Waverider Design Research Articles

Variable leading-edge cone method for waverider design

The optimization of the waverider is constrained by the reversely designed leading edge and the constant shock angle distribution. This paper proposes a design method called the variable Leading-Edge Cone (vLEC) method to address these limitations. In the vLEC method, the waverider is directly designed from the preassigned leading edge and the variable shock angle distribution based on the Leading-Edge Cone (LEC) concept. Since the vLEC method is an approximate method, two test waveriders are designed and evaluated using numerical simulations to validate the shock design accuracy and the effectiveness of the vLEC method. The results show that the shocks of the test waveriders coincide well with the preassigned positions. Furthermore, four specifically designed application cases are conducted to analyze the performance benefits of the vLEC waveriders. The results of these cases indicate that, due to their variable shock angle distributions, the vLEC waveriders exhibit higher lift-to-drag ratios and better longitudinal static stability than conventional waveriders. Additionally, the vLEC waveriders demonstrate superior volumetric capacities near the symmetry plane, albeit with a minor decrease in volumetric efficiency.

Waverider Design Using Osculating Method

Because of the requirements of payload capability, flight range, and maneuverability, hypersonic aircraft demand high aerodynamic performance. Waveriders have attracted significant attention because of their high lift-to-drag ratios in hypersonic states. Many methods to design waveriders have been proposed for more than 60 years, among which the osculating method features unique advantages in terms of design space, efficiency, and flexibility. Moreover, nearly all waverider design methods can be realized using this approach. This paper presents an overview of research on waverider design methodologies using osculating theory developed until 2023. The design theory and detailed implementation of the osculating cone method are first described, followed by the progress and improvement of the method and the derived osculating flowfield method. The planform-customized waverider from the osculating cone method, which has developed rapidly in recent years, is discussed emphatically. In addition, the connection between the osculating cone and other waverider design methods is plotted to show its powerful applicability. The application of the osculating waverider in practical aircraft design is also summarized. Finally, some perspectives and suggestions for future development are concluded.

Stream-Surface Iteration-Based Flowfield Calculation Method for Pressure-Controllable Waverider Design

The performance of waveriders is greatly influenced by the wall pressure distribution. To achieve the goal of designing a waverider based on the complex two-dimensional pressure distribution, this study proposes a methodology called the stream-surface iteration-based flowfield calculation (SIFC) method. This method discretizes the three-dimensional flowfield with curved stream surfaces and approximates the flow around each point with a unique axisymmetric flow. Moreover, this method iteratively solves the shape of each stream surface and the corresponding flowfield to deal with ill-posed problems. To verify its effectiveness, the SIFC method was first applied to inversely solve the two external annular supersonic flowfields. Then, it was used for the waverider design. The computational fluid dynamics results showed that the relative error of the wall pressure was less than 2.6% for the annular supersonic flowfields. The wall pressure determines the geometric shapes and mechanical properties of waveriders. The pressure center of a waverider can be shifted by 12% of the length in the flow direction and 7.4% of the width in the crossflow direction by altering the input wall pressure. This shift will cause the waverider to produce more than 30% extra trim drag when cruising at the design Mach number.

Aerodynamic analysis of an airframe-inlet integrated full-waverider vehicle designed by osculating cone theory

Recently proposed, the airframe/inlet integrated full-waverider vehicle design methodology introduces an innovative approach to the design of air-breathing hypersonic vehicles. This methodology, compared to traditional integrated waverider design methods, leverages the features of the waverider to enhance the compression ability of the precompression surface and the lift-to-drag ratio characteristics of the vehicle. However, existing full-waverider design methods, based on cone-derived waverider theory, result in a gas cross-flow phenomenon at the inlet lip due to the conical shockwave. This paper suggests an airframe/inlet integrated full-waverider vehicle design method that utilizes the osculating cone waverider theory to improve gas intake quality. Initially, we present the method to obtain profile lines and basic flow field models at different osculating planes of the vehicle. We then validate the osculating cone integrated full-waverider vehicle design methodology through computational fluid dynamics. Although the viscous effect slightly reduces the lift-to-drag ratio of the vehicle and the total pressure recovery coefficient at the isolator exit, the shock wave remains attached to the leading-edge. Finally, a comparison with the cone-derived integrated full-waverider vehicle reveals that the osculating cone integrated full-waverider vehicle achieves similar aerodynamic performance, but with superior gas intake quality. The results indicate that the methodology proposed herein holds promise for guiding future engineering applications of integrated full-waverider vehicles.

