Creation and Validation of Early Stage Conceptual Design Methodology for Blended Wing- Body Aircraft

DEGREE PROJECT IN VEHICLE ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2019

ALEXANDER LEJON

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

Creation and Validation of Early Stage Conceptual Design Methodology for Blended Wing-Body Aircraft

ALEXANDER LEJON

Master of Science of Vehicle Engineering Date: July 2, 2019 Supervisor: Alessandro Sgueglia Examiner: Ulf Ringertz School of Engineering Sciences Host organization: Institut Supérieur de l’Aéronautique et de l’Espace, Toulouse, France Swedish title: Formulering och Validering av Designprocess för Flygfarkoster med Sammansmält Kropp och Vinge

iii

Abstract

The current design paradigm for developing tube-and-wing style aircraft has been well documented in literature. This research attempts to develop and validate a similar design methodology to what is presently utilized for tube-and- wing based aircraft, but has so far not been successfully implemented for the blended wing-body. This construction has no clear distinction between the lift generating surfaces and the cargo carrying structure. The methodology that was developed included the concatenation and validation of low-fidelity, low speed and low complexity aerodynamic models in order to allow for quick and simple analysis of a large number of possible geometries. This enables the user efficiently determine the most promising candidate geometries for further study and/or development. Known issues with the low velocity and low complexity aerodynamic models include the absence of shock wave modelling, an important part in determining the aerodynamic performance of a lift generating surface. The result of this work is the creation and documentation of a procedure for early-stage design of a blended wing-body airframe. However, due to convergence issues with the high-fidelity CFD solver, the methodology could not been validated for transonic flow. It can thus be only considered valid for flow velocities for which the Prandtl-Glauert correction is valid. iv

Sammanfattning

Den befintliga konstruktionsmetodiken för utveckling och design av flygfarkoster är väl dokumenterad i tidigare publicerad litteratur. Detta arbete äm- mar utveckla och validera en liknande metodologi som redan existerar för de väl etablerade flygplansgeometrier som baseras på cylinder/vingar-principen. Metoden som utvecklades inkluderade sammansättaning och validering av tidigare existerande lågupplösta samt lågkomplexa aerodynamiska modeller av- sedda för beräkning av flödesekvationer för inkompressibel, friktionsfri och stationär strömning. Detta var avsett att möjliggöra ögonblicksvalidering av en föreslagen sammansmält kropp/vinge-geometri med speciell fokus på vissa prestationsbaserade nyckeltal. För cylinder/vinge-geometrier är dessa lågupp- lösta metoder i litteraturen väletablerat inexakta på grund av en avsaknad av stötvågsmodellering, men då stora delar av de lyftkraftsgenererande ytorna för- ändrats på en sammansmält kropp/vinge är inte nödvändigtvis detta sant för den typen av flygplan också. Då de högupplösta, mer komplexa höghastighets- simuleringarna inte konvergerade inom den utsatta tiden kan den föreslagna metodiken endast anses giltig för det intervall av flödeshastighet vari Prandtl- Glauerts korrektionsfaktor stämmer väl överens med verkligheten. Contents

1 Introduction 1 1.1 Research Question ...... 2

2 Background 3 2.1 Previous studies ...... 3 2.2 Baseline Geometry ...... 4 2.3 The Vortex Lattice Method ...... 5 2.4 Euler Equations ...... 6 2.4.1 Jameson-Schmidt-Turkel ...... 6

3 Method 7 3.1 Requirements on new geometry ...... 7 3.2 Athena Vortex Lattice ...... 7 3.2.1 Verifying the AVL model ...... 9 3.3 SU2 simulations ...... 9 3.3.1 Preprocessing ...... 9 3.3.2 Solver settings ...... 9 3.4 Results Interpretation ...... 10

4 Results 11 4.1 Developed design meators ...... 11 4.2 Results from AVL ...... 11 4.3 The new baseline geometry ...... 12 4.4 Euler veriﬁcation with SU2 ...... 13

5 Discussion 14 5.1 Geometry creation ...... 14 5.2 AVL solution accuracy ...... 14 5.3 SU2 Simulations ...... 15

v vi CONTENTS

6 Conclusions 16 6.1 Method validity ...... 16 6.2 Proposed new geometry ...... 16 6.3 Further studies ...... 16

References 18

A Glossary 21

B Baseline Geometry 22

C Sampling probability distribution 24

D BWB Parameters 25

E AVL Solver settings 26

F Full table of simulation results from AVL 27

G Lift distributions from AVL for new baseline geometry 39

H Overview of new Baseline Geometry 43

I Results from SU2 44 Chapter 1

Introduction

One of the biggest concerns within the field of aerial travel today and aeronautics in particular is the efficiency of short- and medium-range aerial pas- senger and cargo transport. The explosive growth in flown kilometers per year shows no signs of stopping, if anything - it is still on the ascendancy with some authors estimate that by 2050, the emissions caused by aerial transporta- tion would in and of itself account for the total annual CO2 budget - i.e. the amount of carbon dioxide that the ecosystem on Earth can absorb [1]. This leads to the conclusion that either aviation needs to become more efficient or the air travel behaviour of society needs to change. Whilst a com- bination of the two might be possible, with improving socioeconomic status in many high-population countries such as China and India it is not likely that the amount of people using aviation as a form of travel will see a dramatic decline over the coming decades [2]. Aircraft efficiency has developed rapidly since the early days of commer- cial jet travel in the 1960’s. High-bypass turbofans, winglets and changes in material composition of the aircraft have all contributed to the improvement, but there are only so many efficiency improvements that can be made when the principal issue lies with the design of the airframe. [nasabwb] With efficiency being one of the principal concerns today, it is necessary to review whether a change in airframe design would be pertinent. One of the alternative geometries to the tube-and-wing (TW-configuration) is the blended wing-body (BWB), where there is no clear distinction between the body and the wing of the aircraft. Previous studies regarding the blended wing-body’s efficiency have shown a clear improvement with regards to aircraft fuel economy, in the range of a 15-30% reduction in fuel burn per seat. [3]

1 2 CHAPTER 1. INTRODUCTION

However, studies performed on short/mid-range blended wing-bodies have had mixed results - many of the Boeing Company’s results point to short/mid- range blended wing-body designs being unfeasible but a study made at ISAE Supaero/ONERA shows an improvement in efficiency over the A320neo at ranges between 800 and 1200 nautical miles. [4] [5] A study made at NASA Langley and NASA Glenn shows similar results, showing reductions in block fuel burn of up to 45%, compared to the TW. [6] Further studies on the blended wing-body are necessary in order to determine at which ranges it would be advantageous to use over the prevailing tube-and-wing airframe. The present work will attempt to outline an early stage conceptual design procedure for a blended wing-body and suggest an update to the baseline geometry created at ISAE Supaero. [5] The design processes for a BWB are, naturally, not as well developed as they are for the TW-configuration, with the latter having decades of experience and empirical data to draw on. Currently, there exists a gap in the methodology employed for early stage conceptual BWB design, with no clear methodology developed to quickly determine the most basic parameters for a BWB such as lift-to-drag ratio, static margin and stall characteristics. This thesis will aim to compare inviscid high and low fidelity aerodynamic models for a blended wing-body aircraft and thus determine whether a low fidelity aerodynamic model is applicable during the cruise stage (and in extension, during take-off and approach) for a blended wing-body aircraft. The final objective is to allow this method to be integrated into the FAST tool, a multi- parametric optimization design tool developed at Onera and ISAE Supaero as a way of including BWB design into the tool. [7]

1.1 Research Question

Are low ﬁdelity aerodynamic models like the Vortex Lattice Method applicable and valid during early stage conceptual design for transonic cruise stage analysis of a blended wing-body aircraft? Chapter 2

Background

Researchers at ISAE Supaero and ONERA have previously proposed a baseline geometry for a short-medium range blended wing-body (BWB). However, during review of this geometry, issues were found with the aerodynamic performance of the proposed baseline design. The issues that were raised concerned the stall characteristics and a static margin that was far from what was desired. This lead to the conclusion that in order to be able to quickly determine the rough performance of a proposed blended wing-body aircraft, a new methodology that allowed for quick design and simulation was required. The geometry parameters that were theorized to have an effect on the aerodynamic performance of the blended wing-body are listed in appendix D table D.1. The process of designing a BWB has not been extensively documented, but an attempt at saving the accumulated knowledge about specifically flying wings has been made by K. Nickel and M. Wohlfahrt in [8]. The aim of this thesis is to formulate and validate an early stage design process of blended wing-bodies using currently available tools and methods, and use the developed methodology to suggest a replacement baseline blended wing-body geometry.

