIS 45
46 RALLABHANDI AND MAVRIS replaces the closest of these if it has better fitness.Conventional tournament selection picks parent designs randomly and causes crossover between these possibly dissimilar parents,which might disrupt the evolutionary improvement desired in the subsequent populations.To avoid this,mating restriction is applied using a mating-selection algorithm that biases the selection phase of the A algorithm to prefer and cross more phenotypically similar parents [38];o solutions are chosen via standard binary tournament selection with replacement.Of these a candidates,the solution that is most similar or dissimilar from the others is chosen as the first parent.The mate for this first parent is biased by performing B fitness-based tournament selections and then selecting the winner closest to the original parent,as measured in genotypic space.By increasing the magnitude of B,the user increases the strength of similarity between parent solutions.Positive values of B are of special interest for problems with hierarchical encodings,because crossover between 280ft similar solutions is expected to produce children with better fitness Fig.9 Three views of the supersonic reference vehicle provided by values. NASA [36] Maintaining population diversity is another important issue in 3.Multi-Island Strategy and Parallelization using GAs.Restricted tournament replacement [37]is used in this Two of the most frequent criticisms of genetic algorithms are that study to allow a diverse population.Under this method,each child they typically require a very large number of function evaluations to solution is compared with @solutions from the parent population and converge and they are prone to premature convergence in certain circumstances.In an attempt to accelerate the convergence of genetic algorithms,an injection island strategy has been proposed,which Table 3 Technology weighting factors used in weight modification Multiplication factor Value 10 *133 Wing weight 0.75 -Present calculations Fuselage weight 1.05 9.5 ￥Reference results Empennage weight 0.85 9 Table 4 Weight analysis comparison [36] 85 Mass and balance summary Calculated Reference %difference 8 Wing 74.621 84.278 -11.46% Horizontal tail 2952 3084 -4.28% 75 Vertical tail 2375 2385 -0.42% Fuselage 49.996 49.996 0.00% Landing gear 29.998 27.908 7.49% Nacelle (air induction) 0 65 Structural total 159.942 167.652 -4.60% Engines 87,339 89.438 -2.35% Thrust Reversers 0 04 06 08 121416 18 Miscellaneous systems 1463 1463 0.00% Mach number Fuel system:tanks and plumbing 5443 5026 8.30% Propulsion total 94.245 95.926 -1.75% a)Zero lift drag comparison at 50,000 ft Surface controls 9132 0130 0.02% Auxiliary power 1192 1192 0.00% 14 Present calculations Instruments 1366 1546 -11.64% -Reference results Hydraulics 5143 4301 19.58% 12 Electrical 4399 4542 -3.15% Avionics 1983 2718 -27.04% Furnishings and equipment 18.987 19.825 -4.23% Air conditioning 5449 5504 -1.00% Anti-icing 483 363 33.06% 08 Systems and equipment total 48.134 49.121 -2.01% Weight empty 301.779 312.700 -3.49% Cv Crew and baggage:flight,2 450 675 -33.33% 06 Crew and baggage:cabin,4 665 975 -31.79% Unusable fuel 1574 1896 -16.98% 04 Engine oil 367 367 0.00% Passenger service 2681 3318 -19.20% Cargo containers 1575 1575 0.00% 02 Operating weight 309.091 321.506 -3.86% Passengers,175 28.875 28.875 0.00% Passenger baggage 7700 7875 -2.22% 0.05 0.1 0.15 0.2 025030.35 Zero fuel weight 345.666 358.256 -3.51% CD Mission fuel 468237 45564) 2.76% Ramp (gross)weight 813.898 813.898 b)Takeoff drag polar comparison Fig.10 Aerodynamic validation with the reference vehicle [36]
Maintaining population diversity is another important issue in using GAs. Restricted tournament replacement [37] is used in this study to allow a diverse population. Under this method, each child solution is compared with! solutions from the parent population and replaces the closest of these if it has better fitness. Conventional tournament selection picks parent designs randomly and causes crossover between these possibly dissimilar parents, which might disrupt the evolutionary improvement desired in the subsequent populations. To avoid this, mating restriction is applied using a mating-selection algorithm that biases the selection phase of the algorithm to prefer and cross more phenotypically similar parents [38]; solutions are chosen via standard binary tournament selection with replacement. Of these candidates, the solution that is most similar or dissimilar from the others is chosen as the first parent. The mate for this first parent is biased by performing fitness-based tournament selections and then selecting the winner closest to the original parent, as measured in genotypic space. By increasing the magnitude of , the user increases the strength of similarity between parent solutions. Positive values of are of special interest for problems with hierarchical encodings, because crossover between similar solutions is expected to produce children with better fitness values. 