Design and aerodynamic performance analysis of a variable-sweep-wing morphing waverider

Journal Pre-proof Design and aerodynamic performance analysis of a variable-sweep-wing morphing waverider

Pei Dai, Binbin Yan, Wei Huang, Yifei Zhen, Mingang Wang, Shuangxi Liu

PII:

S1270-9638(19)31844-9

DOI:

https://doi.org/10.1016/j.ast.2020.105703

Reference:

AESCTE 105703

To appear in:

Aerospace Science and Technology

Received date:

8 July 2019

Revised date:

10 January 2020

Accepted date:

11 January 2020

Please cite this article as: P. Dai et al., Design and aerodynamic performance analysis of a variable-sweep-wing morphing waverider, Aerosp. Sci. Technol. (2020), 0, 105703, doi: https://doi.org/10.1016/j.ast.2020.105703.

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Design and Aerodynamic Performance Analysis of a

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Variable-sweep-wing Morphing Waverider

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1. Pei Dai: School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China;

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E-mail: [email protected] 2. Binbin Yan * (corresponding author): School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China; E-mail: [email protected] 3. Wei Huang: Science and Technology on Scramjet Laboratory, National University of Defense Technology, Changsha 410073, China; E-mail: [email protected] 4. Yifei Zhen: a. The 9th Designing, CASIC, Wuhan, Hubei 430040, China; b. School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China; E-mail: [email protected] 5. Mingang Wang: School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China; E-mail: [email protected] 6. Shuangxi Liu: School of Astronautics, Northwestern Polytechnical University, Xi’an 710072,

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China; E-mail: [email protected]

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Abstract: The wide speed range and large flight envelope of the hypersonic vehicle require that its

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aerodynamic configuration still has good aerodynamic performance at low Mach number. Therefore,

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the variable Mach number waverider is proposed to achieve good flight performance in a wide speed

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range. In this paper, based on the delta-winged variable Mach number waverider, a

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variable-sweep-wing morphing waverider is proposed and studied, including four specific

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sweep-wing configurations, namely loiter, standard, dash and wing-retracted configurations. In the

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current study, the aerodynamic performances of this variable-sweep-wing morphing waverider with

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four configurations are investigated under subsonic/supersonic/hypersonic flight conditions. At the 1

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same time, the numerical approaches employed are validated against the available experimental data

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in the open literature. The obtained results show that compared with the wing-retracted configuration,

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the best flight performance of this variable-sweep-wing morphing waverider can be achieved using

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different configuration for different flight condition. However, within the hypersonic speed range, the

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aerodynamic performance is improved through morphing but its advantages are not as large as that in

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the subsonic speed. Besides, effects of wing downwash and shockwave are also analyzed. In

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conclusion, the variable-sweep-wing morphing waverider improves both low-speed and high-speed

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aerodynamic performances, and it expands the flight speed range.

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Keywords: Morphing waverider; aerodynamic performance; variable-sweep-wing; wide-speed-range

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vehicle

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1. Introduction

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Traditional aircrafts are designed for specific flight conditions, causing certain mission segments

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to be compromised. One solution of this problem is to design aircrafts for a wide speed range with due

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consideration of different flight scenarios. With the development of the aeronautical and astronautical

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technology, the design of aircrafts aims to the wider velocity range and larger space range, especially

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for the aerodynamic configuration design of the hypersonic vehicle. For example, a reusable launch

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vehicle (RLV) operating at different flight regimes from subsonic to hypersonic speeds was proposed

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in Ref. [1], and aerodynamic control surfaces’ effects were provided as well. Moreover, many novel

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configurations have been proposed for hypersonic vehicles to achieve good flight performance in a

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wide speed range. One solution of this problem is design of the variable Mach number waverider.

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Three design methodologies of the variable Mach number waverider for a wide-speed range are 2

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cone-derived method, osculating-cone-derived method and the tandem/parallel combination of

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different waveriders. In Ref. [2], a variable Mach number waverider was proposed based on the

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cone-derived method. With the variation of Mach number, the vehicle always had the waverider

48

characteristics partly, and its overall performance was robust in the wide-speed range. Ref. [3]

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introduced a novel design approach of the cone-derived variable Mach number waverider based on

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the streamline tracing technique. Compared with the traditional conical-derived waverider, the

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streamlines using to form the vehicle’s lower surface were traced in flow-fields with different Mach

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numbers. The aerodynamic configuration of the vehicle generated by this novel method was mainly

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affected by the upper surface’s base curve, which was parameterized in their paper.

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As for the osculating-cone-derived method, a variable Mach number waverider design method

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was proposed in Ref. [4]. The osculating cone variable Mach number waverider owned higher

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lift-to-drag ratio throughout the flight profile when compared with the osculating cone constant Mach

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number waverider, and it had superior low-speed aerodynamic performance (M=4.0) while

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maintaining nearly the same high-speed aerodynamic performance. Moreover, two kinds of design

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methods for the constant swept waverider were discussed in Ref. [5], and both of them had more

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flexible design curves. Compared with the general osculating cone waverider, the cuspidal waverider

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had better high-speed aerodynamic performance under any flight condition in the high-speed range.

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By means of combination, Wang et al. [6] designed a novel wide-speed-range waverider which

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can level takeoff phase and hypersonic cruising phase by connecting a low-speed waverider and a

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hypersonic waverider. Li et al. [7] also proposed design schemes of the tandem wide-speed-range

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waverider by combining two waveriders which were designed for different Mach numbers (M=4 and

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M=8) in tandem. And the appropriate configuration of the connection section was very important for 3

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this hypersonic vehicle. Besides, the parallel waverider on a wide speed-range with two wings was

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proposed in Ref. [8]. These wings enhanced the pitching moment performance and maneuverability of

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this vehicle. However, the wings increased drag coefficient of the parallel vehicle remarkably, and

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resulted in the decrease of the lift-to-drag ratio. In addition, in order to improve the lift-to-drag ratio in

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the landing phase, Liu et al. [9] designed the wide-ranged multistage morphing waverider which was

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generated in the same conical flow field, and it contained a free-stream surface and different

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compression-stream surfaces.

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The wide speed and large flight envelope of the hypersonic vehicle require that its aerodynamic

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configuration still has good aerodynamic performance at low Mach number. However, the

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above-mentioned papers designed waveriders in the hypersonic speed and they rarely included the

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analysis of the low speed aerodynamic performance in the subsonic/transonic speed. As for other

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researches, the low speed aerodynamic performance of waverider has been examined. In the Langley

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Research Center, Pegg et al. [10] tested two separate waverider-derived vehicles, and these tests

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provided measurements of moments and forces about all three axes, control effectiveness, flow field

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characteristics and the effects of configuration changes. In Ref. [11], the planform generated by the

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optimization of a dual fuel waverider configuration at a hypersonic cruise speed of Mach 10 was

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examined for its low speed performance at Mach 0.25. Takama [12] proposed that outer wings were

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attached to the ideal waverider with analyses of both subsonic and hypersonic aerodynamic

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performances. The proposed practical waverider successfully improved the low-speed performance

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without losing the hypersonic performance. In Ref. [13], the low speed aerodynamic performance

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(from M=0.8 to M=2.5) of vortex lift waveriders with a wide-speed range was investigated, and the

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low speed lift-to-drag ratio of the cuspidal waverider was higher than that of the general osculating 4

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cone waverider.

