Aircraft Configurations With Outboard Horizontal Stabilizers Benjamin DARRENOUGUE
Erasmus Student.
Final Year Project Report
May 14, 2004
School of Aeronautical Engineering Faculty of Engineering Queen’s University Belfast
Abstract Final Year project Advisor: Dr E.Benard
Aerodynamics Of The OHS Configuration By Benjamin Darrenougue, 2004 School of Aeronautical Engineering, Queens University of Belfast, Belfast, BT7 1NN, Northern Ireland
An aircraft configuration with Outboard Horizontal Stabilizers (so called OHS configuration), which is a compromise between a flying wing and the traditional layout, has become of interest because of potential drag reduction. This tailless configuration has two stabilizing surfaces attached to short booms and located outboard and downstream the main wing tips. These horizontal surfaces, located in the upwash flow generated by the lifting main wing would permit to reach relatively high lift to drag ratio due to the additional lift they produce. A model was built to carry out low speed wind tunnel tests at a wing-chord based Reynolds number in the region of 2 x 105 . A numerical analysis based on the panel method was also run to get results at higher Reynolds number, in the region of 3 x 106 . Both the numerical and experimental analysis show comparable results and trends.
Acknowledgements First of all, I would like to thank the Queen’s University of Belfast and the staff of the School of Aeronautical Engineering to have welcome me and enabled me to spend this year studying abroad. Then, I would like to thank Dr. J.D. Muller, in Belfast and Dr. D. Legendre and Dr J. George, my supervisors in Toulouse, who arranged the Erasmus exchange. I am also very thankful to Dr. E. Benard my project supervisor, who was very helpful sharing his knowledge of aerodynamics and providing a lot of advices. It was very pleasant to work with him in a nice atmosphere. I also appreciated very much to relax speaking French with him from time to time. I would also like to thank Craig Algie from the wood workshop for his advices, Raymond Bell, John McCay and Norman Whitley from the metal workshop for their efficiency in manufacturing the wind tunnel model in a very short period of time. I liked working with them as well because they are as friendly as professional. Then, I would like to thank Kafeel Ahmed for all his help during the wind tunnel tests. His knowledge concerning the sting balance and the wind tunnel tests was essential for this project. He also tried to be as available as possible in spite of his own work. I am also grateful to Dan Johnson who let me use some pictures from his website ”luft46”. Last, but not least, I would like to thank Professor Kentfield, J.A.C from the University of Calgary who, kindly, provided me with most of his publications which was the basement of my bibliography.
Belfast, Northern Ireland
Benjamin DARRENOUGUE
May 14, 2004
ii
Nomenclature General Characters A
Aspect ratio
KN
Pitch Static Margin
a
Lift curve slope with respect to α
L
Lift
b
Span
L/D
Lift to Drag Ratio
c
Average Chord
MX
Rolling Moment
CD
Drag Coefficient
MY
Pitching Moment
CDI
Induced Drag Coefficient
MZ
Yawing Moment
CL
Lift Coefficient
N
Neutral Point
CM
Pitching Moment Coefficient
Re
Reynolds Number
D
Drag
r
Gas Constant (=287 J/KgK)
e
Oswald Coefficient
S
Area
FX
Axial Force
V∞
Free Stream Velocity
FY
Side Force
W
Downwash Velocity
FZ
Normal Force
G or CoG
Centre Of Gravity
Greek Characters α
Angle Of Attack (AOA)
η
Tail incidence
λ
Source Strength
ν
Kinematic Viscosity
Φ
Flow Potential
ρ
Density
iii
Nomenclature
iv
Subscripts DW T
Digital Wind Tunnel
d
Downwash (operates on W)
OHS
Outboard Horizontal Stabilizer
T
Tail
u
Upwash (operates on W)
W
Wing
Contents Abstract
i
Acknowledgements
iii
Nomenclature
v
List of Figures
x
List of Tables
xi
1 Introduction 1.1
1.2
1.3
1
Why using an OHS configuration? . . . . . . . . . . . . . . . . . . . . . . . .
2
1.1.1
What is an OHS configuration? . . . . . . . . . . . . . . . . . . . . . .
2
1.1.2
The Lifting Line Theory . . . . . . . . . . . . . . . . . . . . . . . . . .
3
Investigations about OHS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.2.2
OHS configuration in use nowadays . . . . . . . . . . . . . . . . . . . .
10
Aims of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2 Theoretical Review
12
2.1
The main coefficients in Aerodynamics . . . . . . . . . . . . . . . . . . . . . .
12
2.2
Induced Drag and Drag polar . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
2.3
The static stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
3 Numerical Simulations 3.1
17
The package CMARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
17
Contents
3.2
3.3
3.4
vi
The panel method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.2.1
Simple description . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
18
3.2.2
Simplified mathematical model . . . . . . . . . . . . . . . . . . . . . .
18
The numerical models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.3.1
The wing only model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.3.2
The OHS models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.3.3
The traditional configuration . . . . . . . . . . . . . . . . . . . . . . .
22
3.3.4
The flight conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
The numerical results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.4.1
Results for the wing only model
. . . . . . . . . . . . . . . . . . . . .
24
3.4.2
Results for the OHS models . . . . . . . . . . . . . . . . . . . . . . . .
27
3.4.3
Results for the traditional configuration . . . . . . . . . . . . . . . . .
31
4 Wind Tunnel Tests 4.1
4.2
4.3
4.4
33
The Test Model Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
4.1.1
The Test Model Dimensions . . . . . . . . . . . . . . . . . . . . . . . .
34
4.1.2
The Test Model Settings . . . . . . . . . . . . . . . . . . . . . . . . . .