3. Multi-Island Strategy and Parallelization Two of the most frequent criticisms of genetic algorithms are that they typically require a very large number of function evaluations to converge and they are prone to premature convergence in certain circumstances. In an attempt to accelerate the convergence of genetic algorithms, an injection island strategy has been proposed, which Fig. 9 Three views of the supersonic reference vehicle provided by NASA [36] Table 3 Technology weighting factors used in weight modification Multiplication factor Value Wing weight 0.75 Fuselage weight 1.05 Empennage weight 0.85 Table 4 Weight analysis comparison [36] Mass and balance summary Calculated Reference % difference Wing 74,621 84,278 11:46% Horizontal tail 2952 3084 4:28% Vertical tail 2375 2385 0:42% Fuselage 49,996 49,996 0.00% Landing gear 29,998 27,908 7.49% Nacelle (air induction) 0 0 Structural total 159,942 167,652 4:60% Engines 87,339 89,438 2:35% Thrust Reversers 0 0 Miscellaneous systems 1463 1463 0.00% Fuel system: tanks and plumbing 5443 5026 8.30% Propulsion total 94,245 95,926 1:75% Surface controls 9132 9130 0.02% Auxiliary power 1192 1192 0.00% Instruments 1366 1546 11:64% Hydraulics 5143 4301 19.58% Electrical 4399 4542 3:15% Avionics 1983 2718 27:04% Furnishings and equipment 18,987 19,825 4:23% Air conditioning 5449 5504 1:00% Anti-icing 483 363 33.06% Systems and equipment total 48,134 49,121 2:01% Weight empty 301,779 312,700 3:49% Crew and baggage: flight, 2 450 675 33:33% Crew and baggage: cabin, 4 665 975 31:79% Unusable fuel 1574 1896 16:98% Engine oil 367 367 0.00% Passenger service 2681 3318 19:20% Cargo containers 1575 1575 0.00% Operating weight 309,091 321,506 3:86% Passengers, 175 28,875 28,875 0.00% Passenger baggage 7700 7875 2:22% Zero fuel weight 345,666 358,256 3:51% Mission fuel 468,232 455,642 2.76% Ramp (gross) weight 813,898 813,898 Fig. 10 Aerodynamic validation with the reference vehicle [36]. 46 RALLABHANDI AND MAVRIS
RALLABHANDI AND MAVRIS 47 0 404 △Cenerd ⊙bani4 Ama Diet 0 Corventional 06 T-tall Renw】 100 04 0.2 02 Celor By Control Sufacns 92 -04 90 -06 83 08 3000 50 100 150 200 Range (nm) Time (ms) 11653 Range(nm)=3294.6 SPR=0.363 Jet Velocity (ft/s)= 1557.3726 VAPP 126 WeP PL(dB)=89.2563 Cruise Mach #=1.7679 TOGW=98945 Penalty=2262.622 Length 136.256 Fus.Diam 6.9617 1180 Fig.11 Canard performance comparison,visualization,and tradeoff. allows multiple populations to evolve in parallel [39].In this scheme, the thrust-to-weight ratio (TWR)to minimize the excess fuel.The the main GA population evolves normally using the GA operators calculated thrust-to-weight ratios are use to scale the engine deck. and secondary populations are run at regular intervals,and the best FLOPS is run using the scaled engine deck and drag polar results from those are injected into the main GA population.This information.The altitude is allowed to vary to maximize range optimization scheme has been shown to improve the convergence Finally,the engine takeoff power setting is estimated by iterating rate by nearly an order of magnitude when compared with the FLOPS to take off around 7000 feet.This was done to compare conventional GA.This scheme is used in this study to improve the different engine-cycle architecture for takeoff noise.Although noise performance of the GA.Because of the size of the problem,the entire was not considered explicitly during this study,inclusion of jet process could take a long time to run on a single computer.To velocity as one of the objectives makes the final designs acceptable in remedy this issue,parallel-grid computing using CONDOR [40,41] that dimension because of the strong correlation between takeoff has been used in this study. noise and jet velocity. E.Optimization Setup IV.Validation The optimization process begins by creating multiple populations To ensure that the tools and methods being used for the work are In this study,the main population is augmented by a single secondary consistent with those used by other researchers for supersonic aircraft population.Each population member represents a complete analysis,a supersonic reference geometry provided by engineers at geometry,along with propulsion parameters and certain flight NASA was analyzed using the modeling environment.The reference conditions.The engine model is run and the engine deck is generated. vehicle,shown in Fig.9,is based upon a concept developed during Engine-weight regressions are used to calculate the propulsion the High-Speed Research Program.It has been resized