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Another solution for wide speed range vehicle is though morphing technology. Morphing

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aircrafts can change different wing shapes or geometries to achieve the optimal flight performance

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according to various mission scenarios, such as takeoff, loiter, reconnaissance, attack and landing. In

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Ref. [14], the Naval Research Laboratory developed a morphing waveriders with a constant leading

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edge and a top surface with a morphing lower stream surface to enable on-design performance across

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a wide Mach number range from Mach 5 to Mach 10. A multiple joint variable-sweep morphing

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aircraft was developed in Ref. [15], and it allowed independent choice of inboard and outboard for

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each wing. Besides, Chakravarthy et al. proposed a time-varying characteristic equation of the

98

influence of different morphing trajectories in Ref. [16]. A longitudinal LPV model for the Z-wing

99

morphing UAV was proposed in Ref. [17]. An adaptive super-twisting sliding mode control of

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variable sweep morphing aircraft was proposed in Ref. [18]. In order to make this new morphing

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aircraft be able to perform rapid autonomous morphing and aerodynamic performance optimization

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under different missions and flight conditions, Xu et al. developed deep neural networks and

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reinforcement learning techniques as a control strategy in Ref. [19]. A six-degrees of freedom

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nonlinear time-varying model and sliding mode flight controller were proposed in Ref. [20]to enhance

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the lateral maneuverability for a tailless telescopic wing morphing aircraft by using additional

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asymmetric wing telescoping. In Ref. [21], the controller was designed for hypersonic flight vehicle

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(HFV) considering the actuator hysteresis and the angle of attack (AOA) constraint respectively. But,

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researches on the morphing aircraft mainly focus on subsonic/transonic speed.

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The main objective of this paper is to enhance the low speed aerodynamic performance of the

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variable Mach number waverider aiming for a wide-speed range flight. In the subsonic/transonic 5

111

speed range, extended morphing wings can produce a large lift and lift-to-drag ratio. However, in the

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hypersonic speed, wings lead to a larger increment of drag coefficient than lift coefficient, which leads

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to a decrease of the lift-to-drag ratio. Therefore, a wing-retracted configuration is preferred in the

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hypersonic speed. In conclusion, two variable sweep wings are added to the delta-winged waverider

115

which was designed in Ref. [5], namely the variable-sweep-wing morphing waverider.

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The rest of this paper is organized as follows: First, the variable-sweep-wing morphing waverider

117

model and aerodynamic parameters are introduced in Section 2. Next, the numerical approach

118

employed in the current study is verified by two models and the aerodynamic performances of four

119

configurations are analyzed in Section 3. In addition, preliminary discussions on the differences

120

among four configurations are proposed in Section 4. Finally, the conclusion section ends this paper in

121

Section 5.

122 123 124

Fig. 1 Roadmap of this paper 2. Design of the variable-sweep-wing morphing waverider 6

125

The high-speed aerodynamic performance advantages of the delta-winged waverider have been

126

analyzed in detail and it improved the aerodynamic characteristics of wide Mach numbers ranging

127

from 4.0 to 8.0 in Ref. [5]. In this paper, the delta-winged waverider is chosen as the forebody to

128

make use of its good aerodynamic performance with increased lift. To enhance the volumetric

129

efficiency, a fuselage is attached to the forebody with the same cross section at the base plane of the

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delta-winged waverider forebody. Meanwhile, two all-moving elevons and a vertical tail are control

131

surfaces. In Ref. [22], reusable launch vehicle was configured as a winged body vehicle. This vehicle

132

consists of a fuselage, two double delta wings, two vertical tails and two elevons mounted behind the

133

wing. But in this paper, a waverider forebody provides large lift compared with the fuselage and it

134

makes the center of pressure move forward. Therefore, a large pitching moment generated by control

135

surfaces is required to balance this vehicle as desired positive angle of attack and it can be provided

136

by all-moving elevons. And when the deflection of elevon reaches -20° and center of mass is chosen

137

as 0.33 axial length, the balanced angle of attack will be as small as 4° at some flight conditions (such

138

as M=6, standard configuration). Therefore, all-moving elevons are selected in this paper and a

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hypersonic vehicle with control surfaces is designed. And the geometric model of the designed

140

hypersonic vehicle with morphing wings retracted is shown in Fig. 2.

(a) 3D view

(b) Top view

(c) Main view

7

(d) Side View

(e) Top view with size marking (mm) 141

Fig. 2 Geometric model of the variable-sweep-wing morphing waverider (wing-retracted configuration).

142 143

Based on that, two variable-sweep-wings are attached to the fuselage to provide low speed

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aerodynamic performance advantages, especially during the subsonic flight. The loiter configuration

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with a 20°-sweep-angle supercritical airfoil is chosen as the baseline configuration as shown in Fig. 3.

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The wing leading edge radius of this airfoil is 0.873mm. Two variable-sweep-wings rotate about

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rotating shafts continuously near the wing root to suit for different operating regimes. During the

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hypersonic flight, two morphing sweep wings retract in the body to achieve good hypersonic

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aerodynamic performance with a high lift-to-drag ratio thanks to the delta-winged waverider

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forebody.

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Fig. 3 Geometric model of the variable-sweep-wing with the SC(2)-0706 supercritical airfoil.

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In this paper, two variable-sweep-wings can rotate about rotating shaft continuously. Therefore, 8

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three wing configurations are chosen as specific examples to investigate the optimal aerodynamic

155

performance which suits for different operating regimes. Fig. 4 to Fig. 6 show geometric models of

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the variable-sweep-wing morphing waverider of three different configurations (sweep angle Λ =20°,

157

40°, 60°). The configuration with morphing wings retracted (shown in Fig. 2) is denoted as

158

wing-retracted configuration. The configurations with sweep angles of 20° (shown in Fig. 4 ), 40°

159

(shown in Fig. 5) and 60° (shown in Fig. 6) are denoted as loiter, standard and dash configurations,

160

respectively.

(a) 3D view 161

(b) Top view

Fig. 4 Geometric model of the loiter configuration.

(a) 3D view 162

(b) Top view

Fig. 5 Geometric model of the standard configuration.

(a) 3D view

(b) Top view

163

Fig. 6 Geometric model of the dash configuration

164

Wing parameters of different configurations are shown in Table 1. However, as the sweep angle

165

increases, the wing span, wing area and aspect ratio all become lower. 9

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Table 1. Wing parameters of different configurations considered in the current study.

Sweep angle, Λ (°)

20

40

60

Configuration

Loiter

Standard

Dash

Root Chord (m)

0.168

0.228

0.351

Tip Chord (m)

0.168

0.183

0.180

Span (m)

2.0

1.792

1.512

Wing area ( m 2 )

0.240

0.234

0.221

Aspect ratio

16.667

13.723

10.344

167

For comparative purpose, the top view area of the wing-retracted configuration in Fig. 2 (b) is

168

chosen as the reference area, Sref (Sref=1.312 m 2 ), and the axial length is chosen as the reference length,

169

Lref (Lref =1.785m). In addition, in order to compare the aerodynamic performances of the

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variable-sweep-wing morphing waverider with different configurations, the above reference length

171

and area are also used to calculate the aerodynamic coefficients of the loiter, standard and dash

172

configurations.

173

3. Analysis of aerodynamic performances

174

For evaluation of the aerodynamic performances of the variable-sweep-wing morphing

175

waverider designed in this paper, the software Metcomp CFD++ [23] is used to simulate 3D viscous

176

flow fields of the variable-sweep-wing morphing waverider under different flight conditions. For this

177

study, the three-dimensional Reynolds-Averaged Navier Stokes (RANS) equations and the SST k-Ȧ

178

turbulence model [2][2][5][24][25] are adopted in this numerical simulation. The operational fluid is

179

air, and it is treated as an ideal gas with no reactions modeled.

180

3.1. Code validation 10

181

In the 2nd CFD Drag Prediction workshop, the lift, drag, and pitching moments are calculated

182

for the DLR-F6 configuration at subsonic flow conditions by solving the Reynolds-averaged

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Navier–Stokes equations on structured as well as on unstructured, hybrid grids[26]. In addition, to

184

verify the effectiveness of the numerical approach employed in this paper in the hypersonic speed

185

(M=8.2), the hemi-spherically blunted cone-cylinder body model are numerically simulated, and the

186

predicted results are compared with the experimental data.