2.1 Previous studies

A composite study made by Liebeck [3] indicates that the blended wing-body could reduce fuel burn by up to 27% per seat mile. Other studies have indicated a similar eﬃciency improvement over the classical tube-wing-design [4] for large blended wing-bodies. Previous results on short and medium range blended wing bodies have conclusively showed an improvement for medium range blended wing-bodies

3 4 CHAPTER 2. BACKGROUND

but the results for short range BWBs are less positive. This is due to an inherent disadvantage that the BWB has compared to the tube-and-wing setup. A BWB will generally be heavier than a comparable tube-and-wing as the shape of the airframe causes an increase in structural weight. As this is the case, there exists a minimum flight range below which the TW-configuration has superior fuel efficiency. [5][3] This is caused by, in part, the increase of structural weight but also the higher cruise altitude that the BWB needs to climb to. The higher cruise altitude requirement is a result of the increase in overall wing area, requiring a higher cruise altitude to reach maximum aerodynamic efficiency. There has also been studies done regarding design parameter optimization for aerodynamic performance [9] and BWB design using similar approaches. [10] The use of high-fidelity aerodynamic models for the previously selected geometry has also been studied. [11]

2.2 Baseline Geometry

The baseline BWB geometry, as defined by researchers at ONERA and ISAE Supaero, is split into three parts - the central body, the transition zone and the wing. The geometry data of the baseline BWB can be found in appendix B in table B.1. For the baseline geometry, studies have also been made at ONERA/ISAE Supaero regarding the placement of control surfaces on the body. The placement of the elevons (elevator-ailerons) on the center body is unconventional, but studies have shown that the power required to create the required pitching moment would not be too high to motivate the placement of the elevons solely on the center body. [12] In other studies the flow was shown to separate in the "kink" region where the body meets the wing [3] - using the geometry setup proposed by Sgueglia et al. drastically reduces the risk for flow separation as the angle between the body and wing trailing edge is not as severe as in the aforementioned report. The total wingspan of the baseline geometry was 41 meters. The baseline geometry does not include any winglets or wingtip attachments. There are currently studies in progress regarding the aerodynamic and control impact of the addition of winglets on the blended wing-body. The baseline geometry was assumed to have control surfaces stretching the outermost 50% of the span of the wing. The weight of the center body, while not relevant for the pure aerodynamics of the BWB, did affect the cruise altitude. For all purposes where this altitude CHAPTER 2. BACKGROUND 5

was considered, the worst case scenario from [5] was used. This gave a wing area of 340.1 m2 which was rounded down to 340 m2. The cruise altitude was 42400 feet for the worst case scenario BWB, which is 3300 feet higher than the certified ceiling of the unmodified A320Neo. [13] It was also assumed that any change in the geometry would be possible to manufacture, as long as the changes were within reasonable bounds and the geometry created did not seem unreasonable from a structural standpoint. As can be seen in figure B.1, the baseline geometry contains over-wing mounted engine nacelles. These were removed in order to solely focus on the aerodynamic effect of the BWB planform. Previous work on the geometries of a BWB transport have suggested a center body leading edge sweep angle of 45◦, where the baseline geometry proposes a center body sweep of 35◦. These figures were taken into account during the creation of the parameter ranges for which the aerodynamic properties would be investigated. [14]

2.3 The Vortex Lattice Method

The VLM is implemented through the distribution of horseshoe vortices along span and chord. This, together with the Biot-Savart law, the Kutta-Jukowski theorem, Prandtl’s lifting line theory and Herman von Heimholtz vortex fila- ment theory form the basis of analysis. [15] Key assumptions in the VLM are incompressible, irrotational and inviscid flow, thin lifting surfaces and finally small angles of attack and sideslip. As the cruise velocity of the BWB would be above the range for which flow can be considered incompressible (Mcruise > 0.3), the effects of compressibility need to be considered. However, the Prantl-Glauert transformation is only valid up to Mach numbers of 0.7 - after that transonic flow starts to appear. As the BWB is assumed to cruise at Mach 0.78, it is outside the scope for which the Prandtl-Glauert transformation is valid. [16] Even though the Prantl-Glauert transformation is invalid, some useful results can be gained from using the VLM. It is assumed throughout this thesis that the VLM holds for M = 0.78, as the VLM has a good ratio of computational effort to result accuracy - especially when only considering early stage conceptual design. Should the later Euler solution show that the VLM is far away from an accurate solution, the addition of a possible correction factor will be evaluated. The theory behind the Vortex Lattice Method and the method itself is well established and documented in detail in other publications and will thus not 6 CHAPTER 2. BACKGROUND

be elaborated upon further here. [17] [16] [18] [19] Another limitation of the VLM is that it only deals with irrotational flows - the BWB is likely to exhibit significant lateral flow across the center body which can have an impact on the pressure distributions over the airframe. The impact of the lateral flow can only be determined from higher fidelity methods that also allow for rotational flow.

2.4 Euler Equations

For the purpose of verifying the Vortex Lattice calculations through the use of higher fidelity CFD methods, the Euler equations were used. The Euler equations were selected as they offer a good trade-off between computational complexity and accuracy. It was also chosen as it is offered as part of the SU2 suite of software, an open-source code for CFD analysis. SU2 is well documented and has been shown to be reasonably accurate for several different applications. [20] The Euler equations were chosen over other, higher fidelity, CFD methods as they require some of the same assumptions as the VLM (inviscid and adiabatic flow) but incorporates the effect of compressibility and shock waves into the solution. As this work is concerned with the creation and validation of an early stage method, it was determined that the Euler equations were a good trade-off between computational complexity, accuracy and still taking into account the key differences between incompressible flow with the Prandtl- Glauert correction applied and the compressible flow including shock waves that the BWB would experience during the cruise segment. There are several good references detailing the implementation of the Euler equations as well as their specific implementation in SU2, and further elaboration is omitted. [21] [20]

2.4.1 Jameson-Schmidt-Turkel The solution scheme chosen for the solving the Euler equations in SU2 was Jameson-Schmidt-Turkel’s. JST was chosen as it oﬀers a balance between good performance and solution accuracy for the Euler equations, including accounting for the presence of shock waves. It is very well documented in the original article, and will not be elaborated further here. [22] Chapter 3

Method

3.1 Requirements on new geometry

In order to be able to access the same (or with the least amount of modifi- cation) gate infrastructure as the Airbus A320neo, it was determined that the 41 meter wingspan of the old baseline geometry was too long to fit into the currently standard 36 meter wing box available at most airports. There were also issues with stall performance of the baseline geometry, with maximum lift coefficient appearing very close to where the control surfaces. There were also some issues raised regarding the longitudinal static margin of the aircraft with the outboard wings placed closer to the trailing edge of the fuselage. The requirements on the new geometry compared to the old are in full listed in table 3.1.

3.2 Athena Vortex Lattice

The low-ﬁdelity VLM simulations were performed using the MIT-developed Athena Vortex Lattice (AVL) software. AVL implements the Vortex Lattice Method (VLM) which is a numerical method used for calculating (amongst others) induced drag and lift distributions for a certain geometry.

