This study describes the start/unstart characteristics of a finite and rectangular supersonic biplane wing. Two wing models were tested in wind tunnels with aspect ratios of 0.75 (model A) and 2.5 (model B). The models were composed of a Busemann biplane section. The tests were carried out using supersonic and transonic wind tunnels over a Mach number range of
A sonic boom is caused by shock waves and expansion waves generated by a supersonic aircraft. As the sonic boom generates an impulsive noise at the ground, it produces undesirable effects on not only people but also animals and architecture. Sonic boom mitigation is thus required for the development of supersonic commercial aircraft [
The concept of a Busemann biplane, which was first proposed by Busemann in 1935 [
Sketch of shock waves and expansion waves around Busemann biplane.
Start state
Unstart state
The start/unstart characteristics of the Busemann biplane have been investigated. Previous studies demonstrated that the characteristics are similar to those of a supersonic inlet diffuser [
Conceptual drawing of boomless supersonic biplane in supersonic level flight [
This study investigated the start/unstart characteristics of finite rectangular supersonic biplane wings using experimental fluid dynamics. Two biplane models consisting of a Busemann biplane section with aspect ratios of 0.75 and 2.5 were tested in supersonic and transonic wind tunnels. The test was performed for
This paper is organized as follows. Section
Figure
Start/unstart characteristics of supersonic inlet diffuser. The thick solid line shows the Kantrowitz-Donaldson limit, and the broken line shows the isentropic contraction limit. The ratio of the throat-to-inlet-area of the Busemann biplane is
If the design point is defined at
The wind tunnel test was carried out at the intermittent blowdown wind tunnels of the Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (ISAS/JAXA). Figure
Specifications of supersonic and transonic wind tunnels of ISAS/JAXA.
Supersonic wind tunnel | Transonic wind tunnel | |
---|---|---|
Type | Blowdown | Blowdown |
Mach number range | 1.5–4.0 | 0.3–1.3 |
Test section size | 600 mm |
600 mm |
Window size |
|
|
Flow duration | ≥30 s | ≥30 s |
Total pressure | ≥149.1 kPa | ≥149.1 kPa |
Test gas | Dry air | Dry air |
Supersonic wind tunnel facility of ISAS/JAXA. The test section is open to the atmosphere in the figure.
Two models with different aspect ratios were tested: model A (AR = 0.75) and model B (AR = 2.5). Figure
Specifications of test models.
Model A | Model B | |
---|---|---|
Chord length, |
80 mm | 40 mm |
Thickness, |
4 mm | 2 mm |
Distance between wing elements at leading and trailing edges, |
40 mm | 20 mm |
Distance between wing elements at shoulder, |
32 mm | 16 mm |
Span, |
60 mm | 100 mm |
Aspect ratio, AR | 0.75 | 2.5 |
|
0.05 | 0.05 |
|
0.5 | 0.5 |
Overview of finite rectangular supersonic biplane models. Both wings use the Busemann biplane section (shown in black). Numbers denote lengths (in mm). Arrows indicate the positive direction. Shaded parts show connecting pieces.
Model A
Model B
Model design must allow for critical conditions associated with blockage and transient starting loads [
The starting loads and strength calculations were carried out following the procedures described in [
Strength calculations were performed assuming that the maximum load acted at the leading edge of the wing. The moment arm from the leading edge to the root of the sting was 0.4 m. The section modulus of the sting was
Figure
Wind tunnel model supported by sting in test section (model B).
