inlet integration methodology for air-breathing hypersonic vehicles

Accepted Manuscript An overview of waverider design concept in airframe/inlet integration methodology for air-breathing hypersonic vehicles Feng Ding, Jun Liu, Chi-bing Shen, Wei Huang, Zhen Liu, Shao-hua Chen PII:

S0094-5765(18)30788-4

DOI:

10.1016/j.actaastro.2018.09.002

Reference:

AA 7089

To appear in:

Acta Astronautica

Received Date: 2 May 2018 Revised Date:

22 August 2018

Accepted Date: 1 September 2018

Please cite this article as: F. Ding, J. Liu, C.-b. Shen, W. Huang, Z. Liu, S.-h. Chen, An overview of waverider design concept in airframe/inlet integration methodology for air-breathing hypersonic vehicles, Acta Astronautica (2018), doi: 10.1016/j.actaastro.2018.09.002. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

An overview of waverider design concept in airframe/inlet integration methodology for air-breathing hypersonic vehicles

College of Aerospace Science and Engineering, National University of Defense Technology,

Changsha, Hunan 410073, People’s Republic of China b

Science and Technology on Scramjet Laboratory, National University of Defense Technology,

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Changsha, Hunan 410073, People’s Republic of China

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a

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Feng Dinga,b*, Jun Liua,b, Chi-bing Shena,b, Wei Huanga,b, Zhen Liua,b, Shao-hua Chena,b

*Corresponding author. Tel.: +86 731 84576452; fax: +86 731 84576447 E-mail address: [email protected] (F. Ding).

Abstract: A waverider is any supersonic or hypersonic lifting body that is characterized by an

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attached, or nearly attached, bow shock wave along its leading edge. A waverider can possess high lift-to-drag ratio characteristics as well as an ideal precompression surface of the inlet system, and hence has become one of the most promising designs for air-breathing hypersonic vehicles. Two

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classes of general methodologies exist for using the waverider concept in the airframe/inlet

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integration for air-breathing hypersonic vehicles. In the first class, the waverider is used only as the forebody of a vehicle, and behaves as the precompression surface to efficiently provide the inlet system with the required compression flow field. In the second class, and to take advantage of the waverider’s high lift-to-drag ratio characteristics as well as the ideal precompression surface for the engine, the waverider design is used as the basis for the design of the entire vehicle, and the engine is generated within the pristine waverider definition while maintaining the bow shock wave attaching to the leading edge. In this paper, waverider applications developed by domestic

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ACCEPTED MANUSCRIPT and overseas scholars in the airframe/inlet integration methodology for air-breathing hypersonic vehicles are reviewed and classified, and the future research and development trends are presented. The idea for the design of a waverider-derived air-breathing hypersonic vehicle can be

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summarized as follows: the modeling of the basic flow is used to design the waverider in the streamwise direction, and the osculating theory is used to design the waverider in the spanwise direction.

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Keywords: Air-breathing hypersonic vehicle; Waverider; Airframe/inlet integration methodology;

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Forebody/inlet integration methodology; Aerodynamic design methodology

Introduction

A large number of studies conducted since the 1960s have shown that one of the key techniques for ensuring the success of air-breathing hypersonic vehicles is the effective integration

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of the engine with the airframe [1][2][3]. To reduce overall drag and achieve positive thrust margins at hypersonic speeds, the engine must be incorporated as an integral part of the airframe. The engine and airframe aerodynamics therefore become highly associated. Hence, a distinctive

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characteristic of the design of the air-breathing hypersonic vehicle is the degree to which the

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engine, inlet and nozzle (i.e., propulsion system) must be integrated with the rest of the body. The airframe/propulsion integration is of unique significance in the development of the air-breathing hypersonic vehicles, where each component affects every other component. Unfortunately, engineering practice usually leads to a subdivision by components in the design, development, and manufactuing processes, ao that the integration is not well-advanced. The airframe of an air-breathing hypersonic vehicle comprises forebody, fuselage, wings, and afterbody [4]. The wings here also refer to the flat body parts that provide the lifting force on

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ACCEPTED MANUSCRIPT both sides of the fuselage. Hypersonic propulsion systems rely mainly on scramjet engines, including inlets, combustion chambers, and nozzles. The layout, location, and the number of the scramjet engines on the airframe of an air-breathing hypersonic vehicle are varied and should be

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designed according to mission requirements. The inlet needs to provide a compressed air stream for the scramjet combustor, and the upstream capture airflow required may be disturbed by the various components of the airframe. The combustion chamber and the nozzle usually belong to the

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internal components, and their upstream flow mainly depends on the inlet or outlet of the

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combustion chamber performance parameters, without interfering with the flow of the airframe. Hence, one of the core design aspects of airframe/propulsion of the air-breathing hypersonic vehicle is the design of airframe/inlet integration [5].

Considering the working performance and overall design parameters, the requirements

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of hypersonic vehicle design for airframe and inlet are different. The design requirements of the airframe are high lift-to-drag ratio, high effective volume, and good thermal protection performance at the leading edge; the inlet is designed to provide as much effective air source for

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the combustion chamber as possible by minimizing the loss of air flow energy. Because the design

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requirements and methods are different for airframe and inlet, for a long time, airframe/inlet integration could only be designed for integrating two separate high-performance components, and then they are involved simple superposition and compromise. In other words, so far it has been more of an art than a science. There are some vehicle design issues that are sufficiently complex and dependent in some unknown way on scale that they may not be reliably resolved even by combining test results from a number of separate facilities. Thus, it was identified that the key to the improvement of overall performance is an efficient airframe/inlet integration design method

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ACCEPTED MANUSCRIPT [6]. A waverider is any supersonic or hypersonic lifting body that is characterized by an attached, or nearly attached, bow shock wave along its leading edge [7][8][9]. Because of the

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excellent aerodynamic configuration of the waverider, since Nonweiler [10] first proposed the waverider concept in 1959, the waverider has become one of the most promising designs for air-breathing hypersonic vehicles [11][12][13][14]. There are two advantages in using the

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waverider concept in an air-breathing hypersonic vehicle design [3]. First, a waverider can be used

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as an ideal precompression surface of the inlet system because the leading-edge shock wave generated by the waverider can precompress the air and limit the high-pressure air between the lower surface and the shock wave escaping to the upper surface, and the waverider can capture a considerably greater amount of air. Second, the waverider has a higher lift-to-drag ratio than a

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conventional lifting body at the same lift coefficient, owing to the greater pressure difference between the upper and lower surfaces of the waverider [15]. Thus, a waverider can possess high lift-to-drag ratio characteristics as well as an ideal precompression surface of the inlet system.

