development and validation of conceptual design framework

American Institute of Aeronautics and Astronautics

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Development and Validation of Conceptual Design Framework for a Mid-Size

Turbo-Prop Transport

Youngmin Jo1, Seongim Choi

2, and Youngmin Park

3

Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

Korea Aerospace Research Institute, Daejeon, Korea, Republic of Korea

A turboprop aircraft is suitable for mid-range transport as it has high fuel efficiency in specific flying condition. For

this reason, a mid-size turboprop aircraft has been re-drawing great interests in the design community concurrent

with the growth of the airline industry. South Korea is in the process of designing and developing its own mid-size

turboprop transport to keep pace with the international trend. For that purpose, we develop an in-house sizing

program as a conceptual design tool and increase its accuracy by integrating high-fidelity CFD analysis into the

sizing process. The reliability of the conceptual design framework is verified by analyzing the mission profile of

existing turbo-prop aircraft. Moreover, a multi-level design framework is developed which sequentially employs the

conceptual design framework of the sizing and the detailed design of adjoint-based optimization. First, gradient-free

optimization to maximize cruise performance is carried out using the conceptual design framework with a limited

number of geometric design variables to change wing planform. All the mission requirements are well-satisfied as

they are imposed on the design process as the explicit form of the constraints. Second, gradient-based optimization

is carried out to further detail the configuration optimized at the first level. A large number of design variables are

included in this design level to minimize drag. By iterating those two levels, a more comprehensive design can be

achieved with a large number of design variables while taking into account the entire mission from take-off to

landing. As a result, 5.4% increase of L/D based on the inviscid drag is obtained from planform design and the

sequential section design resuls in additional 3%, indicating the current design framework is successful.

Nomenclature

MTOW = Maximum Take-Off Weight

TOW = Take-Off Weight

MZFW = Maximum Zero Fuel Weight

OEW = Operating Empty Weight

Wf = Total Fuel Weight

Wmission = Mission Fuel Weight

Wres = Reserve Fuel Weight

Wtrapped = Trapped Fuel Weight

Wpayload = Payload Weight

L/Di = Lift to Induced Drag Ratio

L/D = Lift to Total Drag Ratio

Wtake-off = Take-Off Weight

Winitial = Initial Cruise Weight

Wfinal = Final Cruise Weight

1 Ph.D. Candidate, Dept. of Aerospace Engineering, AIAA Member.

2 Assistant Professor, Dept. of Aerospace Engineering, AIAA Member, Corresponding Author.

3 Researcher, AIAA Member.


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CL = Lift Coefficient

CDi = Induced Drag Coefficient

CDf = Friction Drag Coefficient

CDc = Compressibility Drag Coefficient

Vstall = Stall Speed

Tavailable = Available Thrust

ESFC = Equivalent Specific Fuel Consumption

TSFC = Thrust Specific Fuel Consumption

TOFL = Take-Off Field Length

LFL = Landing Field Length

AR = Aspect Ratio

AoA = Angle of Attack

I. Introduction

Due to growing attentions in the high fuel price and environmental issues, low priced airliners using the small

aircraft and business jet industries are emerging amidst an industry that has focused mostly on large airliners.

However, the demand for the smaller airliners is increasing in line with the growth of the airline industry1.

The mid-size turboprop aircraft is suitable for this trend. A turboprop engine offers the optimal fuel efficiency on

specific mission and is advantageous in case of the frequent intra-city routes. For these reasons, low price airliners

prefer mid-size turboprop aircraft. The Korean airliner industry is growing in accordance with this international

trend. The nation is recently carrying out a project to develop and manufacture a mid-size transport with target

operation in the near future. The current work is a part of ongoing collaboration work.

This research aims to develop and verify the conceptual design framework of that aircraft, and the key contents of

research are as follow. An in-house sizing program of AMD-Sizing is developed to accurately predict its mission

profiles from take-off to landing. To verify the accuracy of the sinzing process, the mission profile of existing

aircraft, Dash-8 of Bombardier, was analyzed by the AMD-Sizing program and compared against results from the

commercial sizing software of AAA. Comparison shows excellent agreements in the estimation of system weight

and performances in the entire mission profile. Unlike the typical sizing process that is mostly based on the low-

fidelity table-lookups and the empirical models made of statistical data, the AMD-Sizing has major advantages in

that it can integrate higher-fidelity subdisciplinary analysis including CFD (Computational Fluid Dynamics) or CSD

(Computational Structures Dynamics) to increase the accuracy and reliability of the conceptual design. Currently,

AMD-Sizing was further improved by replacing its low-fidelity aerodynamic analysis with a high-fidelity CFD

analysis or less accurate linear potential flow solver. Also the current sizing program is enhanced as a more

comprehensive conceptual design framework by integrating the mathematical design optimization algorithms.

Surface geometry can be paramerized by introducing shape-related design parameters and modified automatically

through parametric relations. Thus, an optimum configuration of the aircraft or mission profiles can be found

through a formal design optimization process.

To fully utilize the developed conceptual design procedure, a multi-level design framework is developed by

sequentially applying the conceptual sizing process and a detailed adjoint-based optimization technique. First,

gradient-free optimization is applied to find an optimum shape of wing planform to maximize cruise performance. A

total of 16 design variables are used to parameterize wing planform, while all other mission constraints ranging from

take-off to landing are imposed as the constraints on the optimization process. At design Mach number of 0.521, a

linearized potential solver is integrated into the AMD-Sizing program to accurately and rapidly predict aerodynamic

performance. A total of 5% improvement was observed while all mission requirements were well satisfied through

the sizing process. Second, a gradient-based design optimization was carried out to further design the wing sections

starting from the optimized planform shape at the first level. For high-fidelity aerodynamic analysis at the second

level, Euler flow solutions were employed. Gradient sensitivity was obtained by solving continuous adjoint

equations with the propoer boundary conditions. A well-constructed gradient-based design process of SU2 (Stanford

University Unstructured) suites was directly adopted to detail the wing sectional airfoil shapes. Total 50 Design

variables were employed in the second level design. By iterating those two design levels of global and local

optimization, a more comprehensive design framework that encompass a larger number of design variables and

explores bigger design space was achived.

