Multipoint optimization on fuel efficiency in conceptual design of wide-body aircraft

Xiao CHAI,Xiongqing YU,Yu WANG

College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

1.Introduction

The continued growth of air traffic has caused increasing demands to improve aircraft fuel efficiency for minimizing aviation’s environmental impact and for counteracting fuel prices.According to the Intergovernmental Panel on Climate Change(IPCC),the civil air transport is expected to continue increasing at a rate of 4.8%by 2036.1The contribution to global anthropogenic carbon emissions by the continued growth in aviation may increase to 15%by 2050.1Ambitious research goals of the reduction of fuel burned have been set by NASA’s Environmentally Responsible Aviation(ERA)Project2and European ‘‘Clean Sky 2” Program.3

Traditionally,aircraft conceptual design optimizations have been generally performed to maximize the aircraft fuel efficiency at a design flight condition,4,5which is referred to as single-point optimizations and may result in designs with unsatisfying performance under off-designflight conditions.To improve the robustness of the designs and increase the aircraft fuel efficiency under actual flight operations,there is a need to consider multipleflight conditions in aircraft conceptual design optimization.The multipoint optimization in this paper means that the objective function in the aircraft conceptual design optimization involves multipleflight conditions.

Early work with a consideration of multiple conditions has been focused on the aerodynamic shape optimizations of airfoils and wings.Buckley et al.6performed an airfoil design optimization under 18flight conditions.Lyu and Martins7investigated the impact of multipoint design optimization on a Navier-Stokes-based aerodynamic shape and planform optimization of a blended-wing-body aircraft.Liem et al.8performed a multipoint aerostructural optimization of a long-rang twin-aisle aircraft,in which high-fidelity aerodynamic and structural analysis models were used.Recently,more studies,which couple aircraft designs and air transport networks,have been conducted with the application of the concept of system of systems oriented design.9Lammering and Schneider10presented an approach focused on singleaisle market requirements.Their results showed that an increase in fuel efficiency and economics of up to 25%was feasible under the consideration of the entire mix of daily operationsofsingle-aisleaircraft.An integrated design and optimization of aircraft families and air transport networks were performed by Jansen and Perez.11Liu et al.12proposed a design index sets evaluation method combining airliner market analysis with aircraft conceptual design.

However,there was few effort made in rapid aircraft conceptual design and optimization with a consideration of the actual uses of these aircraft in an operator’s route networks.In this paper,a new strategy to formulate multipoint design optimization problems is developed to maximize the aircraft fuel efficiency over a large number of different missions.The remainder of the paper is organized as follows:The actualflight operations of a wide-body aircraft are presented in Section 2,in which a civil jet Boeing 787-8 is chosen as the representative of wide-body aircraft based on market analysis,and itsflight missions are analyzed in terms of payloads and ranges.A multipoint optimization problem considering the actualflight missions is formulated in Section 3.A framework to solve both the single-point and multipoint optimization problems is presented in Section 4.The differences between the results from the single-point and multipoint optimizations are discussed in Section 5,followed by conclusions in Section 6.

2.Wide-body aircraft market analysis andflight mission data

Based on the operation capacity of an aircraft,wide-body aircraft can be generally divided into three categories:small widebody,medium wide-body,and large wide-body.According to the Boeing Current Market Outlook13,the design payloads of small wide-body,medium wide-body,and large wide-body aircraft are 200–280,280–400,and more than 400 passengers,respectively.They mainly operate for internationalflights and partially domesticflights.The Boeing current market outlook13predicted that 39620 new commercial aircraft will be delivered over the next 20 years,as shown in Fig.1.

Although the predicted total number of wide-body aircraft to be delivered in the next 20 years is only about one-third of that of single-aisle aircraft,the total market value of widebody aircraft is about the same as that of single-aisle aircraft,as illustrated in Fig.1.The majority of wide-body aircraft is small and medium wide-body aircraft,and Boeing 787-8 is the latest widely operational small wide-body aircraft now.Also considering that China and Russia are co-developing wide-body aircraft14,a wide-body aircraft similar to Boeing 787-8 is chosen as the baseline aircraft in the following optimizations.