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However, with engine integration, the lift-to-drag ratio of the waverider is expected to be

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considerably lower than that of the pure aerodynamic configuration. As a result, over the past 50 years, engine–airframe integration methodologies for the hypersonic waverider vehicle have been extensively studied by many researchers. As a first step in the engine–airframe integration presented herein, problems associated with inlet–airframe integration for waveriders are addressed. Two classes of general methodologies exist for using the waverider concept in an air-breathing hypersonic vehicle design [16]. In the first class, the waverider is used only as the

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ACCEPTED MANUSCRIPT forebody of a vehicle, and it behaves as the precompression surface to efficiently provide the inlet system with the required compression flow field; therefore, the first class is termed as waverider forebody/inlet integration design methodology, and it is the most critical item in the integration

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process. Furthermore, it is worth noting that the design of the forebody not only takes into account lift, drag, and stability, but also considers that the shape of the forebody significantly affects the overall performance of vehicle. In the second class, and to take advantage of the waverider’s high

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lift-to-drag ratio characteristics as well as the ideal precompression surface for the engine, the

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waverider design is used as the basis for the design of the entire vehicle, and the engine are generated within the pristine waverider definition while maintaining the bow shock wave attaching to the leading edge; therefore, the second class is termed as waverider airframe/inlet integration design methodology.

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In this paper, the above two classes of general methodologies by domestic and overseas scholars for using the waverider concept in the airframe/inlet integration design of the air-breathing hypersonic vehicle are reviewed and classified. The idea for the design of a

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waverider-derived air-breathing hypersonic vehicle can be summarized as follows: the modeling

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of the basic flow is used to design the waverider in the streamwise direction, and the osculating theory is used to design the waverider in the spanwise direction. The following is a detailed introduction to the research status of the above two classes of design methodologies.

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Waverider forebody/inlet integration design methodology Many researchers have developed the waverider forebody/inlet integration design

methodologies when the waverider was used as the forebody of the vehicle. Some researchers applied the basic flow models to develop the streamwise-direction design methods, some

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ACCEPTED MANUSCRIPT researchers used the osculating theories to develop the spanwise-direction design methods, and some other researchers proposed several combination design methods of geometric transition or assembly to meet the needs of practical engineering.

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2.1. Streamwise-direction design methods For the streamwise-direction design, the researchers developed a variety of design methods in the following two main approaches. First, the waverider forebody is taken as the

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inlet’s first-stage precompression surface, followed by a multistage wedge or a two-dimensional

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isentropic compression surface to further compress air until the inlet entrance requirements are met, such as the design proposal of Starkey and Lewis [17] from the University of Maryland in the United States, as shown in Fig. 1. In the second approach, the waverider forebody is taken as the inlet’s entire precompression surface, and the flows are directly compressed into the inlet by the

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waverider forebody, as in the design proposal of He et al. [18] from the China Aerodaynmic Research and Development Center, as shown in Fig. 2. Here, we introduce the four classic and commonly used design methods in the

Wedge-derived waverider forebody/inlet integration

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2.1.1.

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streamwise direction.

When Nonweiler [10] first proposed the waverider design concept in 1959, he employed

flows past a wedge to generate the first waverider in the history of aerospace science and technology. This type waverider is termed as wedge-derived waverider, and it is also known as the “Λ” waverider because of the “Λ” shape of the cross-section [19][20][21], as shown in Fig. 3. Although the wedge-derived waverider is of low practical value because of its low volumetric efficiency, its design concept is pioneering, because of which it provides the future research

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ACCEPTED MANUSCRIPT direction for hypersonic vehicle configurations. Furthermore, the wedge-derived waverider is also named the V-shaped wing by Zubin and Ostapenko [22][23][24], Ostapenko [25], Ostapenko and Simonenko [26], Maksimov and

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Ostapenko [27], Zubin et al. [28] from Sussian Moscow State University, and the main design parameters of the V-shaped wing are shown in Fig. 4. Furthermore, there has been widespread investigation of the flow over V-shaped wing [22]-[27]. Both the theoretical and experimental

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results showed that at supersonic or hypersonic speed a V-shaped wing is more efficient in flow

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regimes with a shock attached to the leading edges as compared to a equivalent planar triangular wing, and the former has a larger lift-to-drag ratio than the later (given the specific volumes and lift coefficients of the two configurations being equal) [25].

Mazhul and Rakhimov [29][30] from the Russian Academy of Science investigated

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another type of waverider that was also generated from flows past a wedge. For this type of waverider, the projection curve of its leading edge on the base plane is a power-law curve; therefore, it is termed the power-law-shaped waverider, as shown in Fig. 5.

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The wedge-derived waverider is used as the vehicle forebody for the integration design,

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and its biggest advantage is not only the flow field uniformity but also the suitability for optimal design. This is because the supersonic flow around a wedge is a typical 2D planar flow field, and the geometry and aerodynamic performance parameters can be calculated easily by fast calculation methods such as the analytical method. In view of the above two advantages, the wedge-derived waverider is not only the first kind of waverider which is applied to the forebody/inlet integration, but is also the first to be successfully applied to the demonstration flight test vehicle of the scramjet. Futhermore, such a design concept was first realized by the

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ACCEPTED MANUSCRIPT Boeing X-51A WaveRider scramjet demonstrator [31] as shown in Fig. 6, which implemented a wedge-derived waverider forebody for compression ahead of the inlet. Two methods are used to design the wedge-derived waverider forebody, namely

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constant-wedge-angle and variable-wedge-angle methods [32]. The waverider forebody generated from the constant-wedge-angle method produces a plane shock wave at its leading edge, and the waverider forebody generated from the variable-wedge-angle method produces a 3D shock wave

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at its leading edge. Compared with the constant-wedge-angle method, the variable-wedge-angle

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method is more flexible and convenient, and hence is beneficial to the forebody/inlet integration. Starkey and Lewis [17][33] and Starkey et al. [34] applied the wedge-derived waverider with a variable wedge angle (as shown in Fig. 7) as the first-stage precompression surface of a multiple scramjet, and developed the wedge-derived waverider forebody/inlet integration design method. 2D curved surface compression waverider forebody/inlet integration

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2.1.2.