187

a) DLR-F6 at M=0.75

188

The DLR-F6 model was originally built in the 1980’s and subsequently tested in several

189

investigations at the French ONERA S2MA wind tunnel[27] and main dimensions of the DLR-F6 WB

190

configuration are depicted in Fig. 7. The DLR-F6 model was sting mounted in the 1.77 m × 1.75m

191

transonic test section using a z-sting mount attached to the aft portion of the upper fuselage as shown

192

in Fig. 8 .During experiments, pressure distributions were measured on the right wing by 288 pressure

193

orifices located in 8 span-wise wing sections and total forces were measured by a balance.

194 195

Fig. 7 Main dimensions of the DLR-F6 WB configuration.

11

196 197

Fig. 8 DLR-F6 WB configuration in the ONERA S2MA wind tunnel

198

The numerical results were calculated by Uriel Goldberg [28] using CFD++ codes. In Case 1,

199

single point grid sensitivity study of CFD++ was carried out under the flight condition (Mach number

200

is 0.75, angle of attack is 0.144e, lift coefficient is 0.5) as shown in Table 2. This case was run at a

201

specified lift coefficient (CL=0.5). The numbers of cells of coarse mesh, medium mesh and fine mesh

202

were 5.5 million, 7.4 million and 9.6 million respectively. The maximum increments of drag

203

coefficient and pitching moment coefficient compared with fine mesh were 1.07% and 6.45%

204

respectively.

205

Table 2. Single point grid sensitivity study of CFD++.

Coarse mesh

Medium mesh

Fine mesh

(5.5 million)

(7.4 million)

(9.6 million)

Drag coefficient

0.02915

0.02933

0.02902

Pitching moment coefficient

-0.1388

-0.1385

-0.1394

0.44%

1.07%

------

4.30%

6.45%

------

Grid size

Darg coefficient increment compared with Fine mesh

Pitching moment coefficient increment compared with Fine mesh

12

206

And they were also compared with the experimental data to verify the effectiveness of drag polar

207

study in Case 2 (M=0.75, ¢=-3,-2,-1.5,-1,0,1,1.5,2.0), as shown in Fig. 9. The boundary conditions

208

for the freestream included the Mach number M=0.75, the static temperature T0 = 305 K, and the

209

Reynolds number Re = 3 × 106, in accordance to the experimental setup. And the number of cells is

210

7.4 million. The values of the lift, drag and pitching moment coefficients obtained by the numerical

211

approach are a slightly larger than the experimental data, but their trends with the increase of the angle

212

of attack are the same, and differences between numerical approach and experimental data are shown

213

in Table 3. As shown in Fig. 9 (d), the numerical approach shows very good agreement with the

214

experimental data in the drag polar. According to Ref.[29], there are several reasons why the CFD

215

results were not expected to match the experimental data exactly. First, the CFD runs were all

216

specified to be fully turbulent. Also, the CFD runs were all computed in free air, and the sting mount

217

was not modeled. The effects of these differences are difficult to quantify without specific study to

218

identify them.

(a) Lift coefficient

(b) Drag coefficient

13

(c) Pitching moment coefficient

(d) Drag polar

219

Fig. 9 Comparisons of lift, drag and pitching moment coefficients versus angle of attack.

220

Table 3. Increments of lift, drag and pitching moment coefficients compared with experimental data.

221

Angle of attack (°)

-3

-2

-1.5

-1

0

1

1.5

Lift coefficient increment (%)

42.76

19.84

16.09

13.23

10.36

6.86

4.60

Drag coefficient increment (%)

0.60

2.58

3.62

3.85

5.02

5.51

6.46

Pitching moment coefficient increment (%) 10.89

11.34

11.39

12.16

12.67

10.75

7.60

b) hemi-spherically blunted cone-cylinder body model at M=8.2

222

Singh [30] conducted extensive wind tunnel experiments in the hypersonic speed range on a

223

scale model of a hemi-spherically blunted cone-cylinder body model (shown in Fig. 10). According to

224

Ref. [30], the Mach number is 8.2 and the angle of attack varied from -3° up to 10°. In this paper, the

225

hemi-spherically blunted cone-cylinder body model is numerically simulated, and the computed

226

results are compared with the experimental data to verify the effectiveness of the numerical

227

approaches employed in this paper, and they are shown in Fig. 11. The number of cells is 2 million

228

and the flight condition is M=8.2, Re=9.35h104/cm, the static pressure P0 = 951.5Pa, and the static

229

temperature T0 = 89.3 K. In addition, the length and base area (i.e. 17.7 cm and 3.14 cm2) of the

230

hemi-spherically blunted cone-cylinder body model are used as the reference length and area, 14

231

respectively. In Fig. 11, the red dotted line denotes the experimental data derived from Ref. [30], and

232

the black line denotes the predicted data calculated by CFD++. Differences between numerical

233

approach and experimental data are shown in Table 4.

(a) Grids on the boundary layer

(b) Grids on the surface

234

Fig. 10 Schematic diagram of the grid employed in the hemi-spherically blunted cone-cylinder body

235

model.

236 237

Fig. 11 Comparisons of lift and drag coefficients.

238

Table 4. Increments of lift, drag and pitching moment coefficients compared with experimental data.

Angle of attack (°)

-3

0

3

5

7

10

Lift coefficient increment (%)

4.28

----

4.30

20.01

0.34

20.33

Drag coefficient increment (%)

10.28

25.29

14.78

12.29

12.39

1.74

239

Besides, several hypersonic flow cases of engineering and scientific interest have been computed

240

using various turbulence models available in the CFD++ flow solver in Ref. [31]. In all cases very 15

241

good agreement between predictions and experimental data of pressure, heat transfer and skin friction

242

were obtained. From the above discussions, it can be shown that the numerical approaches applied in

243

this paper are with confidence to study the aerodynamic performances of the variable-sweep-wing

244

morphing waverider, and the predicted results are believable in the following parts.

245

3.2. Aerodynamic performance

246

In Ref. [5], the designed Mach numbers of the delta-winged waverider are 3.86/4.4/8.0. In order

247

to investigate the aerodynamic performance of the variable-sweep-wing morphing waverider, different

248

flight conditions need to be selected for the numerical simulation. In Ref. [3]and [5], the cruising

249

altitude was chosen as 25 km. In Ref. [14], the flight altitude was chosen as 30 km. In Ref. [6], the

250

cruising altitude was chosen as 15 km. At the last flight test of X-51A in 2013, flight altitude was

251

19km. Therefore, the selected supersonic/hypersonic Mach numbers are 3.0/6.0/8.0, and its cruising

252

flight condition is set as 20km with Mach 8. Besides, aerodynamic performances can be easily

253

simulated and analyzed in the different flight altitude by changing free stream parameters in future

254

studies. At this cruising flight condition, the static temperature of the atmosphere is 216K, the static

255

pressure is 5475Pa and the dynamic pressure is 245275Pa. To provide an optimal or steady condition

256

for the propulsion system, the RBCC powered hypersonic vehicle generally climbs with the constant

257

dynamic pressure at the ascent stage [4]. Therefore, the altitude of flight Mach 3 is chosen as 7.25km,

258

while the altitude of flight Mach 6 is chosen as 16.35km according to the constant dynamic pressure

259

trajectory.

260

In addition, the low speed aerodynamic performances are also investigated for the

261

variable-sweep-wing morphing waverider, and the subsonic/supersonic flight conditions are Mach 0.8,

262

H=10km and Mach 1.5, H=10km. All these specific selected flight conditions can refer to Table 5. 16

Table 5. Flight conditions.