36
The Experimental Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
4.2.1
The Free Stream Velocity . . . . . . . . . . . . . . . . . . . . . . . . .
39
4.2.2
Recording the measurements . . . . . . . . . . . . . . . . . . . . . . .
39
4.2.3
The Test Program . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
The Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
4.3.1
The aerodynamics of the OHS varying the tail location . . . . . . . .
40
4.3.2
The aerodynamics of the OHS varying some effects . . . . . . . . . . .
41
4.3.3
The static stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
Correcting the wind tunnel data . . . . . . . . . . . . . . . . . . . . . . . . .
46
5 Discussion 5.1
48
Comparison between numerical and experimental tests . . . . . . . . . . . . .
48
5.1.1
CL vs. α
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
5.1.2
L/D vs. α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
5.1.3
The bad numerical prediction of the drag . . . . . . . . . . . . . . . .
49
vii
Contents
5.2
Structural considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
6 Conclusion
53
A CMARC analysis methods
55
A.1 Boundary layer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
55
A.2 The Induced drag computations . . . . . . . . . . . . . . . . . . . . . . . . . .
56
B All numerical results
57
C All experimental results
62
References
70
List of Figures 1.1
The traditional aircraft design for wing-tail assembly . . . . . . . . . . . . . .
2
1.2
The OHS design for wing-tail assembly . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Lifting Line Theory - Replacement of the finite Wing with a Bound Vortex .
3
1.4
Lifting Line Theory - Velocity Distribution in the YZ-Plane . . . . . . . . . .
4
1.5
Lifting Line Theory - Lift and induced Drag for finite and infinite Wings . . .
4
1.6
Lifting Line Theory - Forces on the Tail located in the Upwash of the Trailing Vortices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.7
OHS configuration during Second World War . . . . . . . . . . . . . . . . . .
6
1.8
The Scaled Composites’ SpaceShipOne . . . . . . . . . . . . . . . . . . . . . .
10
2.1
The 6 main components acting on the aircraft . . . . . . . . . . . . . . . . . .
12
2.2
Theoretical drag polar plot . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
2.3
Conditions of longitudinal static stability . . . . . . . . . . . . . . . . . . . .
16
3.1
Covering the body surface with source panels . . . . . . . . . . . . . . . . . .
19
3.2
The wing is attached a wake . . . . . . . . . . . . . . . . . . . . . . . . . . . .
20
3.3
The wing and stabilizers wakes . . . . . . . . . . . . . . . . . . . . . . . . . .
22
3.4
The wake for a traditional configuration . . . . . . . . . . . . . . . . . . . . .
22
3.5
CL vs. α for the NACA 0015 wing only model
. . . . . . . . . . . . . . . . .
24
3.6
CL vs. α from NACA report 586. . . . . . . . . . . . . . . . . . . . . . . . . .
25
3.7
The drag polar for the wing only model . . . . . . . . . . . . . . . . . . . . .
26
3.8
The drag polar for the NACA 0015 profile from NACA . . . . . . . . . . . . .
26
3.9
Displays using POSTMARC . . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
3.10 CL vs. α for the OHS models . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
viii
ix
List of Figures
3.11 Drag polar for the OHS models . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.12 Lift to Drag ratio from the numerical tests . . . . . . . . . . . . . . . . . . . .
30
3.13 The effect of varying the stabilizers angles . . . . . . . . . . . . . . . . . . . .
31
3.14 Lift to Drag ratio for the traditional configuration . . . . . . . . . . . . . . .
32
4.1
The Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
4.2
The full geometry wind tunnel model . . . . . . . . . . . . . . . . . . . . . . .
35
4.3
Side view of the booms arrangement . . . . . . . . . . . . . . . . . . . . . . .
36
4.4
Picture of the booms arrangement . . . . . . . . . . . . . . . . . . . . . . . .
36
4.5
The mounting cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
4.6
Side view of the overall model . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
4.7
Front view of the overall model . . . . . . . . . . . . . . . . . . . . . . . . . .
38
4.8
Picture of the overall model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
4.9
CL vs. α for the OHS configurations with different tail locations . . . . . . .
41
4.10 L/D vs. α for the OHS configurations with different tail locations . . . . . . .
42
4.11 Influence of various effects on the aerodynamics . . . . . . . . . . . . . . . . .
42
4.12 Experimental CM vs.CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
4.13 CoG location vs. tail location (KN =cste=0.255) . . . . . . . . . . . . . . . .
45
4.14 Influence of η on the longitudinal static stability . . . . . . . . . . . . . . . .
45
4.15 Influence of the dihedral angle on the longitudinal static stability . . . . . . .
46
5.1
Comparing numerical and experimental CL vs. α . . . . . . . . . . . . . . . .
49
5.2
Comparing numerical and experimental L/D vs. α . . . . . . . . . . . . . . .
50
5.3
Comparing corrected numerical and experimental L/D vs. α . . . . . . . . . .
51
B.1 All numerical results - Wing only model . . . . . . . . . . . . . . . . . . . . .
57
B.2 All numerical results - Traditional configuration . . . . . . . . . . . . . . . . .
57
B.3 All numerical results - OHS 0.5 chord . . . . . . . . . . . . . . . . . . . . . .
58
B.4 All numerical results - OHS 1 chord . . . . . . . . . . . . . . . . . . . . . . .
58
B.5 All numerical results - OHS 1.5 chord . . . . . . . . . . . . . . . . . . . . . .
58
B.6 All numerical results - OHS 2 chord . . . . . . . . . . . . . . . . . . . . . . .
58
B.7 All numerical results - OHS 0.5 chord, stabilizer incidence -3 deg . . . . . . .
59
List of Figures
x
B.8 All numerical results - OHS 0.5 chord, stabilizer incidence -5 deg . . . . . . .