Different from the above wedge-derived waverider forebody/inlet integration using 2D flow around a wedge, in 2010, Mazhul [35] first employed a kind of 2D curved surface

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compression flow combined with an oblique shock wave and isentropic compression flow to

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design the waverider shown in Fig. 8; then, he investigated the off-design performance of this type of waverider by using a finite-volume solution of Euler equations by means of higher-order total-variation-diminishing (TVD) Runge–Kutta schemes. Li et al. [36] from the Xiamen University applied the 2D curved surface compression

flow (as shown in Fig. 9) as the basic flow field to develop the waverider forebody/inlet integration configuration (as shown in Fig. 10) with preassigned pressure distribution. The study results showed that compared with the wedge-derived waverider forebody/inlet integration case,

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ACCEPTED MANUSCRIPT the mass flow rate, pressure ratio, and total pressure recovery coefficient of the inlet of the proposed case by Li et al. [36] improved by 5%, 6.4%, and 2.3%, respectively. 2.1.3.

Cone-derived waverider forebody/inlet integration

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The supersonic flow around a cone at a zero angle of attack, which is known as a conical flow field, is a typical 2D axisymmetric basic flow field. In 1968, Jones et al. [37] first used this type of flow field to design a waverider known as the cone-derived waverider. Subsequently, in

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1986 and 1987, Bowcutt [38] and Bowcutt et al. [39] optimized the cone-derived waverider under

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consideration of the detailed viscous effects. Bowcutt’s research showed that the shape of the optimized waverider considering the viscous effects was obviously different from that of the previously optimized waverider without considering the viscous effects [38][39]. Furthermore, the conical flow field is the most widely used basic flow field for waveriders, and the cone-derived

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waverider has become the most widely used waverider owing to its easier calculation and better volumetric efficiency than the wedge-derived waverider on account of the concave streamlines being closer to the shock wave [40][41][42][43].

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Javaid and Serghides [44][45] used the cone-derived waverider as the first-stage

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precompression surface to design the forebody/inlet integration vehicle, and this method is termed as cone-derived waverider forebody/inlet integration method. Bowcutt and Haney [46] also used the cone-derived waverider forebody/inlet integration method to develop a high-performance hypersonic vehicle named the Rockwell Research Vehicle (HRV) that can accelerate from Mach 3 to Mach 8 with hydrocarbon fuels, and the HRV can be used as the second-stage accelerator of the two-stage-to-orbit (TSTO) system; Bowcutt et al. [47] and Bradley et al. [48] applied the integration method to the design of the first-stage vehicle of a TSTO system; subsequently, Glass

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ACCEPTED MANUSCRIPT and Bowcutt [49] used a similar integration method to design a singe-stage vehicle for the ultra-rapid global travel. In the design of Glass and Bowcutt [49], the integrated inlet system consists of three ramps with a variable second ramp and cowl lip that needs to maintain the shock

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wave on the lip for the wide-speed flight from takeoff to Mach 8. Moreover, for the cone-derived waverider forebody, compared with the wedge-derived waverider, the volumetric efficiency increases, but the three-dimensional flow characteristics reduces the inlet’s flow uniformity [50]. Wedge-cone-derived waverider forebody/inlet integration

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2.1.4.

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In 1994 and 1995, Takashima and Lewis [51][52] from the University of Maryland in the United States first used a 3D flow field around a wedge-cone body as shown in Fig. 11 to generate a waverider termed as wedge-cone waverider, and used this type of waverider as the forebody of a vehicle to design a wedge-cone waverider forebody/inlet integration vehicle. Their

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study results indicated that the wedge-cone waverider forebody provided a higher volume than the cone-derived waverider forebody while also providing a comparable lift-to-drag ratio. In 2013, Ming [53] from the Nanjing University of Aeronautics and Astronautics conducted a study on the

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design method and performance characteristics of the wedge-cone waverider forebody/inlet

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integration, and the study results confirmed that a vehicle using this type of integration had the advantages of both the wedge-drived waverider and the cone-derived waverider. 2.2. Spanwise-direction design methods For spanwise-direction design, given the simplicity and accuracy of the design method

of the axisymmetric inviscid basic flow field, researchers have developed three types of waverider design theories: osculating cone [54], osculating axisymmetric [55][56], and osculating flow field [57][58][59][60][61][62] theories. Based on the three osculating waverider design theories, studies

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Osculating cone waverider forebody/inlet integration

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The osculating cone design theory, which was first proposed by Sobieczky et al. [54] in 1990, is the first kind of spanwise design theory of a waverider forebody of a hypersonic vehicle. This theory has been successfully applied to the design of the HIFiRE 4 flight experiment vehicle

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[63], which was successfully tested on the flight Mach number 8 in July 2017 [64]. As shown in

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Fig. 12, the fuselage of the HIFiRE 4 flight experiment vehicle is a truncated osculating cone waverider. The basic concept of the osculating cone design theory is as follows: the 3D flows designed by the osculating cone theory can be approximated locally by applying a conical flow in every osculating plane; in other words, a 3D flow with specific properties is constructed using

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conical flow, which is easy to solve, and specific properties of the constructed flow are obtained by the osculating cone theory. In detail, under the assumption that lateral flow is neglected or that lateral flow is too small to be considered, the 3D supersonic flow constructed by the osculating

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cone theory can be approximated with two-order accuracy by applying the conical flow in the

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local osculating plane; this greatly reduces the computational time of the 3D flow field used as the basic flow field of a waverider forebody. Further, the design basis for the osculating cone waverider forebody is the design of a 3D flow field according to the osculating cone theory. Because of application of this theory, the shock wave profile of the bottom cross-section of the waverider forebody is no longer limited to an arc or a straight line; instead, it can be rationally designed according to the shape of the inlet lip. The use of this theory greatly expands the design space and application range of the waverider forebody.

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ACCEPTED MANUSCRIPT Fig. 13(a) illustrates an osculating plane that is normal to the design shock wave curve at point Pi,4, and Fig. 13(b) illustrates the conical flow field in an osculating plane. The design Mach number and shock wave angle, which define the locally conical flow, are required to be

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maintained constant in each osculating plane to prevent pressure gradients in the spanwise direction. The base radius of the locally conical flow equals the local curvature radius of the shock wave curve. The vertex of the conical flow in each osculating plane is determined by the local

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curvature radius as well as the design shock wave angle. The design shock wave curve is chosen

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such that the variation in the curvature radius is continuous along the curve, and a series of osculating planes are constructed along the design shock wave curve to fully define the flow field [65][67][68][69].

Takashima and Lewis [70], O’Brien[71], O’Brien and Lewis [72][73] used the

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osculating cone waverider forebody as the first stage precompression surface of an integrated vehicle, and developed osculating cone waverider forebody/inlet integration. As the geometry of the middle region of the osculating cone waverider forebody has similar characteristics to that of

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the wedge-derived waverider forebody, the flow field uniformity of the inlet has been improved.

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In addition, as the geometry on both sides of the osculating cone waverider forebody has similar characteristics as the cone-derived waverider forebody, the volumetric efficiency of the forebody has been improved.