263

H(km)

Mach Number

Static pressure (kPa)

Dynamic pressure (kPa)

Velocity (m/s)

10

0.8

26.43

11.84

239.62

10

1.5

26.43

41.63

449.29

7.25

3

39.40

245.28

933.15

16.35

6

98.77

245.28

1770.41

20

8

55.29

245.28

2360.55

264

The lift coefficients, drag coefficients and lift-to-drag ratios of four configurations (loiter,

265

standard, dash and wing-retracted configurations ) with the increase of angle of attack (i.e. í2°, 0°, 2°,

266

5° and 10°) under five flight conditions, are all obtained and depicted in Fig. 12, Fig. 13 and Fig. 14

267

respectively. In Fig. 12 to Fig. 14, the loiter configuration ( Λ =20e) is denoted by marker ƺ and

268

dotted line, the standard configuration ( Λ =40e) is denoted by marker ƶ and dashed line, the dash

269

configuration ( Λ =60e) is denoted by marker Ƹ and dash-dotted line, and the wing-retracted

270

configuration ( Λ =90e) is denoted by marker ͪ and solid line.

271 272

In the following paragraphs, α denotes the angle of attack, CL denotes the lift coefficient,

CD denotes the drag coefficient, and L / D denotes the lift-to-drag ratio.

17

CL

CL

273

(a) M=0.8

(b) M=1.5

0.35 0.3 0.25 0.2

0.25 CL( =20deg)

CL( =20deg)

CL( =40deg)

0.2

CL( =60deg) CL( =90deg)

CL( =40deg) CL( =60deg) CL( =90deg)

0.15

0.15 0.1

0.1 0.05

0.05

0 -0.05 -2

0

2

4

6

8

0 -2

10

(°)

0

2

4

6

8

10

(°)

(d) M=6

CL

(c) M=3

(e) M=8 274 275

Fig. 12 Lift coefficients of the variable-sweep-wing morphing waverider in different configurations.

276 18

CD

CD

(a) M=0.8

(b) M=1.5

0.12

0.08 CD( =20deg)

0.1

0.07

CD( =40deg) CD( =60deg)

0.06

CD( =90deg)

0.08

CD( =20deg) CD( =40deg) CD( =60deg) CD( =90deg)

0.05 0.04

0.06

0.03 0.04 0.02 0.02 -2

0

2

4

6

8

0.01 -2

10

(°)

0

2

4

6

8

10

(°)

(d) M=6

CD

(c) M=3

(e) M=8 277 278

Fig. 13 Drag coefficients of the variable-sweep-wing morphing waverider in different configurations.

279

19

L/D

L/D

(a) M=0.8

(b) M=1.5

3.5

3.5

3

3

2.5 2.5

2 1.5

2

1

1.5 L/D( L/D( L/D( L/D(

0.5 0 -0.5 -2

0

2

4

6

=20deg) =40deg) =60deg) =90deg)

8

L/D( L/D( L/D( L/D(

1 0.5 -2

10

(°)

0

2

4

6

=20deg) =40deg) =60deg) =90deg)

8

10

(°)

(d) M=6

L/D

(c) M=3

(e) M=8 280 281

Fig. 14 Lift-to-drag ratios of the variable-sweep-wing morphing waverider in different configurations.

282

As can be seen from Fig. 12 to Fig. 14, under the same flight condition, lift coefficients and drag

283

coefficients of the four configurations increase with the increase of the angle of attack, and their 20

284

lift-to-drag ratios increase first and then decrease with the increase of the angle of attack. Moreover,

285

under the same angle of attack and the same configuration, the lift, drag coefficients both decrease

286

with the increase of the flight Mach number. The following section provides detailed discussions on

287

drag coefficient, lift coefficient and lift-to-drag ratio.

288

a) Drag coefficient

289

Under different flight conditions, relative changes in drag coefficients with the same angle of

290

attack in different sweep configurations are quite the same; and the drag coefficients become lower as

291

the sweep angle increases. Therefore, drag coefficients at the cruising flight condition (Mach=8.0,

292

H=20km) are chosen as an example to compare the aerodynamic characteristics of the four

293

configurations of the variable-sweep-wing morphing waverider, and they are shown in Table 6.

294

Table 6.

Comparison of drag coefficients of four configurations of the variable-sweep-wing morphing waverider at Mach=8, H=20km

295

Angle of attack (°)

-2

0

2

5

10

Loiter configuration ( Λ =20°)

0.019754

0.022438

0.027548

0.039291

0.070960

Standard configuration ( Λ =40°)

0.018025

0.020702

0.025770

0.037483

0.069082

Dash configuration ( Λ =60°)

0.016476

0.019175

0.024200

0.035976

0.067606

Wing-retracted configuration ( Λ =90°)

0.015335

0.018249

0.022986

0.034679

0.061192

296 297

b) Lift coefficient

298

To further analyze the existing differences, lift coefficients of the variable-sweep-wing morphing

299

waverider in four configurations at flight M=0.8, M=1.5, M=3, M=6 and M=8 are depicted in Table 7,

300

Table 8, Table 9, Table 10 and Table 11, respectively. As can be seen from Table 7 and Table 8, under 21

301

subsonic flight condition (M=0.8) and low speed supersonic flight condition (M=1.5), loiter

302

configuration has the largest lift coefficient compared with other configurations at the same positive

303

angle of attack.

304

However, as can be seen from Table 9 to Table 11, in the high-speed range (M=3, M=6, M=8),

305

the lift coefficients of loiter, standard and dash configurations are nearly the same, but they are all

306

larger than the wing-retracted configuration at positive angles of attack. As can be seen from Table 9,

307

under the flight condition Mach 3, the standard configuration has the largest lift coefficient compared

308

with other configurations at positive angles of attack. As can be seen from Table 10, under the flight

309

condition Mach 6, the dash configuration has the largest lift coefficient compared with other

310

configurations at angles of attack from 0° to 5°. However, at the high angle of attack, the lift

311

coefficient of the standard configuration is the largest. As can be seen from Table 11, under the flight

312

condition Mach 8, the dash configuration has the largest lift coefficient compared with other

313

configurations at positive angles of attack. This shows that different configurations of the

314

variable-sweep-wing morphing waverider suit for different flight conditions with the corresponding

315

largest lift coefficient.

316

Table 7.

Comparison of lift coefficients of four configurations of the variable-sweep-wing morphing waverider at M=0.8, H=10km.

317

Angle of attack (°)

-2

0

2

5

10

Loiter configuration ( Λ =20°)

0.016315

0.129002

0.241981

0.386298

0.577483

Standard configuration ( Λ =40°)

-0.008369

0.087742

0.155285

0.312580

0.537427

Dash configuration ( Λ =60°)

-0.016415

0.058482

0.133100

0.250815

0.483442

Wing-retracted configuration ( Λ =90°)

-0.000625

0.049749

0.102599

0.190366

0.365065

22

318

Table 8.

Comparison of lift coefficients of four configurations of the variable-sweep-wing morphing waverider at M=1.5, H=10km

319

320

Angle of attack (°)

-2

0

2

5

10

Loiter configuration ( Λ =20°)

-0.047298

0.044453

0.137971

0.277054

0.503541

Standard configuration ( Λ =40°)

-0.055504

0.036292

0.129868

0.266058

0.482392

Dash configuration ( Λ =60°)

-0.061294

0.019952

0.102222

0.226396

0.442081

Wing-retracted configuration ( Λ =90°)

-0.038259

0.013649

0.069830

0.160637

0.323762

Table 9.