59
B.9 All numerical results - OHS 0.5 chord, stabilizer incidence -10 deg . . . . . .
59
B.10 All numerical results - OHS 0.5 chord, stabilizer incidence +3 deg . . . . . . .
59
B.11 All numerical results - OHS 0.5 chord, stabilizer incidence +5 deg . . . . . . .
60
B.12 All numerical results - OHS 0.5 chord, dihedral -5 deg . . . . . . . . . . . . .
60
B.13 All numerical results - OHS 0.5 chord, dihedral -10 deg . . . . . . . . . . . . .
60
B.14 All numerical results - OHS 0.5 chord, dihedral -20 deg . . . . . . . . . . . . .
60
B.15 All numerical results - OHS 0.5 chord, dihedral -30 deg . . . . . . . . . . . . .
61
B.16 All numerical results - OHS 0.5 chord, dihedral +5 deg . . . . . . . . . . . . .
61
B.17 All numerical results - OHS 0.5 chord, dihedral +10 deg . . . . . . . . . . . .
61
B.18 All numerical results - OHS 0.5 chord, dihedral +30 deg . . . . . . . . . . . .
61
C.1 All experimental results - Wing only model . . . . . . . . . . . . . . . . . . .
62
C.2 All experimental results - OHS 0.5 chord . . . . . . . . . . . . . . . . . . . . .
63
C.3 All experimental results - OHS 1 chord . . . . . . . . . . . . . . . . . . . . . .
63
C.4 All experimental results - OHS 1.5 chord . . . . . . . . . . . . . . . . . . . . .
63
C.5 All experimental results - OHS 2 chord . . . . . . . . . . . . . . . . . . . . . .
64
C.6 All experimental results - OHS 0.5 chord, stabilizer incidence -3 deg . . . . .
64
C.7 All experimental results - OHS 0.5 chord, stabilizer incidence -5 deg . . . . .
64
C.8 All experimental results - OHS 0.5 chord, stabilizer incidence +3 deg . . . . .
65
C.9 All experimental results - OHS 0.5 chord, stabilizer incidence +5 deg . . . . .
65
C.10 All experimental results - OHS 0.5 chord, dihedral -3 deg . . . . . . . . . . .
65
C.11 All experimental results - OHS 0.5 chord, dihedral -5 deg . . . . . . . . . . .
66
C.12 All experimental results - OHS 0.5 chord, dihedral -10 deg . . . . . . . . . . .
66
C.13 All experimental results - OHS 0.5 chord, dihedral +3 deg . . . . . . . . . . .
66
C.14 All experimental results - OHS 0.5 chord, dihedral +5 deg . . . . . . . . . . .
67
C.15 All experimental results - OHS 0.5 chord, dihedral +10 deg . . . . . . . . . .
67
C.16 All experimental results - OHS 1 chord, stabilizer incidence -3 deg, dihedral +3 deg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
List of Tables 3.1
Numerical Wing model dimensions . . . . . . . . . . . . . . . . . . . . . . . .
20
3.2
The numerical OHS model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
21
3.3
The flight conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
23
3.4
Oswald coefficients for OHS configurations . . . . . . . . . . . . . . . . . . . .
29
4.1
The experimental OHS model . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
4.2
Lift curve slope with respect to α . . . . . . . . . . . . . . . . . . . . . . . . .
41
4.3
Centre of gravity locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
5.1
Numerical drag coefficient correction . . . . . . . . . . . . . . . . . . . . . . .
51
C.1 Variation of the AOA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
xi
Chapter 1
Introduction Traditionally, the conventional aircraft configuration uses a horizontal tail aft the main wing to provide a moment of the same magnitude as the one produced by a lift-producing main plane. The tail moment is directly opposed to the main wing one in order to prevent the airplane from rotating. An innovative concept called Outboard-Horizontal-Stabilizer (OHS) configuration is to place each half of the stabilizing tail surface outboard and downstream the main wing tips. Thus, the stabilizers are located in the upwash flow generated by the lifting main wing which enables them to provide not only pitch control, as in a conventional aircraft but also to counter drag forces using inclined forward lift force vectors due to upwash flow (see lifting line theory). As the two halves of the stabilizer are fixed aft the main plane using short booms, one can understand that the structural design of the OHS configuration is more complicated than traditional ones. On the other hand, this project aims at continuing the initial work of Matthias Randolph[26] and extending numerically and experimentally the assessment of the OHS characteristics to see if the aerodynamic advantages provided by the OHS configuration balance the disadvantages in structural complexity.
1
1.1. Why using an OHS configuration?
1.1 1.1.1
2
Why using an OHS configuration? What is an OHS configuration?
The conventional aircraft uses a horizontal tail aft the main wing to counteract the pitching moment due to the lifting main wing. Traditionally this tail is located aft the main wing and symmetrically to the longitudinal axis of the aircraft (see Fig. 1.1). Alternativelly, the tail can be split into two equal halves, and each half of the stabilizer is moved outboard and downstream the main wing tips (see Fig. 1.2). That is why this configuration is called Outboard Horizontal Stabilizers (OHS). Short booms are attached at each wing tip and each half of the tail is fixed at the corresponding boom on the associated side.
Figure 1.1: Traditional wing-tail assembly design.
Figure 1.2: OHS wing-tail configuration
It can be easily understood that on one hand the structural design of the OHS is more complicated but on the other hand, placing the tails close to the wing tips has an aerodynamic advantage which will be explained with the Lifting Line Theory.
3
Chapter 1. Introduction
1.1.2
The Lifting Line Theory
The first practical theory for predicting the aerodynamics of a finite wing was developed by Ludwig Prandtl and his colleagues (therefore it is called Prandtl’s Theory sometimes). This theory is so useful that it is still used today for preliminary calculations of finite wing characteristics.