In conclusion, a study was successful for the development and verification of the high-fidelity conceptual

framework for the mid-size turboprop transport. The key findings are expected to help increase the industry’s

competitive edge and to seek advancement in the mid-size aircraft market.


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II. Conceptual design method and sizing

A. A Conceptual design program for sizing

For conceptual design of mid-size transport, a in-house program of AMD-Sizing (Aerospace Multidisciplinary

Design-Sizing) is developed and its accuracy of the results including system weight is validated against the data of

existing aircraft of similar size and the results from Darcorporation’s Advanced Aircraft Analysis (AAA)2,3

.

The AMD-Sizing program is developed for a conceptual design of conventional aircraft, although it was fine-

tuned for a mid-size turboprop transport in the current study. Most of the functions related to the estimation of

mission profiles were developed based on the contents of the digital textbook of Program for Aircraft Synthesis

Studies (PASS) of Stanford University4,5

. It can be coupled with high-fidelity analysis like Computational Fluid

Dynamics (CFD) or Computational Structural Dynamics (CSD) to enhance its accuracy to predict mission profile. In

addition, it can be combined with mathematical optimization algorithms to find optimal aircraft configuration for

improved performance, or can define optimum mission profile for a given aircraft configuration. The AMD-Sizing

in the current work combines all to find the optimal wing shape to improve aerodynamic performance while

satisfying a given mission profile from take-off to landing. Figure 1 shows a schematic of analysis done by AMD-

Sizing.

B. Estimation methods of the AMD-Sizing program

Following are brief descriptions of the components of the AMD-Sizing program for the analyses of the sub-

discplines of mission profile. A simple approximation formulation is used in most cases and is corrected based on

empirical data available in the public domain.

1. Weights

For calculation of weights, structural analysis and statistical comparisons are combined5,6,7

. Main wing weight is a

function of fully-stressed bending weight, load factor, and geometric parameters. Fuselage weight is calculated from

gross fuselage wetted area and a pressure-bending load parameter. The tail wing weights including a control surface

are calculated from a exposed and gross wing area, and are adjusted from empirical data. Other component weights

are a function of the number of passengers which are multiplied by empirical constant.

2. Aerodynamics

Prandtl’s lifting-line theory is used for calculating the coefficients of lift and induced drag forces. For parasite

drag calculation, aircraft surfaces are assumed to be a flat plate and the analogy of laminar/turbulent friction drag

correlation on a flat plate is used. Fuselage upsweep and a gap between the wing and the control surfaces are also

considered separately5,6,7

. The markup factor is utilized to consider small gaps, rivets, etc. Although a

compressibility drag coefficient (CDc) can be computed by defining crest critical Mach number(Mcc) and its ratio

with free stream Mach number(M∞), a range of main operation of the mid-size turboprop transport is subsonic and

the consideration of compressibility drag is not made in current work.

As the effects of thickness and camber of airfoil and twist distribution of the wing are not fully considered in the

lifting-line-based method due to its limitations in the accuracy, higher-fidelity aerodynamic analysis is considered in

our work. A panel method which solves the boundary value problem of linear potential flow is integrated in the

Figure 1 Range analysis of a mid-size turboprop transport using AMD-Sizing


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AMD-Sizing program. In fact, CFD analysis to solve Euler and Navier-Stokes governing equations is also carried

out and compared with the panel method.

3. Loads

A load factor is considered for the maneuvering and vertical gust conditions5,6,7

. The vertical gust is calculated

based on FAR25 regulation9. These load factors are used to estimate component weights, and constrain aerodynamic

performance for structural stability.

4. Static Stability and Trim

The aircraft lift curve slope is determined by DATCOM correlation5,6,7

. After the tail lift curve slope is computed,

the location of center of gravity is determined. Lift force of tail is trimmed to obtain zero pitching moment by

adjusting incidence angle.

5. Mission Performance

Take-Off Filed Length (TOFL)

Calculation of take-Off Field Length (TOFL) uses a correlation of Federal Aviation Regulations(FAR) field

length requirements with respect to the number of engine5,6,7

. It is related with take-off weight (TOW), stall speed,

and available thrust. The field length is determined by Eq. (1)5.

( )

( )

(1)

2nd

segment climb gradient

A constraint on climb performance is imposed as specified in FAR. A 2nd

segment climb gradient is defined as a

minimum climb gradient in the case of one engine inoperable. The effect of one engine out decreases a thrust level,

and the inoperable engine generates a windmilling drag component. Control surface should be operated in a way to

trim the asymmetric condition, which makes an additional drag component. Therefore, modification to drag force is

needed. A 2nd

segment climb gradient with the revised drag force is defined as Eq. (2)5 where ke is a correction

factor assumed by constant gas.

(2)

Cruise range, descent and landing

Specific range parameter is defined in Eq. (3)5 as a function of lift-to-drag ratio, cruise speed and the thurst

specific fuel consumption (TSFC). Aircraft range is determined based on integrated Breguet range equation as Eq.

(4)5.

( ⁄ ) (3)

( ) (

)

(4)

Descent operation requires less fuel than cruise, therefore a descent condition is neglected. Landing Field

Length(LFL) is determined by empirical equation as a function of stall speed.