Comparison of lift coefficients of four configurations of the variable-sweep-wing morphing waverider at M=3, H=7.3km

321

322

Angle of attack (°)

-2

0

2

5

10

Loiter configuration ( Λ =20°)

-5.74e-05

0.049551

0.099514

0.175698

0.304030

Standard configuration ( Λ =40°)

-0.000573

0.050192

0.101112

0.178387

0.306489

Dash configuration ( Λ =60°)

-0.001505

0.049701

0.100436

0.175587

0.296456

Wing-retracted configuration ( Λ =90°)

0.005586

0.043188

0.081403

0.141280

0.241506

Table 10.

Comparison of lift coefficients of four configurations of the variable-sweep-wing morphing waverider at M=6, H=16.3km

323

Angle of attack (°)

-2

0

2

5

10

Loiter configuration ( Λ =20°)

0.012974

0.043439

0.073936

0.120931

0.203206

Standard configuration ( Λ =40°)

0.012745

0.043400

0.073990

0.121197

0.204280

Dash configuration ( Λ =60°)

0.012693

0.043893

0.074700

0.122103

0.203642

Wing-retracted configuration ( Λ =90°)

0.016873

0.042163

0.067351

0.106620

0.173450

23

324

Table 11.

Comparison of lift coefficients of four configurations of the variable-sweep-wing morphing waverider at M=8, H=20km

325

Angle of attack (°)

-2

0

2

5

10

Loiter configuration ( Λ =20°)

0.016603

0.042406

0.068370

0.108734

0.181994

Standard configuration ( Λ =40°)

0.016543

0.042323

0.068231

0.108619

0.182294

Dash configuration ( Λ =60°)

0.016480

0.042599

0.068671

0.109377

0.183858

Wing-retracted configuration ( Λ =90°)

0.020275

0.042060

0.063870

0.096006

0.158142

326

As shown in Fig. 15, in order to quantitatively analyze the lift coefficient differences among four

327

configurations of the variable-sweep-wing morphing waverider, the increment or decrement

328

percentages of lift coefficients of the three wing-extended configurations to that of the wing-retracted

329

configuration are calculated for each flight condition. Under the flight condition M=1.5, α =0D , the

330

increment percentage of the loiter configuration is the largest with the value of 225%. Under the flight

331

condition M=0.8, the increment percentage of the loiter configuration exceed 50% of all positive

332

angles of attack. Among all flight conditions, it is in the supersonic speed range (M=1.5) that the

333

increment percentage of the lift coefficient of the standard and dash configurations are the highest,

334

and with further increase of the flight Mach number, the percentage increase of the lift coefficient is

335

gradually reduced. In other words, compared with the wing-retracted configuration, the low speed

336

performances of the three configurations are improved.

24

(a) Loiter configuration

(b) Standard Configuration

(c) Dash configuration 337

Fig. 15 Increment percentage of lift coefficient of the loiter/standard/dash configuration relative to that of the wing-retracted configuration

338 339

c) Lift-to-drag ratio

340

As can be seen from Fig. 14(a), in the subsonic speed range (M=0.8), the lift-to-drag ratio of

341

loiter configuration (L/D=8.43, Į=2°) is always higher than other configurations, but they are close at

342

high angles of attack. The main reason is that at small angles of attack, the drag coefficients of the

343

four configurations are relatively close, but the lift coefficient of loiter configuration is much larger.

344

However, with the increase of the angle of attack, the drag coefficient of loiter configuration highly

345

surpasses that of other configurations, and this makes the lift-to-drag ratios of the four configurations

346

close at high angles of attack. 25

347

In contrast, under the low speed supersonic flight condition (M=1.5), the standard configuration

348

has the largest lift-to-drag ratio of 3.29 when Į=0°, and this is shown clearly in Fig. 14 (b). As can be

349

seen from Fig. 14 (c)-(e), under the high speed supersonic/hypersonic flight condition (M=3, 6, 8),

350

among loiter, standard and dash configurations, the dash configuration has the largest lift-to-drag ratio

351

when Į=0°. The main reason is that among three wing extended configurations, although the lift

352

coefficients of the four configurations are different from each other, but the difference among drag

353

coefficients is much larger than the increment of the lift coefficient. Therefore, a smaller drag

354

coefficient leads to a larger lift-to-drag ratio. It is quite interesting to notice that under some specific

355

flight conditions (M=6, α =0 and M=8, α =0), the wing-retracted configuration has the largest

356

lift-to-drag ratio compared with other three wing-extended configurations. Moreover, it can be found

357

that at the subsonic speed, the increase of the lift-to-drag ratio of loiter configuration relative to the

358

wing-retracted configuration is significantly higher than that at the supersonic/hypersonic speed. This

359

shows that different configurations of the variable-sweep-wing morphing waverider suit for different

360

flight conditions with their different advantages on aerodynamic performance.

361

As shown in Fig. 16, in order to quantitatively analyze the lift-to-drag ratio differences among

362

four configurations of the variable-sweep-wing morphing waverider, the percentages increase or

363

decrease of the lift-to-drag ratio of the three wing-extended configurations versus the wing-retracted

364

configuration are calculated for each flight condition.

26

(a) M=0.8

(b) M=1.5

(c) M=3

(d) M=6

(e) M=8 365 366

Fig. 16 Increment percentage of the lift-to-drag ratio of the loiter/standard/dash configurations relative to that of the wing-retracted configuration

367

As shown in Fig. 16 (a) and (b), at the same subsonic/low-speed supersonic speed, the

368

percentage increases of the lift-to-drag ratio of the three wing-extended configurations versus the 27

369

wing-retracted configuration decrease with the increase of the angle of attack, and this means that the

370

wing-extended configurations’ aerodynamic advantages gradually diminish with the increase of angle

371

of attack.

372

As shown in Fig. 16 (c), at the flight Mach number 3, the percentage increases of the lift-to-drag

373

ratio of the three wing-extended configurations shows a trend of rising first and then falling with the

374

increase of the angle of attack, which means that compared with the three wing-extended

375

configurations, the aerodynamic performance of the wing-retracted configuration is not significantly

376

reduced at the small angle of attack and high angle of attack. As shown in Fig. 16 (d) and (e), at the

377

flight Mach number 6 and 8, the percentage increases of the lift-to-drag ratio of the three

378

wing-extended configurations increase with the increase of the angle of attack. Compared between

379

Fig. 16 (c)-(e), at the same angle of attack, the percentage increase of the lift-to-drag ratio of the dash

380

configuration is the largest, and it decreases with the increase of the flight Mach number. This

381

indicates that the aerodynamic performance advantage of the dash waverider is more pronounced at

382

low hypersonic speed.

383

As shown in Fig. 16 (c)-(e), the black solid line denotes that the percentage increase of the

384

lift-to-drag ratio equals zero and it denotes the wing-retracted configuration. Therefore, it is

385

interesting to notice that under some specific flight conditions, the percentage increase of the

386

lift-to-drag ratio is lower than zero, which means that the aerodynamic performance of the

387

wing-retracted configuration is higher than that of some configurations (especially standard and loiter

388

configurations), and it is more obvious in high speeds and small angles of attack.

389

In conclusion, the variable-sweep-wing morphing waverider proposed in this paper enhances

390

both low speed take-off performance and high-speed cruising performance, and it expands the flight 28

391

speed range. For different flight conditions and different mission scenarios, the best flight

392

performance of this variable-sweep-wing morphing waverider can be achieved using different

393

configurations.

394

d) Pitching moment coefficient

395

The focus of this paper is the investigation of aerodynamic performance of the morphing

396

waverider, and the center of gravity of this vehicle has not been designed. Therefore, the nose at

397

symmetric plane of this vehicle is chosen as the reference center of pitching moment coefficient, as

398

shown in Fig. 17. And in this paper, a negative pitching moment denotes a nose-down pitching

399

moment.