The main idea of the Lifting Line Theory is to replace the wing with a vortex filament, which would produce a lift due to the Kutta-Joukowski theorem[3] . That vortex filament is located at the quarter chord line of the wing and is limited by the wing tips, i.e. it is a finite and bounded vortex filament. However, due to the Helmholtz theorem[4], such a vortex line cannot end in the fluid. Therefore, the vortex filament is assumed to continue as two free vortices trailing from the wing tips to infinity (see Fig. 1.3). This vortex (the bound and the two free vortices) is in the shape of a horseshoe that is why it is called horseshoe vortex.
Figure 1.3: Replacement of the finite Wing with a Bound Vortex Due to their orientation the trailing vortices induce a downwash Wd along the bound vortex (i.e. under the wing) and an upwash Wu beyond the wing tips. Figure (1.4) shows the induced velocity of the trailing vortices in the yz-plane at the quarter cord line. For simplicity, the velocity distribution of a single horseshoe vortex is shown. The induced downwash plays a role in the creation of induced drag whereas the induced upwash is important for the advantages of the OHS-configuration, but that fact will be discussed later.
1.1. Why using an OHS configuration?
4
Figure 1.4: Velocity Distribution in the YZ-Plane First, the downwash of such a horseshoe vortex is considered. That causes a deflection of the free stream velocity because the actual free stream velocity under the wing is the resultant of the infinite free stream velocity and the downwash. But from the Kutta-Joukowski theorem[3] , the produced lift is perpendicular to the free stream velocity. Thus, for a finite wing with an induced downwash the lift is rotated and has to be split in the effective lift (still perpendicular to the reference velocity) and an additional force in the x-direction. That force acts in the downstream direction and therefore it is called induced drag. For a better understanding, Figure (1.5) shows the difference in lift between an infinite wing (without downwash) and a finite wing (with downwash).
Figure 1.5: Lift and induced Drag for finite and infinite Wings In contrast to a traditional configuration the tail of an OHS-configuration is placed aft and next to the wing tips as shown in Figure (1.2). The induced velocity by the trailing
5
Chapter 1. Introduction
vortices is upwards in that area (see Fig. 1.4). Thus, the resultant velocity (free stream plus upwash) is turned upwards. That fact causes the advantage of the OHS-configuration. In Figure (1.6), the lift of an infinite tail and a finite tail located in the upwash are shown. The upwash causes a deflection of the flow like in the discussed downwash above. But this time, the streamline is turned upwards. That does not influence the effective lift but it affects the additional force. That force acts now in the forward direction, i.e. it produces thrust.
Figure 1.6: Forces on the Tail located in the Upwash of the Trailing Vortices
The overall induced drag is the sum of the induced drag of the wing and the tail (the induced drag of the fuselage will be neglected in that project). Thus, for a traditional configuration, the tail increases the overall induced drag. Considering the discussion above, the tail of the OHS-configuration reduces the overall induced drag as it produces thrust. This is a clear advantage of that configuration.
Thus, it can be easily understood that placing the stabilizers close to the wing tips is a drag reduction and so encourages to choose an OHS-design but on the other hand the structural arrangement of the OHS is more complicated than the traditional one. The question is to know if the aerodynamic advantage balances the disadvantages in structural complexity.
1.2. Investigations about OHS
1.2 1.2.1
6
Investigations about OHS Background
Blohm und Voss’ idea The idea of the configuration was firstly investigated in Germany during the Second World War by Blohm und Voss[14]. The idea was to design single seat tailless and aft-swept-wing fighters using either piston engines or turbojets (see Fig. 1.7). Then, the idea was not really exploited.
Figure 1.7: The Blohm und Voss. P.210
Kentfield’s investigations Nowadays, the most relevant studies were achieved by DR. Kentfield J.A.C., professor in the department of Mechanical Engineering at the University of Calgary (Canada).
In Kentfield’s first departmental report[15], in 1990, were presented some results from the study of an aircraft configuration in which the aft tail assembly is divided in two halves and mounted on a boom aft and downwind from each wing tips in order to use it as an efficient lifting surface: this configuration is called OHS configuration. His investigations were about drag reductions and major aerodynamic and gravitational structural loads acting on the air-
7
Chapter 1. Introduction
craft. The first result was that in the comparison of both an OHS and a traditional configuration having a main wing aspect ratio of AW = 6, a tail aspect ratio of AT = 3 and a horizontal tail semi-span of 40% of the wing semi-span, significant lift-related drag reductions exist. These tests were based on NACA 0012 airfoil surfaces with a Reynolds number of Re = 6 x 106 . Thus, for the design of a small 17m span-mainplane commuter aircraft with 26 seats using Outboard Horizontal Stabilizers, the total drag was 14% less than the corresponding traditional configuration. Then, it was worked out that major structural loadings of OHS configuration are comparable to those of a corresponding conventional aircraft. Last, it was shown that an OHS using airplane has a centre-of-gravity location 65% of the chord aft the wing leading edge and that the horizontal stabilizer is able to carry about 20% of the gross weight of the vehicle.
In his engineering notes[16], professor Kentfield described some of the results presented before. So, it is shown that with a horizontal stabilizer semispan of about 40% of the mainplane semispan, the conservatively estimated spanwised-average upwash angle is 18.3 deg (CLW /AW ). As far as longitudinal stability is concerned, the contribution of the stabilizers to the pitching moment is much more effective than the usual tail contribution.