To further improve the ability of the waverider forebody to precompress air flow into the

inlet of an integrated vehicle, a design method of a multistage compression waverider forebody was developed by Lyu and Wang [74], and Wang et al. [76], from the Nanjing University of Aeronautics and Astronautics, in 2015 and 2016, respectively. According to the conical flow field

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ACCEPTED MANUSCRIPT theory and the osculating cone design theory, a waverider forebody configuration with multiple compression ramps was obtained by the streamline tracing method. The basic flow field with three-stage compression ramps used in Lyu and Wang’s waverider forebody design [74] is shown

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in Fig. 14, and the designed three-stage compression cone-derived waverider forebody and three-stage compression osculating-cone-derived waverider forebody are shown in Fig. 15(a) and Fig. 15(b), respectively. The basic flow field with two-stage compression ramps used in the design

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and study of the multistage compression waverider forebody/inlet integration by Wang et al. [76]

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is shown in Fig. 16, and the integration configuration is shown in Fig. 17.

In order to achieve better compression efficiency than the 2D ramps and larger capture area than the axisymmetric inlet, an osculating cone waverider aircraft integrated with an external inlet compression system (a two stage compression inlet system) was developed by Kontogiannis

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et al. [75] from the University of Southampton in 2016. In the design of Kontogiannis et al., as shown in Fig. 18, an osculating cone waverider forebody is designed as the first stage precompression surface of a mixed compression inlet system, and then another osculating cone

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waverider located on the the underside of the waverider forebody is utilized as the second stage

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compression surface before the inlet cowl. Both the two osculating cone waveriders make up the external inlet compression system of the integrated aircraft.

2.2.2.

Osculating axisymmetric waverider forebody/inlet integration The osculating axisymmetric design theory is an extension of the osculating cone design

theory developed by Sobieczky et al. [55][56] in 1997 and 1999. The 3D flows designed by the osculating axisymmetric theory can be approximated locally by applying a type of axisymmetric

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ACCEPTED MANUSCRIPT flow in each osculating plane. In other words, the basic flow field in the osculating plane is no longer limited to the conical flow; rather it is an appropriate axisymmetric flow field that meets design requirements. The basic flow field in each osculating plane can be scaled by the same

the shock wave profile of the bottom cross-section of the waverider.

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axisymmetric basic flow field model, and the scaling ratio is determined by the curvature radius of

Wang and Qian [77] from the Beijing University of Aeronautics and Astronautics

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performed a comparison study of three types of waverider forebodies: those derived using the

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conical flow field theory, osculating cone design theory, and osculating axisymmetric design theory. Their study results showed that the design method of using the conical flow field theory is relatively simple and it provides a high lift-to-drag ratio, but the inlet flow field is not quite uniform; thus, this approach is not beneficial for the engine and forebody/inlet integration. In

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contrast, application of both the osculating cone design theory and the osculating axisymmetric design theory can generate waverider forebodies that are more universal and improve the inlet flow field quality. Additionally, all three design methods have a high computational speed, which

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is quite promising for the subsequent integration design and optimization process.

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In the study of He et al. [18][78], they used, in each osculating plane, a curved conical flow around a concave curved cone consisting of a straight shock wave along with a group of isentropic compression waves as the basic flow field and developed an osculating curved-cone-derived waverider forebody/inlet integration. They then verified this waverider design method via numerical simulation [18]. and subsequently compared and analyzed both the osculating curved-cone-derived waverider forebody and the osculating cone-derived waverider forebody. The study showed that the osculating curved-cone-derived waverider forebody

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ACCEPTED MANUSCRIPT successfully overcomes the shortcoming of insufficient compression of air flow at the exit cross-section of the waverider forebody and also provides an obviously improved volumetric efficiency in comparison to the osculating cone-derived waverider forebody.

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Subsequently, He et al. [79][80][81] used the inward-turning cone flow with a straight shock wave as the basic flow to develop the osculating inward-turning cone waverider forebody/inlet integration (OIC waveriders for short); the basic flow field structure in each

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osculating plane is shown in Fig. 19, and the typical configuration of this kind of integration

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vehicle is shown in Fig. 20. Numerical and experimental studies of this kind of waverider forebody/inlet integration were conducted under both design and off-design conditions. The results indicated that this kind of waverider forebody has small flow spillage under both design and off-design conditions.

Osculating flow field waverider forebody/inlet integration

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2.2.3.

(1) Rodi’s osculating flow field waverider forebody/inlet integration The osculating flow field design theory was first proposed by Rodi [57][59][60][61][62]

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from the American Lockheed Martin Corporation. It is an extension of the osculating cone and

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osculating axisymmetric design theories: the basic flow field in each osculating plane is no longer confined to the same axisymmetric flow field; rather, different axisymmetric flow fields can be chosen in each osculating plane according to the design requirements. Fig. 21 shows the basic flow field with an external compression shock wave in an osculating plane used in Rodi’s osculating flow field design theory. As shown in Fig. 21, the local air properties just downstream of the leading-edge shock wave are calculated using the initial flow turning angle for the given osculating plane using Rankine-Hugoniot equations. Downstream of the leading-edge shock wave,

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A preliminary study [57] showed that the waverider forebody/inlet integration vehicle derived from the osculating flow field theory has the following advantages over those derived from the osculating cone theory: (1) reduced trim drag through an improved streamwise lift

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distribution, (2) an increased vehicle volume for a given aerodynamic performance, (3) a forward

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shift in the center-of-mass position, (4) reduced viscous drag through delayed boundary-layer transition, and (5) an improved aft body close-out geometry.

A further study [58] showed that for a given volumetric efficiency under a design Mach number of 16.0, the waverider forebody derived from the osculating flow field theory shows up to

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a 7% increase in the inviscid lift-to-drag ratio over the waverider forebody derived from the osculating cone theory, and this increase percentage improves with a decrease in the design Mach number.

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Another study showed [61] that the hypersonic air-breathing vehicle created using

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waverider forebodies generated from the osculating flow field theory can include multiple characteristics favorable for the integration of the air-breathing propulsion systems. A preliminary examination of integration using such waverider forebodies, directed towards cruise aircraft applications, has been performed. A range of waverider forebodies are introduced to demonstrate the flexibility and utility of the osculating flow field theory in this integration application. Such vehicles have been analyzed to quantify the potential for both propulsion and aerodynamic performance improvements when using osculating flow field theory. The results showed that the

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ACCEPTED MANUSCRIPT waverider forebody/inlet integration vehicle derived from the osculating flow field theory shows up to a 15% increase in the propulsion efficiency, a 3% increase in the lift-to-drag ratio, and a 18.5% increase in the flying range compared to the integration vehicle derived from the osculating

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cone theory. (2) You’s internal and external dual waverider forebody/inlet integration

Unlike Rodi’s osculating flow field theory, which is limited to the basic flow field with

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an external compression shock wave, a new osculating flow field theory developed by You et al.