400 401

Fig. 17 Reference point

402

The pitching moment coefficients of four configurations (loiter, standard, dash and

403

wing-retracted configurations ) with the increase of angle of attack (i.e. í2°, 0°, 2°, 5° and 10°) under

404

five flight conditions, are all obtained and depicted in Fig. 18. In Fig. 18, the loiter configuration

405

( Λ =20e) is denoted by marker ƺ and dotted line, the standard configuration ( Λ =40e) is denoted

406

by marker ƶ and dashed line, the dash configuration ( Λ =60e) is denoted by marker ƻ and

407

dash-dotted line, and the wing-retracted configuration ( Λ =90e) is denoted by marker ƺ and solid

408

line.

409

Under the subsonic flight condition (M=0.8) and the low speed supersonic flight condition 29

410

(M=1.5), the differences among different configurations are quite large. And with morphing wings

411

sweeping backwards, a smaller nose down pitching moment is induced. When aircraft changes from

412

loiter configuration to dash configuration, lift coefficient becomes smaller and center of pressure

413

shifts backwards resulting in a larger moment arm of lift. However, the decrease magnitude of lift is

414

bigger than the increase magnitude of moment arm of lift resulting in a smaller pitching moment

415

coefficient. Under the high speed supersonic (M=3) or hypersonic speeds (M=6, M=8), the

416

differences among three wing-extended configurations are very small. Under hypersonic speed, the

417

lift of morphing wings is very small compared with the lift generated by the waverider forebody and

418

the difference of lift among three wing-extended configurations can be neglected.

419

30

420

(a) M=0.8

(b) M=1.5

(c) M=3

(d) M=6

(e) M=8 421 422 423

Fig. 18 Pitching moment coefficients of four configurations versus angle of attack. 4. Preliminary discussion on differences among four configurations To explore the reasons for differences in the aerodynamic performances among four 31

424

configurations of the variable-sweep-wing morphing waverider proposed in this paper, the flow field

425

characteristics of two specific flight conditions (Mach 0.8, Į=0° and Mach 8, Į=0° ) of the four

426

configurations and effects of wing downwash and shock wave are analyzed in detail in this section.

427

4.1. M=0.8, Į=0°

428

According to the analysis in Section 3.2, under the flight condition Mach 0.8, the loiter

429

configuration has the largest lift coefficient, drag coefficient, and lift-to drag ratio compared with

430

other configurations. Besides, the drag coefficients of the four configurations are quite close at low

431

angle of attack, while at high angle of attack, the drag coefficients of the four configurations are quite

432

different.

433

Fig. 19 illustrates the pressure contours at the lower and upper surfaces of four configurations of

434

the variable-sweep-wing morphing waverider, and the pressure coefficient levels in eight contours are

435

the same for an accurate figure-to-figure comparison. For each subfigure, the upside and downside

436

figure denote different configuration for comparison. Moreover, apart from two variable-sweep-wings,

437

the pressure contours of upper and lower surfaces of all the four configurations are nearly the same,

438

which means that different configurations of the variable-sweep-wing lead to differences in pressure

439

distribution over wings and it is the main reason for different aerodynamic performance. Besides, the

440

lower surface pressure coefficients of four configurations are all higher than the corresponding upper

441

surface pressures. In addition, as can be seen from Fig. 19 (a) and (c), the upper surface of the wing of

442

the loiter configuration has a low pressure area drawn in the dark blue, and the lower surface of the

443

wing of it has a high pressure area drawn in the dark red. Therefore, the biggest difference between

444

pressure coefficients of upper and lower surfaces at the wing area of the loiter configuration makes it

445

have the largest lift coefficient. 32

a)

Upper surface, loiter vs standard

b)

configuration

c)

Upper surface, dash vs wing-retracted configuration

Lower surface, loiter vs standard

d)

configuration

Lower surface, dash vs wing-retracted configuration

Fig. 19 Comparisons of pressure coefficient contours of four configurations 446

Pressure coefficient contours on wing’s cross-section in a chord-wise direction (Y=0.46m) with

447

flowfield streamtraces of three wing-extended configurations are shown in Fig. 20. A high-pressure

448

area near the leading edge of the wing and pressure distribution of both wing and tail can be

449

investigated at this cross section. A small sweep angle of the loiter configuration leads to a

450

high-pressure area near the leading edge, and it results in a large drag coefficient.

33

a)

loiter configuration

b)

standard configuration

c)

dash configuration

Fig. 20 Pressure coefficient contours on a wing's cross-section in a chord-wise direction (Y=0.46m) with flowfield streamtraces of three wing-extended configurations (M=0.8, Angle of attack = 0°) 451

Fig. 21 presents pressure coefficient distributions of lower and upper surfaces of three

452

configurations on different wing’s cross sections (Y=0.46m and Y=0.66m). X/b denotes the ratio of x

453

coordinate with semi-span width. High pressure coefficients at the leading edge and following edge

454

can be observed, and the difference between pressure coefficients of upper and lower surfaces of the

455

loiter configuration is the biggest. The lift coefficient generates by the wing can be approximated by

456

calculating the area enclosed by Cp curves of upper and lower surfaces. Therefore, the loiter

457

configuration has the largest lift. As shown in Fig. 21 (a) and Fig. 20 (c), as to the dash configuration,

458

the pressure coefficient of the upper surface is even large than that of the lower surface when X/b is

459

smaller than 0.3, and it leads to a negative lift coefficient near this area. Therefore, the dash

460

configuration has the smallest lift. Meanwhile, by sweeping the wing, a streamline effectively sees a

461

thinner airfoil. As stated above, caused by a large sweep angle, the airfoil of dash configuration is

462

thinner than the loiter configuration at the same position, and the pressure at its lower surface is

463

smaller, so the dash configuration has the smallest pressure component in the drag direction.

34

a)

Y=0.46m

b)

Y=0.66m

Fig. 21 Pressure coefficients of lower and upper surfaces of three wing-extended configurations at different wing’s cross-section in a chord-wise direction (Y=0.46m and Y=0.66m) 464 465

4.2. M=8, Į=0°

466

Fig. 22 denotes pressure coefficient contours on the waverider forebody and surface of the

467

wing-retracted configuration. As shown in Fig. 22 (d)-(f), the good waverider performance of the

468

variable-sweep-wing waverider in Mach 8 can be observed. The shock wave on the forebody prevents

469

the leakage of the high-pressure gas on the lower surface of the waverider, and the waverider exhibits

470

good shock effect. As can be seen from Fig. 22 (c), the lower surface of the forebody has a

471

homogeneous pressure distribution while the upper surface is surrounded by the free flow condition.

35

472

a) 3D view with three planes

d) X=0.16m

b) Upper surface

c) Lower surface

e) X=0.31m

f) X=0.46m

Fig. 22 Pressure coefficient contours on the waverider forebody cross sections and surface of the wing-retracted configuration. 473

Fig. 23, Fig. 24 and Fig. 25 denote pressure coefficient contours on wing cross sections and

474

upper/lower surfaces of the loiter, standard and dash configurations, respectively. The high-pressure

475

area at the wing leading edge of the loiter configuration is more obvious than the other two

476

configurations, and it leads to a large drag coefficient. Compared with Fig. 20, the difference between

477

the pressure coefficients of upper and lower surfaces of the variable-sweep-wing is very small at the

478

hypersonic speed. In other words, in the hypersonic speed range, the aerodynamic performance

479

advantages of the wing-extended configurations are not as large as those in the subsonic speed. For

480

different flight condition and mission scenarios, the best flight performance of this

481

variable-sweep-wing morphing waverider can be achieved using different configuration. 36

a) 3D view with six planes

d) Y=-0.46m

b) Upper surface

c) Lower surface

e) Y=-0.55m

f) Y=-0.66m

Fig. 23 Pressure coefficient contours on wing cross sections and surfaces of the loiter configuration. 482

a) 3D view with six planes

d) Y=-0.46m

b) Upper surface

c) Lower surface

e) Y=-0.55m

f) Y=-0.66m

Fig. 24 Pressure coefficient contours on wing cross sections and surfaces of the standard configuration. 483

