Effects of stability margin and thrust specific fuel consumption constrains on multi-disciplinary optimization for blended-wing-body design

Minghui ZHANG, Zhenli CHEN,*, Zhogung TAN, Wenting GU,Dong LI, Chngsheng YUAN, Binqin ZHANG

a School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

b Shanghai Aircraft Design and Research Institute, Commercial Aircraft Corporation of China, Ltd., Shanghai 200232, China

KEYWORDS

Abstract Blended-Wing-Body (BWB) configuration, as an innovative transport concept, has become a worldwide research focus in the field of civil transports development.Relative to the conventional Tube-And-Wing(TAW)configuration,the BWB shows integrated benefits and serves as a most promising candidate for future‘‘green aviation”.The objective of the present work is to figure out the effects of the stability margin and Thrust Specific Fuel Consumption (TSFC) on the BWB design in the framework of Multi-Disciplinary Optimization (MDO). A physically-based platform was promoted to study the effect static stability margin and engine technology level. Low-order physically based models are applied to the evaluation of the weight and the aerodynamic performance.The modules and methods are illustrated in detail,and the validation of the methods shows feasibility and confidence for the conceptual design of BWB aircrafts.In order to find out the relation between planform changes and the selection of stability and engine technology level,two sets of optimizations are conducted separately. The study proves that these two factors have dominant effects towards the optimized BWB designs in both aerodynamic shapes,weight distribution,which needs to be considered during the MDO design process. A balance diagram analysis is applied to find out a reasonable static stability margin range.It can be concluded that a recommended stability margin of a practical BWB commercial aircraft can be half of that of a conventional TAW design.©2019 Chinese Society of Aeronautics and Astronautics.Production and hosting by Elsevier Ltd.This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction

Blended-Wing-Body (BWB) configuration is a revolutionary concept for commercial transports and a potential option for future civil aircrafts.1By integrating wings, centerbody,engines and tails into a single lifting surface, the BWB configuration achieves a substantial performance improvement.As an advanced technology collector,the BWB configuration preserves advantages of aerodynamics improvement,weight reduction, noise shielding, and emissions reduction,compared with the conventional Tube-And-Wing(TAW)configuration.The aviation industries have performed continuous investigations on the BWB as long-haul civil aircrafts for decades.2-8Because of the unique geometry feature that the lifting body,wing,control surfaces and engines are highly integrated,the aerodynamics,structure and stability and control issues are highly interrelated. BWB has an inherent multidisciplinary integration and appears as a Multidisciplinary Design Optimization (MDO) problem. Trade-offs between different disciplines are obligated. In fact, the BWB configuration appears frequently as a sample problem of MDO design. However,most of the MDO designs were performed on specified planform and engine technologies.

Since the beginning of BWB development,the Stability and Control (S&C) design exhibited as a challenge. The Boeing Company applied WingMOD to realize the early stage MDO designs of BWB.1,2The WingMOD adopts traditional vortex lattice method for aerodynamic estimation and monocoque beam simplification for structural weight estimation.With the help of MDO method, Boeing BWB-450 was trimmed at the stability margin Kn=+5%, by changing the planform, centerbody airfoil and twist distribution, which is quite different from that of the first generation Boeing BWB-800-I (Kn=-15%). The second generation Boeing BWB-800-II is still statically unstable to achieve high lift-to-drag ratio(L/D).The Central Aerohydrodynamic Institute(TsAGI)of Russia investigated a large capacity aircraft of multiple layouts.9Based on the consideration of possible variants of the control system, the Knof IWB-750 was assumed to be -3%at cruise Mach number of 0.85. Under this constraint, a final design achieves a high L/D of 24.5,while the highest L/D could be realized at a higher instability level of about 12-14%.It was also concluded that the allowable Center of Gravity (CG)range for BWB would be lower than that for current TAW airplanes. In ACFA2020 (Active Control for Flexible Aircraft)Project10-12an ultra-efficient 450 passenger BWB design was realized by using new controllers to improve ride comfort and handling qualities, as well as load reduction. An adaptation of the CG by fuel redistribution is proposed to obtain a reasonable Knaround 5%to improve high cruise performance.Otherwise,the Kncould reach a level of 13%with a large trimdrag penalty.These investigations show that the stability margin is highly interrelated with aerodynamic efficiency of BWB,and that a high aerodynamic efficiency should be realized under SC constraints Due to the inherent wing-body integration, the magnitude of Kncan have effects on the layout, e.g.aerodynamic configuration, weight distribution and control strategy, which is much stronger than that of TAW design.Distinct planforms can be observed for different BWB concepts with different stability margin, as shown in Fig. 1.