To obtain a set of missions that is representative of the actual operations of the baseline aircraft,we referred to the American Research and Innovative Technology Administration (RITA)’s Bureau of Transportation Statistics flight database.15The payload and range data for all Boeing 787-8flights that took off from the United States,landed in the United States,or both was extracted.Since such data is only available for the United States market,we assume that the data can also be used to reflect other markets.These data consists of 60453flights,of which the payload and range distribution(surface)in reference to the design payload-range envelope(solid line)of Boeing 787-816is shown in Fig.2.This distribution is plotted using a 26×42 grid of bins.Each bin is 500 km in range by 1000 kg in payload.We chose the midpoint to represent the range and payload of a bin that contains at least oneflight mission.The color map shown in Fig.2 represents the number offlight missions contained within each bin.There are 426 representativeflight missions in our analysis.A more detailed analysis is provided in Fig.3.The white circle in Fig.2 represents the design point of Boeing 787-8.It can be seen that the majority of allflights were operated within a range of around 8000 km and a 30000 kg payload,respectively.It can also be observed that noflights were operated at the maximum range.Hence,current utilization in daily operations yields potential for optimization of the aircraft efficiency by means of considering off-design conditions.As Boeing 787-8 is the main competitive aircraft of our study aircraft and Boeing 787-8flight operation data in other regions is not easy to obtain,the Boeing 787-8flight data in the United States is chosen as a representative of the actual operations of the baseline aircraft and used in the following multipoint optimization study.

Fig.1 Boeing current market outlook 2016 to 203513.

Fig.2 Distribution of 60453flights for Boeing 787-8 and its payload-range envelope.

Fig.3 Range and payload distributions of Boeing 787-8.

3.Optimization problem definition

As previously mentioned,a baseline aircraft similar to Boeing 787-8 was taken as an example for the optimizations.The range of the aircraft was designed to be 12000 km with a payload of 280 passengers,and the design cruise Mach number is 0.85,which is chosen as the same as that of the aircraft being co-developed by China and Russia.14The initial configuration of the baseline aircraft is shown in Fig.4.

3.1.Objective function

Generally,minimizing Direct Operating Costs(DOCs)is used as the objective of a conceptual design optimization towards improving aircraft economics.However,DOCs are sensitive to many uncertainties and scenario parameters such as fuel price,wages of crew,or operational fees.Therefore,the Speci-fic Hourly Productivity(SHP)17was chosen as the optimization objective for evaluation of aircraft economics.The parameter is defined as

Fig.4 Configuration of baseline aircraft.

wherempayloadis the payload,Rmissionis the range,mblockfuelis the block fuel burned,andtblocktimeis the block time.‘Block’in this paper refers to the completion of an entireflight mission,starting from taxing out and ending by taxing in.Consequently,the block fuelmblockfueland the block timetblocktimeare the total fuel burned and the total time spent in the entire trip,respectively.The parameters in Eq.(1)only depend on technical parameters that directly result from aircraft design analysis.

For the single-point optimization problem discussed in this paper,only oneflight condition is considered.The objective of the single-point optimization,SHPsingle,is the specific hourly productivity in a designflight mission in which the aircraft is designed to transport 280 passengers over 12000 km.The expression is as follows:

In the multipoint optimization,the objective function,SHPtotal,is defined as the weighted sum of all SHPiof each single mission.The relative frequency of each mission is obtained by normalizing its frequency with respect to the total number offlight missions.Therefore,SHPtotalis expressed as

whereflightiis the number of each flight mission,and flighttotalis the total number of allflight missions.The Boeing 787-8flight operation data shown in Figs.2 and 3 were used in the calculation of SHPtotal.There were 426 representativeflight missions evaluated using the SHP_total analysis module(see Section 4.6).Then they were summed up to formulate SHPtotalby weighing their frequencies.

3.2.Design variables

There are totally eleven design variables,of whichfive geometric variables are wing configuration parameters,while the other six are engine thermodynamic cycle parameters.The design variables and their bounds are listed in Table 1.

