CFD Analysis and Assessment of the Stability and Control of a
Supersonic Business Jet
Irene Borillo Llorca
Supervisor: Arthur Rizzi
Royal Institute of Technology (KTH) Stockholm, Sweden
March 2015
Abstract
Extensive research has been done on the aerodynamics of supersonic aircrafts, especially in the military and commercial airplanes’ field. Regarding supersonic business jets (SSBJs), two major problems have been addressed in past investigations: reducing the sonic boom and decreasing the NOx emissions. This report focuses on a different aspect, the controls and stability of this type of aircrafts. This field has not been addressed thoroughly by the different companies and universities investigating SSBJs, as most of the existing concepts are preliminary designs that have not been developed extensively. With this report I try to put my two cents in analyzing the longitudinal stability and control surfaces of three different SSBJs designs.
Acknowledgements
First of all, I would like to thank my supervisor Arthur Rizzi for all his guidance. Whenever I was stuck, he always tried helping me or putting me in contact with someone that could help me solve my problem.
His comments always gave me more ideas that would eventually make me advance in my thesis. Jesper Oppelstrup, Mengmeng Zhang and Maximilian “Mio” Tomac have also been a great support, helping me when I had problems with one of the multiple programs that I had to learn how to use, for which I am very grateful. Special thanks to Evelyn Otero and Dr. Raj Nangia. Evelyn was the one who put me in contact with Arthur Rizzi, without her I would not be writing these words. Raj Nangia visited us at the KTH just in the right moment, he offered me lots of advice and comments on my thesis which allowed me to continue the process more smoothly.
GoCart has been one of the main programs I have been using to complete the Thesis. Many thanks to Colin Johnson and Janet Zhen, president and product manager of Desktop Aeronautics, for giving me free access to this software, always answering my emails and offering me help with my doubts.
I cannot obviously forget to mention my Swedish “family”, all the great people I met here which have made my stay in Stockholm unforgettable. They have been besides me for the good and the bad.
We hung out, we traveled and we discovered together a new culture and exciting places, but they also listened to me talking about my thesis during hours and complaining because a program would not work.
They know who they are and I could not have dreamt of meeting better people.
Finally and most importantly, thank you to my parents and my sister. They have always supported me and they have allowed me to follow my dreams. I am who I am because of them and I will never be able to thank them enough for all they have done for me.
Contents
I Introduction 7
1 Justification for a Supersonic Business Jet 7
2 Objectives 8
3 Chosen Designs of Study 8
3.1 Aerion AS2 . . . 8
3.2 HISAC . . . 9
3.3 LM1021 . . . 9
3.4 Main Parameters . . . 10
4 Sonic Boom and Mitigation Techniques 11 5 SSBJs Design Aspects 11 5.1 Fuselage Sizing . . . 11
5.2 Control Surface Sizing . . . 11
5.3 Aerodynamic Considerations . . . 12
6 Methodology 13 6.1 Programs Used . . . 13
6.1.1 CATIA V5 . . . 13
6.1.2 CEASIOM . . . 13
6.1.3 Digital DATCOM . . . 16
6.1.4 MSES . . . 16
6.1.5 Edge . . . 17
6.1.6 ANSYS ICEM CFD . . . 17
6.1.7 Tornado . . . 18
6.1.8 GoCart . . . 18
6.1.9 RAGE . . . 18
6.2 Procedure Followed . . . 18
II Work Done 20
7 CAD Models 20 7.1 Assumptions . . . 207.2 Determination of the Wing’s Airfoil . . . 22
8 Comparison of Airfoils using MSES 23 8.1 Objective . . . 23
8.2 Chosen Airfoils . . . 23
8.3 Procedure of Calculation . . . 23
8.4 Conclusions . . . 23
9 Finding the Mean Aerodynamic Chord 28 10 Estimation of the Center of Gravity and Moments of Inertia 29 10.1 AcBuilder’s Models . . . 29
10.2 Estimation using Weight and Building Module . . . 30
11 Building the Aerodynamic Database 30
11.1 Why Use GoCart Instead of Edge? . . . 32
11.2 Effects of Geometry, Mesh and Calculation Methods in GoCart’s Results . . . 33
11.2.1 Different Geometries . . . 33
11.2.2 Different Meshes . . . 36
11.2.3 Different Calculation Methods . . . 38
11.2.4 Conclusions . . . 41
12 Longitudinal Static Stability 41 12.1 Theoretical Background . . . 41
12.1.1 Neutral Point . . . 41
12.1.2 Static Margin . . . 43
12.1.3 Trimming Conditions . . . 43
12.2 Analysis of the SSBJs . . . 43
12.3 Optimizing the Elevators’ Size . . . 44
12.3.1 First Iteration . . . 45
12.3.2 Second Iteration . . . 46
13 Dynamic Stability and Aircraft Performance 48 13.1 Theoretical Background . . . 48
13.1.1 Longitudinal Dynamics . . . 49
13.1.2 Lateral dynamics . . . 50
13.1.3 Handling Qualities . . . 51
13.2 Analysis of the SSBJs . . . 53
13.2.1 AS2 . . . 53
13.2.2 LM1021 . . . 54
III Conclusions 58
14 Main Goals 58
15 Learned Notions 59
16 Experience Using GoCart 59
17 Future Work 60
Bibliography 62
Appendix: Database with "Existing" Supersonic Business Jets 64
List of Figures
3.1 Aerion AS2. Image obtained from Aerion’s webpage. . . 9
3.2 HISAC low noise configuration. Image from final report of HISAC project. . . 9
3.3 LM1021 N+2 low-boom model. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program". . . 10
3.4 Evolution of Lockheed Martin’s N+2 project. Left to right: 1021, 1040, 1043 and 1044. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program". . . 10
6.1 AS2 model built in CATIA . . . 13
6.2 LM1021 model built in CATIA . . . 13
6.3 CEASIOM architecture and data flow. . . 14
6.4 Surface and volume example mesh created in SUMO and visualized with SCOPE. . . 14
6.5 AcBuilder’s user interface. . . 15
6.6 User interface of the Weight and Balance module. . . 15
6.7 MSES roadmap from "A User’s Guide to MSES 3.04" . . . 17
6.8 Box diagram showing the procedure followed to complete this thesis. The programs that were finally used are the ones inside the red box. . . 19
7.1 CAD models built with RAGE (left) and SUMO (right). From top to bottom: AS2, HISAC and LM1021. . . 21
7.2 Projection of reference profile (SUMO). . . 22
8.1 Different wing sections of the LM1021. . . 24
8.2 NACA airfoils chosen for study . . . 24
8.3 Distribution of pressure around airfoil (MSES results). . . 25
8.4 Mach number distribution around airfoil (MSES results). . . 25
8.5 Boundary layer thickness on top surface of the airfoil (MSES results). . . 26
8.6 Boundary layer thickness on bottom surface of the airfoil (MSES results). . . 27
8.7 Mach number and angle of attack sweep for LM1021 airfoil and NACA 15003 (MSES results). . . 27
9.1 Method to find MAC of a tapered or delta wing. . . 29
10.1 Aircrafts built in AcBuilder. Left to right: AS2, HISAC and LM1021. . . 30
11.1 Aerodynamic coefficients of AS2 for different geometries. . . 34
11.2 Aerodynamic coefficients of HISAC for different geometries. . . 35
11.3 Aerodynamic coefficients of LM1021 for different geometries. . . 36
11.4 Meshes obtained with different number of refinements. Top (from left to right): HISAC 14, HISAC 11, HISAC 10. Bottom (from left to right): AS2 14, AS2 10. . . 37
11.5 Aerodynamic coefficients obtained for the AS2 with different mesh refinement. . . 37
11.6 Aerodynamic coefficients obtained for the HISAC with different mesh refinement. . . 38
11.7 Aerodynamic coefficients of AS2 for different methods of calculation. . . 39