37

a) 3D view with six planes

d) Y=-0.46m

a) Upper surface

b) Lower surface

e) Y=-0.55m

f) Y=-0.66m

Fig. 25 Pressure coefficient contours on waverider forebody, wings and surface of the dash configuration. 484 485

4.3. Analysis of wing downwash

486

Pressure coefficient contours on a chord wise wing and tail cross section (Y=0.46m) with

487

flowfield streamtraces of three wing-extended configurations are shown in Fig. 26. This flow

488

establishes a circulatory motion that trails downstream of the wing. These wing-tip vortices

489

downstream of the wing induce a small downward component of air velocity in the neighborhood of

490

the wing itself. This downward component is called downwash in Ref. [32]. As can be seen in Fig. 26,

491

the flowfield near the leading edge of the horizontal tail is nearly the same as far field air flow. And

492

the downward component induced by the wing downwash is very small.

38

a)

loiter configuration

b)

standard configuration

c)

dash configuration

Fig. 26 Pressure coefficient contours on a wing and tail cross section (Y=0.5m) with flowfield streamtraces of three wing-extended configurations (M=0.8, Angle of attack = 10°) 493

The dash configuration is chosen as an example to investigate the downwash effect on the tail,

494

since the distance between wing and tail of the dash configuration is the nearest. Pressure coefficient

495

contours on a chord wise wing and tail cross section (Y=0.5m) of dash configuration with flowfield

496

streamtraces of three flight condition are shown in Fig. 27. As can be seen in Fig. 26, the differences

497

of downwash effects among three supersonic/hypersonic flight conditions are quite small.

a)

M=3

b)

M=6

c)

M=8

Fig. 27 Pressure coefficient contours on a wing and tail cross section (Y=0.5m) of dash configuration with flowfield streamtraces of three flight condition (Angle of attack = 10°) 498

39

499

4.4. Effects of shock wave

500

Under the supersonic flight condition(M=3, AoA=0deg), comparisons of Mach number contours

501

of loiter, standard and dash configurations at seven cross sections are shown in Fig. 28, Fig. 29 and

502

Fig. 30, respectively. For a clear demonstration, the grids with Mach number greater than 2.9 are not

503

drawn in the right subfigure. Attached bow shock on leading edge of the forebody can be observed

504

explicitly as shown in X direction cross sections at Fig. 28 (b) to Fig. 30 (b). The shock wave on the

505

forebody prevents the leakage of the high-pressure gas on the lower surface of the waverider. The

506

Mach contours along the wing span wise direction shows that effect of forebody shock wave

507

gradually decreases with increase of the distance of y direction from wing root.

a) Z=-0.09m

b) X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 28 Comparisons of Mach number contours of loiter configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m and Z=-0.09m) under the flight condition (M=3, AoA=0e) 508

40

a) Z=-0.09m

b) X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 29 Comparisons of Mach number contours of standard configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m and Z=-0.09m) under the flight condition (M=3, AoA=0e) 509 510

As shown in Fig. 30, two variable-sweep-wings are totally under the influence of forebody shock wave.

a) Z=-0.09m

b) X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 30 Comparisons of Mach number contours of dash configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m and Z=-0.09m) under the flight condition (M=3, AoA=0e) 511

Under the supersonic flight condition(M=6,AoA=0°), comparisons of Mach number contours of

512

loiter, standard and dash configurations at seven cross sections are shown in Fig. 31, Fig. 32 and Fig.

513

33, respectively. For a clear demonstration, the grids with Mach number greater than 5.9 are not

514

drawn in the right subfigure. Mach number contours in Fig. 31 to Fig. 33 allow assessing the bow 41

515

shock shape that takes place past the vehicle. Attached bow shock on leading edge of the forebody can

516

be observed explicitly as shown in X direction cross sections at Fig. 31 (b) to Fig. 33 (b).

a) Z=-0.09m

b) X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 31 Comparisons of Mach number contours of loiter configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m and Z=-0.09m) under the flight condition (M=6, AoA=0e) 517

a) Z=-0.09m

b) X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 32 Comparisons of Mach number contours of standard configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m and Z=-0.09m) under the flight condition (M=6, AoA=0e) 518

42

a) Z=-0.09m

b) X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 33 Comparisons of Mach number contours of dash configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m and Z=-0.09m) under the flight condition (M=6, AoA=0e) 519

Under the hypersonic flight condition(M=8,AoA=0°), comparisons of Mach number contours of

520

loiter, standard and dash configurations at seven cross sections are shown in Fig. 34, Fig. 35and Fig.

521

36, respectively. For a clear demonstration, the grids with Mach number greater than 7.9 are not

522

drawn in the right subfigure. Attached bow shock on leading edge of the forebody can be observed

523

explicitly as shown in X direction cross sections at Fig. 34 (b) to Fig. 36 (b).

a)

Z=-0.09m

b)

X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 34 Comparisons of Mach number contours of loiter configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m) under the flight condition (M=8, AoA=0e) 524 43

a)

Z=-0.09m

b)

X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 35 Comparisons of Mach number contours of standard configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m) under the flight condition (M=8, AoA=0e) 525

a)

Z=-0.09m

b)

X=0.1m, 0.2m, 0.3m and Y=0.42, 0.5, 0.6m

Fig. 36 Comparisons of Mach number contours of dash configuration at seven cross sections (X=0.1m, 0.2m, 0.3m, Y=0.42, 0.5, 0.6m) under the flight condition (M=8, AoA=0e) 526

5. Conclusions and future work

527

In this paper, the design methodology and aerodynamic performances of a variable-sweep-wing

528

waverider are proposed and analyzed respectively. Besides, the aerodynamic performances of four

529

different configurations are compared with each other, and we have come to the following

530

conclusions:

531

z

Under the same flight condition, the drag coefficient of the four different sweep 44

532

configurations increases with the increase of the angle of attack, and it becomes lower as the

533

sweep angle increases. Under the same angle of attack and the same sweep configuration,

534

the drag coefficient decreases with the increase of the flight Mach number.

535

z

In terms of the increase in the lift, under the flight conditions (M= 0.8, M=1.5), the loiter

536

configuration has the largest lift coefficient. The optimal configurations with the largest lift

537

coefficient for different flight conditions are the followings, the standard configuration for

538

Mach 3, and the dash configuration for Mach 6 and Mach 8. This shows that different

539

configurations of the variable-sweep-wing morphing waverider suit for different flight

540

conditions with the largest lift coefficient.

541

z

Under the same flight condition, the lift-to-drag ratio of the four different sweep

542

configurations increases first and then decreases with the increase of the angle of attack.

543

Under the flight condition (M=0.8), the lift-to-drag ratio of the loiter configuration

544

(L/D=8.43, Į=2°) is the highest, but they are close at high angles of attack. In contrast,

545

under the flight condition (M=1.5), the standard configuration has the largest lift-to-drag

546

ratio of 3.29. Under the flight condition (M=3,6,8), the dash configuration has the largest

547

lift-to-drag ratio when Į=5°.

548

z

Though analyses of effects of wing downwash and shock wave, the flowfield near the

549

leading edge of the horizontal tail is nearly the same as far field air flow. And the downward

550

component induced by the wing downwash is very small. Attached bow shock on leading

551

edge of the forebody can be observed. The Mach contours along the wing span wise

552

direction shows that effect of forebody shock wave gradually decreases with increase of the

553

distance of y direction from wing root. 45

554

In conclusion, the variable-sweep-wing morphing waverider proposed in this paper improves

555

both low speed take-off and high-speed cruising performances, and it expands the flight speed range.