3.3.Design constraints

There are several constraints imposed in the optimization problems,which are listed in Table 2.These constraints need to be satisfied at the design condition to ensure that the optimized aircraft meets the performance and geometrical requirements,including mission range,takeoff and landingfield lengths,available fuel volume,engine-out climb gradient,and rate of climb at Top Of Climb(TOC).

4.Overall solution framework

A multidisciplinary integrated framework for aircraft conceptual analysis and optimization18was applied to solve the optimization problems described above,as illustrated in Fig.5.The aircraft conceptual analysis framework consists of several disciplinary analysis modules,including propulsion,geometry,aerodynamics,weight,and mission performance analysis modules.Empirical formulations with various statistical data,semi-empirical equations,and some simplified numerical methods are used in the modules under considerations of rapid execution and robustness of the framework.Each module is independent and easy to be modified.The analytical methods in each discipline are briefly described below.The optimization algorithm specifies a new combination of input parameters in every loop in the optimization studies.

4.1.Propulsion

The propulsion module is used to estimate thrust and fuel consumption performance for various engine configurations.The basic engine architecture for the optimization performed in this study is a two-spool,separate-flow turbofan as shown in Fig.6.

The code for calculating the engine performance is a zerodimensional steady thermodynamics analysis program.19At the engine design point,the program automatically ensures continuity of mass,speed,and energy by varying the scale factors on the performance maps for the compressor and turbine components.Off-design operation of the engine is handled through the use of component performance tables and minimization of work,flow,and energy errors.The engine is then balanced by altering the free variables of available components.The propulsion code is run for various conditions required by the performance module,and the results of engine performance are then exported in a three-dimensional array of altitude,Mach number,and thrust setting.

Table 1 Design variables and their bounds.

Table 2 Design constraints.

4.2.Geometry

A parametric geometric model based on the quasi-analytical methods20is used to define the aircraft configuration geometry.The functionality of this model is to estimate the wetted area of the aircraft and the volume of the fuel tank required by the aerodynamics and weight modules.A typical geometrical model of the aircraft configuration generated by the geometry module is shown in Fig.4.

4.3.Aerodynamics

The low-and high-speed aerodynamic characteristics of the aircraft are calculated by the aerodynamics module.The lift characteristics of a clean wing are computed using a quasianalytical technique.20A detailed component build-up method is used to calculate the zero-lift drag,which takes into consideration the viscous separation and the mutual interference effects between components.21The method used to estimate the lift-induced drag is the Oswald span efficiency method.20The wave drag is calculated based on the modified Korn’s equation.22The lift increment produced by flap and slat deflections at low speed is estimated based on the methods presented by Isikveren.20The total incremental drag due to one engine’s inoperative condition is also estimated in this module.

4.4.Weight

The weight module is used to predict the weight of each component of the aircraft.The maximum takeoff weight of the aircraft is calculated iteratively by adding the component weight,which is estimated using empirical methods.23The fuel required for the design mission is estimated by the iteration of the weight andflight performance modules.Fig.7 illustrates the definition and breakdown of the aircraft weight.

4.5.Performance

The performance module estimates the mission required fuel,takeofffield length,landing field length,and second-segment gradient.A typical airliner mission profile is illustrated in Fig.8.The takeoff and landing performances are calculated using a parametric expression24The main mission performance is obtained using a piecewise analytic model based on simpli-fied motion equations for typicalflight segments.25The fuel burned in a reserve mission is predicted based on the fraction of the aircraft’s maximum takeoff weight.Additional performance constraints in the optimization studies are also evaluated in the performance module.

Fig.5 Framework of multidisciplinary analysis and optimization.

Fig.6 Turbofan engine model with two-spool separate exhaust.

4.6.Objective evaluation

The specific hourly productivities,as the optimization objective,are evaluated in the SHP_single and SHP_total analysis modules as shown in the overall solution framework in Fig.5.

In the single-point optimization,given the design payloadmpayload,designand the design rangeRmission,design,the design block fuel burnedmblockfueland the design block timetblocktimecan be predicted by the performance module detailed in Section 4.5.Based on the above information,SHPsinglecan be calculated using Eq.(2).