Experimental Investigation for Subsonic, Transonic, and Supersonic Performances of Double-Swept Waverider

The wind-tunnel experiments for the double-swept waverider were carried out in subsonic, transonic, and supersonic states, aiming to validate its potential advantages in wide-speed performances. The test configurations were generated using the planform-customized waverider design, which was developed from the osculating-cone method. Two experimental models of the double-swept waveriders with bend and cusp heads were fabricated, and a single-swept configuration was built as a comparable model. A series of experiments were performed in the FD-06 wind tunnel of the China Academy of Aerospace Aerodynamics at a subsonic Mach number of ; transonic Mach numbers of , 0.8, and 0.9; and a supersonic Mach number of . The results from the wind-tunnel tests were examined by combining the numerical simulations. As the Mach number increased, the lift-to-drag () ratios of the double-swept waveriders decreased slightly when ; but when , their dropped sharply. Moreover, the double-swept waveriders were unstable in the longitudinal direction in the subsonic state, and their longitudinal stability was obviously improved as the Mach number went up. When the Mach number was greater than 0.9, they became statically stable. Compared with the single configuration, the double-swept waverider exhibited increased in subsonic and transonic states, as well as improved longitudinal stability in the wide-speed range, but it exhibited a decreased in the supersonic state.

Influence of Non-Uniform Bluntness on Aerodynamic Performance and Aerothermal Characteristics of Waverider

The waverider is widely used in hypersonic vehicles with its high aerodynamic performance, but due to the serious aerothermal environment, its sharp leading edge should be blunted. Circular blunt is one of the commonly used aerothermal characteristic protection methods. Circular blunt with larger diameter can reduce peak heat flux, but at the same time, it will lead to larger drag. The existing research shows that under the same blunt diameter in two-dimensions, the non-uniform blunt can reduce the peak heat flux by 20%, and the difference of drag is small. In this paper, the non-uniform blunt profile is applied to the three-dimensional waverider, and the influence of the non-uniform blunt profile on the aerothermal characteristic performance and aerodynamic performance of the waverider is studied, and the results are compared with those of circular blunt. The numerical simulation is used to compare and analyze the waverider under different angles of attack, flight altitudes, and Mach number. The results show that the peak heat flux of the waverider with non-uniform blunt reduces by about 17% compared with that with circular blunt under a small angle of attack range, Mach 2-10, and a flight altitude of 15–35 km. Meanwhile, when the blunt height/diameter is 20 mm, the aerodynamic performance difference between the two different blunt profiles does not exceed 3% within a 15 degrees angle of attack, Mach 2-10, and flight altitude of 15–35 km. The non-uniform blunt profile can be applied to the design of the three-dimensional waverider.

Artificial neural network-based streamline tracing strategy applied to hypersonic waverider design

Streamline tracing in hypersonic flows is essential for designing a high-performance waverider and intake. Conventionally, the streamline equations are solved after obtaining the velocity field over a basic flow field from simplified flow differential equations or three-dimensional computational fluid dynamics. The hypersonic waverider shape is generated by repeatedly applying the streamline tracing approach along several planes. This approach is computationally expensive for iterative waverider optimization. We provide a novel strategy where an Artificial Neural Network (ANN) is trained to directly predict the streamlines without solving the differential equations. We consider the standard simple cone-derived waverider using Taylor–Maccoll equations for the conical flow field as a template for the study. First, the streamlines from the shock are solved for a wide range of cone angle and Mach number conditions resulting in an extensive database. The streamlines are parameterized by a third-order polynomial, and an ANN is trained to predict the coefficients of the polynomial for arbitrary inputs of Mach number, cone angle, and streamline originating locations. We apply this strategy to design a cone-derived waverider and compare the geometry obtained with the standard conical waverider design method and the simplified waverider design method. The ANN technique is highly accurate, with a difference of 0.68% from the standard method in the coordinates of the waverider. The performance of the three waveriders is compared using Reynolds averaged Navier–Stokes simulations. The ANN-derived waverider does not indicate severe flow spillage at the leading edge. The new ANN-based approach is 20 times faster than the standard method.

Experimental Investigation on Off-Design Performances of Double-Swept Waverider

Wind-tunnel tests of the double-swept waverider were performed in the off-design states, aiming to analyze its potential advantage in wide-speed performances. The test configurations were generated using the planform-customized waverider design, developed from the osculating-cone method. Then models of double-swept waveriders with the bend and cusp head were fabricated, and compared with a model of a single-swept waverider also built using the same method. A variety of experiments in their on-design and off-design states were performed in the hypersonic wind tunnel FD-07 of our institute, and computational fluid dynamics were employed to simulate flowfields as a supplement. According to the wind-tunnel tests and flow simulations, the aerodynamic forces and longitudinal stability were obtained and analyzed. The aerodynamic performance of the double-swept waverider did not fall significantly when deviating from the design states. The general trend was that, as Mach number increased, the lift-to-drag ratios dropped slightly. The double-swept waverider featured large longitudinal stability margin in hypersonic states, and the change in Mach number had little effect on longitudinal stability. Compared with the single configuration, the double-swept waverider suffered a decrease in lift-to-drag ratio, but showed a significant improvement in longitudinal stability.