Propulsion system

Rather than having the analysis for the specific propulsion system, a table of turboprop engine performance is

used. Engine performance is defined at wide range of Mach number and flight altitude and is shown graphically in

Figure 7. The engine performance at specific condition is determined by interpolating datas of the table.

Optimization algorithm for design


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In addition to the subdiscipinary analysis components, a design process based on mathematical optimization

algorithms is integrated in the sizing program to provide optimum mission profiles at a given shape or to generate

the optimum aircraft shape to satisfy mission requirements. In combination with the surface kernel method that can

modify the boundary definition of the aircraft configuration, the shape of aircraft can be easily parameterized

through the definition of the design variables. In fact, the current sizing program of AMD-Sizing has an optimization

algorithm of genetic algorithm (GA). With the definition of design variables, objectives, and mission constraints, an

optimum shape or mission profiles of the aircraft of interests can be found.

C. Comparison of weight estimation methods

Weight estimation is a major process in the conceptual design process as it initially determines the size of the

aircraft. The accuracy of the weight estimation method is critical in the fidelity and reliability of aircraft design. We

chose two sizing programs to compare their accuracy: AAA and AMD-Sizing. A major difference of the two

programs is a detailed procedure of how they estimate it. AAA uses a fuel-fraction method while the AMD-Sizing

program employs the component weight estimation method. Moreover, the AMD-Sizing considers MTOW or fuel

weight as a constant, and system weights are estimated based on the constant . Each procedure is shown in Figure 2.

Figure 2 Comparison of weight estimation methods: fuel-fraction method(left),

component weigths estimation method with fixed MTOW(center) and total fuel weight(right)

D. Validation of Sizing Programs

To validate the accuracy of the two sizing methods, weights of an existing aircraft was referenced and compared.

Dash-8 of Bombardier was chosen as a reference aircraft and is shown in Figure 3. It is a representative model of

mid-size turbo-prop aircraft. Series 400 of Dash-8 has 78 of typical passenger capacity which is close to the payload

target of design aircraft in our study.

Figure 3 Bombardier Dash-8 (Series 400)

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Table 1 Comparison of system weight estimation for Bombardier Dash-8 (Series 400)

Weight Dash-8 Estimation of AAA

(% error in difference)

Estimation of the AMD-

Sizing program with fixed

MTOW


Total Fuel (lb) 7,500 7,517 (0.23) 7,648 (0.81)

OEW (lb) 37,700 37,421 (-0.74) 37,952 (0.90)

MZFW (lb) 57,000 56,646 (-0.62) 56,826 (-0.15)

TOW (lb) 64,500 64,164 (-0.52) 64,500 (0)

Results of weight estimation carried out by both sizing programs are compared against the values of Dash-8 in

Table 1. The two results have differences less than 1% compared to the reference values of Dash-8. As AAA has

been widely used for numerous aircraft designs and its reliability is somewhat proven, very little discrepancy of the

current sizing program both from AAA results and data of Dash-8 implies that the AMD-Sizing program can be

safely used as a reliable conceptual design tool for the mid-size turbo-prop transport.

A main difference between the AAA and AMD-Sizing is an ability to integrate high-fidelity sub-disciplinary

analysis into the conceptual sizing process. For example, in terms of aerodynamics analysis, AAA uses statistical

data collected from existing aircraft and has well built-in tables using curve-fitting of the data, but it cannot predict

the aerodynamic analysis accurate enough to be compatible with the high-fidelity CFD computations. On the other

hand, the AMD-Sizing program was constructed using advanced programming language based on the database

stuctures, and each subdiscipline can be easily added or replaced by higher-fielity analysis methods. Aerodynamic

analysis tools with different fidelities from less accurate discrete vortex method, linear potential flow solver to

highly accurate viscous Navier-Stokes flow solver can be seamlessly integrated into the sizing program, and thus the

accuracy of the overall sizing process can be greatly enhanced. The same idea can be extended to the computational

structural analysis based on finite element analysis or aeroelastic analysis to tightly integrate aerodynamics and

structures analyses. For these reasons, We chose the AMD-Sizing as the design optimization tool as well as the

sizing program.

A modified version of the AMD-Sizing program is also made by integrating higher-fidelity aerodynamic analysis

of CFD computation or the panel method into the sizing procedure in lieu of the lifting-line-based prediction. An

increase of computational cost for the modified version of AMD-Sizing is also compared against the original sizing

process.

III. Target aircraft design

A. Design requirements analysis

Design requirements of target aircraft are summarized in the Table 2 and the values are not much different than

those of the reference aircraft of Dash-8. A design payload is determined such that the aircraft can take about 94

passengers including flight crew. A total of 1,000 nmi for the missin range is amount that can cover all domestic

region of Korea.

Table 2 Design requirements

Segment Notes Segment Notes

Regulation FAR259 Take-Off & Landing

Field Length

≤ 4,500 ft

Mission Range 1,000 nmi Cruise Altitude 25,000 ft

Passenger Number 92 Cruise Speed 310kts (M=0.521)

Design payload 20,700lb Alternate Mission Range 100 nmi

Max. fuel capacity 12,300lb Hold Mission Time 45 min

B. Mission profile

Based on the given design requirements, entire mission profile is defined as in Figure 4. The mission profile is

similar to that of typical commercial transport and includes taxing, take-off, climb, cruise, descent, landing, alternate

mission of 100nmi, and hold mission of 45 minutes. In the simulation of mission profile for the conceptual design

purpose, the profile was simplified as in Figure 5. The first and second climb missions were combined into a single


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climb mission. At constant cruise speed, the initial cruise altitude is determined as 24,000ft whereas the final cruise

altitude is 25,000ft as the requirement. The descent mission is integrated into the cruise mission. In addition, the

alternate mission and hold mission are not considered specifically in the sizing process.