However, most of the previous studies were performed to study the effects of SC constraints on specified configurations with fixed planforms.13-15More recently, MDO optimizations were applied for BWB design with variable planform and constraints on S&C.

A series of RANS-based aerodynamic shape optimization studies on BWB design was performed to understand the tradeoffs between aerodynamic performance, and constraints on trim,stability,and bending moment.16The effects of different geometry design variables, e.g. twist, airfoil shape, and planform shape are explored with CG travels in a limited range. It was concluded that a balanced and stabilized design could be achieved through profile camber or wingtip twisting combining with sweep. The results demonstrated that the trimmed and stable configuration with lowest cruise drag could be obtained by enforcing a Knof 1%. A multi-fidelity MDO method was also developed, which incorporates low-fidelity weight and balance models, and a Reynolds Averaged Navier-Stokes (RANS) solver for aerodynamic performance and S&C.17The method was applied on a regional BWB design under S&C constraints, the resultant designs are trimmed in pitch, and satisfy the constraint on Kn≥-4% at cruise. However, when a more stringent requirement was applied, the optimizer preferred to move the neutral point aft by tailoring of the wing pressure distributions, instead of variations on the planform.The result turns to be a local optimized, as it would exhibit significantly degraded performance at off-design conditions. ONERA conducted a multi-control surface optimization for an Airbus long-range BWB under handling quality constraints,18where the design challenges on control sizing and control-surface minimization of BWB were pointed out when the adequate closed-loop handling qualities were ensured by limited deflections and deflection rates at the preliminary design level.

Through the previous studies, it can be concluded that the design of a stable and highly cruise-efficient BWB is still an open question,specifically what is a suitable longitudinal static stability margin.It is also obvious that by integrating the S&C constraints into the MDO conceptual design is essential.However, when conducting a three-dimensional optimization, special attention should be paid to avoid a local optimization obtained by aerodynamic tailoring. Therefore, it is preferred to perform a direct planform optimization in a much larger design space to find out a balance between tradeoffs.

Meanwhile fuel efficiency is a driven design matrix for BWB design,because it is an important determinant of aircraft range, size, economics, noise and emissions. During the past 70 years, a great progress has been made on engine design,contributing around half of the aircraft fuel efficiency.The efficiencies of turbofan engines are improved by increasing Overall Pressure Ratio (OPR) and ByPass Ratio (BPR) and by decreasing Fan Pressure Ratios (FPR) to obtain lower Thrust Specific Fuel Consumption(TSFC).19The BWB configuration provides opportunity to adopt larger BPR engines because of upper-surface mounting position. Historically, most representative works concerning about the engine technology level is carried out by the National Aeronautics and Space Administration (NASA).20-23NASA investigated BWB configurations and accumulated knowledge and technologies on BWB design.Several different BWB configurations were developed with increasing fidelity. In 2004, a 300 passenger BWB transport powered by two General Electric (GE) GE-90-like engines was designed using NASA standard toolset (FLOPS, NPSS and WATE) aiming at down-select and assessment of candidate Propulsion Airframe Aeroacoustics (PAA) technologies under NASA’s quiet aircraft technology project.20In 2009, a 305 passenger Hybrid-Wing-Body (HWB) configurations(HWB300-2009)21was designed for system study using the same toolset based on the Boeing BWB-450, whose cruise TSFC is 0.516 lb·lbf-1·h-1, specific fuel consumption is measured in fuel mass flow per hour per unit thrust force,which is commonly used in pounds of fuel per hour, per pound of thrust.In 2012,the scaling effects of HWB22were studied with improved FLOPS, a higher order centerbody weight estimation methodology and technology assumptions on advanced propulsion system and hybrid laminar flow control, and several advanced subsystems. With a TSFC of 0.49 lb·lbf-1·h-1,it was concluded that the HWB configuration have the potential to simultaneously reduce fuel burn and noise level compared to an TAW configuration using equivalent technologies. In 2016, the performance potential of several advanced subsonic concepts including BWB configuration were assessed.23Three categories of HWB were designed using the advanced technology and updated weight estimation method. The engine technologies included a low fan pressure ratio with short inlet, swept and leaned fan exit stators, a highly loaded high-pressure compressor enabling higher overall pressure ratios,and a low NOxcombustor,and the TSFC is assumed to be 0.485 lb·lbf-1·h-1for direct drive turbofan. By examining the noise, fuel burn, and emissions, the HWB concepts adopting GTF engines provide the best overall performance. It can be concluded that the TSFC is the key parameter to represent the engine technology level.Direct benefit due to the improvement of engine technologies could be obtained according to the NASA’s design.The effect of TSFC on the BWB configuration should be considered to realize a more aerodynamic efficient design.