The Schlieren system was used for both the supersonic and transonic wind tunnel tests. Figure
Schematic of Schlieren system for wind tunnel test. “PM” denotes a paraboloidal mirror; “
Table
Experimental conditions. The Mach sweep is described in Section
Wind tunnel | Designation | Model |
|
|
|
|
Re [ |
---|---|---|---|---|---|---|---|
Transonic | Case 1 | A | Mach sweep, 0.9–0.3 | 0 | 0 | 150.5 ( |
1.8–0.8 |
Case 2 | A | Mach sweep, 1.3–0.6 | 0 | 0 | 150.6 ( |
2.0–1.5 | |
Case 3 | A | 1.0 | Pitch pause, 0–4 | 0 | 150.5 | 1.9 | |
Case 4 | A | 1.1 | Pitch pause, 0–4 | 0 | 150.3 | 1.9 | |
Case 5 | A | 1.2 | Pitch pause, 0–4 | 0 | 150.6 | 2.0 | |
Case 6 | A | 1.3 | Pitch pause, 0–4 | 0 | 151.0 | 1.9 | |
Case 7 | A | 1.0 | 0 | 90 | 150.7 | 1.9 | |
Case 8 | A | 1.1 | 0 | 90 | 150.3 | 1.9 | |
Case 9 | A | 1.2 | 0 | 90 | 150.6 | 2.0 | |
Case 10 | A | 1.3 | 0 | 90 | 150.8 | 2.0 | |
| |||||||
Supersonic | Case 11 | A | 1.5 | Pitch pause, 0–4 | 0 | 200.2 | 2.4 |
Case 12 | A | 1.6 | Pitch pause, 0–4 | 0 | 201.1 | 2.4 | |
Case 13 | A | 1.7 | 0 | 0 | 200.5 | 2.3 | |
Case 14 | A | 1.7 | 2 | 0 | 201.1 | 2.3 | |
Case 15 | A | 1.7 | 4 | 0 | 200.4 | 2.3 | |
Case 16 | A | 1.8 | Pitch pause, 0–4 | 0 | 200.6 | 2.2 | |
Case 17 | A | 1.9 | Pitch pause, 0–4 | 0 | 200.4 | 2.1 | |
Case 18 | A | 2.1 | Pitch pause, 0–4 | 0 | 250.4 | 2.5 | |
Case 19 | A | 2.3 | 0 | 0 | 301.4 | 2.7 | |
Case 20 | B | 1.5 | Pitch pause, 0–4 | 0 | 200.7 | 1.2 | |
Case 21 | B | 1.6 | Pitch pause, 0–4 | 0 | 200.7 | 1.2 | |
Case 22 | B | 1.7 | Pitch pause, 0–4 | 0 | 201.4 | 1.1 | |
Case 23 | B | 1.8 | Pitch pause, 0–4 | 0 | 200.2 | 1.1 | |
Case 24 | B | 1.9 | Pitch pause, 0–4 | 0 | 200.0 | 1.0 | |
Case 25 | B | 2.0 | 0 | 0 | 249.8 | 1.3 | |
Case 26 | B | 2.1 | 0 | 0 | 250.8 | 1.2 |
Figure
Schlieren images of flow field around model A (AR = 0.75,
Figure
Schlieren images of flow field around model A (AR = 0.75,
Figure
Time series Schlieren images of model A (AR = 0.75,
It is important to mention here the effect of connecting pieces on the aerodynamics. A connecting piece is a prism shape attached to the top and bottom of the wing elements (Figure
Figure
Schlieren images of flow field around model B (AR = 2.5,
Figure
Time series Schlieren images of model B (AR = 2.5,
The implications of the difference in state between the former
Irikado et al. [
The former
The Busemann biplane (two dimensional) was in the start state at
Schlieren images of flow field around model A in unstart state (AR = 0.75,
The difference in start/unstart characteristics between models A and B is discussed here. The start/unstart characteristics varied with the aspect ratio. Model A (AR = 0.75) was in the start state at a lower Mach number
Regions of influence in supersonic flow on finite biplane wings: (a) model A (AR = 0.75) and (b) model B (AR = 2.5). The illustrations show the upper surface of the lower wing element (plan view). The broken lines indicate the Mach cone generated from each tip at
Model A
Model B
The start/unstart characteristics of the finite rectangular supersonic biplane wings were investigated by wind tunnel tests for
Inlet area, m2
Throat area, m2
Aspect ratio (=
Chord length, m
Focal length, m
Distance between wing elements, m
Distance between wing elements at the shoulder, m
Mach number
Pressure, Pa
Reynolds number
Wing area, m2; total model planform area, m2
Wing thickness, m
Wing span, m
Cartesian coordinates
Section modulus, m3
Angle of attack, deg
Angle of yaw, deg
Ratio of specific heats
Mach angle, deg
Maximum stress, Pa
Yielding stress, Pa
Diameter of window and mirror, m; angle of roll, deg.
Ambient; total
Freestream.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported financially by Grants-in-Aid for Scientific Research (no. 15206091 and no. 19206086) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and the Tohoku University 21st Century Center of Excellence Program. The authors wish to thank Dr. K. Kusunose of JAXA and Professor K. Matsushima of Toyama University for their invaluable comments regarding this work. The authors would like to thank Dr. T. Irikado and Mr. K. Sato of ISAS/JAXA for their considerable support in performing wind tunnel tests. The authors would like to express their gratitude to Dr. M. Kurita of the Wind Tunnel Technology Center, JAXA, for his helpful suggestions regarding wind tunnel model design. The authors wish to acknowledge their colleagues, Dr. K. Shimoyama, Dr. A. Toyoda, and Mr. S. Ozaki, for their helpful technical assistance concerning wind tunnel tests.