C. Baseline Configuration of Aircraft

A shape of the three-dimensional full configuration is shown in Figure 6. Most of the details of the initial

geometries were given and some parts were designed to satisfy the mission profile and design requirements. Details

of the geometric parameters are omitted for a security reason.

Figure 4 Overall mission profile

Figure 6 CAD 3-view drawing of aircraft geometry

Figure 5 Simplified mission profile


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System Weight Estimation

Estimation of system weight of design target were summarized in Table 3. They have maximum error of 3% in

comparison with the given values, but this error can be negligible at this conceptual design level where all the details

of the geometries are not been fully defined. Because a fuel weight is directly used to determine cruise range, the

accuracy in predicting the fuel weight less than 1% with fixed MTOW is greatly appreciated and the reliability of

the design that tries to maximize the cruise range can be increased. In addition, the error of TOW with fixed fuel

weight can be negligible on performance estimation of designed aircraft.

Table 3 Estimation results of system weight

D. Initial designed aircraft performance

1. Engine performance

Engine performances were suggested with satisfying the requirements. The engine ESFC and thrust along altitude

and machnumber are plotted as Figure 7. Specific values of the ESCF and the thrust are omitted for a security reason.

2. Take-off performance

Take-off field length is important to estimate take-off performance of aircraft. For the shorter take-off field length,

low stall speed is needed by large deflection angle of flap. Length of flap was set to be 75% of wing span with its

width 35% of mean chord length. Estimation results of take-off field length with respect to the flap deflection angle

can be seen in left on Figure 8. The take-off field length is less than 4,500ft as design requirements as long as

deflection angle is larger than 17deg, which is acceptable for typical aircraft.

Figure 7 Engine performance along altitude and machnumber

Segment

Estimation of AMD-

Sizing with fixed MTOW


Estimation of AMD-Sizing

with fixed fuel weight


Given

Fuel (lb) 9,008 (0.09) 9,000 (0) 9,000

MEW (lb) 38,666 (-2.56) 38,666 (-2.56) 39,680

OEW (lb) 42,142 (-0.02) 42,142 (-0.02) 42,150

ZFW (lb) 62,842 (-0.01) 62,842 (-0.01) 62,850


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Figure 8 Initial design aircraft performance:

Take-off field length along flap deflection(left), Payload-range diagram(center),

Landing field length along flap deflection(right)

3. Cruise performance

At cruise mission, an altitude of 25,000ft and a velocity of 310kts (M=0.521) were specified as design

requirements. Maximum fuel weight that can be loaded on the aircraft was given as 12,300lb. Based on these values,

a payload-range diagram was constructed. As shown in center on Figure 8, harmonic range is larger than 1,000nmi

and satisfies the design requirement. Of course, Max. Fuel Range and Ferry Range are larger than 1,000nmi.

4. Landing performance

Variation of landing field length with respect to flap deflection angle is seen in right on Figure 8. It can be

referred that the requirement of 4,500ft is satisfied with 47deg of the flap deflection.

5. Climb performance

FAR25 defines 2nd

segment climb gradient larger than 0.024 for twin-engined aircraft. AMD-Sizing estimated the

gradient as 0.024836, which satisfies the regulation with very little margin. The margin is expected to be increased

with design process.

IV. Mid and high-fidelity aerodynamic analysis and design framework

AMD-Sizing uses multi-fidelity aerodynamic analysis methods, lifting-line theory as a low-fidelity, potential flow

solver as a mid-fidelity, and Euler and Navier-Stokes(N-S) solvers as a high-fidelity analysis. In order to supplement

inaccuracy of the low-fidelity analysis, the mid and high-fidelity analysis are considered in this section. Based on

these methods, multi-level design framework is introduced as very efficient design method.

A. Mid-fidelity based global design tools

1. Aerosurf for shape deformation and panel generation

In order to use potential flow solver on design process, shape deformation and panel generation techniques are

needed. On this study, Aerosurf was utilized. The Aerosurf, developed at Stanford University, parameterizes aircraft

shape as more than 100 design variables and generates points, lines, and surface panels for CFD or CSD. With the

many variables, It has a flexibility on aircraft shape generation. Futhermore, Using Parallel Virtual Mechine(PVM)

library, it can be cooperated with Computational Analysis Programming Interaface(CAPRI). The Shape generation

process is seen in Figure 9. The baseline configuration was regenerated with surface panels as Figure 10.

2. PAN-AIR for potential flow solution

PAN-AIR was develoed at BOEING company, uses higher-order panel method based on linearized potential flow.

It calculates pressure, moment on aircraft surface, including mass-flux or velocity components within near flow field.


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Figure 9 Aircraft shape generation process of Aerosurf

3. NSGA-2 for constrained global optimization

Based on short time consumption of the shape generation and the flow calculation, genetic algorithm as a global

optimization algorithm was considered in this design process. NSGA-2, widely used in many engineering fields, was

utilized on this study. It is based on nondominated sorting algorithm, has abilities to treat multi objectives and

constraints.

B. Mid-fidelity based global design framework

As previously described, the mid-fidelity tools have immediacies on shape deformation and aerodynamic analysis.

These characteristics offer a potential for designing aircraft planform. We constructed a mid-fidelity based design

framework available for aircraft planform design by tightly coupling the mid-fidelity tools and the AMD-Sizing.