The static stability margin and engine technology level are dominant design aspects.24It is inspiring to find out that whether there is any more aerodynamic efficient BWB configuration under different stability margin range and engine technology level constrains, when a free deformation of configuration is permitted. A MDO framework is constructed permitting a large design space,which can represent the typical stable and unstable BWB planforms.Two sets of MDO studies of a BWB configuration was conducted to understand the interrelation among planform changes, aerodynamic performance,and constraints on stability margin and engine technology level. The optimization results indicate that these two design factors have strong influences on the BWB planforms.To figure out a reasonable static stability margin combining with center of gravity, a balance diagram analysis is also conducted.

2. MDO design methods and validations

The overall structure of the conceptual design platform is accomplished under MATLAB and can be seen in Fig. 2.The program structure can be divided into a design evaluation loop and an optimization design loop.This two-level structure enables the platform to act as both a quick evaluation tool and an MDO design tool.

The optimization design utilizes the Multi-Objective Genetic Algorithm (MOGA) to perform the multi-objective conceptual design of a BWB configuration. The design begins with the definition of the mission profile, the design objective and the selected technology level. After defining the design space of each variable, Latin hypercube sampling is applied to ensure proper spatial distribution of the first generation.Then the geometry module translates the design variables into geometry files of different formats, laying the foundation for the following analysis module. An integration process is applied to the weight and aerodynamic analysis and engine modules to ensure proper coupling of the disciplines. After the convergence of both the weight and aerodynamics,the performance module is applied to the evaluation of the characteristics of the design.Geometry limitations,stability and control,payload and fuel capacity requirements are treated as optimization constraints to achieve a feasible design. The optimized results that achieve the design objectives and meet the design constraints are further analysis by high-order methods.If the performance is not acceptable,adjustments will be made in technology and configuration selections until the MDO design process find the acceptable optimization results.

2.1. MDO design methods

2.1.1. Geometry module

The geometry module provides both the outside aerodynamic shape and the inside arrangements,such as the cabin,the cargo and the fuel volume. It prepares the input files needed in the other modules. The parametric definition of the BWB geometry is preferred in accomplishing the exploration of the design space.In the geometry module,the BWB configuration geometry is decomposed into the planform and the section airfoils.

As exhibited in Fig. 3, the planform incorporates four parts: the cabin, the rear cabin, the trapezoidal wings, and the outboard wing. The cabin section is the pressurized bay,which is sized by the number of passengers. The rear cabin is the area attached with the engines and the trailing-edge elevon of the centerbody.The outboard wing is similar to the conventional kink-wing design. The trapezoidal wings provide smooth transition from the centerbody to the outboard wing sections. Fuel tanks are placed in the outboard and the trapezoidal wings. It is a design constraint to ensure the sufficient volume of the fuel tanks.

Fig. 2 Program structure of conceptual design platform.

Fig. 3 Planform of geometry parametric definition.

The planform is defined by explicit physical parameters,grouped into chord-wise lengths C1-C5, span-wise lengths B1-B4and sweep angles Λ1-Λ3.To realize a quick transition from the outer-wing to the centerbody and reduce the empty space,an additional control section is added at the kink position.The design parameters lead to a linear planform represented by the red dashed lines, while a smooth outline planform is obtained by applying the piecewise cubic splines.This method is convenient and efficient to describe a reasonable planform and arrangement. The representation capability of parametric geometry module for BWB planform is tested in a large initial design space, as shown in Fig. 3. A variety of planforms that differ in chords, widths and sweep angles are generated.