11.8 Aerodynamic coefficients of HISAC for different methods of calculation. . . 40
11.9 Aerodynamic coefficients of LM1021 for different methods of calculation. . . 42
12.1 Static stability of an aircraft determined by the derivative of Cmwith respect to α . . . . 43
12.2 Determining the trimming point. . . 44
12.3 Aerodynamic coefficients obtained for HISAC with canard (v2) and without a canard (v1) 46 12.4 Aerodynamic coefficients obtained for LM1021 for different elevator sizing (first iteration) 47 13.1 Forces, moments, velocities and angles affected by the longitudinal motion of the aircraft. 49 13.2 Longitudinal modes represented in a Im-Re axis diagram. . . 50
13.3 Forces, moments, velocities and angles affected by the lateral motion. . . 50
13.4 Cooper-Harper scale. . . 51
13.5 Classification of aircrafts. . . 52
13.6 Classification of flight phases. . . 52
13.7 Flying quality levels. . . 52 13.8 Longitudinal dynamic behavior of the Aerion AS2: short-period mode (top) and phugoid
mode (bottom). . . 53 13.9 Angle of attack (top) and elevator deflection (bottom) needed to trim the AS2. . . 54 13.10Static margin of the AS2 for different flying speeds and altitudes. . . 55 13.11Static margin of the LM1021 for different flying speeds and altitudes (original CG position). 55 13.12Static margin of the LM1021 for changed CG location. . . 55 13.13Longitudinal dynamic behavior of the LM1021: short period mode (top) and phugoid
mode (bottom). . . 56 13.14Trimming conditions for the LM1021: angle of attack (top), elevator deflection (bottom). 57
List of Tables
3.1 Main characteristics of the chosen designs . . . 10
5.1 Fuselage length in meters function of the type of aircraft . . . 12
8.1 Main characteristics of the chosen airfoils . . . 23
8.2 MSES results for M=0.5 and α=2o . . . 28
9.1 Mean aerodynamic chord of the SSBJs . . . 29
10.1 Weight breakdown. . . 31
10.2 SSBJs’ total center of gravity for different weights. . . 31
10.3 SSBJs’ moments of inertia. . . 31
11.1 SDSA aero matrix structure . . . 32
11.2 SDSA control matrix structure . . . 32
11.3 Aerodynamic coefficients obtained with Edge and GoCart for M = Mcruise and α = 3deg 33 11.4 Mesh parameters . . . 38
11.5 Different calculation methods used for the Aerion AS2 model. . . 39
11.6 Different calculation methods used for the HISAC model. . . 41
11.7 Different calculation methods used for the LM1021 model. . . 41
12.1 Neutral point and static margin for each SSBJ . . . 44
12.2 Trimming conditions when changing elevator deflection . . . 45
12.3 First iteration of AS2 elevator’s optimization . . . 45
12.4 HISAC elevator’s optimization . . . 47
12.5 LM1021 elevator’s optimization . . . 48
Part I
Introduction
1 Justification for a Supersonic Business Jet
The idea of a supersonic business jet (SSBJ) seems quite futuristic and unreachable for most of the population, but it is a great opportunity for those who have enough resources to afford this kind of aircraft. The business jet market is a growing sector whose costumers would be more than interested in a supersonic version. The market for SSBJs would include public company owners, private owners, fractional ownership and charter flights. In order for SSBJs to become a success in the aircraft business, the following key points need to be addressed: safety, security, reliability, comfort, productivity and performance.
The major advantage of a SSBJ is its speed. Assuming a cruise Mach of 1.8 and a range of 5000 NM, a current 2 days business trip can be reduced to 12 hours, and worldwide coverage is achieved within 10 hours (with no range limitation). Point to point journeys, reduced security measures and being able to set the timetable are also other factors that allow the costumer to save time, when compared to regular existing flights.
However, all that glitters is not gold. Three main technical issues avoid SSBJs to become a reality which are the airport noise, the sonic boom and the engine emissions. Many investigations are currently studying or have studied these matters trying to find ways to diminish these effects. Nonetheless, it is not only technical research what has to be done, regulations need to be modified and amplified to cover these issues effectively, especially those concerning supersonic flight overland, as it is a key point to achieve maximum time savings. Nowadays, the International Civil Aviation Organization (ICAO) regulation states that supersonic flight overland is allowed as long as no disturbance is created at the ground. On the other hand, supersonic flight is prohibited over the United States by an act of Congress.
Another downfall in the market is its cost. The target unit cost for an SSBJ is around $85 million and one might think there are not enough costumers for this type of airplane. A few studies have been analyzing possible SSBJs sales. According to an internal market research done by Gulfstream, around 180 to 350 units would be sold over 10 years, without including special mission, government sales or fractional ownership needs. An independent market research estimates sales in 250-450 units costing between $50M and $100M per unit over a 10-20 year period. The typical threshold of a business jet is around 200 units, so it is realistic to assume that a supersonic version would be successful.
When designing a SSBJ a few requirements have to be followed in order to make them attractive for the future buyers and avoid technical complications at the same time. The cruising Mach for market viability has to be higher than 1.3. The higher limit is marked by kinetic heating (which occurs at Mach numbers higher than 2) and the complexity of the intakes (increased complexity for Mach higher than 1.7). As for range, transatlantic capability is the minimum requirement for which at least 3500 NM of range are necessary. SSBJs would be even more appealing if they had transpacific capability (range higher than 5000 NM). However, this might imply too many technical complications, therefore, a range of approximately 4500 NM is a low risk compromise.
2 Objectives
The objective of this thesis is to analyze the stability of three different supersonic business jet designs and optimize the size of their control surfaces, focusing on the longitudinal behavior. Thus the main goals of this research are the following:
1. Study the longitudinal static stability of the three chosen designs 2. Optimize the size of their elevators
3. Study their longitudinal dynamic stability and flight performance
3 Chosen Designs of Study
Three different designs have been selected in order to study their stability and optimize their control surfaces. By choosing different designs, it is possible to compare the results and try to find an explanation to the differences obtained. The objects of study of this thesis are the Aerion AS2, the low boom configuration from project HISAC and the LM1021. The characteristics of these and similar aircrafts can be found in the appendix.
3.1 Aerion AS2
During many years, different research studies and companies have tried to find an efficient design for a supersonic business jet, but none of them has become a reality so far. In the present, two major projects seem to evolve forward: the one conducted by the company based in Boston, Spike Aerospace, and the AS2 (figure 3.1) designed by Aerion Corporation headquartered in Reno.The most advanced in the design process is the AS2.