This design framework uses AMD-Sizing with the mid-fidelity based tools. First of all, the genetic algorithm

previously described generates variable sets, and each the AMD-Sizing and aerosurf performs design process

respectively. At aerodynamics design process, the AMD-Sizing estimates target lift coefficient for initial and final

cruise condition. Then, PAN-AIR calculates aerodynamic performances of generated shape at the cruise condition.

Since The panel method only calculates inviscid drag, friction drag is estimated in the AMD-Sizing’s aerodynamic

subdiscipline. After calculation, the results are applied to the AMD-Sizing, and it continues the design process.

Finally, evaluated performances are transformed as objective functions and constraints in optimization algorithm,

and the optimizer repeats this design process. This design process can be seen in Figure 11.

Figure 10 Proposed CAD geometry(left) and generated shape on Aerosurf(right)


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Figure 11 Tightly coupled mid-fidelity based design framework

C. High-fidelity based local design tools

For high-fidelity aerodynamics analysis and shape optimization of the current mid-size turbo-prop transport,

SU2(Stanford University Unstructured) Suite was used in this study10

. SU2 was originally developed at Stanford

University, has an unstructured CFD flow solver, continuous adjoint solver, and shape optimization module that is

tightly coupled with the CFD flow and adjoint solvers. Components of SU2 Suite are listed below:

1. SU2_CFD and SU2_DDC for Euler and N-S flow solution

SU2_CFD is a software, used for fluid dynamics simulation in parallel computation environment and SU2_DDC

partitions the volumetric grid as a pre-processor to parallel flow computation10

. This calculates direct flow solutions

and adjoint solutions for potential, Euler, N-S, Reynolds Averaged Navier-Stokes (RANS) equation. It uses a Finite

Volume Method (FVM). Both explicit and implicit methods are available for time integration, and central difference

or upwind method for space integration. In order to improve robustness and convergence of the flow solution,

advanced numerical techniques of residual smoothing and agglomeration multi-grid are also available.

2. SU2_MDC for surface and mesh deformation

SU2_MDC module deforms the boundary surface and corresponding surface/volume mesh10

. To deform of the

surface, the bump functions or Hicks-Henne curve is used for 2D and FFD for 3D. The method is based on the

transfer functions instead of defining the geometry explicitly. This optimization process can be effectively

decoupled from the geometric parameters and the geometry can be deformed freely. An example of FFD is in Figure

12. The movement directions of FFD are determined by SU2_GPC, and the movement distance is calculated from

the optimizer. Once the aircraft surfaces are deformed by FFD points, overall inner nodes are moved

correspondingly in a way of spring analogy. Since the method does not generate a new grid and modifies an existing

grid, computational efficiency regarding the mesh topology can be greatly saved.

Figure 12 Free form deformation (FFD)

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3. SU2_GPC for gradient computation

SU2_GPC computes sensitivity information through the partial derivatives of a functional with respect to

variations in the geometries of the boundary surface10

. Surface sensitivity, flow solution, and geometrical variable

are used to evaluate the derivative of particular functions (drag, lift, etc).

4. BFGS and SLSQP for unconstrained and constrained local optimization

Broyden-Fletcher-Goldfarb-Shanno(BFGS) and Sequential Least Square Programming(SLSQP) were considered

as gradient based unconstrained and constrained algorithms. The BFGS is a quise-Newton method which

approximates Hessian matrix. SLSQP algorithm is based on Han and Powell method with BFGS-update of Hessian

matrix and L1-test function of step-length algorithm. For handling constraints, It solves quadratic programming

subproblem. Though the optimizer searches local design area, optimization process can be converged an optimum

quickly with an advantage of gradient based algorithm, resulting in a capability of optimization with high-fidelity

aerodynamic analysis.

D. Comparison of multi-fidelity flow solutions

For validation of the flow solvers, aerodynamic characteristics were compared. For potential and euler solver, For

euler compution, geometry generated from Aerosurf was reconstructed smoothly. The shape of nacelle was

regenerated properly. panels and surface grids were generated as Figure 13.

Figure 13 Panels and grid on surface of baseline: 1,346 panels(left) and 222,460 t elements(right)

A total 1,346 panels and 222,460 tetrahedral elements were generated for each computation. On the euler

computation, ROE-2nd

-order flux scheme and LU-SGS time integration scheme were used. For accelerating

computation speed, 1 level with W-cycle based multigrid method was considered. Flow solution was converged to

10-5

order of residual of density variable. Computed drag polars with inviscid drag ared compared in Figure 14.


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Figure 14 Comparison of drag polars

In the Figure 14, line theory based drag polar have different tendency compared to other drag polars. But the order

of 3 inviscid drags is not different larger within range of 0.58-0.62 of lift coefficient as a lift of cruise condition. In

addition. The difference of drag values between panel and euler computation is caused by the nacelle geometry

consideration. But, the drag polar tendencies of two method is very similar. Thus, the line theory can be used on

conceptual design level. In addition, design process is valid using mid and high-fidelity flow solutions.

E. Multi-level design framework

The design process comprised two levels, combining global and local design. As previously described, in the first

global design level, a gradient-free optimization was carried out under the platform of AMD-Sizing program.

Mission profile and other design requirements were specified as the constraints in the optimization module of AMD-

Sizing and geometry-related parameters are defined as design variables of the optimization problem. As mentioned

before, to increase the accuracy of the sizing process, higher-fidelity of aerodynamics analysis is replaced to

compute aerodynamic performances during cruise condition. However, as the gradient-free optimization method

such as genetic algorithm is used, corresponding function evaluations are required in large numbers and limit the

number of design parameters to be less than about 20. But gradient information is not required in the optimization

process, relatively large variations in the shape design parameters are allowed. As this first level, optimization is

carried in tight coupling with AMD-Sizing, all the mission requirements are automatically satisfied.