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[82] from the Nanjing University of Aeronautics and Astronautics, can combine the basic flow field with an external compression shock wave with that with an internal contraction shock wave; this new theory was termed the internal and external dual waverider forebody/inlet integration design concept (dual waverider design concept for short). Through the design of a unique inlet lip

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shock wave with a continuously changing curvature in the spanwise direction, the basic flow field in the osculating plane can be continuously transferred from the internal contraction shock wave on the forebody’s inner side to the external compression shock wave on the forebody’s outer side.

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Thus, two completely different basic flow fields—the inner-side basic flow field with an internal

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contraction shock wave and the outer-side basic flow field with an external compression shock wave—are closely and effectively combined. The internal contraction shock wave can be used to design the internal waverider forebody as the precompression surface to provide high-efficiency compression air flow for the engine, and the external compression shock wave can be used to design the external waverider forebody as the lift surface to provide a high lift-to-drag ratio for the airframe; the internal waverider forebody and the external waverider forebody together constitute the dual waverider forebody. As shown in Fig. 22 of the schematic representation of the dual

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ACCEPTED MANUSCRIPT waverider design concept, at any cross-section before the inlet lip, the forebody’s inner side rides on the internal contraction shock wave, i.e., the internal waverider forebody, and the forebody’s outer side rides on the external compression shock wave, i.e., the external waverider forebody.

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The two aerodynamic configurations of the dual waverider forebody/inlet integration vehicles with a single flowpath studied by You et al. [82] and with double flowpaths studied by Li et al. [83] are shown in Fig. 23 and Fig. 24, respectively.

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The design concept of the dual waverider has greatly expanded the scope of the

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osculating flow field design theory. Although the volumetric efficiency and the lift-to-drag ratio of the dual waverider forebody/inlet integration configuration are still worthy of examination and study, it is an ideal design method for the concept of combined internal and external waverider forebodies.

2.3.1.

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2.3. Other combination design methods

Star-shaped waverider forebody/inlet integration Ostapenko and Zubin et al. [84]-[89] from the Sussian Moscow State University

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combined several V-shaped wings (i.e. “Λ” waveriders) along the circumference and designed a

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pyramidal body with a star-shaped cross-section, which is termed the star-shaped body, the star-body waverider, or the star-shaped waverider. The star-shaped waverider with four petals (i.e. four V-shaped wings) are shown in Fig. 25. Both the theoretical and experimental results indicated that the star-shaped waverider has a much lower wave drag than the body of revolution of the equivalent length and midsection area [87][90]. The marked reduction of the wave drag is explained physically by the formation of a system of weak shocks which arise from the star-shaped body in place of the strong axisymmetric wave which arises from the body of

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ACCEPTED MANUSCRIPT revolution [92]. Thus, the star-shaped waveriders can be regarded as promising supersonic and hypersonic flight vehicles because of the low drag and high lift-to-drag ratio [86]. Subsequently, Ferguson et al. [93]-[99] used the star-shaped waverider as the forebody

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of the vehicle, and developed a family of hypersonic slender vehicles integrated with a scramjet. Fig. 26(a) shows the flow model of this kind of vehicle, and Fig. 26(b), (c) and (d) shows three kinds of star-shaped waverider forebody/inlet integrated configurations. As shown in Fig. 26(b), (c)

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and (d), they are composed of four, five, and six “Λ” waveriders, respectively, so they are named

2.3.2.

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the four-point, five-point and six-point star-shaped waverider forebody/inlet integration. Geometric transition waverider forebody/inlet integration

Nan et al. [100] from Nanjing University of Aeronautics and Astronautics refered to the Falcon hypersonic cruise vehicle (HCV) [101][102] jointly developed by the Defense Advanced

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Research Projects Agency (DARPA) and the United States Air Force, and developed the geometric transition waverider forebody/inlet integration. A pair of inward-turning inlets are placed on both sides of the osculating cone waverider forebody, and then the inlet surface and the forebody

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surface are connected by a simple transition surface. This type of integrated vehicle configuration

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through the geometric transition method is shown in Fig. 27. Although the integration of the forebody and the inlets is to achieve through the geometric transition method, but the numerical results showed that at any cross-section before the lip, the forebody’s outer side rides on the internal contraction shock wave, and the forebody’s inner side rides on the external compression shock wave. 2.3.3.

Double-flanking waverider forebody/inlet integration To meet the design requirements of a high lift-to-drag ratio and high volumetric

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ACCEPTED MANUSCRIPT efficiency of an integrated hypersonic airplane, a type of hypersonic airplane configuration with double-flanking waverider forebody integrated with double-flanking air inlets was proposed by Cui et al. [103] from the Chinese Academy of Sciences, and the design method of a

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double-flanking waverider forebody, which entailed rotation and assembling of two waverider-based surfaces, was first introduced. The geometric model of the double-flanking waverider forebody is shown in Fig. 28, and the design example of double-flanking waverider

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forebody/inlet integration vehicle is shown in Fig. 29. It is worth noting that the double-flanking

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waverider concept of Cui et al. [103] differs from the above-described dual waverider concept of You et al. [82]. The former concept is that both the left and right sides of the forebody ride on the shock wave; the latter concept is that the forebody’s inner side rides on the internal contraction shock wave, i.e., the internal waverider, and the forebody’s outer side rides on the external

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compression shock wave, i.e., the external waverider, and the internal waverider and external waverider together constitute the dual waverider. 2.3.4.

Wide-speed morphable waverider forebody/inlet integration

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A morphable waverider design method used for the wide-speed vehicle was proposed by

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Maxwell [104][105][106] from the US Naval Research Laboratory. This method attempts to achieve on-design waverider performance across a range of speeds by maintaining shock wave attachment through morphing the waverider’s lower stream surface as well as maintaining a fixed leading edge and upper surface of the waverider. Subsequenlty, Phoenix and Maxwell [107][108] evaluated the complexity, accuracy and structure of the morphing system required to enable a high-performance morphing waverider. Next, Goodwin and Maxwell [109][110] applied this morphable waverider design theory

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ACCEPTED MANUSCRIPT to develop a wide-speed morphable waverider forebody/inlet integration. As shown in Fig. 30, the lower surface of the waverider forebody under the different flight Mach number is different, but the leading edge is fixed. The research results showed that the morphable waverider forebody/inlet

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scramjet is capable of significantly higher performance than the traditional rigid planar inlet scramjet across a broad range of flight conditions.