Aerion has recently (September 2014) signed an agreement with the multinational company Airbus to start a collaboration project to further develop the AS2. This news was determining when choosing the configurations that would be studied, as the probabilities of this aircraft becoming a reality increased considerably.
The AS2 is not a low-boom design; therefore it needs to make use of a phenomenon known as “Mach cut-off”, which will be explained in detail later in the paper. The materials used will be the following:
carbon fiber for wings, fuselage, empennage and engine nacelles; the leading edge of the wing will be made of a titanium alloy to avoid erosion; and the internal fitting will consist in aluminum, steel and titanium.
The most unique feature of this aircraft is the barely swept wing. It is designed so that it creates Neutral Laminar Flow, reducing friction a 50% compared to conventional swept or delta wings. It is rather thin and smooth to obtain 90% of laminar flow around the airflow, resulting in a considerable drag reduction, and its leading edge is relatively sharp. The airfoils used are modified bi-convex airfoils with the upper and lower surfaces slightly curved. To be able to achieve approach and landing speeds comparable to those of subsonic business jets, the wing will have high-lift flaps. Aerion and NASA have been working together to determine manufacturing tolerances and verifying that the amount of laminar flow is the expected one.
About its performance, the AS2 will be both efficient at supersonic (Mach 1.4) and subsonic (Mach 0.95) speeds. The subsonic efficiency is necessary to allow viable routes over the US, as the Federal law
forbids supersonic flight. Above the rest of populated areas, the only concern is not to create a sonic boom on ground. This is achieved by flying between Mach 1.1 and 1.2 and thanks to the Mach cut-off phenomenon mentioned before. Finally, over water, the AS2 will be able to fly at 1.4 Mach.
Figure 3.1: Aerion AS2. Image obtained from Aerion’s webpage.
3.2 HISAC
The High Speed Aircraft (HISAC) program was launched in 2005 and co-funded by the European Com- mission to find a feasible design of a small supersonic aircraft that would meet certain environmental standards including sonic boom, engine emissions and noise. The project was coordinated by Dassault Aviation and included 37 partners from 13 countries. Four different configurations were developed and each one focused on a different aspect: low noise, long range, variable geometry and low boom.
The reduction of noise is one of the biggest obstacles that has to be overcome for SSBJs to become a reality, therefore it was decided to focus the study on the low noise configuration (figure 3.2). Luckily, the department of Aerodynamics at KTH had done previous studies on this configuration, so the amount of information available was noteworthy. As for the design itself, the low noise configuration has a low aspect ratio, cranked arrow delta wing.
Figure 3.2: HISAC low noise configuration. Image from final report of HISAC project.
3.3 LM1021
NASAs supersonic project tries to overcome the technology barriers (environmental and concerning efficiency) for civil supersonic airliners. Three main programs were developed: N+1 Supersonic Business Class Aircraft (was not studied in detail), N+2 Small Supersonic Airliner, and N+3 Efficient Multi-Mach Aircraft. Two different concepts were studied in the N+2 program, being one of them the LM1021 (figure 3.3).
The LM1021 is a low-boom model with capacity for 82-100 passengers developed by Lockheed Martin together with General Electric, Liberty Works and Standford University. Its sonic boom signature is 1/100 of the one of the Concord. This is achieved by creating a series of closely timed small shocks
instead than a big one. This is possible thanks to a very long fuselage that allows volume and lift to build up and decrease gradually.
It is obvious that this model is not a business jet, but it was decided to scale it down as it had been developed more extensively and the information available was greater than with the N+1 designs. It is also important to note out that the LM1021 is only the first phase of Lockheed Martin’s project (figure 3.4) so it is expected to obtain some non-desirable behaviors when studying this model. The reason why it was chosen to study this first phase instead of other more developed stages was the lack of information about the geometry for these other phases.
Figure 3.3: LM1021 N+2 low-boom model. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program".
Figure 3.4: Evolution of Lockheed Martin’s N+2 project. Left to right: 1021, 1040, 1043 and 1044. Image from "Overview of Sonic Boom Reduction Efforts on the Lockheed Martin N+2 Supersonic Validations Program".
3.4 Main Parameters
The main characteristics of the chosen designs are presented in table 3.1.
HISAC Low Noise Configuration Aerion AS2 LM1021 Low-Boom Model (Scaled Down)
Capacity [PAX] 8 11 8-10
Length [m] 40.9 49 49
Wing Area [m2] 139 125 230
Wing Span [m] 19.1 21 17.7
Maximum Take-Off Weight [kg] 53300 52163 54890
Operational Empty Weight [kg] 25100 22588 24901
Cruise Mach Number [-] 1.8 1.4 1.6
Cruise Altitude [m] 15750 15500 15240
Table 3.1: Main characteristics of the chosen designs
4 Sonic Boom and Mitigation Techniques
The sonic boom is the audible component of a shock wave. It sounds like a loud explosion and follows the path of the aircraft as long as it flies at speeds greater than Mach 1. A way of characterizing the sonic boom level of an aircraft is the figure of merit (equation 4.1) which was described by Seebass and George in 1974. A figure of merit of less than 1 is considered acceptable.
F M = W eight
3
2Length (4.1)
Length and weight are the primary parameters affecting the boom. Therefore, a SSBJ must be as long as possible, light weighted and must have a slender configuration for low boom design.
The three designs chosen for study mitigate the sonic boom in different ways. The Aerion AS2 uses a technique known as “Mach cut-off”. Not all booms reach the ground; some may be refracted at 1520 m above the ground depending on the atmospheric conditions (mainly temperature and winds). For this phenomenon to occur, the aircraft must be flying at a speed less than 1.2 Mach and an altitude higher than 10700 m. Lockheed Martin used shaped boom design processes to achieve a design with an acceptable quiet flight over land (less than 85 PLdB of sonic boom and 10-20 EPNdb of airport noise).
As for the HISAC model, it was designed with the main objective of reducing the external noise.
5 SSBJs Design Aspects
Supersonic business jets have not become yet a reality, so there is no way to know which specific design aspects they should follow. Daniel P. Raymer gives some general ideas for supersonic aircrafts and business jets in his book “Aircraft Design: A Conceptual Approach”. In this chapter the three chosen designs will be analyzed following Raymer’s methods for initial sizing and configuration layout of an aircraft.
5.1 Fuselage Sizing
For some aircrafts, the fuselage size is determined by the payload it has to transport. This is not the case for SSBJs. Other considerations have to be taken into account like aerodynamic smoothness to diminish drag as well as the sonic boom, and being able to fit the huge fuel tanks, among others. Raymer offers a formula (equation 5.1) to calculate the initial size of the fuselage depending on the type of airplane.
Obviously, SSBJs do not appear on the list but the most similar fuselage length is obtained using the values for the twin turboprop (table 5.1).