After that, Kentfield, J.A.C.[17], continued his investigations with water and wind tunnel tests at the University of Calgary (Canada). A full wing model (starboard and backboard side) without fuselage was used. The tests were restricted to relatively low Reynolds numbers, in the region of 6 x 104 based on the main wing chord, due to the dimensions, and flow speed of the open-jet wind tunnel. The model span was 0.795 m; the aspect ratio was 6.19 (including booms). The planform area of both halves of the horizontal stabilizer was 40% of the main wing area and the tail chord was equal to the wing chord. The model was constructed in such a way that it could be used for tests of a normal configuration as well, i.e. the same main wing and the same tail. The purpose of the normal configuration test was to compare the results of the OHS-design with it. Kentfield worked out that the OHS model increases the maximum lift to drag ratio up to 30%.
1.2. Investigations about OHS
8
Structural loading considerations were also carried out. Although such a configuration seems to involve major structural problems, the study of torsional loadings and bending moments showed that a properly designed OHS configuration does not rise to major structural difficulties. It was shown that the maximum torsional loading for the OHS configuration exceeds by only 17% the corresponding one of the conventional aircraft. However, at the 65% chord centre-of-gravity location, this maximum torsional loading occurs at the wingtips whereas it occurs at the wing root for the traditional version. At the 50% chord centre-of-gravity location, this maximum torsional loading occurs at the wing root for both of the configurations. As far as wing-root bending moments are concerned, they have approximately the same magnitude for both of the designs. Last, professor Kentfield mentioned that students from the Mechanical Engineering department built OHS radio-controlled free-flight models to participate to a contest. According to pilots, these models were ”easy to fly with good stability”.
In 1997, Kentfield, J.A.C.[21], compared the influence of the aspect ratios on the OHS and traditional aircrafts. It was found that for equal cruise drags the conventional configurations employ mainplane aspect ratios two or three times those of the OHS ones. It was also concluded that although the advantage of an OHS version relative to a conventional one diminished with increasing aspect ratio, for equal aspect ratios, the OHS version enables approximately 20% less drag and 15% smaller planform areas than comparable conventional aircraft. Another consideration was that the elevator deflections required to maintain level flight over a lift coefficient range from 0.2 to 1.2 were approximately double for the conventional aircraft.
A few years ago, in 2000, Kentfield, J.A.C.[18], published the results of some wind tunnel tests undertaken at the University of Calgary (Canada). The main objectives were to give a statement about the OHS-configuration for different aspect ratios, from AW = 6, to AW = 15. The wing-chord-based Reynolds number was 6 x 104 . The first result was that the upwash flow at the tails is essentially independent of main-plane aspect ratio but proportional to the main-plane lift coefficient. Then, it was shown that OHS configurations are more efficient than classical ones concerning
9
Chapter 1. Introduction
L/D ratios. However, this advantage based on L/D considerations tends to diminish as AW increases. The maximum values of L/D ratios occur at CLW values that are from 16 to 30% greater for conventional aircraft. The last result was that for equal CLW , AW and gross lift, an OHS-configuration is, typically, 15% smaller in wing planform area than a traditional one.
One of the last published documents of Kentfield, J.A.C.[20], was about structural considerations such as bending moments or torsional loadings. It was found that the wing-root bending moment loads were, for equal CLW , AW and vehicle gross weights less for the OHS version of the aircraft than those of the conventional one. This is because on one hand, the main-plane area is 15% smaller for the OHS version and on the other hand, there is a bending moment relief from the weight of the booms and tail surfaces attached to the wing tips. Also, the torsional loading at the wing root of the OHS configuration is generally less than the corresponding loading of a comparable classical version due to nose-down moment applied at the wing-tip and countering positive pitching moment resulting from wing lift. Thus, contrary to what can be thought about OHS configurations, they do not suffer from excessive structural bending moments or torsional loadings in comparison with traditional aircrafts. Another consideration was about the movement of the vehicle centre-of-gravity, which has a strong influence on wing-root shear loads and a small influence on corresponding bending moment loads.
Doctor Kentfield is still investigating about OHS configurations as it can be seen with the poster[19] he used in July 2003 during a conference at Dayton to present some results from his anterior studies. Last, he published a paper concerning high subsonic aircrafts with OHS configuration in January 2004[22]. For high subsonic Mach number vehicles, the wing has to be swept to reduce the number of regions of supersonic flows. For an OHS version, the wing has to be swept forward to achieve structural stability. Then, the effects of washout and twist were
1.2. Investigations about OHS
10
investigated. Last, the supercritical airfoil section, which provides large negative pitching was tested as it is likely to be employed for high subsonic speeds. The negative pitching moment developed, degraded the performances of both OHS and traditional configurations but, the OHS superiority was conserved.
1.2.2
OHS configuration in use nowadays
In order to meet the X-prize, a privately funded competition requiring that three people be taken to 100 km and that the ship repeat the flight within two weeks, Scaled Composites[9] and its president Burt Rutan[11] used the OHS technology (see Fig. 1.8). This configuration should enable them to fly in space for very low cost. The overall system includes a turbojet-powered carrier aircraft called the ”White Knight” and designed to drop the spaceship from about 50,000 ft. The spaceship itself is called the ”SpaceShipOne” and is powered by a hybrid rocket engine that should enable it to reach Mach 3.5. It uses the OHS configuration for a high angle of attack entry at supersonic speeds. Pneumatic actuators drive the two stabilizers. There are no control surfaces on the wing and pitch and roll are controlled by elevons on the tail booms driven manually by the control stick. This model was realized without wind tunnel tests. Rutan wanted to use only CFD and to collect real data during flight tests. However, the White Knight was also used as a flying wind test tunnel with the SpaceShipOne in captive carry. The 17 December 2003, the sub-orbital rocket broke the sound barrier and reached mach 1.2.
