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