Issue Solution Wingspan 41m Reduce to 36m Static margin too high Move wings forwards along center body chord Unsafe stall properties Change wing geometry to move stall location Table 3.1: Requirements on new geometry

7 8 CHAPTER 3. METHOD

Parameters used in AVL simulations Value Mach number 0.78 Velocity 233.34 [m/s] Air density 0.3937 [kg/m3] g 9.81 [m/s2] Weight 80 000 [kg] Table 3.2: AVL simulation parameters

The calculations are based on the vortex lattice method, as detailed in section 2.3. In AVL, the BWB is represented as a set of six wing sections. The center body was considered a wing as well, in order for AVLto correctly model the lift and drag force that the center body contributes with. The VLM has no inherent support for solutions regarding compressible flow, so AVL also implements the Prandtl-Glauert correction to obtain a more accurate solution for higher mach numbers. [23] The AVL software takes input files containing the geometry of the aircraft that has been exported from OpenVSP. L The results from AVL that were deemed of most importance were the D ratio, the CL,tip and the CL,max over the wing. The max value of the lift coefficient and the location thereof indicates the stall performance of the aircraft, as the location of the maximum local lift coefficient would be the location of initial flow separation. The location of the flow separation is important as for a BWB it is imperative that the elevons maintain functionality, should the aircraft enter a stalling state in order to recover the stall. With the control surfaces of a BWB within the turbulent section of the airflow, the BWB would become extremely difficult to control and the stall would be extremely difficult to recover. Thus, assuring that the point of initial stall would not be at the location of the elevons of the BWB was a key metric for determining the feasibility of a new BWB baseline geometry. The lift distribution curves from AVL were also overlain with the spanwise distributions obtained from the SU2 simulations in order to give another metric for model validation. The simulation in AVL was run for two cases: one for a trimmed cruise 1 2 stage (where mg = 2 ρv SCL and also for a series of angles of attack to create a drag polar for the prospective BWB design. CHAPTER 3. METHOD 9

3.2.1 Verifying the AVL model As specified in section 2.3, some assumptions are required for the VLM. In the case presented here, the Mach number is far above the region for which incompressible flow can be assumed (M >> 0.3) and the airfoil that the center body is built upon is thick to allow for passengers and cargo. This means that lifting line theory (and in extension the VLM) could possibly be inadequate. However, the current work aims develop a framework for early- stage conceptual design of a blended wing-body aircraft. Should it become evident during model verification that the VLM based AVL simulations are far from the results from the more accurate Euler, the difference will be studied. To verify the model, the top performing geometry with respect to wing load distribution, lift-to-drag ratio and static stability was run through an Euler simulation and the results compared to those obtained from the VLM/AVL. The reason behind Euler being chosen as a method for verification was that both the VLM and the Euler equations are inviscid, holding as many assumptions as possible constant across the two different methods and assuring that any possible difference in results calculated with the two methods would be to the addition of compressibility and shock waves that is included in the Euler equations.

3.3 SU2 simulations

3.3.1 Preprocessing In order to run the SU2 simulations the geometries had to be meshed. The software chosen for the meshing was ICEM CFD. [24] When meshing the geometries, extra care was taken to increase the resolution of the mesh close to the leading edge as well as where the (potential) recompression shocks would be located. This was of utmost importance, as for the Euler equations the shock waves are solution singularities without width. Using a finer mesh over the areas where the shock waves would exist reduces the probability of solution divergence due to the stiffness of the differential equation.

3.3.2 Solver settings The solver was set to use a JST numerical scheme, a Jacobi smoother and a Jacobi preconditioner for the Krylov linear solver that SU2 implements. It was set to iterate a maximum of 10 000 times. These settings were obtained in part 10 CHAPTER 3. METHOD

from previous SU2 simulation work done by L. Cerquentani [11] and in part from experimentation done in order to obtain solution convergence. The JST convective method was used instead of Roe or Lax-Freidrich as JST allowed for increased convergence speed a higher success rate than either Roe or Lax-Freidrich in the previous study. [11] No multi-grid was set, as the multi-grid option has been established as a cause of solution divergence for some users.

3.4 Results Interpretation

The results from the Euler simulations were then compared to the results from the Vortex Lattice simulations in order to determine whether the accuracy of the VLM was suﬃcient for early stage BWB design. Chapter 4

Results

4.1 Developed design meators

The proposed methodology for creating and quickly determining the aerodynamic performance of several BWB geometries involves OpenVSP, AVL and a python script that connects the two together and parses the results. First, many geometries are generated using programmatic calls to OpenVSP. These geometries are then projected onto plate representations, suitable for use with AVL. AVL then runs simulations for a set case, where the case can either be to generate a drag polar (multiple angles of attack) or run for a trimmed, level flight cruise condition analogue. The results from these simulations are then put into an excel sheet as well as drawn into graphs, allowing at-a-glance de- termination of lift-to-drag ratio, maximum local lift coefficient and location thereof, maximum global lift coefficient, Oswald efficiency ratio and other performance indicators. This methodology was then used to propose a new baseline geometry for further studies at ISAE Supaero/Onera.

4.2 Results from AVL

The full table of results from the Vortex Lattice simulations are presented in appendix F in table F.2. The four top geometries and their results are presented in tables 4.1 and 4.2. In ﬁgure 4.1, the distributions of wing loading and lift coeﬃcient are shown as output from AVL. This plot is for the trimmed cruise case, with parameters shown in table E.1 in appendix E.

11 12 CHAPTER 4. RESULTS

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 68 40.23 0 0.623 59.54 0.548 26.70 0.478 -4.49 48 37.23 0 0.673 58.21 0.581 34.97 0.332 -1.46 70 40.52 0 0.668 59.78 0.621 38.66 0.257 -2.03 168 55.25 0 0.549 43.44 0.682 28.358 0.519 -0.48

L Table 4.1: Top four geometries (Highest D max) from AVL

L 2 Geo no. D Oswald coeﬀ. at max L/D Aspect ratio Wing area [m ] 68 22.839 0.9815 4.412 287.22 48 22.671 0.9818 4.335 298.94 70 22.461 0.9815 4.328 299.47 168 22.239 0.953 4.391 295.18 Table 4.2: Results of top four geometries from AVL

The stall characteristics of geometry 70 were also determined to be safer than the baseline geometry, as the location of the maximum lift coeﬃcient according to the AVL simulations was located towards the body and not at locations where future control surfaces would be located. Similar conclusions could be drawn about the static margin of the aircraft. With the outboard wing moved further forward, the downward pitching moment was reduced as the outboard wing lifting force would be closer to a theorized center of gravity at approximately 35% chord of the center body.

4.3 The new baseline geometry

From the four geometries in table 4.1, number 70 was chosen as the new baseline geometry on which the Euler verification would be performed. Geometry no. 70 was chosen as a new baseline BWB geometry from the AVL simulations. A view of this geometry can be seen in figure H.1 in appendix H. During the process it was determined that in order to make the wing load distribution more elliptical the center body twist angle was to be set to 0, and geometries were re-generated. This lead to a final geometry parameter probability distribution similar to the one in table C.1, but with φcb = 0 deg. CHAPTER 4. RESULTS 13

Figure 4.1: Treﬀtz plane plot of the chosen geometry 70, trimmed cruise case

4.4 Euler veriﬁcation with SU2

During the process of creating the SU2 model and config file, it was found that the CFD model repeatedly failed to converge despite using solver settings that have been proven to work in previous studies. The reason for the convergence failures are discussed and explored further in the discussion section in chapter 5.3. No verification of the AVL results could thus be done using the SU2 Euler simulations. Chapter 5

Discussion

5.1 Geometry creation

During initial results parsing, it was determined that the center body twist angle φcb needed to have a zero (or close to) twist, as it otherwise adversely aﬀected the Oswald coeﬃcient and the spanwise load distribution of the BWB. Positively twisting the center body was found to have very little improvement on the aerodynamic performance of the airframe, so leaving the center body untwisted was determined to be the best option in order to minimize drag.

5.2 AVL solution accuracy

As noted in section 3.2, the accuracy of the AVL software for transonic re- gions is debateable. However, as the design methodology development concerns early stage BWB design, some accuracy deficiencies would be deemed acceptable. As discussed previously in section 3.2, one of the major differences with regards to accuracy is the absence of transonic effects at a flight velocity where transonic effects would be inevitable (M > 0.7). These effects cannot be said to be equal across all aircraft geometries, as multiple factors affect the severity of the wave drag caused by the shock waves such as lifting surface sweep angle against the oncoming flow. In this case, the leading edge sweep angle is varied on all three lifting surfaces of the BWB. In previous studies, the shock wave intensity (and thus wave drag contribution) has been show to greatly vary with wing sweep, but also that that the general trend is that for higher sweep, the wave drag is reduced on a similar BWB as studied here. [25]

14 CHAPTER 5. DISCUSSION 15

In order to fully explore the aerodynamic characteristics of the BWB developed throughout the current work, higher resolution and ﬁdelity studies are needed. Characteristics such as vortex lift/drag caused by the delta-wing like shape of the center body and boundary layer eﬀects cannot be determined using inviscid methods and require the solution of other, more complex gov- erning equations, such as the Reynolds-Averaged Navier-Stokes equations.