Waverider airframe/inlet integration design methodology

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3.

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Based on the above waverider forebody/inlet integration, other researchers studied airframe/inlet integration when the waverider design was used as the basis for the design of the entire air-breathing hypersonic vehicle.

3.1. Basic-flow-field-containment waverider airframe/inlet integration

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O’Neill and Lewis [2][111] from University of Maryland, and O’Neill [1] developed a series of air-breathing hypersonic integration vehicle using the basic-flow-field-containment method, and the generated integration vehicle configuration is shown in Fig. 31 (a). Their design

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idea is to take the forebody, wedge-surface, and inlet wrapped with a conical shock wave as shown

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in Fig. 31 (b), and the entire vehicle rides on the conical shock wave, causing the conical shock wave to remain attached to the leading edge for the entire length of the vehicle. Thus, this type of method is named the cone-derived waverider airframe/inlet integration wrapped by conical shock wave.

As shown in Fig. 32, Tapley [112], and Tapley and Lewis [113] arranged the engine on the underside of the wedge-derived waverider airframe, and developed the wedge-derived waverider airframe/inlet integration.

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ACCEPTED MANUSCRIPT According to the characteristics of the above two design methods, the two design methods can be summed up as the basic-flow-field-containment waverider airframe/inlet integration method. The expected goal of this method is to take full advantage of the waverider’s

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high lift-to-drag ratio characteristics and the ideal precompression surface for the inlet. However, the engine is arranged on the underside of the airframe by the geometric modification, shown in Fig. 31 (c) and Fig. 32 (b), which partly destroys the waverider characteristics, i.e., this type of

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design method cannot take full advantage of the waverider characteristics.

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3.2. Basic-flow-field-intersection waverider airframe/inlet integration

Smith and Bowcutt [114] from the Boeing Company used the intersection line of the external compression conical shock wave and the internal compression conical shock wave as the common segment of the leading-edge curve of the airframe and the leading-edge curve of the inlet,

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and developed the integration design method of the waverider airframe and the inward-turning inlet. As the two leading-edge curves are connected by a common section, the waverider airframe and the inward-turning inlet can be better integrated. According to the characteristics of this type

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of integration design method, it can be termed basic-flow-field-intersection waverider

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airframe/inlet integration, and this type of integration design method is shown in Fig. 33. 3.3. Geometric fusion waverider airframe/inlet integration As Bowcutt et al. [115] discussed, in order to enable the generation of a more complex

hypersonic vehicle configuration incorporating the advanced high-performance 3D aerodynamic and propulsion flowpath shapes, the integration design method of the waverider airframe and the inward-turning inlet has become a kind of research hotspot. Zuo and Huang et al. [116][117], and Wang and Cai [118] has done a lot of research on

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ACCEPTED MANUSCRIPT the design principles and the engineering applications of the inward-turning inlet, especially the application of the variable-geometry design to the inward-turning inlet for the wide-speed flight range [119][120]. As shown in Fig. 33, the strategy of enlarging throat is to rotate the moveable

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inlet surface around the rotating shaft. Referring to another hypersonic cruise vehicle (HTV-3X) from the Falcon program of the United States [121], in 2013, Tian et al. [122] from Beihang University realized an integration

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design method of the waverider airframe and double inward-turning inlets by the geometric fusion

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method, which can be termed the geometric fusion waverider airframe/inlet integration, and then modified and optimized the integration design through the parametric method. The designed integration vehicle configuration is shown in Fig. 35.

In 2017, Xiang et al. [123] used a similar geometric fusion method to achieve a novel

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wide-range adaptable dual-waverider integration which can take into account both the external waverider characteristics of the airframe and the internal waverider characteristics of the 3D inward-turning inlet. In Xiang et al.’s design, as shown in Fig. 36, the airframe is designed as a

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complete waverider, and then double inward-turning inlets are embedded into the upper surface of

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the vehicle rather than the lower surface by the geometric fusion. The advantage of this design is that the external waverider characteristics of the airframe will not be disturbed by the inlet, and the internal waverider characteristics of the 3D inward-turning inlets are not affected by the airframe. In 2015 and 2018, Ferguson et al. [124][125] studied an integrated vehicle with a single

inward-turning inlet embedded into the vehicle head through the geometric fusion method. As shown in Fig. 37, the external configuration was designed for the maximum aerodynamic efficiency, whereas the integrated scramjet engine was designed for efficient mass capture over a

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ACCEPTED MANUSCRIPT wide variety of flight condtions. Because the vehicle is designed to operate in flight regimes ranging from Mach 3 through 6, it is named a Generic Hypersonic Vehicle (GHV). The HIFiRE 6 [126][127] as shown in Fig. 38 is the first flight research vehicle with a highly integrated

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inward-turning inlet, and its integration method is similar to that of Ferguson et al. [124][125].

3.4. Full-waverider airframe/inlet integration

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With the aim of integrating a ramjet or scramjet with an airframe, an airframe/inlet

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integration method for the hypersonic waverider vehicle was proposed by Ding and Liu et al. [3] from National University of Defense Technology in Chinese. In Ding and Liu et al.’s work, a novel airframe/inlet-integrated axisymmetric basic flow model (as shown in Fig. 39 (a)) that accounts for both external and internal flows was first designed using the method of characteristics

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and the streamline tracing technique. Subsequently, the design of the waverider airframe/inlet integration vehicle is generated from the integrated axisymmetric basic flow model using the streamline tracing technique. The isentropic and the rear views of the integrated waverider vehicle

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and the bow shock wave of the basic flow model are shown in Fig. 39 (b) and (c), respectively.

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The obtained numerical results showed that this proposed approach is effective in designing this type of integrated hypersonic waverider vehicle. For the specified flight conditions, not only the forebody of the vehicle but also its engine cowl and wings can ride on the bow shock wave, causing the bow shock wave to remain attached to the leading edge for the entire length of the vehicle. Thus, this integrated vehicle can take full advantage of the waverider’s high lift-to-drag ratio characteristics and the ideal precompression surface for the engine. According to the above two waverider characteristics, this type of integrated vehicle method can be termed as the

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ACCEPTED MANUSCRIPT full-waverider airframe/inlet integration method.

4.

Conclusions: development trend analysis The following trends can be identified from a review of developments of the waverider

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applications in the airframe/inlet integration methodology for the air-breathing hypersonic vehicles made by local and foreign scholars.

(1) The general concept for the design of a waverider-derived air-breathing hypersonic

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vehicle is to design the waverider vehicle in the flow direction through the design of the basic

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flow field and to apply the osculating cone theory to design the waverider vehicle in the spanwise direction.