Figure 1.8: The Scaled Composites’ SpaceShipOne
11
Chapter 1. Introduction
1.3
Aims of the project
The project aims at continuing the initial work of Matthias Randolph[26] and extending numerically and experimentally the assessment of the OHS characteristics. As far as the experimental tests are concerned, the low speed wind tunnel of the Queen’s University of Belfast will be used. These tests will be run at a wing-chord based Reynolds number in the region of 2x 105 .A new sting balance will enable me to calculate most of the classical coefficients used in aerodynamics. Numerical simulations will be run using the package CMARC which is composed of three simulation programs: LOFTSMAN, Digital Wind Tunnel and POSTMARC. LOFTSMAN converts geometry data into basic points and tangential panels for a Digital Wind Tunnel simulation which is based on the panel method. Then, POSTMARC plots the geometry, the wakes and the streamlines based on Digital Wind Tunnel data. These tests will be run at higher wing-chord based Reynolds numbers in the region of 3 x 106 . Thus, this project aims at doing extensive numerical and wind tunnel tests to assess the aerodynamic efficiency of the OHS configuration. Then, it will be work out what is the most aerodynamically efficient arrangement, keeping in mind the stability conditions, in order to provide guidelines for future designs.
Chapter 2
Theoretical Review To work out the aerodynamic efficiency of the OHS configuration, this project will focus on the main aerodynamic forces and coefficients. Both the numerical and experimental tests will enable to get the six components acting on a body under flying conditions, i.e. forces and moments acting in the 3 directions (x,y,z).
2.1
The main coefficients in Aerodynamics
During this study, we will be interested in the 6 main aerodynamic components (see Fig. 2.1) which are acting on the aircraft in the 3 following directions (Considering to simplify that body axes and wind axes are the same, ie α=0 here) :
Figure 2.1: The 6 main aerodynamic components acting on the aircraft.
12
13
Chapter 2. Theoretical Review
• In the X-direction: The axial force is the drag force: D and the associated non-dimensional coefficient: CD =
D 1 2 2 ρV ∞ S
(2.1)
The rolling moment: MX • In the Y-direction: The side force: FY The pitching moment: MY • In the Z-direction: The normal force is the lift force: L and the associated non-dimensional coefficient: CL =
L 1 2 2 ρV ∞ S
(2.2)
The yawing moment: MZ However, as the model used for the tests is a symmetrical one and the flow comes from the front, the side force, the yawing moment and the rolling moment should be equal to zero and so out of interest. Thus, we will mainly focus on the lift, the drag and the pitching moment.
2.2
Induced Drag and Drag polar
It was shown in the first chapter that every lift-producing wing also produces drag, even if the flow is inviscid. In the case of a finite wing the Lifting Line Theory provides equations for lift and induced drag and their coefficients[5]. In general, lift and induced drag are related[6], i.e. the coefficients are related as well and assuming an elliptical lift distribution the induced drag coefficient is:
C DI =
C L2 πAW
(2.3)
2.2. Induced Drag and Drag polar
14
But usually, the lift distribution of a finite wing is not elliptical. Thus, the results given by equation (2.3) are in error. In order to correct the results a coefficient has to be added, which is called Oswald coefficient or span efficiency factor. The symbol used for it is e. That coefficient is related to the wing geometry, whereby a value of e = 1 represents a wing with elliptical wing loading. Hence the corrected induced drag coefficient is:
C DI =
C L2 eπAW
(2.4)
The Oswald coefficient is an indicator for the efficiency of a wing as the induced drag decreases with increasing Oswald coefficient. As stated above the limit is e = 1, which represents the optimum case.
It is common to plot the drag coefficient against the lift coefficient for aircrafts or wings only. That graph is called drag polar and can be divided in two parts, the lift independent and the lift dependent drag. The lift independent drag is the form or viscous drag. It is naturally caused by any shape of body in a viscid flow. The lift dependent drag is the contribution of the induced drag. Hence the total drag of a wing can be written as equation (2.5):
C D = C D0 + kC L 2
and
k=
1 eπAW
Where CD0 is the independent drag, drag at zero lift.
For a better understanding, Figure (2.2) shows a theoretical drag polar plot.
Figure 2.2: The drag polar plot
(2.5)
15
Chapter 2. Theoretical Review
2.3
The static stability
During this study, we will focus on the aerodynamic performances of this configuration but also on the stability of such a model. The longitudinal static stability will be of great interest. If an aircraft is disturbed from steady, trimmed flight, it is said to be Statically Stable if it tends to return to the original flight state (speed and attitude)[28].
The Aerodynamic Centre of a body is the point about which the pitching moment is independent of angle of attack. The Aerodynamic Centre must be distinguished from the Centre of Pressure, which is the point about which the aerodynamic pitching moment is zero. • Aerodynamic center: dC M =0 dC L
(2.6)
CM = 0
(2.7)
• Center of pressure:
The Aerodynamic Centre for an aircraft is often called the Neutral Point. The lift may be said to act through the Neutral Point, provided the necessary pitching moment is supplied.
The Static Margin is defined as: KN = −
dC MG dC L
(2.8)
It is the (non-dimensional) distance between the neutral point N and the centre of gravity G.
Two criteria must be met for an aircraft to be statically stable in the longitudinal direction (see Fig. 2.3): • Positive static margin (centre of gravity forward of the neutral point), i.e. the slope of the CMG versus CL curve must be negative at the trimmed point. • CMG at CL = 0 must be positive so that a trimmed condition CMG = 0 exists for CL > 0. This is the same thing as saying that the pitching moment about the neutral point must be positive, i.e. CMN > 0.