Specially designed airfoils are required in BWB configurations. With the stability and control requirements, the cabin,and the cargo arrangement taken into consideration, thick leading-edge curving airfoils are preferred in the centerbody section while typical super-critical airfoils are preferred in the outboard wing to improve the transonic aerodynamic efficiency. Different parametric approaches can be utilized to express the airfoils. However, it will considerably increase the number of design variables and decrease the speed of planform exploration, which is more important in conceptual design phase.Thus,properly designed airfoils in former studies are used here with thickness variations to satisfy the capacity requirements.

With the help of OpenVSP,25a quick geometry is created to provide a first glance of the design configuration to avoid potential mistakes in the input parameters, while the final three-dimensional geometry is obtained by interpolating the section airfoils along the planform with the assistance of the CATIA scripts.

2.1.2. Weight module

The weight module estimates the weight of the major components such as the structure, the propulsion, the fixed equipment, the landing gear, the fuel and payload. The overall aircraft CG is provided by calculating the weights and the locations of the components.

The BWB structural weight calculation presents a serious challenge as this configuration incorporates a non-cylindrical pressurized cabin into the centerbody,which serves as a lifting surface and a fuselage with internal pressure.Several structureestimation methodologies26-29have been put forward to evaluate the BWB centerbody weight with consideration of the complicated loading problem. However, it remains a problem which needs to be further validated. In this study, the structural weight consists of four parts: the cabin, the rear cabin,the trapezoidal wing, and the outboard wing. The centerbody weight prediction routinely implemented is based on a regression of the BWB centerbody FEM analyses for different passenger-size classed aircrafts.26These equations are suitable for the design and analysis of a 200 to 450 passenger BWB transport. The equations are shown as follows:

where MTOW is the maximum take-off weight,KSis a scaling factor equal to 5.698865, Nengthe number of engines supported by the centerbody, Scabinthe cabin planform area, Saftthe planform area of the aft centerbody, and λaftis the taper ratio. Eq. (1) is applied for the cabin weight while Eq. (2) for the rear cabin.

The structural weights of the taper wing and the outer-wing are estimated by the physically-based method promoted by Drela.27The wing is assumed to be cantilevered and the material gauges are sized to undertake the critical loading cases.The resulting wing-box volumes, together with specified material density, provide the primary wing structural weight. A modification has been made to use the wing loading calculated from the vortex lattice method instead of the empirical loading factors.The secondary structural weights are estimated via the historical weight fractions.

The other component weight calculations share the methods of the conventional commercial aircraft, and empirical relationships29-32can be used appropriately. Payload weights are estimated according to the number of passengers. The propulsion weight is provided by the propulsion module,which is presented in Section 2.1.4. The fuel weight is calculated based on the specific mission profile during iteration.The fixed system weight is obtained by the estimation similar to conventional aircrafts.

2.1.3. Aerodynamics module

Better aerodynamic performance is the key feature of BWB configurations. The accuracy of aerodynamic analysis method must be high enough to provide basic aerodynamic features of the design,which is utilized for the performance evaluation.To gain confidence in the aerodynamic results,multi-fidelity aerodynamic models are implemented in the framework. Lowfidelity methods are used to realize quick evaluation during the optimization process, while high-fidelity calculations are applied to the further validation of the optimization results.The low-fidelity aerodynamic method is developed with high efficiency and adequate accuracy. The calculation methods are applied according to the breakdown of the aerodynamic coefficients, as is shown in Fig. 4. The lift induced drag is estimated by a vortex lattice method. The twist angle distributions of the section airfoils are integrated to obtain a desired lift distribution to minimize the induced drag at cruise.The friction drag is calculated using standard flat plate skin friction formulas with compressibility correction,and the form drag is estimated by the form factor. Finally, the wave drag is estimated by the Korn equation. The calculations of the other aerodynamic characteristics such as the lift coefficient,the zero lift moment,and the longitudinal stability also rely on the vortex lattice method. The positive zero lift moment with reasonable static longitudinal stability is essential for the realization of a naturally balanced tailless design. Moreover, the vortex lattice method is applied to the trim control ability evaluation of the centerbody elevon.

Fig. 4 Aerodynamic analysis methods.