(2) The basic flow field for the design of the air-breathing hypersonic waverider vehicles is no longer confined to a conical flow field with a straight shock wave but is instead

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further extended to an axisymmetric flow field with a curved shock wave. Through application of the osculating axisymmetric design theory and the osculating flow field design theory, the basic flow field can be extended to a more complicated, 3D nonaxisymmetric flow field.

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(3) In the aerodynamic configuration design of the air-breathing hypersonic waverider

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vehicle, the studies of the waverider forebody/inlet integration design method have been further developed, involving most types of basic flow fields and waverider design methods, and some configurations with excellent aerodynamic performances have been obtained. (4) As the shock wave characteristics in the inner flow field of the inlet are obviously

different from those in the outer flow field of the waverider airframe, there are still great difficulties for the integration design of the airframe and inlet. Studies on the waverider airframe/inlet integration design method are at the preliminary stage of development, and the

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ACCEPTED MANUSCRIPT current

design

methods

are

more

of

some

combination

methods,

such

as

the

basic-flow-field-containment method, basic-flow-field-intersection method, and geometric fusion method, et al. There has not been a perfect theoretical system of the waverider airframe/inlet

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integration design method similar to the waverider forebody/inlet integration design method. The designers are still looking for more flexible and useful design methods for the design of the waverider airframe/inlet integration.

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Conflict of interest statement

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The authors declare that they have no conflict of interest.

Acknowledgements

The authors would like to express their gratitude for the financial support provided by the National Natural Science Foundation of China (grant number 11702322) and the Natural Science

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Foundation of Hunan Province of China (grant number 2018JJ3589). The authors are also grateful to the reviewers for their extremely constructive comments.

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star-shaped bodies at supersonic velocities. Fluid Dynamics, 1971, 6(1): 86-89. [92] A.L. Gonor, A.I. Shvets. Study of the shock system for flow past star-shaped bodies. Fluid Dynamics, 1966, 1(3): 65-67.

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atmospheric entry [R]. AIAA Paper 2017-5357, 2017. [107] G.B. Goodwin, J.R. Maxwell. Performance analysis of a hypersonic scramjet engine with a morphable waverider inlet [R]. AIAA Paper 2017-4651, 2017.

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Paper 2017-1385, 2017.

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morphable waverider inlet [R]. AIAA Paper 2017-4651, 2017.

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flight and static margin constraints. College Park, MD: University of Maryland College Park (Ph.D.), 1995.

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ACCEPTED MANUSCRIPT mutidisciplinary design optimization applied to hypersonic vehicles to achieve closure [R]. AIAA Paper 2008-2591, 2008. [116] F.-y. Zuo, G.-p. Huang. A preliminary overview analysis on the internal waverider inlets for

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ramjet [R]. AIAA Paper 2017-2420, 2017. [117] G.-p. Huang, F.-y. Zuo, W.-y. Qiao, C. Xia. Design method of internal waverider inlet with bump compression surface [R]. AIAA Paper 2017-4654, 2017.

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[118] J.-f. Wang, J.-s. Cai. Multistage optimization applied to the hypersonic inward turning inlet

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design [R]. AIAA Paper 2016-1019, 2016.

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internal waverider concept [R]. AIAA Paper 2017.

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[122] C. Tian, N. Li, G.H. Gong, Z.Y. Su. A parameterized geometry design method for inward

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turning inlet compatible waverider. Chinese Journal of Aeronautics, 2013, 26(5): 1135-1146. [123] X.-h. Xiang, Y. Liu, Z.-s. Qian. Investigation of a wide range adaptable hyersonic dual-waverider integrative design method based on two different types of 3D inward-turning inlets [R]. AIAA Paper 2017-2110, 2017.

[124] F. Ferguson, N. Dasque, H. Mrema, J.P. Kizito. A coupled aerodynamic and propulsive performance analysis of a generic hypersonic vehicle [R]. AIAA Paper 2015-3839, 2015. [125] F. Ferguson, N. Dasque, M. Dhanasar, L. Uitenham. An aerodynamic analysis of the generic

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ACCEPTED MANUSCRIPT hypersonic vehicle [R]. AIAA Paper 2018-0637, 2018. [126] N.J. Bisek. High-fidelity simulations of the HIFiRE-6 flow path [R]. AIAA Paper 2016-1115, 2016.

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update 2015 [R]. AIAA Paper 2015-3537, 2015.

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[127] B.H. Dauby, D.W. Adamczak, J.A. Muse, M.A. Bolender. HIFiRE 6: overview and status

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Figure captions Fig. 1. Waverider forebody used as first-stage precompression surface [17]. Fig. 2. Waverider forebody used as whole precompression surface [18].

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Fig. 3. Wedge-derived waverider (“Λ” waverider) [19]. Fig. 4. V-shaped wing [27].

Fig. 6. Boeing X-51A WaveRider scramjet demonstrator [31].

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Fig. 7. Wedge-derived waverider with variable wedge angle [34].

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Fig. 5. Power-law-shaped waverider [30].

Fig. 8. Waverider generated from 2D curved compression flow field [35]. Fig. 9. Basic flow field of 2D curved surface-compression flow [36].

Fig. 10. 2D curved surface-compression waverider forebody/inlet integration configuration [36].

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Fig. 11. Wedge-cone generating body and pressure contours around the body [52]. Fig. 12. Three-view of HIFiRE 4 flight experiment vehicle with osculating cone waverider fuselage [63].

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Fig. 13. Schematic illustration of osculating cone theory [65]. Fig. 14. Schematic illustration of basic flow field of multistage compression waverider with three-stage

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compression ramps [74].

Fig. 15. Geometric models of three-stage compression cone-derived waverider and three-stage compression osculating-cone-derived waverider [74]. Fig. 16. Schematic illustration of basic flow field of multistage compression waverider with two-stage compression ramps [76]. Fig. 17. Three-stage compression osculating-cone-derived waverider forebody/inlet integration configuration [76].

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ACCEPTED MANUSCRIPT Fig. 18. Osculating cone waverider aircraft integrated with an external inlet compression system (i.e., two stage osculating waverider compression surfaces) [75]. Fig. 19. Basic inward-turning cone flow field structure in osculating plane [79].

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Fig. 20. Osculating inward-turning cone waverider/inlet integrated vehicle [79]. Fig. 21. Rodi’s basic flow field with an external compression shock wave in an osculating plane [61]. Fig. 22. Schematic representation of dual waverider [82].

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Fig. 23. Dual waverider forebody/inlet integrated vehicle with single flowpath [82].