5.3 SU2 Simulations

As described in section 4.4, the CFD simulations using the SU2 repeatedly failed to converge, despite using settings that have been used previously to obtain convergence on similar geometries. [11] During investigation of these convergence issues it was found that the methodology was flawed, as the base geometry file that was used included severe faceting. The (albeit slight) faceting of the base geometry file was propagated into the mesh file and the issues that this caused were difficult to diagnose. Eventually this issue was discovered through a very thorough, close-up visual inspection of the mesh. Reviewing the (unconverged) plot of the pressure distribution in figure I.1, the non-smooth pressure distributions of the upper and lower side with clear pressure valleys that are consistent with the position of the geometry facet edges. In order to test this theory, the geometry was exported again but was interpolated during preprocessing to create continuous and smooth surfaces. Due to time constraints, only a single simulation was run on this version of the geometry in order to test the theory, resulting in the plot in figure I.2. It is clear when comparing these two pressure distributions that the smooth geometry is much more reasonable, as it lacks the intermittent pressure drops of the faceted geometry. Thus, further studies are required to determine whether the VLM gives results that are close enough to the results when taking wave drag and other compressibility effects that cannot be accurately modelled using the Prandtl-Glauert correction. Chapter 6

Conclusions

6.1 Method validity

Given the failure in obtaining convergence of the higher fidelity method that was intended to be used in validation of the VLM based method, no conclusions can be drawn regarding whether using the VLM through the AVLcode is a feasible method for the determining the transonic aerodynamic performance of a BWB at an acceptable degree of accuracy for early stage design. However, a methodology for designing and determining low-velocity performance of an early stage BWB has been defined, using previously proven valid methods for low velocity flows. Further studies are required to determine the validity of this methodology for transonic flows, as the efforts made within the scope of the current work were insufficient to determine this.

6.2 Proposed new geometry

The new baseline geometry proposed in the results section improves upon the old baseline geometry in all of the areas where the previously decided geometry was deemed insuﬃcient. The static margin is lower and while the maximum lift coeﬃcient appears close to the tip, it is not located close to the where the highest wing loading is located.

6.3 Further studies

The methodology developed herein does not contain the addition of any control surfaces. The eﬀect on the VLM results caused by the control surface

16 CHAPTER 6. CONCLUSIONS 17

induced trim drag could be studied. As AVL also returns results concern- ing the moment coefficients, it could be of interest to further expand upon the methodology and also include whether the VLM gives accurate enough results to review the lateral and longitudinal stability of the BWB. It would also be interesting to determine whether changing the very sharp geometry transitions between the sections in the proposed geometry to smoother transitions would have a meaningful impact on the aerodynamic performance. In this study, the center body used the NACA23018 airfoil. In reality, it is likely that a final iteration of the BWB would use a reflex cambered airfoil for the center body in order to improve the longitudinal stability of the airframe much like many other tailless aircraft. Thus, further studies regarding the effect of a reflex cambered airfoil on the overall performance in general and the longitudinal stability in particular would be necessary. Since the selected geometry only has been analysed using inviscid methods, the viscous drag (CD,0) of the proposed geometry should be calculated through use of viscous methods such as the Reynolds-averaged Navier-Stokes equations. These studies could also aid in determining whether there would be any change in aerodynamic performance due to the introduction of vortices, investigating whether significant sweep of the center body of the blended wing- body would result in vortex lift. This vortex lift could also be studied for higher angles of attack, reviewing whether the same high lift devices (slats and slots) are necessary on a BWB as on a contemporary aircraft. Finally, the geometry proposed is missing a lot of necessary parts for a final iteration production aircraft. Adding some form of propulsion, either in the two-engine constellation seen in the previous, baseline BWB geometry in figure B or distributing the power plants along the center body trailing edge and studying the aerodynamic and stability impact of this on the BWB would also be necessary before the geometry proposed could become reality. References

[1] Bows, A. Anderson, K. Upham, P. Aviation and Climate Change, Lessons for European Policy, 1st Edition. University of Manchester: Routledge, 2008. [2].“ IATA Forecast Predicts 8.2 billion Air Travelers in 2037 ”. In: (Re- trieved 30/6). url: %7Bhttps://www.iata.org/pressroom/ pr/Pages/2018-10-24-02.aspx%7D. [3] Liebeck, R.H. “Design of the Blended Wing Body Subsonic Transport”. In: Journal of Aircraft Vol 41 (January–February 2004). [4] Bonet, J. T. “Blended Wing Body Transport Aircraft Research & De- velopment”. In: 31st Congress of the International Council of the Aero- nautical Sciences (September 2018). [5] Sgueglia, A. Schmollgruber, P. Benard, E. et al. “Preliminary sizing of a Medium Range Blended Wing-Body using a Multidisciplinary Design Analysis Approach”. In: (2017). [6] Nickol, C. Haller, W. “Assessment of the Performance Potential of Ad- vanced Subsonic Transport Concepts for NASA’s Environmentally Re- sponsible Aviation Project”. In: 54th AIAA Aerospace Sciences Meeting (2016). [7] Schmollgruber P. Bartolim N. Bedouet, J. Defoort, S. Gourinat, Y. Be- nard, E. Lafage, R. Sgueglia, A. “Use of a Certiﬁcation Constraints Module for Aircraft Design Activities”. In: (). url: %7Bhttps:// arc.aiaa.org/doi/abs/10.2514/6.2017-3762%7D. [8] Nickel, K. Wohlfahrt, N. Tailless Aircraft in Theory and Practice. Washington DC, United States of America: American Institute of Aeronautics and Astronautics, Inc, 1994.

18 REFERENCES 19

[9] Lyu, Z. Martins, J. R. R. A. “Aerodynamic Design Optimization Studies of a Blended-Wing-Body Aircraft”. In: Journal of Aircraft, Vol. 51, No. 5 ((September–October 2014)). [10] Qin, N. et al. “Aerodynamic Considerations of Blended Wing Body Air- craft”. In: Progress in Aerospace Sciences, vol. 40, no. 4, pages 321–343, (2004). [11] Cerquentani, L. High Fidelity Aerodynamics Models for Blended Wing Body Design. 2018. [12] Cerquentani, L. Control surfaces and laws of a Blended Wing Body. 2019. [13] EASA. “Type certiﬁcate Data sheet for Airbus A318 – A319 – A320 – A321”. In: ((6 March 2017)). [14] Bradley, Kevin R. “A Sizing Methodology for the Conceptual Design of Blended-Wing-Body Transports”. In: NASA/CR-2004-213016 (2004). [15] Budziak, Kinga. Aerodynamic Analysis with Athena Vortex Lattice (AVL). Department of Automotive and Aeronautical Engineering, Hamburg University of Applied Sciences, 2015. [16] Shapiro, A.H. Compressible Fluid Flow I. Wiley, 1953. [17] Falkner. V.M. The Accuracy of Calculations Based on Vortex Lattice Theory. Rep. No. 9621, British A.R.C., 1952. [18] E.L. Houghton, P.W. Carpenter. Aerodynamics for Engineering Students, 5th ed. Butterworth-Heinemann, 2003. [19] Bertin, J., Smith, M. Aerodynamics for engineers (3.rd ed.) Upper Sad- dle River, N.J.: Prentice Hall, 1998. [20] Economon et al. “SU2: An Open-Source Suite for Multiphysics Simula- tion and Design”. In: AIAA Journal Vol. 54, No. 3 (March 2016). [21] Ferziger, J.H. Perić, M. Computational Methods for Fluid Dynamics, third edition. Springer, 2002. [22] Jameson, A. Schmidt, W. Turkel, E. “Numerical Solution of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes”. In: http://www.cs.tau.ac.il/ turkel/PSmanuscripts/jst.pdf (). [23] Drela, M. Youngren, H. “AVL Webpage”. In: http://web.mit.edu/drela/Public/web/avl/ (Retrieved 190612). 20 REFERENCES

[24] ANSYS, Inc. ANSYS ICEM CFD User Manual. ANSYS, Inc., 2012. [25] Siouris, S Qin, N. “Study of the eﬀects of wing sweep on the aerodynamic performance of a blended wing body aircraft”. In: Proc. IMechE Vol. 221 (2007). [26] Harris, Charles D. “NASA Supercritical Airfoils, A Matrix of Family- Related Airfoils”. In: NASA Technical Paper 2969 (1990). Appendix A