The RANS simulation is used for the high-fidelity aerodynamic analysis. A script is developed to realize the automated structural mesh generation for the typical BWB configuration.The initial spacing normal to all viscous walls is limited as y+＜1 based on the Mean Aerodynamic Chord length(MAC), and the growth rate is limited within 1.2. The total number of grid points is nearly 6 million for a clean BWB configuration. The mesh is then applied to the evaluation of the optimized result by conducting RANS calculations with a CFD solver. In this way, the aerodynamic forces of the lowfidelity method are examined and the details of the flow phenomena are revealed.

2.1.4. Propulsion module

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The propulsion system is determined by the maximum thrust facing the most demanding of several design constraints such as the balanced field length for take-off and the climbgradient requirements demanded by the certification specification.29

In this study, we assume two high-bypass-ratio turbofan engines are installed as the podded engines on the back of the BWB centerbody. A rubber-engine method30is used to scale the engine to meet the thrust requirements. The performance changes in the thrust and the TSFC along with the altitude and the airspeed, and is simulated utilizing the Gundlach’s method33which is constructed by the regression analysis of the engine data. The engine model is shown as

where Thrust is the engine thrust at the given altitude and Mach number; Thrust0is the max sea level static thrust; Ma is the Mach number; ρ is the air density at the given altitude and ρslsis the air density at the sea level.

where T is the air temperature at the given altitude, Tslsthe temperature at the sea level, and TSFCslsis the sea level static specific fuel consumption.The thrust and TSFC of an advance turbofan engine with the N+2 timeframe are shown in Fig.5,H is the cruise altitude, 1 kft=0.304 78 km. The engine performance and the weight of the propulsion system are fed back to the weight module for iterations.

2.2. Methods validation

2.2.1. Weight module validation

Due to the complicated loading phenomenon and the indeterminate structure of the centerbody,uncertainty remains in the weight estimation. Furthermore, the sensitivity of the regression equations to the geometry changes in the centerbody is unknown. However, the weight module proves to be feasible in providing similar results and reasonable trends of the weight variation by comparing the detailed component weight data with the H-series BWB. As shown in Table 1, the component weights show good agreement with H2 and H3.2 aircrafts.34The detailed comparisons of component weights between calculation results and reference weights are provided. The relative errors Δ of each component are also given in percentage.Although the same assumption is applied that improvements in material properties lead to 30% reduction in the structural weight by the N+3 time frame,results indicate that the structural weight is slightly over predicted. The accuracy of weight estimation is adequate for the conceptual design platform, as the relative errors of the MTOW are below 2%.

Fig. 5 Engine performance overview.

2.2.2. Aerodynamic module validation

3. Multidisciplinary optimization design

3.1. Optimization design set up

The constructed MDO conceptual design platform is utilized to design a 300-passenger BWB commercial aircraft with cruise speed of Ma=0.85. The top-level requirements used for the present study are listed in Table 2, which are similar to those of a Boeing-777 aircraft.

The optimization objectives are to maximize the cruise aerodynamic efficiency and minimize the maximum take-off weight under the design constraints, as shown in Eq. (5). The cruise lift to drag ratio is the key design objective of the BWB configuration, while the gross weight objective utilized to constrain the outline of the design to maximize the utilization of its interior space. To realize the practical design, constraints are formulated into penalty factors during the optimization process. The planform geometry parameters are inherently limited by the design space as illustrated in Table 3.The chord length value of the second control section C2is implicitly determined C1and Λ1with the consideration that the aft of centerbody has a plane end.The total span of the aircraft is further limited to 65 m, which is the typical value of a conventional TAW aircraft of same size. The cabin area and the fuel capacity are also required to satisfy the design requirements.

where b is the span of the BWB design,Scabinis the cabin area,Vfuelis the fuel capacity, Knis the longitude static stability margin.The design requirements of each variable are identified by the suffix ‘‘req”.

Table 1 Weight validation with H-series aircrafts.

Fig. 6 Aerodynamic validation.

Table 2 Top level requirements.

Table 3 Parameter design space.

3.2. BWB optimization with different static stability margin

Since the static stability margin chosen is still an open issue,a series of optimization have been carried out to study the effect of Knselection on the BWB MDO designs,and aim to find out the suitable range for BWB design. The Knof the three optimizations are limited to the range as follows.

(1) The typical Knfor conventional configuration is selected in OPT1, which is 10-20%.