Lengthf us= aWc (5.1)
5.2 Control Surface Sizing
The whole purpose of this thesis is to study the control surfaces of the supersonic business jets, as it has not been studied before, but in Raymer’s book a few things are specified concerning conventional business jet configurations. Subsonic business jets normally have a tail with a horizontal stabilizer in
AS2 HISAC LM1021 MTOW [kg] 52163 53300 54890
a c Fuselage Length [m]
Sailplane-unpowered 0.383 0.48 70.39 71.13 72.14
Sailplane-powered 0.316 0.48 58.08 58.68 59.52
Homebuilt-metal/wood 1.35 0.23 16.42 16.50 16.61 Homebuilt-composite 1.28 0.23 15.57 15.64 15.75 General aviation-single engine 1.6 0.23 19.46 19.56 19.69 General aviation-twin engine 0.366 0.42 35.06 35.38 35.82 Agricultural aircraft 1.48 0.23 18.00 18.09 18.21
Twin turboprop 0.169 0.51 43.03 43.50 44.16
Flying boat 0.439 0.4 33.84 34.13 34.54
Jet trainer 0.333 0.41 28.61 28.87 29.22
Jet fighter 0.389 0.39 26.90 27.13 27.44
Military cargo/bomber 0.104 0.5 23.75 24.01 24.37
Jet transport 0.287 0.43 30.64 30.93 31.32
SSBJ (real one) 49 40.9 49
Table 5.1: Fuselage length in meters function of the type of aircraft
which the elevator is included. The hinge-line of the elevator should be perpendicular to the aircraft centerline to allow connecting the left and right side elevator surfaces with a torque tube, diminishing the elevator flutter tendencies. For a conventional business jet, the elevator chord should be 32% of the horizontal tail’s chord (ce/c = 0.32).
The HISAC and LM1021 model have non-conventional elevator configurations (elevons and rudder- vators), therefore an idea about the initial sizing of the controls cannot be made. On the other hand, the Aerion’s AS2 model does have a conventional tail with elevator. In the AS2 3-views obtained from Aerion’s webpage, the elevator occupies 32% of the horizontal stabilizer’s total chord therefore it seems that is well sized. Nonetheless, the final sizing of the control surfaces is based on the dynamic analysis of control effectiveness, which is one of the goals of this project.
5.3 Aerodynamic Considerations
Friction drag is directly proportional to the total wetted area, so excess wetted area should be avoided.
This can be accomplished by diminishing the fineness ratio (W idthLength
max), but fat fuselages have a lot of flow separation at the back which increases greatly the pressure drag. SSBJs have large fineness ratios, therefore, to counteract the high friction drag, the fuselage is as smooth as possible (avoiding longitudinal breaks in the contour) and the aft-fuselage deviation from the freestream is less than 12 degrees to prevent flow separation.
Finally, when dealing with supersonic airplanes, the greatest concern is the supersonic wave drag (drag due to the formation of shock waves). The wave drag depends on the curvature (2ndderivative) of the volume distribution of the aircraft; therefore, it is directly related to the longitudinal change of the vehicle’s cross-sectional area. To reduce the drag as much as 50% the area rule is used, which consists in squeezing the fuselage at the point where the wing has its maximum cross-sectional area, softening the volume distribution shape. This squeezing or “coke-bottle” shaping of the fuselage can be clearly observed in the AS2 and is also visible in the HISAC and LM1021 models, but it is less obvious.
6 Methodology
6.1 Programs Used
6.1.1 CATIA V5
CATIA (Computer Aided Three-dimensional Interactive Application) is a 3D design commercial software developed by Dassault Systems. Engineers all around the world use it to design, simulate, analyze and manufacture a wide range of products in a variety of industries, including aerospace. For this particular thesis, three specific modules (part design, assembly design, and wireframe and surface design) were used to create initial 3D models of two of the aircrafts that were going to be studied (the AS2 and the LM1021, figures 6.1 and 6.2, respectively).
Figure 6.1: AS2 model built in CATIA
Figure 6.2: LM1021 model built in CATIA
6.1.2 CEASIOM
CEASIOM (Computerized Environment for Aircraft Synthesis and Integrated Optimization Methods) is a tool developed within the SimSAC project (Simulating Stability and Control Characteristics for Use in Conceptual Design). Although the project started in November of 2006 and lasted three years, all CEASIOM modules keep being improved up to this date.
Usually, in a traditional design process, the dynamic characteristics of the aircraft are not computed until the design is in a quite mature stage, which means that any modifications will imply high costs.
CEASIOM’s main purpose is to enable a preliminary analysis of the aircraft’s flying qualities in the early conceptual design phases, reducing financial and technical risks. To be able to achieve this objective, CEASIOM combines different modules (figure 6.3), each one focusing on a specific field of the design
process. The following subsections will explain in detail the modules that have been used for this project (SUMO, AcBuilder, Weights and Balance, and SDSA).
Figure 6.3: CEASIOM architecture and data flow.
SUMO
SUMO is a graphical tool that allows the creation of aircraft geometries in an easy and intuitive way. It also generates the airplane’s surface and volume meshes automatically (figure 6.4). This surface modeler was developed by Larosterna, a software development business started by Dr. David Eller from the Flight Dynamic Lab at KTH. It was first developed following the requests of the Swedish National Aeronautics Research Project DirSim and it has been further developed thanks to the SimSAC project sponsored by the European Union.
Figure 6.4: Surface and volume example mesh created in SUMO and visualized with SCOPE.
Two different surfaces can be used when defining the geometry: body surfaces or wing surfaces. Body surfaces are used for the fuselage and engine nacelles, and its shape is determined by its top and side view as well as different sections. Meanwhile, the wing surfaces are used for wings, lifting surfaces, and horizontal and vertical stabilizers. Its profile can be determined using a standard airfoil (i.e. NACA airfoil), defining your own airfoil or copying the one from the overlaid geometry.
AcBuilder
The AcBuilder module allows building conventional aircraft geometries (one fuselage, one main wing, one horizontal tail, etc.) by defining its components and their dimensions. The mass and position of the fuel tanks, as well as the cabin parameters (volume, number of seats, pressure) can be specified which allows plotting the center of gravity of the different elements and the total one. Different technology parameters such as beam model, spar location and material properties can also be defined in preparation for the structural module NeoCASS. The output file is an “.xml” file, specifically created for CEASIOM, which is the input of the other modules.
Figure 6.5: AcBuilder’s user interface.
Weight and Balance
The W&B module is used to calculate the weights of the aircraft as well as its total center of gravity and the moments of inertia. These calculations are done introducing the AcBuilder “.xml” file as an input and using a semi-empirical method. Depending on the aircraft size and type, different estimation methods, mainly based on statistical handbooks, are suggested (Howe, Torenbeek, Raymer, USAF and Cessna). The user is also able to set all of the weights or some of them manually.
Figure 6.6: User interface of the Weight and Balance module.
SDSA
SDSA is CEASIOM’s module specialized in studying the stability and flying qualities of an aircraft.
Different studies can be performed such as determining the eigenvalues of the system, thus finding the different dynamic flying modes (phugoid mode, short period mode, roll mode, etc.), finding the static margin, executing a flying maneuver, etc.
As an input, SDSA needs all the aerodynamic coefficients (stability derivatives and control derivatives) as well as mass and geometric properties, information about the landing gear and power unit properties.