Glossary

Abbreviation Elaboration BWB Blended Wing Body RANS Reynolds-Averaged Navier-Stokes AVL Athena Vortex Lattice OpenVSP Open Vehicle Sketch Pad MTOW Maximum Takeoﬀ Weight OEW Operational Empty Weight MZFW Maximum Zero Fuel Weight T&W Tube and wing LHS Latin Hypercube Sampling JST Jameson-Schmidt-Turkel

21 Appendix B

Baseline Geometry

General parameters Wing Area 340 m2 Total wingspan 36 m Center body Halfspan 3.9 m ◦ Λ25% 35 cb 0.575 ◦ φcb 0 Airfoil NACA23018 Transition zone Halfspan 2 m ◦ Λ25% 30 tz 0.3739 ◦ φtz -3 Airfoil NACA0018 Wing Halfspan 12.1 m ◦ Λ25% 30 w 0.211 ◦ φw 0 Airfoil SC410 [26] Table B.1: Geometry data for reference geometry of BWB

22 APPENDIX B. BASELINE GEOMETRY 23

Figure B.1: OpenVSP Baseline Geometry overview Appendix C

Sampling probability distribution

Parameter Min Max µ σ2 ◦ Λw,25 [ ] 20 45 32.5 52.0833 ◦ Λtz,25 [ ] 20 60 50 300 ◦ Λcb,25 [ ] 30 60 45 75 w 0.2 0.6 0.4 0.0133 tz 0.4 1 0.7 0.03 cb 0.575 1 0.7 0.03 ◦ φw [ ] -5 0 -2.5 2.0833 ◦ φcb [ ] 0 0 0 0

Table C.1: Uniform probability distribution characteristics for geometry input parameters

24 Appendix D

BWB Parameters

Parameter Name

Λbody Body sweep angle φbody Body twist angle body Body taper ratio Λtz Transition zone sweep angle tz Transition zone taper ratio Λwing Wing sweep angle φwing Wing twist angle wing Taper ratio of outer wing Table D.1: Parameters of interest

25 Appendix E

AVL Solver settings

Parameter Value ρ 0.3739 [kg/m3] g 9.81 Mass 80 000 [kg] Cd,0 0.00622 v 233.34 [m/s] M 0.78 Table E.1: AVL simulation parameters

26 Appendix F

Full table of simulation results from AVL

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 1 30.12 0 0.669 0.879 52.4 0.238 -0.35 28.38 2 30.25 0 0.741 0.648 47.11 0.328 -1.6 23.77 3 30.41 0 0.65 0.853 33.34 0.432 -2.8 42.73 4 30.5 0 0.718 0.899 57.96 0.428 -4.43 34.77 5 30.65 0 0.771 0.784 56.09 0.278 -2.97 25.24 6 30.92 0 0.797 0.802 55.34 0.348 -1.68 37.84 7 31.13 0 0.729 0.663 34.18 0.556 -1.93 33.52 8 31.28 0 0.965 0.68 40.17 0.359 -4.5 40.78 9 31.46 0 0.678 0.823 47.92 0.469 -0.55 33.43 10 31.53 0 0.797 0.625 35.42 0.439 -0.15 39.77 11 31.71 0 0.707 0.745 51.37 0.225 -4.33 28.63 12 31.89 0 0.746 0.902 40.78 0.315 -3.81 41.51 13 32.03 0 0.916 0.425 33.64 0.302 -3.08 35.7 14 32.24 0 0.99 0.57 58.06 0.47 -2.06 21.05 15 32.32 0 0.679 0.75 45.24 0.296 -1.87 41.02 16 32.46 0 0.733 0.953 40.23 0.379 -2.41 23.48 17 32.69 0 1.059 0.501 52.55 0.393 -4.27 23.64 18 32.8 0 0.937 0.637 59.02 0.337 -3.23 37.16 19 32.9 0 0.96 0.505 44.89 0.326 -0.98 27.88 20 33.03 0 0.636 0.895 48.37 0.386 -2.35 42.01

27 28 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL

Figure F.1: Drag polar for −3 < α < 15 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL 29

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 21 33.24 0 0.648 0.863 33.11 0.384 -1.24 21.99 22 33.41 0 0.794 0.698 42.04 0.275 -1.82 22.96 23 33.57 0 0.862 0.475 33.89 0.529 -0.73 27.17 24 33.61 0 0.805 0.776 32.31 0.245 -0.64 33.77 25 33.87 0 0.853 0.54 34.96 0.503 -2.94 22.67 26 34.03 0 0.722 0.766 31.98 0.456 -4.01 29.78 27 34.13 0 0.737 0.566 50.18 0.563 -3.1 36.82 28 34.33 0 0.769 0.989 39.84 0.283 -0.6 32.22 29 34.36 0 0.803 0.692 44.21 0.442 -2.33 31.13 30 34.59 0 0.783 0.541 43.6 0.435 -3.73 29.88 31 34.67 0 0.966 0.436 48.86 0.55 -2.02 30.78 32 34.93 0 0.778 0.514 30.64 0.547 -3.32 26.48 33 35.07 0 0.952 0.443 39.99 0.51 -2.73 41.44 34 35.17 0 0.761 0.432 54.93 0.585 -2.53 38.33 35 35.27 0 0.732 0.536 45.82 0.417 -0.39 34.14 36 35.53 0 0.784 0.455 53.94 0.545 -3.05 28.55 37 35.65 0 0.54 0.905 48.16 0.351 -3.55 25.08 38 35.83 0 0.886 0.601 31.09 0.578 -2.51 39.26 39 35.87 0 0.988 0.556 34.91 0.316 -4.66 29.58 40 36.01 0 0.88 0.716 57.08 0.483 -0.35 43.26 41 36.16 0 0.769 0.545 37.1 0.312 -3.02 34.26 42 36.3 0 0.813 0.741 55.42 0.339 -3.96 20.05 43 36.46 0 0.766 0.993 49.67 0.214 -4.47 34.73 44 36.63 0 0.886 0.714 30.48 0.39 -2.65 30.18 45 36.77 0 0.808 0.739 48.67 0.557 -3.9 36.96 46 37.04 0 0.64 0.852 44.48 0.291 -0.01 36.43 47 37.18 0 1.066 0.569 50.82 0.377 -0.7 36.22 48 37.23 0 0.672 0.581 58.21 0.332 -1.46 34.97 49 37.36 0 0.879 0.483 47.83 0.239 -2.98 30.03 50 37.55 0 0.67 0.703 41.99 0.596 -4.05 22.13 51 37.77 0 0.673 0.807 32.82 0.433 -4.39 40.98 52 37.9 0 0.85 0.49 56.57 0.446 -3.52 43.96 53 37.96 0 0.656 0.653 59.2 0.581 -3.36 24.38 54 38.2 0 0.775 0.837 49.08 0.59 -0.88 42.42 55 38.32 0 0.781 0.697 46.77 0.421 -0.11 28.09 56 38.5 0 0.752 0.747 37.34 0.355 -4.99 21.81 57 38.69 0 0.812 0.885 39.51 0.419 -4.9 26.22 58 38.77 0 0.653 0.845 55.53 0.232 -1.32 30.32 59 38.89 0 0.704 0.817 39.75 0.203 -1.45 21.22 60 39.07 0 0.812 0.652 40.91 0.56 -0.94 20.25 30 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 61 39.24 0 0.721 0.686 59.98 0.553 -0.77 26.87 62 39.35 0 0.628 1.068 56.98 0.265 -2.85 40.24 63 39.58 0 0.67 0.62 55.14 0.513 -1.67 43.44 64 39.74 0 0.623 0.749 45.94 0.261 -4.7 35.62 65 39.77 0 0.748 0.82 53.48 0.415 -4.53 31.04 66 39.97 0 0.739 0.821 36.79 0.507 -3.62 37.71 67 40.16 0 0.739 0.768 31.33 0.521 -0.3 32.33 68 40.23 0 0.623 0.548 59.54 0.477 -4.49 26.7 69 40.42 0 0.689 0.917 53.6 0.366 -3.86 44.2 70 40.52 0 0.668 0.621 59.78 0.256 -2.03 38.66 71 40.76 0 0.627 0.736 48.01 0.591 -2.59 41.25 72 40.95 0 0.925 0.453 44.27 0.463 -0.27 38.24 73 41.01 0 0.84 0.396 43.94 0.452 -3.77 23.96 74 41.23 0 0.678 0.719 45.6 0.509 -1.89 27.71 75 41.39 0 1.085 0.5 58.38 0.381 -1.04 36.25 76 41.54 0 0.751 0.767 47.29 0.437 -4.94 39.15 77 41.57 0 0.853 0.412 46.49 0.349 -4.28 41.69 78 41.75 0 0.736 0.649 36.98 0.252 -2.13 38.82 79 41.95 0 0.846 0.597 34.32 0.274 -4.11 32.85 80 42.01 0 0.672 0.816 34.51 0.218 -4.24 26.36 81 42.29 0 0.689 0.785 30.23 0.465 -2.88 21.72 82 42.35 0 0.866 0.644 57.47 0.522 -0.1 29.3 83 42.51 0 0.86 0.534 37.69 0.207 -1.17 44.88 84 42.75 0 0.842 0.701 54.74 0.561 -4.76 41.89 85 42.77 0 0.99 0.495 41.28 0.549 -4.03 35.41 86 42.94 0 0.893 0.425 37.59 0.486 -1.28 22.56 87 43.14 0 0.58 0.869 50.63 0.308 -2.26 43.65 88 43.26 0 0.961 0.596 50.44 0.249 -3.43 44.62 89 43.41 0 0.888 0.774 45.04 0.285 -0.18 25.97 90 43.56 0 0.798 0.931 45.5 0.313 -0.66 40.11 91 43.77 0 0.701 0.631 30.95 0.472 -2.29 43.51 92 43.84 0 0.606 1.034 32.24 0.304 -2.8 35.21 93 43.96 0 0.924 0.449 41.72 0.396 -3.47 34.48 94 44.15 0 0.855 0.554 53.2 0.423 -4.15 43.86 95 44.3 0 0.793 0.507 31.94 0.308 -0.21 31.8 96 44.4 0 0.766 0.816 48.47 0.402 -1.92 20.96 97 44.55 0 0.707 0.856 41.17 0.403 -0.06 44.4 98 44.75 0 0.635 0.851 36.61 0.49 -0.61 37.98 99 44.9 0 0.84 0.642 58.84 0.396 -2.19 37.55 100 45.07 0 0.732 0.654 42.24 0.282 -4.32 20.78 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL 31