In the second gradient-based design level, an adjoint-based optimization is carried out using SU2. Gradient-based

optimization methodology such as BFGS or SLSQP requires gradient sensitivity information to find search direction.

Adjoint solution approach is used for sensitivity analysis in an efficient and accurate technique. As the deformation

amount is limited mostly by the extent of the mesh deformation capability, only small variations in the shape, such

as sectional airfoil changes with bump functions and FFD technique, are considered. Improved aerodynamic

performance is again input to the AMD-Sizing to estimate further improvement in the mission profiles.

This multi-level design framework is first introduced by Choi et al12

as a method to integrate the conceptual sizing

process as well as high-fidelity CFD-based detailed design in an efficient way. A total number of design parameters

that are included in multi-level design framework is in an order of hundreds and yet the large variation of the design

parameters are allowed including wing planform shapes. A brief procedure of the design process is follows:

1. A Conceptual design is proceeded satisfying overall mission constraints

1.1 An aerodynamic analysis of AMD-Sizing is replaced by high-fidelity of CFD solver or medium-fidelity

linear potential solver

1.2 Optimization algorithm of AMD-Sizing defines the objectives, constraints and geometric design parameters

1.3 A random search process of evolutionary algorithms of the AMD-Sizing finds the optimum configuration

2. Detailed design process is performed using SU2

2.1 After that, using euler and continuous adoint equations are solved sequentially from SU2_CFD.


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2.2 Gradient-based optimizer determines the skip distance and the movement directions based on the sensitivity

which is calculated from the results of the adjoint equataion.

2.3 The movement directions are projected to new FFD points using SU2_GPC.

2.4 Target surfaces are deformed with near new FFD points. And the inner nodes are moved using SU2_MDC.

2.5 For parallel computation, SU2_DDC decomposes the deformed grid.

3. The aerodynamics of the optimized shape are updated to the AMD-Sizing to check the mission profile.

4.가 없음

V. Design Results

A. Design condition

As cruise performance is most important aspect of commercial transport airliners, the steady cruise condition was

focused as a design condition. Considering that lift value is equivalent to weight value of aircraft on the steady

cruise condition, A lift coefficient during initial cruise was fixed at a specific value with the angle of attack was

allowed to vary to accommodate the lift value. Operating Mach number and altitude were considered as 0.521 and

25,000ft. All other mission requirements specified in Table 2 were imposed as constraints on the design

optimization process. In order to replace low-fidelity aerodynamic analysis in a conceptual design level of AMD-

Sizing, the mid and high-fidelity inviscid Euler computation was introduced. Previously, a Kriging response surface

of the Euler CFD computations was constructed to replace the low-fidelity aerodynamic analysis module of the

AMD-Sizing. However, in this study, the mid-fidelity of the panel method was utilized mainly for the computational

efficiency. The flow condition was such that the free stream Mach number is well below the transonic regime, the

panel method was sufficient to accurately predict the inviscid components of overall drag12

. In order to take into

account the friction-induced viscous drag component, it was computed by a simple approximation method of AMD-

Sizing based on flat plate analogy and explicitly added to the inviscid drag component.

1. Design conditions for wing planform design

An objective function and equations of constraints were formulated for the wing planform design. The NSGA-2

basically considers minimizing objective and positive sign of equations of constraints. For maximizing the cruise

range, objective function was formulated as inverse proportion to the range. The TOW is constained to not be

heavier than the MTOW with fixed fuel weight, resulting in inducing aerodynamic optimization. The take-off field

length, landing field length, and 2nd

climb segment gradient are constrained to satisfy the mission requirements. Also,

the minimum static margin is considered as larger than zero. In addition, for comfortability of passengers, AoA is

considered as not too be high. Therefore, on wing planform design, total one of objective function and seven of

constraints are considered as below:

- Optimization problem: minimize 1000.0/cruise range

- Subject to: TOW ≤ MTOW

Take-off field length ≤ 4,500ft

Landing field length ≤ 4,500ft

2nd

segment climb gradient ≥ 0.024

Minimum static margin ≥ 0.0

AoA at cruise condition ≤ 3.5deg

2. Design conditions for sectional airfoil design

At second design level, wing planform design result is considered as a starting point of sectional airfoil design.

First of all, the target CL is fixed in this process whereas AoA is varied. Instead, In order to retain cruise altitude, the

cruise lift coefficient must be higher than that of the design result. This condition is considered as a constraint on

this process. Objective function is minimizing drag coefficient. Finally, an objective function and a constraint are

considered in this process as below:

- Optimization problem: minimize CD

- Subject to: CL ≥ CL_target

B. Design variables


15

1. Variables for wing planform design

Wing reference area and AR are major variables on aircraft wing design. On this study, the reference area is fixed

as given design consideration. But, the AR is still varied, resulting in large variation of the wing planform. In

order to design wing planform, a break section is defined as a section at 30% location of half length of the main

wing. Root, break, and tip sections are varied with thickness, twist angle, and camber line. The camber line is a

function of location and height of camber point, deflects sectional airfoils slightly. Total 16 of wing planform

design variables are defined in Table 4.