All this information can be loaded separately in multiple text file structures or in a single XML file. This second option is the one used when using SDSA combined with other CEASIOM modules. It allows combining the information gotten from the rest of modules in an easy way, as all of the other modules output is given in XML format.
6.1.3 Digital DATCOM
The Digital DATCOM is a computer program that implements the methods contained in the United States Air Force DATCOM, which allows estimating the stability and control characteristics of an aircraft for preliminary design applications. It calculates, in a rapid and economical way, the static stability, high-lift and control device, and dynamic-derivative characteristics. Moreover, a trim option is available that allows to compute the control deflection and aerodynamic data for aircraft trim at subsonic speed.
The inputs for this program can be divided in 4 groups. In group I, the flight conditions and reference dimensions of the aircraft are defined. The second group contains the basic geometric parameters for a conventional configuration (body, wing and tail). Group III inputs define unconventional configurations or other configuration parameters (i.e. engines, flaps, control tabs). Finally, the inputs in group IV are used to control the execution of the case.
Digital DATCOM was the first approach used for finding the aerodynamic coefficients of the chosen designs. Nonetheless, as DATCOM is based in experimental and semi-empirical data and supersonic business jets are something very new, it was decided to solve the flow around the aircrafts using CFD software.
6.1.4 MSES
MSES is an airfoil design and analysis system developed by Dr. Mark Drela from the Department of Aeronautics and Astronautics at the MIT. Single and multi-element airfoil can be analyzed, modified and optimized for a wide range of Mach and Reynolds number. Problems such as shock-induced separation, shock waves or transitional separation bubbles can be solved. To represent the inviscid flow, the steady Euler equations in integral form are used; to represent the boundary layers and wakes, a compressible lag- dissipation integral method is implemented. Both flows are coupled through the displacement thickness of the boundary layer (δ*) and solved using a global Newton-Raphson method. One of the innovative features of this code is that it uses an intrinsic streamline coordinate grid which assumes that there is no convection across streamline cell faces. This turns the grid into an unknown; therefore the mesh is part of the solution and has to be stored continuously.
This code has different programs which are used for different purposes. MSET is the grid and flowfield initializer. The inputs for this program are the files “blade.xxx” and “mses.xxx”. “Blade.xxx” contains the x-y coordinates of the airfoil while “mses.xxx” defines the runtime parameters. The output given by MSET is an “mdat.xxx” file which is the main solution state file. MSES itself is the flow solver, which needs the “mses.xxx” and “mdat.xxx” files as inputs and rewrites the solution on “mdat.xxx”. To be able to visualize the results, either as plots or coefficients, the MPLOT program has to be run. Finally, parameter-sweep calculations can be done using MPOLAR. In this case, apart from needing “mdat.xxx”
and “mses.xxx” as inputs, another file determining the desired sweep has to be introduced (“spec.xxx”).
To plot the results, PPLOT or SPLOT have to be used. A clear roadmap of MSES is shown in figure 6.7, including only the programs and data files that have been used during the realization of this Master Thesis.
Figure 6.7: MSES roadmap from "A User’s Guide to MSES 3.04"
6.1.5 Edge
Edge is a CFD flow solver for unstructured grids of arbitrary elements (www.foi.se) developed by the Swedish Defence Research Agency (FOI). KTH, SAAB Aerosystems, TUB (Germany) and University of Britsol (UK) have helped in its development which started in 1997. In this case, Edge was used as an Euler solver to find out the aerodynamic coefficients of the chosen models.
Three different files are needed as input: a “.ainp” file with the input values, the model’s volume mesh (“.bmsh” file) and a “.aboc” file with its boundary conditions; these two last files are obtained with SUMO. It is very important to define the projection of the forces (lift, drag and side force), which change depending on the angle of attack and side angle (equations 6.1, 6.2 and 6.3), as well as the point of reference to calculate the moments. The process of choosing a moment reference point will be explained in a later section.
L1= sin α × (−1); L2= 0; L3= cos α (6.1)
D1= cos β × cos α; D2= sin β; D3= cos β × sin α (6.2)
S1= cos α × sin β × (−1); S2= cos β; S3= sin α × sin β × (−1) (6.3) Once everything is defined properly, the preprocessor has to be executed. The elements are discretized to control volumes surrounding each vertex and then control volumes are fused to coarser the grid cells (this will be used for multigrid). To improve the performance of the CPU with the cache memory, the nodes and edges are reordered, only in case cache reordering is previously selected. Finally, Edge has to be started either with a parallel or a sequential calculation.
6.1.6 ANSYS ICEM CFD
ICEM is a meshing software developed by ANSYS that allows the user to import a geometry from a CAD program and fix it to produce a high quality surface or volume mesh. It includes mesh diagnostic
and interactive tools for editing the mesh. The obtained mesh can be exported to various formats that can be after introduced in computational fluid dynamics and finite element analysis solvers.
6.1.7 Tornado
Tornado is a vortex lattice method for wings thought for conceptual design and educational purposes.
It can solve the aerodynamic coefficients very fast by modelling the lifting surfaces as thin plates. This allows the user to get a first approximation of the effects of modifying the geometry without the time delays that entail the more accurate whole-body calculations. The code is implemented in MATLAB and developed by the Swedish Royal Institute of Technology (KTH), the University of Bristol, Linköping University and Redhammer Consulting Ldt.
This program has been used to complete the aerodynamic database for our chosen SSBJs. The lifting surfaces of the aircrafts are needed as input, as well as the flying conditions. Tornado can calculate static cases or different sweeps and also other more complex cases as the trimmed aircraft polar point, unsteady cases, viscous drag estimations, etc.
6.1.8 GoCart
GoCart implements NASAs CDF solver code (CART3D) in a simple and user friendly GUI developed by Desktop Aeronautics. It is used to perform inviscid aerodynamic analysis and is mainly thought for design purposes. It is divided in four sections: “preprocessor”, “volume mesh”, “flow solver” and
“postprocessor”.
In the preprocessor the geometry has to be introduced either using CART3D files “.tri”, RAGE input files or a “.stp”/“.stl” CAD integration file. The preprocessor checks that the model is watertight and that all its components intersect. Once this is done, the volume mesh is generated. The parameters of the mesh can be modified and the changes are quickly visualized. If everything works properly and cubes can be ran, the volume mesh will be generated and the user will pass to the flow solver section.
Several parameters can be modified in the flow solver section. First, and maybe most important, the reference values (length, area, moment reference point) and flight conditions (Mach and angle of attack) need to be introduced. The value of these parameters affects greatly the results; therefore, it is crucial to use the correct ones. Some cases are more challenging than others and may require modifying the flow solver settings to obtain good convergence: lower the CFL number, lower the number of multigrid levels, use a more dissipative limiter, run first order, etc.
Finally, when the user determines that a good convergence is obtained, the results can be visualized in the postprocessor. The aerodynamic forces and moments can be seen both in the aerodynamic and body frame. The distribution around the aircraft of other parameters (e.g. pressure coefficient, Mach number) can be observed in a 3D view of the model with a color scale. Additionally, Mach and alpha sweeps can be done once one calculation is completed.