to carry 150 system weights.The aerodynamics,stability,noise,and other passengers over a 5500-n-mile,50%Mach 0.95,50%Mach 2.0 relevant analyses are run over each geometry.FLOPS runs the mission.The power plant was also supplied by NASA and includes a geometry through arepresentative mission by parametrically varying mixer-ejector nozzle sized to meet FAA stage-III noise levels.To simulate present-day composite technology effects,the technology weighting factors listed in Table 3 were applied to the weights Table 5 Effect of horizontal stabilizer type computed by FLOPS.These same factors were used to generate the NASA-supplied results.To obtain results for comparison,the present Objective T-tail Canard modeling environment was run in analysis mode with the same gross Range,n mile 3330.7 4362.6 weight as that of the supplied reference vehicle. Jet velocity for 7000-ft takeoff,ft/s 1554.45 1420.8 Shock pressure rise,psf 0.32 0.33 A.Weight Comparison Sonic boom,PL (dB) 88.447 94.848 Approach velocity,kt 137.9 133.1 Table 4 depicts the comparison between the weight breakdown Static stability penalty 2577.75 168.2 from the NASA reference with those calculated using the analysis tools mentioned earlier in this paper.The predicted weights are
allows multiple populations to evolve in parallel [39]. In this scheme, the main GA population evolves normally using the GA operators and secondary populations are run at regular intervals, and the best results from those are injected into the main GA population. This optimization scheme has been shown to improve the convergence rate by nearly an order of magnitude when compared with the conventional GA. This scheme is used in this study to improve the performance of the GA. Because of the size of the problem, the entire process could take a long time to run on a single computer. To remedy this issue, parallel-grid computing using CONDOR [40,41] has been used in this study. E. Optimization Setup The optimization process begins by creating multiple populations. In this study, the main population is augmented by a single secondary population. Each population member represents a complete geometry, along with propulsion parameters and certain flight conditions. The engine model is run and the engine deck is generated. Engine-weight regressions are used to calculate the propulsion system weights. The aerodynamics, stability, noise, and other relevant analyses are run over each geometry. FLOPS runs the geometry through a representative mission by parametrically varying the thrust-to-weight ratio (TWR) to minimize the excess fuel. The calculated thrust-to-weight ratios are use to scale the engine deck. FLOPS is run using the scaled engine deck and drag polar information. The altitude is allowed to vary to maximize range. Finally, the engine takeoff power setting is estimated by iterating FLOPS to take off around 7000 feet. This was done to compare different engine-cycle architecture for takeoff noise. Although noise was not considered explicitly during this study, inclusion of jet velocity as one of the objectives makes the final designs acceptable in that dimension because of the strong correlation between takeoff noise and jet velocity. IV. Validation To ensure that the tools and methods being used for the work are consistent with those used by other researchers for supersonic aircraft analysis, a supersonic reference geometry provided by engineers at NASA was analyzed using the modeling environment. The reference vehicle, shown in Fig. 9, is based upon a concept developed during the High-Speed Research Program. It has been resized to carry 150 passengers over a 5500-n-mile, 50% Mach 0.95, 50% Mach 2.0 mission. The power plant was also supplied by NASA and includes a mixer-ejector nozzle sized to meet FAA stage-III noise levels. To simulate present-day composite technology effects, the technology weighting factors listed in Table 3 were applied to the weights computed by FLOPS. These same factors were used to generate the NASA-supplied results. To obtain results for comparison, the present modeling environment was run in analysis mode with the same gross weight as that of the supplied reference vehicle. A. Weight Comparison Table 4 depicts the comparison between the weight breakdown from the NASA reference with those calculated using the analysis tools mentioned earlier in this paper. The predicted weights are Fig. 11 Canard performance comparison, visualization, and tradeoff. Table 5 Effect of horizontal stabilizer type Objective T-tail Canard Range, n mile 3330.7 4362.6 Jet velocity for 7000-ft takeoff, ft/s 1554.45 1420.8 Shock pressure rise, psf 0.32 0.33 Sonic boom, PL (dB) 88.447 94.848 Approach velocity, kt 137.9 133.1 Static stability penalty 2577.75 168.2 RALLABHANDI AND MAVRIS 47