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 101 45.21 0 0.777 0.713 59.6 0.231 -1.11 27.55 102 45.43 0 1.023 0.549 38.72 0.57 -0.96 33.31 103 45.45 0 0.738 0.654 57.75 0.343 -1.77 21.51 104 45.7 0 0.729 0.603 48.92 0.497 -4.96 25.7 105 45.87 0 0.67 0.833 58.55 0.494 -4.56 28.25 106 45.96 0 0.632 0.734 49.99 0.572 -1.02 32.01 107 46.17 0 0.674 1.106 49.91 0.236 -0.5 38.51 108 46.34 0 0.953 0.504 54.44 0.453 -0.91 20.26 109 46.4 0 0.779 0.865 56.15 0.34 -2.67 39.67 110 46.54 0 0.787 0.505 35.8 0.6 -4.85 35.01 111 46.8 0 0.951 0.61 43.78 0.243 -0.78 39.96 112 46.89 0 1.045 0.506 55.68 0.532 -4.62 31.95 113 47.02 0 0.913 0.407 42.58 0.586 -1.74 22.04 114 47.17 0 0.662 0.619 43.13 0.333 -0.45 21.35 115 47.26 0 0.696 0.589 53.37 0.321 -2.77 25.84 116 47.44 0 0.761 0.817 51.22 0.534 -2.16 29.19 117 47.61 0 1.121 0.525 31.66 0.299 -2.1 24.26 118 47.74 0 0.587 0.912 39.14 0.499 -3.59 32.66 119 47.9 0 0.801 0.624 38.29 0.598 -4.37 39.55 120 48.09 0 0.66 0.901 59.37 0.358 -2.47 29.49 121 48.24 0 0.894 0.699 31.45 0.386 -1.58 42.55 122 48.34 0 0.708 0.811 44.82 0.583 -4.6 26.6 123 48.51 0 0.942 0.642 51.64 0.366 -3.63 26.96 124 48.68 0 0.836 0.459 30.33 0.461 -1.98 36.07 125 48.89 0 0.878 0.912 40.4 0.228 -3.13 39.39 126 48.92 0 0.868 0.794 32.91 0.208 -3.19 23.55 127 49.15 0 0.664 1.004 33.25 0.23 -1.65 38.91 128 49.28 0 0.81 0.63 34.77 0.579 -4.73 33.69 129 49.42 0 0.677 0.867 35.21 0.295 -1.53 22.42 130 49.57 0 0.684 0.876 34.35 0.294 -3.71 20.46 131 49.74 0 0.783 0.811 31.52 0.448 -1.37 24.04 132 49.86 0 0.779 0.82 54.17 0.264 -4.89 23.25 133 50.04 0 0.659 0.678 52.75 0.564 -1.57 43.04 134 50.11 0 0.751 0.588 52 0.574 -2.1 42.31 135 50.26 0 0.773 1.011 54.78 0.362 -1.08 22.79 136 50.52 0 0.784 0.45 51.03 0.567 -2.68 26.09 137 50.58 0 0.77 0.495 37.95 0.496 -1.79 44.77 138 50.76 0 0.801 0.893 56.74 0.254 -3.83 24.19 139 51 0 0.846 0.78 41.41 0.269 -0.13 29.7 140 51.13 0 0.618 1.102 46.62 0.24 -4.79 33.21 32 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 141 51.19 0 0.92 0.699 32.54 0.374 -3.68 30.68 142 51.31 0 0.763 0.56 30.01 0.475 -2.92 25.26 143 51.51 0 0.591 0.981 57.21 0.426 -0.82 42.19 144 51.62 0 0.836 0.697 49.3 0.246 -3.21 28.83 145 51.78 0 0.974 0.51 46.91 0.528 -1.95 35.92 146 52.02 0 1.03 0.387 41.6 0.371 -1.41 24.81 147 52.09 0 0.953 0.467 47.03 0.407 -3.66 20.53 148 52.29 0 0.744 0.636 33.99 0.594 -1.33 31.66 149 52.49 0 0.822 0.615 36.12 0.516 -4.08 22.31 150 52.53 0 0.716 0.768 56.36 0.345 -1.51 33.98 151 52.67 0 0.802 0.688 39.39 0.25 -3.99 42.8 152 52.91 0 0.818 0.449 55.83 0.41 -4.64 37.42 153 53.1 0 0.912 0.547 51.88 0.223 -0.28 32.98 154 53.23 0 0.93 0.596 49.46 0.373 -0.83 44.11 155 53.36 0 0.77 0.965 30.77 0.267 -0.53 34.07 156 53.51 0 0.562 0.93 37.81 0.412 -1.06 27.25 157 53.61 0 0.852 0.709 47.45 0.354 -2.71 43.15 158 53.82 0 0.753 0.605 56.42 0.538 -0.41 36.71 159 53.95 0 0.767 0.663 42.31 0.304 -1.2 25.49 160 54.07 0 0.488 1.048 43.32 0.219 -1.38 28.95 161 54.18 0 0.856 0.764 38.92 0.467 -1.18 35.33 162 54.3 0 0.835 0.947 39.15 0.286 -3.89 23.12 163 54.47 0 0.751 0.891 37.44 0.322 -3.38 38.11 164 54.65 0 0.55 1.024 46.21 0.27 -3.27 27.03 165 54.83 0 0.689 0.776 51.5 0.535 -4.16 41.75 166 54.93 0 0.83 0.694 54.51 0.288 -4.22 40.25 167 55.09 0 0.869 0.689 57.75 0.542 -2.43 24.88 168 55.25 0 0.549 0.682 43.44 0.519 -0.48 28.36 169 55.45 0 0.723 0.623 57.37 0.363 -3.04 27.87 170 55.59 0 0.802 0.838 33.45 0.258 -4.8 42.91 171 55.8 0 0.726 0.578 36.25 0.482 -1.83 23.18 172 55.81 0 0.851 0.646 50.85 0.537 -3.49 41.2 173 56.03 0 0.704 0.905 42.77 0.5 -3.41 24.62 174 56.3 0 0.653 1.032 52.2 0.479 -2.31 37.03 175 56.49 0 0.627 0.625 40.54 0.413 -3.29 21.45 176 56.59 0 0.738 0.621 44.64 0.215 -2.57 30.42 177 56.81 0 0.776 0.756 42.7 0.22 -4.42 29.07 178 56.98 0 0.863 0.805 58.68 0.2 -2.24 31.34 179 57.08 0 0.729 0.744 38.57 0.443 -0.25 40.69 180 57.25 0 0.888 0.552 47.62 0.505 -0.68 31.57 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL 33