6.1.9 RAGE
RAGE is Desktop Aeronautics’ aircraft geometry generator. An aircraft can be easily implemented by defining its different components one by one (fuselage, wing, control surfaces, horizontal tail, vertical tail, etc.). The output file can be exported to a file extension which some CAD programs can read.
Wings and wing-like components are defined determining the chord and airfoil of different sections. The fuselage is also defined by sections, specifying the type of shape and the variables defining it. Introducing control surfaces is quite simple, as they are characterized as wing-like components.
When using GoCart to analyze the flow around an object, it is preferable to define this object in RAGE and not using other CAD programs. This way, problems will be avoided when using GoCart (more details are given in chapter 16).
6.2 Procedure Followed
The primary goal of this thesis is to find the early flying and handling qualities of a group of supersonic business jets as well as studying their stability. In order to do this, an reverse engineering process has
been followed, trying to determine the design decisions the designers made. The starting point was the existing conceptual designs which already had some control surfaces drawn on them. From there, a study of the static stability was done to rate the suitability of these surfaces and determine if changes had to be done. Once decided the proper size of the control surfaces to achieve good static stability characteristics, a dynamic stability study was conducted. The steps followed to achieve this goal are schematized in figure 6.8.
Figure 6.8: Box diagram showing the procedure followed to complete this thesis. The programs that were finally used are the ones inside the red box.
The first step consisted in defining the geometry of the aircraft. This was done using different programs depending on the type of input needed for the CFD code: SUMO, RAGE, AcBuilder and Tornado. Without a geometry, there is no way to start the process. Once we had a defined geometry, a surface and volume mesh had to be obtained for each model. SUMO and GoCart do their own meshes;
ICEM can be used to modify the surface meshes obtained with SUMO. No mesh is needed for Tornado as it uses a vortex lattice method.
To be able to run proper computational fluid dynamic calculations, it was necessary to calculate the center of gravity of the aircraft, this was done using W&B CEASIOM’s module. This module also allows to calculate the moments of inertia of the SSBJ which would be used later as part of the input for the SDSA module. Once all the different CFD calculations were done and the aerodynamic database built, all this information plus other parameters were introduced to the stability and control module of CEASIOM (SDSA) as an .xml file, obtaining as an output the flying and handling qualities of the vehicle.
It is important to note out that, even though all the programs mentioned were used during the thesis, some of them were discarded as they were not the most convenient for the purpose of this study (will be explained later on in chapter 7 and section 11.1). The programs that were finally used to obtain the flying and handling qualities of the SSBJs are the ones inside the red box in figure 6.8.
Part II
Work Done
7 CAD Models
The three different aircraft configurations needed to be introduced into a CAD program to obtain a 3D model from which extract a mesh for the Computational Fluid Dynamics (CFD) calculations. With this aim, the program chosen to build the SSBJs was SUMO (Surface Modeler).
To be able to model the desired aircraft configurations, the geometry of the jet was imported to SUMO using an “.stl” file by using the option “Load overlay geometry. . . ”. The “.stl” file was obtained differently in each case. For the low noise configuration of HISAC, the geometry was extracted from a mesh that had been generated during previous studies at KTH. A wind tunnel model of the LM1021 was found on the website of the American Institute of Aeronautics and Astronautics (AIAA) Sonic-Boom Workshop of January 2014 and was adapted using the 3D CAD design program CATIA from Dassault Systems. Finally, only the 3 views and some dimensions of the AS2 were available, so the model had to be done from scratch using CATIA.
When trying to introduce the control surfaces into the SUMO models, a few problems aroused.
Implementing the control surfaces directly with SUMO was quite challenging, therefore it was decided to use the software ICEM to deflect the surface mesh directly. This procedure involved an arduous task of reparation as, when deflecting the desired surface, the mesh ruptured and it had to be fixed node by node. This process had to be repeated for every specific deflection which was very time consuming. The next problem appeared when introducing the modified surface mesh into GoCart. If the mesh had not been properly repaired, which occurred more often than desired, GoCart was not able to create a volume mesh for it. For all these reasons, it was decided to take another course of action.
GoCart permits deflecting surfaces very easily by defining a rotation axis via two points selected by the user. Unfortunately, the input file introduced in GoCart with the vehicle’s geometry has to be divided into its different components to be able to select the specific component that wants to be deflected (i.e. the control surfaces). This can be achieved using Desktop Aeronautics’ CAD software, RAGE. The RAGE models were built based on the SUMO models; on figure 7.1 (left side) the elevator surfaces can be distinguished as independent components of the aircraft (each component has a different color). To assure the water-tightness of the models, the RAGE files (“.input”) were exported to Cart3D files (“.tri”) before introducing them into GoCart.
7.1 Assumptions
Due to the fact that the amount of information available for these designs is scarce and that SUMO is a fairly simple modeler, some assumptions had to be made in order to be able to create the 3D models.
For all the configurations, the engines were deleted in the model, as its inclusion did not add any benefit to our calculations. Nonetheless, for the LM1021, the tail is embedded in one of the engines
Figure 7.1: CAD models built with RAGE (left) and SUMO (right). From top to bottom: AS2, HISAC and LM1021.
therefore this one could not be simply removed. Instead, the fuselage was lengthened and the shape slightly modified so that the tail would lay on the fuselage without the need of including the shape of the engine. This way, calculation problems when using CFD were avoided.
It was decided to simplify the wings as much as possible to be able to obtain a mesh. Therefore, planar wings with no camber and no twist were implemented (zero lift coefficient design to start with).
The airfoils used for the wings and tails of all the models were NACA 66003 airfoils. The election of the airfoils is explained in detail in section 7.2.
7.2 Determination of the Wing’s Airfoil
The major problem when creating the 3D models was determining the wing airfoil. The profile for the HISAC design was extracted from the geometry available by using the SUMO option “Wing sections from overlay. . . ”. Unfortunately, the results obtained were not the desired ones; strange curves and edges appeared at the leading edge (LE). What SUMO does to copy the airfoil from an overlay is to use a reference profile with a thickness of 18% and project 120 points. As HISAC’s profile is basically a thin plate, only one point got projected to the LE (figure 7.2), making it impossible for SUMO to carry out a proper interpolation of this part of the airfoil. To be able to define the wing’s nose properly, more than 100 points would be needed to create the spline. SUMO’s code can be changed for it to be able to do this, but it would be useless as commercial CAD programs (i.e. CATIA, NX, etc.) would not be able to read the “.iges” or “.stp” files because they cannot open splines with more than 100 points.
Figure 7.2: Projection of reference profile (SUMO).
A similar problem was detected when working with the LM1021 model. In this case, SUMO was able to copy the overlay geometry quite properly (the nose definition was acceptable), but the LE was too sharp for SUMO to mesh it. To overcome this problem, some cuts were performed to the CATIA model obtained from the AIAA website in order to find the airfoils used and try to determine if any existing airfoil (i.e. NACA airfoil) was similar to it. Three different NACA airfoils were chosen to further study their aerodynamic characteristics and compare them to the real airfoil by using MSES. The details of this study can be found in chapter 8. Unfortunately, none of the studied NACA airfoils behaved like the airfoil extracted from the LM1021 CAD model.