2.3. The static stability
16
Figure 2.3: Conditions of longitudinal static stability Then, consider a disturbance causing a nose up rotation of an aircraft, which is caused by a positive pitch moment. A nose up movement increases the angle of attack and hence the lift coefficient increases as well. The slope of CMG is negative, i.e. the pitching moment decreases and becomes negative. Thus the aeroplane returns to its original flight state. The second criterion is necessary to keep the aircraft in a trimmed flight. The steady flight condition requires a CMG = 0 and on the other hand a lift force equal to the weight of the aircraft (CL > 0).
Chapter 3
Numerical Simulations To work out the efficiency of the Outboard Horizontal Stabilizer configurations, numerical simulations were run. The main goal was to obtain a first set of data to be kept as a reference for future comparisons with the coming wind tunnel tests. These simulations were run using the package CMARC which is based on the panel method. These tests were run at a wing-chord based Reynolds number in the region of 3x 106 where some data for wing only models exist and had been previously collected.
3.1
The package CMARC
This package is composed of three softwares: LOFTSMAN, Digital Wind Tunnel (DWT) and POSTMARC. Basically, LOFTSMAN is a program for developing shapes for streamlined bodies, such as aircraft fuselages, nacelles, boat hulls and lifting and control surfaces like wings. Its function is to define geometries and to export points, lines and wireframes in various formats. It converts the geometry data into basic points and tangential panels in an input file for a Digital Wind Tunnel analysis. Digital Wind Tunnel (DWT) uses the input file generated by LOFTSMAN and runs a simulation based on the panel method. Then, the post-processor POSTMARC, plots the geometry, the wakes and the streamlines based on DWT data. It provides pressure data and then, by integration (see appendix A), provides aerodynamic coefficients, boundary-layer characteristics, velocity scans, and so on.
17
3.2. The panel method
3.2 3.2.1
18
The panel method Simple description
The Panel Method is commonly used for aerodynamic applications. The concept is to cover the surface of the concerned body with a finite number of small areas called panel. Each of them is distributed by singularities of a certain kind that have an undetermined uniform density. In general, source or doublet panels are used on non-lifting surfaces, and vortex panels are used on the lifting surfaces of a body. The oncoming flow, which is assumed to be incompressible, irrotational, and inviscid, has to be tangent to every panel at a particular location. That gives a set of equations, which is used to compute the singularity densities on the panels. Thus, the flow, composed of the uniform freestream flow and the flow induced by the singularities on the finite number of panels, becomes determined, and the velocities and pressures at any point in the flow field can be calculated.
3.2.2
Simplified mathematical model
A panel can be regarded as a two-dimensional line of length 2L in the two-dimensional flow field. This line is distributed by an infinite number of sources of strength λ per unit length. The potential at any point (x,y) in the flow caused by an entire vertical source panel, which centre is located at the centre of the coordinate system, is: λ Φ= 2π
Z
+L
h
i
ln x2 + (y − y 0 )2 dy 0
(3.1)
−L
If we now consider a body of any form in a uniform flow, distributed by a number of control points, this body can be meshed by a set of panels covering its surface. Each panel is tangentially in contact with the body shape at only one of the control points (see Fig. 3.1): Let m be the total number of panels around the body. Sources of a uniform density are distributed on each panel. λ1 ,λ2 ,...,λm represent the sources strength per unit length. The velocity potential at any point (xi ,yi ), caused by the j th panel is generalized by equation (3.2):
Φ=
λ 2π
Z
+L
ln −L
hq
i
(xi − xj )2 + (yi − yj )2 ds
(3.2)
19
Chapter 3. Numerical Simulations
Figure 3.1: Covering the body surface with source panels This time, the centre of the source panel is not located in the centre of the coordinate system and the orientation of the source panel is not vertical any more. Let rij =
q
(xi − xj )2 + (yi − yj )2 be the the distance between the points (xi ,yi ) and (xj ,yj ).
Then, the potential at any point (xi ,yi ), sum of the uniform flow potential plus the panel potentials (from 1 to m) is given by equation (3.3):
Φ(xi , yi ) = U xi +
Z m X λ i=1
2π
ln(rij )dsj
(3.3)
Then, we can compute the boundary condition at each body surface, i.e. the normal velocity on the body shape is zero (see equa 3.4): ∂ Φ(xi , yi ) = 0 ∂ni
(3.4)
Thus, combining equation (3.3) and equation (3.4), the velocity distribution can be calculated anywhere in the flow1 . With the same method, the velocity at any point of a lift-producing surface, like a wing, immerged in a uniform flow, can be calculated. But this time, instead of using a source singularity, a vortex is used. One has also to remember that the Kutta condition[7] has to be satisfied, i.e. the flow smoothly leaves the top and the bottom surfaces of the airfoil trailing edge. That causes a stagnation point at the trailing edge if the trailing edge angle is finite. If the trailing edge is cusped, then, the velocities leaving the top and bottom surfaces are finite and equal in magnitude and direction. 1
Note that the surface of the body is represented by the control points and not by the panels themselves
because the boundary condition is only valid at the control points.
3.3. The numerical models
3.3 3.3.1
20
The numerical models The wing only model
The first model I created for the numerical simulations was a simple symmetrical and rectangular wing of NACA 0015 profile because the wind tunnel model will be made in the same aerofoil. This wing model was generated and meshed with LOFTSMAN. Table (3.1) summarizes the main dimensions of this wing only model. Aerofoil
Chord
Span
Reference Area
Aspect Ratio
NACA 0015
cW = 1m
bW = 6m
SW = 6 m2
AW =6
Table 3.1: Numerical Wing model dimensions For a wing shape, about 1000 panels are recommended[1] to have a good compromise between accuracy and time of calculation. Then, to satisfy the Kutta condition[7], a wake has to be attached at the wing trailing edge. It is a two-dimensional panel sheet separating the flows on the upper and lower surface of the wing. An option is ticked in LOFTSMAN to add the wake to the wing geometry but it can be modified from the input file in DWT afterwards anyway. The wake is appended from the wing trailing edge and is 20 panels large chordwise. It also extends to 20 chords downstream (see Fig. 3.2). This wake will be critical for the simulations of the OHS models and will be considered with care.