Fig. 25. Star-shaped body with four petals [91].

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Fig. 24. Dual waverider forebody/inlet integrated vehicle with double flowpaths [83].

Fig. 26. Design principle and configuration of star-shaped waverider forebody/inlet integration [94]. Fig. 27. Configuration of geometric transition waverider forebody/inlet integration [100].

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Fig. 28. Double-flanking waverider forebody [103].

Fig. 29. Design example of double-flanking waverider forebody/inlet integration vehicle [103].

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Fig. 30. A wide-speed morphable waverider forebody/inlet integration [107]. Fig. 31. Cone-derived waverider airframe/inlet integration wrapped by conical shock wave [1].

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Fig. 32. Wedge-derived waverider airframe/inlet integration [112]. Fig. 33. Schematic representation of basic-flow-field-intersection waverider airframe/inlet integration [114]. Fig. 34. Variable-geometry scheme for inward-turning inlet [120]. Fig. 35. Configuration of geometric fusion waverider airframe/inlet integration [122]. Fig. 36. Configuration of wide-range adaptable dual-waverider integration by use of geometric fusion method [123]. Fig. 37. Generic hypersonic vehicle integrated with a single inward-turning inlet [125]. 41

ACCEPTED MANUSCRIPT Fig. 38. HIFiRE 6 Flight Vehicle integrated with inward-turning inlet [127].

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Fig. 39. Schematic representation of integrated waverider vehicle and axisymmetric basic flow model [3].

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Fig. 1. Waverider forebody used as first-stage precompression surface [17].

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Fig. 2. Waverider forebody used as whole precompression surface [18].

(a) Type 1

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(b) Type 2

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Fig. 3. Wedge-derived waverider (“Λ” waverider) [19].

Fig. 4. V-shaped wing [27].

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Fig. 5. Power-law-shaped waverider [30].

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Fig. 6. Boeing X-51A WaveRider scramjet demonstrator [31].

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Fig. 7. Wedge-derived waverider with variable wedge angle [34].

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Fig. 8. Waverider generated from 2D curved compression flow field [35].

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Fig. 9. Basic flow field of 2D curved surface-compression flow [36].

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Fig. 10. 2D curved surface-compression waverider forebody/inlet integration configuration [36].

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Fig. 11. Wedge-cone generating body and pressure contours around the body [52].

Fig. 12. Three-view of HIFiRE 4 flight experiment vehicle with osculating cone waverider fuselage [63].

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(b) Osculating plane (plane AA′)

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(a) Base plane of waverider

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Fig. 13. Schematic illustration of osculating cone theory [65].

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Third generating cone

Fig. 14. Schematic illustration of basic flow field of multistage compression waverider with three-stage compression ramps [74].

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(b) Three-stage compression osculating-cone-derived waverider

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(a) Three-stage compression cone-derived waverider

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Fig. 15. Geometric models of three-stage compression cone-derived waverider and three-stage compression

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osculating-cone-derived waverider [74].

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compression ramps [76].

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Fig. 16. Schematic illustration of basic flow field of multistage compression waverider with two-stage

(a) Side view.

(b) Perspective view. Fig. 17. Three-stage compression osculating-cone-derived waverider forebody/inlet integration configuration [76]. 49

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Fig. 18. Osculating cone waverider aircraft integrated with an external inlet compression system (i.e., two stage

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osculating waverider compression surfaces) [75].

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Fig. 19. Basic inward-turning cone flow field structure in osculating plane [79].

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Fig. 20. Osculating inward-turning cone waverider/inlet integrated vehicle [79].

Fig. 21. Rodi’s basic flow field with an external compression shock wave in an osculating plane [61].

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Fig. 22. Schematic representation of dual waverider [82].

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Fig. 23. Dual waverider forebody/inlet integrated vehicle with single flowpath [82].

Fig. 24. Dual waverider forebody/inlet integrated vehicle with double flowpaths [83].

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Fig. 25. Star-shaped body with four petals [91].

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(a) A 2D centerline cross-section of star-shaped waverider forebody/inlet integrated configuration

(b) Four-point star-shaped waverider forebody/inlet integrated configuration

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(c) Five-point star-shaped waverider forebody/inlet integrated configuration

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(d) Six-point star-shaped waverider forebody/inlet integrated configuration

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Fig. 26. Design principle and configuration of star-shaped waverider forebody/inlet integration [94].

Fig. 27. Configuration of geometric transition waverider forebody/inlet integration [100].

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Fig. 28. Double-flanking waverider forebody [103].

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Fig. 29. Design example of double-flanking waverider forebody/inlet integration vehicle [103].

(a) Morphable Cone-derived waverider

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(b) Cross-section at inlet lip

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(a) Configuration view.

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Fig. 30. A wide-speed morphable waverider forebody/inlet integration [107].

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(b) Schematic representation of integration principle.

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Engine box

Element Shock wave

(c) Arrangement position of engine boxes in waverider airframe.

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(a) Configuration view.

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Fig. 31. Cone-derived waverider airframe/inlet integration wrapped by conical shock wave [1].

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Inlet surface

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Nozzle Surface

Start of inlet Cowl leading edge End of inlet Cowl trailing edge (b) Arrangement position of engine boxes in waverider airframe. Fig. 32. Wedge-derived waverider airframe/inlet integration [112].

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(b) Schematic 2.

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(a) Schematic 1.

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Fig. 33. Schematic representation of basic-flow-field-intersection waverider airframe/inlet integration [114].

Fig. 34. Variable-geometry scheme for inward-turning inlet [120].

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Fig. 35. Configuration of geometric fusion waverider airframe/inlet integration [122].

Fig. 36. Configuration of wide-range adaptable dual-waverider integration by use of geometric fusion method

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[123].

Fig. 37. Generic hypersonic vehicle integrated with a single inward-turning inlet [125].

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Fig. 38. HIFiRE 6 Flight Vehicle integrated with inward-turning inlet [127].

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(a) Schematic illustration of airframe/inlet integrated axisymmetric basic flow model.

Axisymmetric bow shock Axisymmetric generating body

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M0 > 1, P0, T0

Axis of symmetry

Integrated waverider vehicle Base plane

(b) Isentropic view of integrated waverider vehicle and bow shock wave of basic flow model.

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(c) Rear view of integrated waverider vehicle and bow shock wave of basic flow model.

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Fig. 39. Schematic representation of integrated waverider vehicle and axisymmetric basic flow model [3].

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ACCEPTED MANUSCRIPT Highlights Waverider design concept in airframe/inlet integration is reviewed and classified. Modeling of basic flow field is used to design integration in streamwise direction.

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Osculating theory is used to design integration in spanwise direction.