556

For different flight conditions and mission scenarios, the best flight performance of this

557

variable-sweep-wing morphing waverider can be achieved using different configurations.

558

46

559 560 561 562

Conflicts of interest The authors declare there is no conflict of interest regarding the publication of this paper. Acknowledgments The authors would like to express their thanks for the support from NSAF (Grant No:

563

U1730135).

564

References

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[1] G. Pezzella, and A. Viviani, Aerodynamic performance analysis of a winged re-entry vehicle from hypersonic down to subsonic speed, Aerosp. Sci. Technol. 52(2016) 129-143. [2] S. B. Li, Z. G. Wang, W. Huang, J. Lei, S. R. Xu, Design and investigation on variable Mach number waverider for a wide-speed range. Aerosp. Sci. Technol. 76(2018) 291-302. [3] T.T. Zhang, Z.G. Wang, W. Huang, S.B. Li, A design approach of wide-speed-range vehicles based on the cone-derived theory, Aerosp. Sci. Technol. 71 (2017) 42–51. [4] Z.T. Zhao, W. Huang, S.B. Li, T.T. Zhang, L. Yan, Variable Mach number design approach for a parallel waverider with a wide-speed range based on the osculating cone theory, Acta Astronaut. 147 (2018) 163–174. [5] Z.T. Zhao, W. Huang, B.B. Yan, L. Yan, T.T. Zhang, R. Moradi, Design and high speed aerodynamic performance analysis of vortex lift waverider with a wide-speed range, Acta Astronaut. 151 (2018) 848–863. [6] F.M. Wang, H.H. Ding, M.F. Lei, Aerodynamic characteristics research on wide speed range waverider configuration, Sci. China Ser. E-Tech. Sci. 52 (10) (2009) 2903–2910. [7] S.B. Li, S.B. Luo, W. Huang, Z. G. Wang, Influence of the connection section on the aerodynamic performance of the tandem waverider in a wide-speed range, Aerosp. Sci. Technol. 30 (2013) 50–65. [8] S.B. Li, W. Huang, Z.G. Wang, J. Lei, Design and aerodynamic investigation of a parallel vehicle on a wide-speed range, Sci. China Inf. Sci. 57 (12) (2014) 128201:1-128201:10. [9] Z. Liu, J. Liu, F. Ding, Z. X. Xia, Novel methodology for wide-ranged multistage morphing waverider based on conical theory, Acta Astronaut 140(2017) 362-369. [10] R.J. Pegg, D.E. Hahne, C.E. Cockrell, et al., Low-speed wind tunnel tests of two waverider configuration models, 6th International Aerospace Planes and Hypersonics Technologies Conference, AIAA Paper. (1995) 6093. [11] C. Tarpley, D. J. Pines, A. P. Kothari, Low-speed stability analysis of the dual fuel waverider configuration. Space Plane & Hypersonic Systems & Technology Conference. (2013) [12] Y. Takama, Practical waverider with outer wings for the improvement of low-speed aerodynamic performance. Aiaa International Space Planes & Hypersonic Systems & Technologies Conference. (2011) [13] Zhao Z. T., W. Huang, L. Yan, T. T. Zhang, S. B. Li, F. Wei, Low speed aerodynamic performance analysis of vortex lift waveriders with a wide-speed range, Acta Astronaut. 161(2019) 209-221. 47

597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638

[14] A. P. Austin, E. R. Robert, E. R. Jesse, B. G. Gabriel, Mach Five to Ten Morphing Waverider: Control Point Study,J. Aircr. 56(2)(2019) 493-504. [15] D. Grant, M. Abdulrahim, R. Lind, Flight dynamics of a morphing aircraft utilizing independent multiple-joint wing sweep, in: AIAA Atmospheric Flight Mechanics Conference and Exhibit, (2006) 6505. [16] A. Chakravarthy, D. Grant, R. Lind, Time-varying dynamics of a micro air vehicle with variable-sweep morphing, J. Guid. Control Dyn. 35 (3) (2012) 890–903. [17] T. Yue, L. Wang, J. Ai, Longitudinal linear parameter varying modeling and simulation of morphing aircraft, J. Aircr. 50 (6) (2013) 1673–1681. [18] B. B. Yan, P. Dai, R. F. Liu, M. Z. Xing, S. X. Liu, Adaptive super-twisting sliding mode control of variable sweep morphing aircraft, Aerosp. Sci. Technol. 92 (2019) 198-210. [19] D. Xu, Z. Hui, Y. Q. Liu, G. Chen, Morphing control of a new bionic morphing UAV with deep reinforcement learning, Aerosp. Sci. Technol. 92 (2019) 232-243. [20] T. Yue, X. Zhang, L. Wang, J. Ai, Flight dynamic modeling and control for a telescopic wing morphing aircraft via asymmetric wing morphing, Aerosp. Sci. Technol. (2017) 328-338. [21] Y. Y. Guo, B. Xu, X. X. Hu, X. W. Bu, Y. Zhang. Two controller designs of hypersonic flight vehicle under actuator dynamics and AOA constraint. Aerosp. Sci. Technol. 80 (2018) 11-19. [22] S. B. Tiwari, R. Suresh, C. K. Krishnadasan, Design, Analysis and Qualification of Elevon for Reusable Launch Vehicle. J. I. of Eng (India): Series C. (2017). [23] S. Chakravarthy, O. Peroomian, U. Goldberg, S. Palaniswamy, Parallel personal computer applications of cfd++, a unified-grid, unified physics framework, Parallel Comput Fluid Dyn. (1999) 127-134. [24] W. Huang, W.D. Liu, S.B. Li, Z.X. Xia, et al., Influences of the turbulence model and the slot width on the transverse slot injection flow field in supersonic flows, Acta Astronaut. 73 (2012) 1–9. [25] W. Huang, S.B. Li, L. Yan, Z.G. Wang, Performance evaluation and parametric analysis on cantilevered ramp injector in supersonic flows, Acta Astronaut. 84 (2013) 141–152. [26] O. Brodersen, M. Rakowitz, S. Amant, Airbus, ONERA, and DLR Results from the Second AIAA Drag Prediction Workshop, J. Aircr. 42 (2005) 932-940. [27] R. Rudnik, M. Sitzmann, J. L. Godard, F. Lebrun, Experimental Investigation of the Wing-Body Juncture Flow on the DLR-F6 Configuration in the ONERA S2MA Facility, Aiaa Applied Aerodynamics Conference. (2013). [28] https://aiaa-dpw.larc.nasa.gov/Workshop2/ pdf/53Goldberg_cfd++.pdf [29] K. R. Laflin, S. M. Klausmeyer, T. Zickuhr, J. C. Vassberg, R. A. Wahls, J. H. Morrison, Data summary from second aiaa computational fluid dynamics drag prediction workshop, J. Aircr. 42(5)(2005) 1165-1178. [30] A. Singh, Experimental Study of Slender Vehicles at Hypersonic Speeds, Cranfield University, Cranfield, 1996 (Ph.D.). [31] U. Goldberg, Hypersonic Turbulent Flow Predictions Using CFD++, AIAA/CIRA 13th International Space Planes and Hypersonics Systems and Technologies Conference. (2005). [32] Fundamentals of aerodynamics(fifth edition). John Anderson Jr.

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Declaration of Competing Interest Š‡ ƒ—–Š‘”• †‡…Žƒ”‡ –Š‡”‡ ‹• ‘ …‘ˆŽ‹…– ‘ˆ ‹–‡”‡•– ”‡‰ƒ”†‹‰ –Š‡ ’—„Ž‹…ƒ–‹‘‘ˆ–Š‹•’ƒ’‡”Ǥ