(2) With the consideration that the MAC of BWB is about two times to that of conventional TAW configuration,the Knof OPT2 is limited within 0-10%, which is half of the conventional aircraft.

(3) Many recently designed BWB configurations are still having stability relaxed, the OPT3 optimization represents this trend, and the Knis limited within -10%-0.

The propulsion system is assumed to use an advance engine with thrust specific fuel consumption of 0.485 lb·lbf-1·h-1.The design objectives and constraints are the same as illustrated in Section 3.1, except that the stability margins are limited within different ranges.

The optimization is conducted by the MOGA method with the population of 100. After integrated for more than 80 generations, all the optimizations reach convergence. The results of the static stability margin optimizations are shown in Figs.7-9.As can be seen from the Pareto fronts,all optimizations present the results to meet the objectives of lower MTOW and higher L/D, and the evolution trends of each generation are to meet the design constraints during the optimization.Three designs are selected on each Pareto front followed the same rule, that the designs with best high-speed aerodynamic efficiency are marked by Point A; the designs with the lowest MTOW are marked by Point C; the coordinate designs for both objectives are marked by Point B.

By comparisons of the configurations along the Pareto fronts, as the lift-to-drag ratios increase, the configurations changes of the three optimizations follow the same design features. The centerbody and blended area become slimmer to save spanwise space for the wing, which is the most aerodynamics efficient. Due to the cabin area constraint, the center-bodies grow longer to provide enough space for the passengers. The wings sweep backward to reduce wave drag.The designs pay a price to realize the geometry modifications.The body and wing structure weight has increased due to the extension of the body and the swept angle change of the wing.

In order to unveil the influence of Kn, the optimization results are put together for further analysis. As shown in Fig. 10, the comparison of Pareto fronts is shown on the left with dashed curves provided by the regression analysis. It is obvious that designs with neutral or unstable longitudinal stability have the highest aerodynamic efficiency. The Pareto fronts shows that if the Knrelaxed by 10%, the MTOW of optimized BWB will reduce 5% with the same L/D, otherwise the L/D will increase 4%with the same MTOW.The comparison of the coordinate design configurations is shown on the right. The differences prove that the selection of Knhas great influence on the aerodynamic shape and weight distribution.The wing of unstable result moves forward, which is similar to the design of IWB-750,as shown in Fig.1.The wing moves backward as the design become more stable,which is similar to the design of ACFA-2020.

Fig. 7 Optimization results for OPT1 (10%≤Kn ≤20%).

Fig. 8 Optimization results for OPT2 (0 ≤Kn ≤10%).

Fig. 9 Optimization results for OPT3 (-10%≤Kn ≤0).

Fig. 10 Comparison of optimization results with different Kn.

3.3. BWB optimization with different TSFC

After the primary study about the static stability margin,another set of optimizations is conduct to explore the configuration and performance change due to the improvements of engine technologies. Different thrust specific fuel consumptions are applied to reflect the changes in fuel efficiency due to engine technology improvement.

(1) A GEnX like turbofan is selected, which represents the current propulsion technology with bypass ratio 10,whose TSFC is estimated as 0.532 lb·lbf-1·h-1.

(2) An advanced propulsion with N+2 technology assumptions is utilized, by consider the fuel consumption drops about 10%. In another words, the TSFC is about 0.485.

(3) An aggressive TSFC of 0.451 lb·lbf-1·h-1is applied to study the changes of BWB configuration design cause by another 10% of engine technology improvement.With the Knlimited within 0 to 10%, two more optimization needs to be conduct, which are marked as OPT4 and OPT5.

By applying the same optimization strategy, the optimization results of the TSFC optimizations are shown in Figs. 11 and 12. The planform changes of the optimization result follow the same trend as the static stability margin study. As lift-to-drag-ratios become larger, the centerbody become slimmer and longer. The swept angles of wing increase to reduce wave drag.

The optimization results of OPT2, OPT4 and OPT5 are plotted together to analysis the effect of different engine technology.As shown in Fig.13,it is obvious that the engine technology have great impact on the BWB weight and aerodynamic efficiency. By comparing the coordinate designs of OPT2 and OPT4, the TSFC reduces 10%, the MTOW will reduce about 4% at the same L/D, which is a result for both configuration variation and TSFC.Coincidently,the planform happen to be the same for OPT2 and OPT5,which provide an opportunity to wipe off the effect of configuration change,the weight reduce about 1%.As fuel is stored in the wing,the fuel consumption show influences on the geometry of configuration,as it will change the weight distribution. However, it will become less influential as lower TSFCand less fuel is needed.