Geo no. Λ25,cb θcb cb Λ25,tz tz Λ25,w θw w 181 57.39 0 0.782 0.737 32.56 0.57 -2.62 34.51 182 57.55 0 0.841 0.569 35.37 0.404 -4.19 36.51 183 57.7 0 0.969 0.509 38.11 0.334 -0.86 32.47 184 57.89 0 0.763 0.672 54.08 0.485 -1.5 20.71 185 57.97 0 0.839 0.826 50.31 0.525 -0.03 30.98 186 58.13 0 0.704 0.833 35.92 0.458 -3.93 40.61 187 58.27 0 0.789 0.657 35.65 0.369 -1.25 38.47 188 58.47 0 0.873 0.549 45.34 0.212 -2.84 35.83 189 58.6 0 0.951 0.448 36.44 0.515 -3.34 44.29 190 58.76 0 0.655 0.788 46.16 0.54 -3.17 25.55 191 58.89 0 0.887 0.588 41.04 0.426 -0.47 24.64 192 59.06 0 0.711 0.981 52.83 0.4 -4.87 33.02 193 59.23 0 0.785 0.926 49.59 0.327 -1.71 40.39 194 59.3 0 0.795 0.658 52.28 0.49 -3.79 32.51 195 59.41 0 1.076 0.452 53.72 0.447 -2.21 30.54 196 59.64 0 0.865 0.818 43.01 0.204 -2.49 27.48 197 59.79 0 1.083 0.567 38.49 0.388 -4.69 31.49 198 59.99 0 0.847 0.647 44.09 0.455 -3.56 39.03 Table F.1: Geometries used in AVL, all angles given in degrees 34 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL

L A Geo no. D Tip CL Max CL e Wing area 1 20.343 0.39 1.305 0.936 3.637 356.36 2 21.357 0.328 1.309 0.986 3.825 338.81 3 20.476 0.244 1.045 0.977 3.517 368.46 4 18.929 0.199 0.943 0.944 3.152 411.1 5 19.669 0.295 1.123 0.949 3.411 379.89 6 19.146 0.275 1.085 0.948 3.195 405.59 7 20.545 0.223 1.141 0.974 3.552 364.92 8 18.593 0.237 0.978 0.992 2.988 433.7 9 19.681 0.244 1.125 0.931 3.424 378.52 10 20.264 0.29 1.208 0.954 3.548 365.29 11 20.777 0.371 1.243 0.957 3.827 338.64 12 19.219 0.265 1.005 0.969 3.186 406.72 13 21.138 0.401 1.401 0.991 3.996 324.29 14 18.903 0.214 1.109 0.987 3.102 417.86 15 21.434 0.369 1.272 0.972 3.832 338.24 16 18.593 0.209 0.968 0.936 3.048 425.2 17 18.887 0.236 1.124 0.984 3.216 402.97 18 19.174 0.278 1.097 0.982 3.196 405.47 19 20.254 0.347 1.339 0.992 3.539 366.21 20 20.078 0.267 1.072 0.951 3.535 366.57 21 20.407 0.259 1.158 0.965 3.561 363.94 22 20.254 0.33 1.233 0.978 3.556 364.46 23 20.766 0.268 1.322 0.977 3.728 347.62 24 19.73 0.377 1.259 0.975 3.356 386.22 25 20.278 0.229 1.208 0.993 3.554 364.64 26 19.948 0.214 1.064 0.978 3.41 380.04 27 21.231 0.232 1.167 0.992 3.819 339.35 28 18.107 0.28 1.036 0.919 2.981 434.77 29 19.855 0.238 1.111 0.982 3.335 388.64 30 21.195 0.271 1.249 0.994 3.875 334.49 31 20.162 0.245 1.245 0.987 3.532 366.97 32 21.046 0.236 1.258 0.992 3.86 335.72 33 20.205 0.254 1.153 0.99 3.587 361.29 34 22.138 0.265 1.269 0.983 4.219 307.22 35 21.908 0.345 1.399 0.97 4.116 314.88 36 21.713 0.261 1.333 0.995 4.074 318.11 37 21.447 0.28 1.191 0.955 4.037 321.06 38 19.139 0.199 1.031 0.979 3.187 406.64 39 19.068 0.277 1.121 0.977 3.311 391.45 40 18.262 0.226 1.013 0.925 2.994 432.89 41 21.634 0.373 1.357 0.99 4.067 318.63 42 19.026 0.233 1.052 0.939 3.298 392.91 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL 35

L A Geo no. D Tip CL Max CL e Wing area 43 18.143 0.296 0.982 0.918 3.073 421.8 44 18.931 0.232 1.043 0.983 3.083 420.32 45 18.892 0.178 0.961 0.988 3.073 421.71 46 20.649 0.378 1.319 0.934 3.75 345.61 47 18.524 0.278 1.137 0.972 3.016 429.76 48 22.671 0.398 1.443 0.982 4.335 298.94 49 21.165 0.447 1.462 0.981 3.975 326.01 50 20.533 0.188 1.141 0.982 3.626 357.43 51 20.426 0.23 1.027 0.988 3.53 367.14 52 20.973 0.274 1.142 0.993 3.804 340.73 53 21.312 0.213 1.212 0.978 3.851 336.57 54 17.916 0.18 0.928 0.903 2.917 444.31 55 19.631 0.27 1.203 0.965 3.421 378.88 56 19.555 0.231 1.071 0.956 3.474 373.08 57 17.855 0.174 0.892 0.96 2.889 448.64 58 20.708 0.406 1.333 0.937 3.794 341.63 59 20.591 0.398 1.292 0.961 3.688 351.39 60 19.416 0.205 1.146 0.976 3.286 394.36 61 20.006 0.226 1.183 0.948 3.517 368.53 62 18.926 0.308 1.059 0.892 3.377 383.72 63 21.509 0.264 1.158 0.974 3.976 325.93 64 21.732 0.371 1.267 0.97 4.145 312.65 65 19.145 0.209 0.998 0.97 3.234 400.7 66 19.07 0.192 0.971 0.97 3.159 410.21 67 19.176 0.223 1.102 0.947 3.27 396.34 68 22.839 0.275 1.351 0.982 4.512 287.22 69 19.36 0.243 0.971 0.947 3.297 393.05 70 22.462 0.464 1.466 0.982 4.328 299.47 71 20.915 0.211 1.068 0.975 3.725 347.94 72 20.381 0.308 1.296 0.962 3.679 352.24 73 21.522 0.298 1.415 0.985 4.213 307.59 74 20.624 0.234 1.182 0.973 3.649 355.16 75 19.084 0.295 1.198 0.977 3.171 408.77 76 19.634 0.214 0.994 0.986 3.327 389.49 77 21.592 0.355 1.277 0.971 4.216 307.4 78 21.483 0.432 1.387 0.989 3.946 328.45 79 20.138 0.345 1.237 0.97 3.662 353.89 80 20.318 0.361 1.212 0.951 3.804 340.72 81 20.037 0.215 1.11 0.977 3.481 372.27 82 18.729 0.225 1.131 0.95 3.179 407.7 83 21.205 0.544 1.507 0.99 3.904 331.95 84 18.823 0.172 0.92 0.992 3.059 423.61 85 19.336 0.205 1.08 0.999 3.257 397.92 86 20.975 0.289 1.398 0.992 3.867 335.11 36 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL

L A Geo no. D Tip CL Max CL e Wing area 87 21.276 0.349 1.208 0.956 3.974 326.08 88 19.508 0.374 1.2 0.996 3.346 387.34 89 18.445 0.296 1.117 0.967 3.06 423.48 90 17.818 0.279 1.038 0.904 2.962 437.51 91 21.034 0.267 1.139 0.987 3.861 335.69 92 19.478 0.288 1.086 0.911 3.484 371.97 93 20.45 0.304 1.268 0.996 3.769 343.89 94 20.342 0.259 1.086 0.996 3.589 361.09 95 21.548 0.433 1.529 0.984 4.112 315.21 96 18.988 0.222 1.054 0.962 3.201 404.82 97 19.104 0.273 1.09 0.909 3.315 390.97 98 19.854 0.243 1.111 0.924 3.511 369.14 99 19.832 0.274 1.142 0.976 3.406 380.53 100 20.354 0.314 1.233 0.957 3.903 332.06 101 20.287 0.403 1.34 0.968 3.632 356.8 102 18.384 0.204 1.072 0.963 2.986 434.02 103 20.85 0.308 1.285 0.979 3.8 341.04 104 20.735 0.221 1.183 0.984 3.802 340.84 105 19.47 0.192 1.019 0.959 3.404 380.78 106 20.564 0.23 1.184 0.942 3.732 347.28 107 17.793 0.341 1.111 0.834 3.162 409.89 108 19.757 0.259 1.262 0.988 3.425 378.41 109 18.477 0.258 1.013 0.919 3.121 415.29 110 20.768 0.209 1.151 0.989 3.806 340.53 111 19.621 0.417 1.329 0.979 3.341 387.91 112 18.812 0.193 1.049 0.997 3.1 418.11 113 20.711 0.248 1.36 0.991 3.773 343.48 114 22.079 0.374 1.471 0.986 4.253 304.75 115 21.927 0.359 1.389 0.983 4.215 307.49 116 18.572 0.186 0.999 0.944 3.064 422.97 117 18.763 0.295 1.158 0.984 3.097 418.43 118 20.139 0.208 1.052 0.966 3.575 362.51 119 19.689 0.185 1.011 0.996 3.36 385.77 120 19.133 0.258 1.082 0.897 3.458 374.76 121 18.874 0.262 1.06 0.967 3.1 418.05 122 19.035 0.165 0.992 0.982 3.209 403.86 123 18.73 0.237 1.059 0.97 3.139 412.91 124 21.136 0.302 1.302 0.987 3.956 327.63 125 17.642 0.301 0.998 0.918 2.873 451.05 126 18.365 0.317 1.069 0.927 3.166 409.3 127 19.253 0.37 1.186 0.914 3.4 381.17 128 19.524 0.184 1.038 0.996 3.336 388.45 129 19.956 0.3 1.169 0.962 3.55 365.05 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL 37

L A Geo no. D Tip CL Max CL e Wing area 130 19.442 0.262 1.075 0.928 3.502 370.12 131 18.648 0.211 1.042 0.967 3.1 418.05 132 18.653 0.261 1.017 0.928 3.317 390.68 133 20.679 0.234 1.104 0.966 3.783 342.63 134 20.422 0.228 1.105 0.981 3.679 352.25 135 17.065 0.205 0.914 0.877 2.833 457.43 136 21.45 0.257 1.357 0.993 4.072 318.24 137 21.334 0.283 1.182 0.98 4.023 322.17 138 18.018 0.257 0.97 0.929 3.1 418.03 139 18.744 0.33 1.182 0.962 3.187 406.64 140 18.749 0.286 1.003 0.898 3.389 382.41 141 18.542 0.227 1.012 0.973 3.044 425.81 142 20.941 0.255 1.261 0.993 3.838 337.69 143 18.802 0.253 1.047 0.874 3.498 370.49 144 19.588 0.34 1.192 0.96 3.453 375.37 145 19.348 0.229 1.127 0.979 3.269 396.51 146 20.647 0.346 1.423 0.996 3.727 347.75 147 19.922 0.263 1.255 0.979 3.604 359.61 148 20.038 0.218 1.161 0.966 3.533 366.86 149 19.536 0.199 1.115 0.983 3.406 380.5 150 19.969 0.305 1.196 0.949 3.569 363.11 151 20.144 0.369 1.199 0.991 3.584 361.58 152 21.301 0.301 1.255 0.983 4.119 314.61 153 20.424 0.488 1.51 0.984 3.67 353.11 154 19.332 0.303 1.156 0.958 3.29 393.92 155 18.076 0.304 1.078 0.923 3.042 426.04 156 20.302 0.268 1.19 0.928 3.77 343.73 157 19.227 0.276 1.07 0.971 3.238 400.21 158 20.19 0.254 1.203 0.942 3.656 354.5 159 20.468 0.342 1.306 0.983 3.71 349.29 160 21.106 0.438 1.39 0.892 4.223 306.87 161 18.199 0.214 1.008 0.945 2.967 436.76 162 17.282 0.213 0.878 0.931 2.856 453.76 163 18.783 0.261 1.018 0.943 3.184 407.04 164 20.11 0.313 1.156 0.931 3.831 338.3 165 19.856 0.195 0.979 0.983 3.416 379.36 166 19.556 0.313 1.121 0.983 3.427 378.22 167 18.446 0.183 1.022 0.957 3.028 427.94 168 22.239 0.292 1.381 0.953 4.391 295.18 169 21.043 0.306 1.278 0.981 3.929 329.89 170 18.92 0.301 1.031 0.97 3.208 404.01 171 21.161 0.265 1.308 0.99 3.915 331.06 38 APPENDIX F. FULL TABLE OF SIMULATION RESULTS FROM AVL

L A Geo no. D Tip CL Max CL e Wing area 172 19.153 0.198 0.993 0.99 3.203 404.64 173 18.417 0.177 0.967 0.935 3.105 417.42 174 17.716 0.191 0.917 0.891 3.067 422.63 175 21.923 0.289 1.344 0.981 4.297 301.61 176 21.339 0.471 1.466 0.98 4.074 318.13 177 19.34 0.346 1.162 0.953 3.54 366.05 178 18.446 0.364 1.146 0.914 3.168 409.08 179 19.555 0.27 1.14 0.934 3.46 374.6 180 19.586 0.25 1.201 0.963 3.405 380.63 181 18.984 0.187 1.008 0.967 3.145 412.09 182 20.161 0.266 1.146 0.997 3.612 358.83 183 19.997 0.346 1.318 0.983 3.49 371.39 184 19.821 0.229 1.176 0.97 3.479 372.55 185 17.17 0.189 0.966 0.887 2.817 460 186 19.407 0.212 0.984 0.981 3.313 391.13 187 20.126 0.311 1.214 0.971 3.565 363.58 188 20.685 0.472 1.427 0.985 3.801 340.95 189 20.186 0.241 1.091 0.995 3.565 363.56 190 19.916 0.2 1.099 0.964 3.523 367.89 191 19.451 0.266 1.219 0.973 3.381 383.31 192 18.004 0.19 0.89 0.917 3.046 425.5 193 17.659 0.26 0.993 0.875 2.994 432.85 194 19.551 0.215 1.079 0.978 3.4 381.12 195 19.417 0.26 1.197 0.985 3.284 394.68 196 18.333 0.336 1.096 0.923 3.127 414.43 197 18.273 0.219 1.004 0.981 2.968 436.69 198 19.32 0.227 1.045 0.991 3.304 392.27 Table F.2: Results of all geometries from AVL Appendix G

Lift distributions from AVL for new baseline geometry

Figure G.1: Treﬀtz plane plot of geometry 70, α = −2

39 40 APPENDIX G. LIFT DISTRIBUTIONS FROM AVL FOR NEW BASELINE GEOMETRY

Figure G.2: Treﬀtz plane plot of geometry 70, α = 0 APPENDIX G. LIFT DISTRIBUTIONS FROM AVL FOR NEW BASELINE GEOMETRY 41

Figure G.3: Treﬀtz plane plot of geometry 70, α = 5 42 APPENDIX G. LIFT DISTRIBUTIONS FROM AVL FOR NEW BASELINE GEOMETRY

Figure G.4: Treﬀtz plane plot of geometry 70, α = 10 Appendix H

Overview of new Baseline Ge- ometry

Figure H.1: New baseline geometry overview

43 Appendix I

Results from SU2

Figure I.1: Upper/lower side pressure distribution (faceted geometry)

44 APPENDIX I. RESULTS FROM SU2 45

Figure I.2: Upper/lower side pressure distribution (interpolated geometry)