Figure 3.2: The attached wake
21
Chapter 3. Numerical Simulations
3.3.2
The OHS models
The OHS models created for the numerical simulations were also designed and meshed with LOFTSMAN. The model is also made of a main rectangular wing of NACA 0015 profile and of two stabilizers of the same profile. The wing and the stabilizers are realized independently, so that it is easy to realise different arrangements. This will be useful for instance to change the stabilizers incidence or their location downstream the main wing without doing an entire new model. Table (3.2) summarizes the main dimensions of the OHS numerical models. Aerofoil
Chord
Span
Reference Area
Aspect Ratio
Main Wing
NACA 0015
cW = 1m
bW = 6m
SW = 6 m2
AW =6
Each Stabilizer
NACA 0015
cT = 1m
bT = 1.5m
ST = 1.5 m2
AT =1.5
Global OHS model
NACA 0015
cOHS = 1m
bOHS = 9m
SOHS = 9 m2
AW =6
Table 3.2: The numerical OHS model First of all, the choices for all the model dimensions will be justified later on, with the experimental study. The configurations investigated in the numerical study include only the aerodynamic surfaces of the OHS arrangement. It means that no fuselage or tail booms were designed. One should note that for the OHS configurations, the reference area used for the calculation of the aerodynamic coefficients is the area of the sum of the main wing area and the stabilizing surfaces area because these are now lifting surfaces. This has to be taken into account in the coefficient calculations. Identically, the reference span is based on the main wing span plus the tail span. Then, the aspect ratio of the main wing is used to reference the aspect ratio of the OHS models.
One important problem raised during the OHS arrangement design was that it turned to be impossible to append a wake to the stabilizing surfaces directly from the LOFTSMAN software. That is to say that either the results obtained from the simulations with the wake appended with LOFTSMAN were not realistic or it was impossible to achieve an input file for DWT. This is probably due to the fact that as the aerofoils used for the wing and the
3.3. The numerical models
22
tail surfaces are both symmetric, the wakes extend in the same plane and interact one with the other: the wake separation line for the wing collides with the stabilizers. The solution was to create only the wing wake with LOFTSMAN and to compute the tail wake directly from DWT. Figure (3.3) shows respectively the wing and the stabilizers wakes simulated with POSTMARC. The rolling tip vortices can be seen at the aerofoils trailing edges.
(a) The wing wake
(b) The stabilizers wake
Figure 3.3: The wing wake (a) and the stabilizers wake (b)
3.3.3
The traditional configuration
A traditional wing-tail arrangement was also realized to obtain some data to be compared with the OHS models. This traditional configuration was simplified to the aerodynamic surfaces only. This model was also realized to see the influence of the tail immerged in the wake of the main wing (see Fig. 3.4). For this study, the distance between the main wing and the tail was set according to a previous study[26], so that it can be compared to an OHS configuration of equal static margin.
Figure 3.4: The tail is immerged in the main plane wake
23
Chapter 3. Numerical Simulations
3.3.4
The flight conditions
Once the models were ready, the flight conditions had to be set. That is to say: • The free stream conditions: free stream velocity, sound velocity. • The fluid properties: kinematic viscosity. • The flight conditions: the Reynolds number2 , the range of angles of attack. The easiest way to set these conditions was to compute them directly from the DWT input file. Table (3.3) summarizes the general flight conditions I chose for the numerical simulations. Free Stream
Sound
Kinematic
Reynolds
Range of
Velocity
Velocity
Viscosity
Number
AOA
40 m/s
340 m/s
1.43x10−5 m2 /s
3x106
-2 to 16 deg
Table 3.3: The flight conditions The Reynolds number value was chosen that way to reduce the profile drag and because at lower Reynolds number, DWT is quite bad at predicting the separation that occurs.
Finally, before starting the simulations, an option was ticked to include on-body streamlines calculations in DWT. This will permit to include boundary layer calculations and displays with POSTMARC. However, the boundary layer considerations and analysis will be discussed later.
3.4
The numerical results
This section will present the results for the wing only model, they will be compared with existing data for such a wing. Then, the results for the OHS configurations will be presented. Different arrangements will be tested: with varying distances between the wing trailing edge and the stabilizer leading edge, with varying incidences of the stabilizers and with varying dihedral and anhedral angles. Then, the OHS models will be compared to the wing only and the traditional models. 2
The Reynolds number is based on the wing chord
3.4. The numerical results
3.4.1
24
Results for the wing only model
CL vs. α The first result is the plot of the lift coefficient versus the angle of attack. Figure (3.5) shows my results whereas Figure (3.6) shows the results for a NACA 0015 aerofoil of an infinite aspect ratio from a NACA report[13].
Figure 3.5: CL vs. α for the NACA 0015 wing only model from the numerical simulations
As it can be seen, the general trend is good. For α = 0, CL =0 which is normal for a symmetric profile. However, the stall is not simulated by the panel method. The slope I obtained with the panel method is 4.54 per rad., which is slightly lower than the slope of the linear part of the curve provided by the NACA (about 5.73 per rad.). This is due to the fact that for my simulations, AW =6 whereas in the NACA experiments, AW =∞. The aspect ratio influence[8] is given by equation (3.5):
a= 1+
a0 a0 (1+τ ) πAW
(3.5)
Where τ represents the difference from the elliptical distribution. In general, 0.05