Table 4 Design variables in the wing planform design

Variable

x(i)

Note

x(1) AR

x(2) Fuselage longitudinal wing location (ft)

x(3) Sweep angle (deg)

x(4) Taper ratio

x(5) Section thickness at root

(proportion of chord length at root)

x(6) Section thickness at break


x(7) Section thickness at tip


x(8) Twist angle at root (deg)

x(9) Twist angle at break (deg)

x(10) Twist angle at tip (deg)

x(11) Section camber location at root


x(12) Section camber location at break

(proportion of chord length at break)

x(13) Section camber location at tip

(proportion of chord length at tip)

x(14) Section camber height at root


x(15) Section camber height at break

(proportion of chord length at break)

x(16) Section camber height at tip

(proportion of chord length at tip)

2. Variables for sectional airfoil design

Starting from the wing planform design result that was previously performed at the first level, further optimization,

changing the shape of wing sectional airfoils, was considered. Aircraft surface was deformed through FFD technique.

Corresponding FFD box was constructed as Figure 15. The FFD box covering the main wing has 84 (7x6x2) FFD

points. In order to prevent wrong deformation, 24 points on the first and last sections and 5 points on the root section

were not permitted to move, reducing total 55 design variables in the end. It is assumption that wetted area of the

wing is constant with very small perturbations.

b/2

wing location

sweep angle

chord

camber height

camber location


16

Figure 15 Control points on FFD box

C. Wing planform design results

1. Geometric variation

First, as the global design level, a design of wing planform was carried out. The details of the baseline design

variables and their bounds are not allowed to be published for security reasons, but the overall comparison of the

optimized shape(named ‘candidate1’) with the baseline can be shown in Figure 16. Since the root section was

combined with the fuselage, near root section(2y/b=0.1) was compared. Corresponding shape variables are listed in

Table 5.

Figure 16 Shape comparison between baseline and candidate1:

(a) overall shape (b) wing shape (c) sectional shape at near root(2y/b=0.1), break(2y/b=0.3), and tip(2y/b=1.0)

Table 5 Values of the optimized design variables in the wing planform design

Design variables Candidate1

(% of difference)

Design variables Candidate1

(% of difference)

AR 13.209 (5.67) Twist angle at break (deg) -1.007 (-191.51)

Fuselage longitudinal wing

location (ft)

41.446 (-18.58) Twist angle at tip (deg) -0.143 -85.73)


17

Sweep angle

(deg)

5.978 (159.90) Section camber location at root

(proportion of chord length at

root)

0.418 (-)

Taper ratio 0.197 (-50.85) Section camber location at

break


break)

0.210 (-)

Section thickness at root


root)

0.147 (-8.38) Section camber location at tip


tip)

0.222 (-)

Section thickness at break


root)

0.161 (0.74) Section camber height at root


root)

-0.005 (-)

Section thickness at tip


root)

0.154 (-3.59) Section camber height at break


break)

0.024 (-)

Twist angle at root (deg) 1.068 (46.59) Section camber height at tip


tip)

0.006 (-)

The main wing of the candidate1 have longer span, larger sweep angle, and smaller taper ratio. These changes are

expected to contribute to reduce induced drag. Also, the wing has been moved forward evidently, bringing a change

of aircraft stability. In addition, deformed sectional shapes by each 4 design variables are expected to make better

aerodynamic performance.

2. Aerodynamic performance

The flow characteristics can be confirmed in Figure 15. The designed wing has more lower pressure on upper

surface. On lower surface of both the baseline and candidate1, Similar pressure distribution can be seen. Thus, It is

expected that the candidate1 has larger pressure difference between the upper and lower surfaces of main wing. It

can be proven in Figure 16. The difference was slightly decreased on near root section. But, the difference become

larger from near root to tip on designed wing. At tip section, the designed wing has almost twice as many pressure

difference as baseline wing. These aerodynamic characteristics were quantitized as Table 6.

At both initial and final cruise condition, inviscid and friction drag was decreased, whereas lift was increased. A

14% and 5% of increase in inviscid and total L/D were obtained from the decrease of the inviscid drag by 12counts.

The increase of total L/D is directly connected to increase of cruise range.


18

Figure 17 Pressure coefficient distribution on wing surface in wing planform design:

(a) upper-baseline (b) upper-candidate1 (c) lower-baseline (d) lower-candidate1

Figure 18 Pressure distribution at near root(left), break(center), and tip(right)

Table 6 Aerodynamics difference between the baseline and candidate1

Baseline Candidate1 (difference)

Initial cruise condition

AoA (deg) 2.9 3.2 (10.34%)

CL 0.60580 0.60741 (16.11counts)

CDi 0.01008 0.00888 (-12.03counts)

CDf 0.01973 0.01950 (-2.32counts)

L/Di 60.097 68.423 (13.85%)

L/D 20.282 21.637 (5.35%)

Final cruise condition

AoA (deg) 2.72 3.02 (11.03%)

CL 0.58300 0.58457 (15.71counts)

CDi 0.00933 0.00823 (-11.03counts)

CDf 0.01982 0.01958 (-2.34counts)

L/Di 62.497 71.071 (13.72%)

L/D 19.964 20.981 (5.10%)

3. Performance of optimized planform design


19

Performances of the candidate1 were evaluated. Overall performances were summarized in Table 7. As a most

important performance facter, 5% of cruise range improvement was achived. 67 nmi as the improvement is

equivalent to a distance from Daejeon to Seoul, Republic of Korea. It is thought that this improvement is very

successful for a regional aircraft.

Also, take-off field length and landing field length were reduced by 6% and 7%. Reduction of field length causes

the advantage on take-off and landing availability of aircraft, and these reductions are meaningful on airport

operation. Left and right figures on Figure 19 show take-off field length and landing field length of the design result.

Deflection angle at landing mission of the baseline was large by 47 degree. The design result satisfies the landing

field requirement at 35 degree. Therefore, decrease of the angle is good design direction.

The 2nd

segment climb gradient was increased as compared with baseline. The target altitude can be obtained

more easily by the aircraft with the greater cilmb gradient. Also, the gradient that is greater than double the baseline

allows an altitude climb with less thrust, thus, it is a positive optimization result.