3.4. Analysis of balance diagram for static stability margin optimization results

Fig. 11 Optimization results for OPT4 (TSFC=0.532 lb·lbf-1·h-1).

In order to decide the suitable range of stability margin, the analysis of the variations of the CGs of these three configurations is also carried out in this study.Stating from the position of the aircraft CG in the operational empty condition, 3%variations about the nominal position is applied to account for variations of operational items. Then the aft and forward CG position is obtained with passengers arranged from front to back and from back to front. After that, the fuel is added to both conditions.Finally,fuel can be added at the most critical situation on the rear loading position to indicate the most aft CG position.

Fig. 12 Optimization results for OPT5 (TSFC=0.451 lb·lbf-1·h-1).

Fig. 13 Comparison of optimization results for different TSFC.

The statistical data of the CG variation and changes of static margin are summarized in Table 4 and Table 5. The CG location relative to the MAC is slightly larger for unstable result and smaller for more stable result, due to the wing position relative to the centerbody. Except for the extreme loading situation, the CGs of OPT2 and OPT3 travel within the static stability margin limits for most of the nominal situations. However, the range is much larger for OPT1. The balance diagrams provide a straight way to see the changes of static margins and movements of CGs, as shown in Fig. 14. The CGs at different situations are provided, e.g.OEW, Zero Fuel Weight (ZFW), Maximum Landing Weight(MLW), weight at middle of the cruise and the MTOW. In general, the larger of the CG range the harder it will be to keep the aircraft in balance.

Table 4 Comparison of CG locations.

Table 5 Comparison of static stability margin Kn.

Fig. 14 Balance diagram for optimization results.

The static stability margin of conventional civil aircraft does not apply to BWB configuration, due to the much larger reference surface area and chord length.In our experience,the recommended stability margin can be half of the conventional aircraft, which means the Knlimited within 0 to 10%. Within this limit, the design realized a positive zero-lifting moment coefficient(Cm0)with positive Kn,which almost achieves a naturally trimmed design at the design lift coefficient. The optimized results with relaxed static stability also have the opportunity to realize a trimmed design, if its Cm0is negative.However, typical centerbody airfoils with leading loading are applied in current study, which provides a great amount of positive Cm0. In order to realize a naturally trimmed unstable design, further study will be conducted employing the centerbody airfoil with released the positive moment constraints.

The configuration of Point B from OPT2 represents a design with advanced propulsion system under the Knlimited within 0-10% constraint. The aerodynamic shape and characteristics is shown in Fig. 15. The aerodynamic result confirms the view that the design almost realized a positive Cm0with positive Kn, which almost achieves a naturally trimmed design at the design lift coefficient.The static stability range for under different flight conditions is summarized in Table 6.The result approves that the stability does not change much for different conditions, which may reduce the pressure of control system design.

Fig. 15 Aerodynamic shape and characteristics for Point B of OPT2.

Table 6 Static stability margin analysis for Point B of OPT2.

4. Conclusion

(1) An MDO platform is constructed to study the effect static stability margin and engine technology level. Physically based models are applied to the evaluation of the weight and aerodynamic performance. The modules and methods adopted are illustrated in detail. The validation of the methods shows feasibility of the conceptual design platform of BWB aircrafts.

(2) A set of direct planform optimizations in a much larger design space is conducted to study the effect of static stability margin.The optimized results prove that the static stability margin have great influence on the configuration as suspected. The results also indicate that aerodynamics improvement and weight reduction of BWB can be realized by applying a higher instability level, which also requires the wing to move forward.

(3) The effect of thrust specific fuel consumption is studied by optimization approach. The technology assumptions on advanced propulsion system should be made carefully, as TSFC also has strong influence on the BWB configuration.The optimized results approve that better BWB design can be obtained by considering both the TSFC improvement and the planform variation.

(4) A balance diagram analysis is applied to further discuss the effect of static stability margin. The stability margin of a BWB commercial aircraft is recommended to be half of the conventional aircraft,which offers an opportunity to achieve a naturally trimmed design at the design lift coefficient.

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (Nos. 3102019JC009 and G2016KY0002).