As for the Aerion AS2, the only information found with respect to the wings was that they were designed to create laminar flow around themselves. No specific details on the airfoils used were given.
As a consequence of all these difficulties, an educated guess had to be done to determine the airfoil that would be used in the SUMO models. All the airfoils (in all the images available) seemed extremely thin and with little curvature. Experience determines that for supersonic leading edges, biconvex airfoils with a thickness of 2-3% at 50% of the chord should be used. On the other hand, for subsonic leading edges, very thin airfoils with a zero lift coefficient design are required. As already mentioned, SUMO has problems meshing very sharp leading edges (like the ones of a biconvex airfoil), therefore it was decided to use the NACA 66003 airfoil, which has a maximum thickness of 3% quite back in the airfoil, for all the cases.
8 Comparison of Airfoils using MSES
8.1 Objective
As already mentioned in chapter 7, a major problem was encountered when deciding the airfoil for the CAD models’ wings, especially for the LM1021, which will be the focus of this parallel study from now on. An airfoil could be obtained from the CATIA CAD model, but its geometric characteristics made it impossible for SUMO to mesh it, as the LE was too sharp. To overcome this matter, an airfoil 2D analysis was done using the CFD nonlinear viscous-inviscid code MSES. A comparison between the LM1021’s airfoil and similar airfoils was executed to try to find one that had resembling aerodynamic performance.
8.2 Chosen Airfoils
After performing several cuts to the wing of the CATIA model, it was determined that the airfoil was kept constant along the wing (figure 8.1). Therefore, the wing’s airfoils study was reduced to one airfoil.
It was decided to compare this profile with NACA 4-digit airfoils, as they are easily defined with the maximum chamber, the maximum chamber position and the thickness. In accordance to the values obtained for the LM1021 airfoil, three different NACA airfoils where chosen for further study (figure 8.2 and table 8.1).
Figure 8.1: Different wing sections of the LM1021.
LM1021 NACA0002 NACA1502 NACA1503
Maximum chamber [%] 0.4 0 1 1
Maximum chamber position [%] 50 0 50 50
Thickness [%] 1.8 2 2 3
Table 8.1: Main characteristics of the chosen airfoils
Figure 8.2: NACA airfoils chosen for study
8.3 Procedure of Calculation
The first step consisted in initializing the grid and the “mdat.xxx” file by using MSET. Once this was done, calculations could be started using MSES. To be able to find a solution, it is necessary to start the calculation with a converged point or a point which is easy solvable (i.e. low Mach number and low angle of attack). For that reason, the first case to be solved was for M=0.5, α=0.5 and Re=4E6, which results were used to make an initial comparison.
When analyzing the results obtained for the pressure coefficient distribution (figure 8.3), Mach number distribution (figure 8.4) and boundary layer thickness (figures 8.5 and 8.6) along the airfoil, it seemed that the NACA 1503 was the one with the closest behavior to the LM1021 airfoil. Although the aerodynamic coefficients (table 8.2) differed quite a lot, it was decided to do more calculations with these two airfoils in different regimes to keep comparing them.
LM1021 NACA0002 NACA1502 NACA1503
CL 0.29505 0.57554 0.37315 0.38201
CD 0.005306 0.04748 0.008681 0.005743
Cm -0.00876 -0.00995 -0.03186 -0.0329
L/D 55.606 12.122 42.983 66.513
CD v 0.005306 0.04748 0.008681 0.005743
CD w 0 0 0 0
CD f 0.003966 0.000997 0.003463 0.003931
CD p 0.001341 0.046483 0.005218 0.001812
dCL/dα 0.1606 0.0945 0.1146 0.1227
dCD/dα 0.001381 0.01986 0.005816 0.001379
dCm/dα -0.00719 -0.01962 0.0028 0.00138
Top Xtr 0.0099 0.0025 0.0034 0.0081
Bottom Xtr 0.9896 1 1 1
Table 8.2: MSES results for M=0.5 and α=2o
Figure 8.3: Distribution of pressure around airfoil (MSES results).
Figure 8.4: Mach number distribution around airfoil (MSES results).
Figure 8.5: Boundary layer thickness on top surface of the airfoil (MSES results).
Figure 8.6: Boundary layer thickness on bottom surface of the airfoil (MSES results).
It was decided to do two sweeps using MSES command MPOLAR. First, the angle of attacked was fixed to 0.5 degrees and the Mach varied. On the second sweep, the Mach was fixed to 0.5 and this time α was the varying parameter. This way we were able to figure out the divergence Mach number and the polar curves of the studied airfoils (figure 8.7).
8.4 Conclusions
MSES has some difficulties calculating the aerodynamic coefficients of the LM1021 airfoil for high angles of attack (> 4 degrees). Most probably, this is due to the fact that it is a supersonic airfoil which normally cannot fly at high α’s. Even with the lack of data for the Lockheed Martin’s airfoil, it is obvious from the polar curves that this airfoil and the NACA 1503 have a fairly different behavior. From the Mach sweep, it can be concluded that the LM1021’s airfoil divergence Mach number is around 0.8. It seems that the divergence Mach for the NACA 1503 is also around 0.8, but MSES was not able to calculate the drag coefficient for higher Mach numbers in this case, so it cannot be assured.
Due to all the facts explained above, it was decided that no NACA airfoil from the ones studied could be used for our CAD models, as their properties were not similar to the ones of the LM1021’s airfoil extracted from the CATIA model. Further studies could have been done using MSES and other standardized airfoils, but MSES offers many limitations for supersonic calculations and it was decided to base the airfoil decision in experience.
Figure 8.7: Mach number and angle of attack sweep for LM1021 airfoil and NACA 15003 (MSES results).
9 Finding the Mean Aerodynamic Chord
The mean aerodynamic chord (MAC) of an aircraft is used to normalize the aerodynamic forces to obtain the lift, drag and pitching moment coefficient. It is also used to figure out the static margin of an aircraft and make sure it is always stable. Therefore, it is very important to know the MAC of the studied SSBJs.
In the case of a tapered or delta wing, the MAC is easily found graphically (figure 9.1). Unfortunately, none of the airplanes that are being studied in this thesis have a tapered or delta wing, they all have multi-crank wings. To find the MAC of a generalized multi-crank wing, ESDU 76003 has been used.
The results are shown in table 9.1.
• Aerodynamic mean chord: c = 23
m+1
P
i=1
c2i−1(1+λi+λ2i)ηi
m+1
P
i=1
ci−1(1+λi)ηi
being ηi= si−sb/2i−1 and λi=cci
i−1
- For a single-crank wing: cc
0 =23η1(1+λ1η+λ21)+λ21(1−η1)(1+λ2+λ22)
1+λ1+λ1λ2(1−η1) being λ1= cc1
0 and λ2= cct
1
• Chordwise position of MAC (from wing apex):
x1/4 = 12A[
m+1
P
i=1
ηici−1(3(1 + λi)
i−1
P
j=1
ηjtan ∆0,j+ (1 + 2Λi)ηitan ∆0,i)] +4c being A = bS2 and ∆n,i
the sweepback of the nthchordline between spanwise stations si−1and si
- For a single-crank wing:
x1/4=12A[η1(η1(1 − λ1) + 3λ1λ2(1 − η1)3η1) tan ∆0,1+ λ1(1 + 2λ2)(1 − η1)2tan ∆0,2] +14cc
0
AS2 HISAC LM1021 MAC [m] 8.2603 9.8427 16.2533 x1/4 [m] 1.49 9.8382 22.3169
Table 9.1: Mean aerodynamic chord of the SSBJs
Figure 9.1: Method to find MAC of a tapered or delta wing.