Center on Figure 19 is payload-range diagrams of baseline and design result. The red line and black line are the

diagrams of candidate1 and baseline using lifting-line theory.

Comparing two diagrams, candidate1’s cruise performance was improved a lot, compared to baseline. Also,

calculating the cruise performance of candidate1 by panel method, much accurate performance value can be

estimated. Of course, all ranges of the candidate1 is larger than the requirement. Since magnitude of inviscid drag of

panel method is smaller than that of line theory, values of the 3 cruise ranges are larger.

Table 7 Aircraft performance difference in the optimized planform design

Performance factor Baseline Candidate1 (% of difference)

Range (nmi) 1297.53 1364.25 (5.14)

TOW (lb) 71843.52 71841.68 (-0.00)

Take-off field length (ft) 4468.39 4203.92 (-5.92)

Landing field length (ft) 4469.05 4113.42 (-7.96)

2nd

segment climb gradient 0.02484 0.052611 (111.83)

Minimum static margin 1.38619 0.68460 (-50.61)

Figure 19 performance of the optimized planform design:

Take-off field length along flap deflection(left), Payload-range diagram(center),

Landing field length along flap deflection(right)

4. Validation of cruise performance using high-fidelity tools

For more accurate cruise performance, Euler computations were done. Aerodynamic performances were carried

out about both baseline and candidate1. Initial and final cruise conditions were considered. Calculated coefficients

and harmonic cruise range are shown in Table 8.

The inviscid drag were decreased at both initial and final cruise conditions, the amounts were about 8counts.

Since the magnitudes inviscid euler computation were higher than those of panel computation, resulting in lower

increase of inviscid L/D and total L/D. Even this discrepancy, about 3% of improved cruise range was carried out.

This is still meaningful on aircraft design process with more accurate values. Thus, design results are validated

successfully by the high-fidelity tools.


20

Table 8 Aerodynamic performance and cruise range comparison between the baseline and the candidate1

Baseline Candidate1 (% of difference)


AoA (deg) 2.95 3.24 (9.83)

CL 0.60736 0.60675 (-0.10)

CDi 0.01448 0.01373 (-5.18)

CDf 0.01973 0.01950 (-1.17)

L/Di 41.944 44.194 (5.36)

L/D 17.724 18.260 (3.02)


AoA (deg) 2.82 3.07 (8.87)

CL 0.58979 0.58383 (-1.01)

CDi 0.01392 0.01305 (-6.25)

CDf 0.01982 0.01958 (-1.21)

L/Di 42.376 44.741 (5.58)

L/D 17.452 17.893 (2.53)

Cruise performance

Harmonic cruise range (nmi) 1133.2 1162.7 (29.5 nmi)

D. Sectional airfoil design results

Based on the candidate1, sectional airfoil design was performed. For efficient design, configuration without tail

wings was considered. Basically, flow characteristics around main wing are dominant to aerodynamic performances

of aircraft. Also, very small perturbations are done for designing sectional airfoil. It is thought that flow

characteristics without tail-wings are similar to that with tail-wings. After designing wing sections, it is validated

using full configuration.

Sectional airfoil design was performed with high-fidelity based design framework. Optimization history is as

Figure 20. The lift coefficient was converged near a constraint. Since optimization of 3-D wing section is hard to

converged, we chose a result (named ‘candidate2’) which have good aerodynamic performance in the design history.

Figure 20 Lift(left) and drag(right) history of sectional design

Table 9 shows aerodynamic performances of the candidate1 and candidate2.

Table 9 Aerodynamic performance and cruise range comparison between the candidate1 and the candidate2

Candidate1 Candidate2 (% of difference)


AoA (deg) 3.24 3.23 (9.49)

CL 0.60675 0.60699 (-0.06)


21

CDi 0.01373 0.01358 (-6.22)

CDf 0.01950 0.01950 (-1.17)

L/Di 44.194

L/D 18.260


AoA (deg) 3.07 3.06 (8.51)

CL 0.58383 0.58409 (-0.97)

CDi 0.01305 0.01291 (-7.24)

CDf 0.01958 0.01958 (-1.21)

L/Di 44.741 45.236 (6.75)

L/D 17.893 17.976 (3.00)

Harmonic cruise range (nmi) 1162.7 1168.4 (3.11)

VI. Conclusions and future work

A sizing program of AMD-Sizing was developed to design a Korean mid-size turbo-prop aircraft. Major advantage

of the sizing program is its capability to be used as a high-fidelity conceptual design tool by integrating high-fidelity

sub-disciplinary analyses of CFD and CSD methods. To verify the accuracy of the AMD-Sizing, mission profile of

Dash-8 of Bombardier was analyzed along with the commercial sizing software of AAA. It shows excellent

agreements for system weight values and other mission values. AMD-Sizing was further improved by replacing its

low-fidelity aerodynamic analysis by high-fidelity CFD analysis.

A multi-level design framework was also developed by sequentially applying AMD-Sizing with CFD analysis and

SU2-based adjoint optimization method. First, wing planform was optimized with a total of 10 design variables and

a genetic algorithm was used to find the optimum configuration to maximize cruise range. At design Mach number

of 0.521, a linearized potential solver was used in AMD-Sizing to accurately predict aerodynamic performance. A

ten percent improvement in total was observed while all mission requirements are well satisfied through the sizing

program. 5% increased cruse range was carried out, this is very successful design result.

Second, sectional airfoil design was performed. Based on the optimized planform, additional 3% of L/Di can be

achived, this is meaningful result in design process.

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development and validation of conceptual design framework

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