In the multipoint optimization,the data of Boeing 787-8flight missions is adopted in the computation of the total speci-fic hourly productivity.For each flight mission(the given payload and range),the block fuel and block time can be obtained from the results of the mission performance analysis described in Section 4.5,and consequently the specific hourly productivity SHPifor each mission can be calculated using Eq.(2).Finally,the total specific hourly productivity SHPtotalcan be calculated according to Eq.(3).However,in the multipoint optimization loops,all designs need to meet the design condition with a design payload of 280 passengers and a design rang of 12000 km.The design condition of the current study aircraft(black circle)is slightly different from that of Boeing 787-8(white circle),as shown in Fig.2.As a result,when the aircraft operates atflight conditions near the margin of the payloadrange envelope of Boeing 787-8,it would need so much fuel that its takeoff weight may exceed its maximum takeoff weight.Thus these missions are infeasible;the productivity is set to zero on such a few missions(SHPi=0).

Fig.7 Aircraft weight breakdown and definition.

Fig.8 Typical airliner mission profile.

4.7.Optimization strategy

A Multi-Island Genetic Algorithm(MIGA)26was used to optimize both the single-point and multipoint optimization problems defined in Section 3.The technique options of the MIGA were set as shown in Table 3.

Table 3 Technique options of MIGA.

5.Results

In this section,we present the results of the single-point and multipoint optimizations for a wide-body aircraft.Both the single-point and multipoint optimizations spent about 48 h on computation using a desktop PC(CPU@2.90 GHz and RAM@4.0 GB)after 5000 iterations.Table 4 lists the optimal design variables for both optimization cases,as well as additional key performance parameters.Figs.9 and 10 show the optimization convergence histories of SHPsinglein the singlepoint optimization and SHPtotalin the multipoint optimization,respectively.To clearly show the optimization convergence histories,only the best feasible design points of each generation are shown in thefigures.

As shown in Table 4,the multipoint optimal design has a 7.72%greater total specific hourly productivity of entire flight missions compared to that of the baseline aircraft,while the increase in the total specific hourly productivity of the singlepoint optimized design is only 5.73%.

Both the multipoint and single-point optimal designs have higher aspect ratio wings,which can reduce the induced drag of the aircraft.The multipoint optimal design has a smaller wing area and a smaller wing sweep than those of the singlepoint optimal design.The reason is that the payload,range,or both of the aircraft operating at most off-designflight conditions are smaller than those at the designflight condition.Consequently,the aircraft takeoff weight operating at offdesign flight conditions is lighter than that at the design flight condition,resulting in a smaller wing area and wing sweep in the multipoint optimal design.

Table 4 Results of single-point and multipoint optimizations.

Fig.9 Optimization convergence history of SHPsinglein singlepoint optimization.

Fig.10 Optimization convergence history of SHPtotalin multipoint optimization.

The two optimized designs have similar engine cycle parameters.Both have a moderate bypass ratio and higher overall pressure and turbine inlet temperature,which can reduce the engine thrust specific fuel consumption.

6.Conclusions

To consider the actual use of aircraft in route networks,this paper performed single-point and multipoint optimizations of a wide-body aircraft for the maximum fuel efficiency.The data of Boeing 787-8 flight missions was used to reflect the true objective function in the multipoint optimization.The design from the multipoint optimization results in a smaller wing area and a smaller wing sweep compared to those of the design from the single-point optimization.In addition,the design from the multipoint optimization has a 7.72%total specific hourly productivity increase of entireflight missions compared to that of the baseline aircraft,while the increase in the total specific hourly productivity of the design from the singlepoint optimization is only 5.73%.The difference between the results of the single-point and multipoint optimizations show that the multipoint optimization is a good option to further improve the aircraft efficiency by considering actualflight conditions in the aircraft conceptual design and optimization.This capability to analyze a large number offlight conditions could be extended with a little modification to other objective functions of interest for any commercial aircraft.

Acknowledgement

This study was supported by the Fundamental Research Funds for Central Universities(NUAA NS2016010).

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