10 Estimation of the Center of Gravity and Moments of Inertia
In order to be able to carry out the CFD calculations properly, it was necessary to find the center of gravity (CG) of the aircrafts in advance. The moments created in a vehicle are dependent on the position of its CG, therefore, any calculations done without introducing properly the CG would be incorrect. As for the moments of inertia, they are essential when estimating the behavior of the SSBJs using SDSA.
To obtain these values, CEASIOM’s module Weight and Balance (W&B) was used. Nonetheless, prior to using it, it was necessary to build the CAD models of the aircrafts using CEASIOM’s CAD software AcBuilder, as it is a necessary input for W&B.
10.1 AcBuilder’s Models
As already mentioned, the Weight and Balance module only accepts as an input the “.xml” file created by AcBuilder. There is no other way of introducing the geometry into CEASIOM, therefore, building the models with AcBuilder became necessary (figure 10.1). This CAD modeler has some limitations:
• Only conventional configurations can be introduced. The components of the aircraft are already determined and none can be added.
• The fuselage cannot be defined in detail. It is divided in four parts (nose, for-fuselage, aft-fuselage and tail) and the aft-fuselage section is maintained constant.
• The wing’s airfoil has to be selected from a list given, which is not too extended.
A very tricky part of building the models was determining the size and location of the fuel tanks. No information about this was available for the chosen SSBJs, so an estimated guess had to be done. It was basically a guess and error process, in which the position and volume of the tanks was modified until the local and total centers of gravity obtained seemed reasonable.
Figure 10.1: Aircrafts built in AcBuilder. Left to right: AS2, HISAC and LM1021.
10.2 Estimation using Weight and Building Module
Once the input “.xml” file is chosen, the W&B module runs different semi-empirical methods to calculate the estimated weights of the aircraft: structure (wing, tail, fuselage, etc.), systems (electric system, flight control, avionics, etc.), total empty weight, payload, fuel weight and total weight. Each method of calculation is supposed to be accurate for a certain type and size of aircraft. However, as supersonic business jets are very uncommon, this approach of choosing a method was not appropriate. Instead, as the empty weight, fuel weight and maximum take-off weight of the Aerion AS2 and the Hisac low noise configuration were known, the method which obtained the most similar values was selected. In both cases, it was the Torenbeek method which is initially thought for big transport aircrafts with take-off weights above 5700 kg and with design dive speeds above 250 knots.
Once the method was selected, the values of the EW, FW and MTOW were modified to make them coincide with the known real values. The final weight distribution as well as the different centers of gravity and moments of inertia, can be found in tables 10.1, 10.2 and 10.3
Different Weights [kg] AS2 HISAC LM1021
Wing 4796.85 5193.10 6354.44
Horizontal Tail 522.58 693.30
Vertical Tail 265.62
Fuselage 6747.76 10910 11606.64 Landing Gear 1617.65 1932.37 2331.66 Total Structure 13950.46 18035.48 20986.04 Fuel System 288.67 281.40 291.79 Flight Control 473.15 535.35 577.73
Avionic 937.73 984.41 1107.67
Electric System 566.48 443.41 790.13 Air Conditioning 237.76 190.91 647.81
Furnishing 550 400 500
Total Systems 3053.78 2835.48 3915.12 Total Empty Weight 22588 25208 24901.16
Payload 1089 792 990
Fuel 28486 27300 29000
Total Weight 52163 53300 54890.80
Table 10.1: Weight breakdown.
[m] AS2 HISAC LM1021 CG at Empty Weight X 31.6257 24.9598 32.4578
Y 0 0 0
Z -0.0644 -0.1946 0.01
CG at Zero Fuel Weight X 29.1529 24.5975 32.2432
Y 0 0 0
Z -0.0710 -0.1670 0.0365 CG at Take-Off Weight X 29.9184 26.8858 33.4206
Y 0 0 0
Z -0.2537 -0.1030 0.1101
Table 10.2: SSBJs’ total center of gravity for different weights.
Moments of Inertia AS2 HISAC LM1021 Ixx [kgm] 479615.39 142897.00 514486.46 Iyy [kgm] 1060296.24 4229928.44 6142560.28
Izz [kgm] 1532515.28 4323392.95 6617113.74 Ixz [kg2m] 16011.30 1888.56 9662.70
Ixy [kg2m] 0 0 0
Iyz [kg2m] 0 0 0
Table 10.3: SSBJs’ moments of inertia.
11 Building the Aerodynamic Database
In order to be able to study the stability and performance of an aircraft it is essential to build a database with all the aerodynamic coefficients for certain flight conditions. This has been done using different CFD codes, one solves the flow around the aircraft using Euler equations (inviscid flow) and the other one uses the Vortex Lattice Method (VLM). The fact of using Euler or VLM to solve the flow around the aircraft gives low-fidelity results, but this is not a major concern. Many of the inputs used for the CFD codes are based in approximations and educated guesses due to the little information that is known about the chosen SSBJs, which means that the aerodynamic coefficients found are approximations (even if solved with higher fidelity methods).
To study static stability during cruise phase, only a few calculations where needed for each model and they were performed using GoCart. An alpha sweep from 0 to 6 degrees was performed for different elevator deflections (0, -1, -3 and -5 degrees) at Mcruise. The control deflections were done directly in GoCart. As already mentioned in chapter 7, the input file used for GoCart has been built with Desktop Aeronautics’ aircraft geometry generator (RAGE), which divides the geometry into different component, being the control surfaces independent components. The deflection of the control surfaces is done with a geometrical rotation around an axis, defined during the preprocessor section of GoCart.
As for studying the dynamic stability and behavior of the vehicles, a broader aerodynamic database was necessary, including situations with non-zero angular velocities. Nowadays, GoCart is not able to implement rolling, yawing or pitching speeds into its calculations, therefore, another program had to be used for these cases. The chosen code was Tornado, which offers good approximations quickly, allowing the user to carry out many calculations in a very short time. Two different matrices had to be build, an aerodynamic matrix containing the stability derivatives (structure shown in table 11.1) and the control matrix with the control derivatives (structure shown in table 11.2). In both cases the angle of attack was varied from -2 to 6 degrees every one degree and the Mach number modified from the subsonic (0.2, 0.4, 0.6) to the supersonic region (1.1, 1.2, 1.3 and 1.4 for the AS2; 1.15, 1.3, 1.45 and 1.6 for the LM1021; 1.2, 1.4, 1.6 and 1.8 for HISAC) avoiding the nonlinearities of the transonic regime. As for the side-slip angle it was varied from -4 to 4 degrees every 2 degrees, and the rolling, yaw and pitch speed