Inverse Design of Hypersonic Waveriders with Variable Cross-Section Shock Waves

A new inverse design methodology for a variable cross-section shock waverider (VCSW) is proposed to extend the flexibility of waverider design based on the local-turning osculating cones method. The proposed waverider is designed to ride on the top of a variable cross-section shock wave, whose cross-sectional shape is an ellipse with different eccentricity ratios. The feasibility and effectiveness of this method are verified using inviscid computational fluid dynamics simulations. To investigate the influence of the eccentricity ratio on the shape and aerodynamic performance of waveriders, five VCSW cases with different eccentricity ratio distributions are derived and numerically analyzed in detail. The results demonstrate that the VCSW with an increasing eccentricity ratio along the streamwise direction has a larger volumetric efficiency but a smaller lift-to-drag ratio. There is a contradiction between the volumetric and aerodynamic performances, and the tradeoff should be considered in the design process. In addition, the growth rate of the eccentricity ratio along the streamwise direction is also an important factor to design VCSW, which can be used to improve the performance of hypersonic waverider vehicles.

Simulation of high-temperature flowfield around hypersonic waverider using graphics processor units

Provision of flight safety during hypersonic flight is a challenging scientific and technical problem. Waverider concept is based on matching the wing leading edge of the shock formed off the vehicle forebody. A hypersonic vehicle spends the major part of its cruise flight in high temperature flow. Design and optimization of waverider at hypersonic speeds is a challenging problem because a large number of variants are required to be computed to achieve a larger lift-to-drag ratios. Numerical simulation of the flowfield around a hypersonic waverider is performed using a high-temperature air model and a hybrid architecture based on graphics processing units. The mathematical model and computational algorithm are verified and validated against CFD benchmark problems. The results obtained show flowfield around hypersonic waverider and its aerodynamic quality at different angles of attack. The scalability of the developed model is investigated, and the results of the study of the efficiency of calculating hypersonic fluidflows on graphics processors are presented. The computational times achieved with the perfect and real gas models are compared.

Experimental and numerical investigation for hypersonic performance of double swept waverider

The planform-customized waverider developed from the osculating-cone method enables the design of a double swept waverider to remedy some deficiencies for the waverider. To analyze the aerodynamic performances, two models of the double swept waveriders, with cusp head and bend head shape, respectively, were fabricated for the wind-tunnel test, and a single swept waverider model was constructed as the compared configuration. A set of experiments at the design Mach number were performed in the hypersonic wind tunnel FD-07 of our institute. Combining computational fluid dynamics (CFD) simulations, the effect of leading-edge bluntness, the aerodynamic forces and longitudinal stability were studied experimentally and numerically. The bluntness of leading-edge area reduced the lift-to-drag ratio (L/D) significantly. The aerodynamic performances obtained from wind-tunnel tests and CFD simulations were very close, marking a difference in L/D of less than 1% in the design state. The data from both wind-tunnel experiments and CFD simulations implied that the double swept waverider maintained “wave-riding” performance in the hypersonic state, and their longitudinal stability improved dramatically compared with the single swept configuration. The results verified the design method of the double swept waverider and its advantages in aerodynamic performance.

Design and Analysis of Double-Swept Waverider with Wing Dihedral

A waverider design given a three-dimensional leading edge is developed from the osculating-cone method, and double-swept waveriders with wing dihedral were generated by customizing the shape of leading edges. Using computational fluid dynamics, the hypersonic performances of the waveriders were evaluated in the Mach number 5 states with the angle of attack ranging from 0 to and angle of side ranging from to . The effect of the wings with positive and negative dihedral angles, namely, the wing dihedral and anhedral, on the longitudinal, lateral, and directional stability was also studied. Results show that both the dihedral and anhedral made nearly no difference to the wave-riding performance, and hence a high lift-to-drag ratio was maintained in hypersonic state. However, compared with the configuration without wing dihedral and the configuration with a ventral fin, the effects of wing dihedral and anhedral on stabilities were different: wing dihedral reduced the longitudinal stability and improved the lateral and directional stability; wing anhedral improved the longitudinal and directional stability but reduced the lateral stability. Lateral–directional dynamic stability was also predicted. This research proposes an idea to promote the engineering application of waveriders when considering the stability requirements.

Mathematical Expression of Geometric Relationship in Osculating-Cone Waverider Design

Waveriders have a high lift-to-drag ratio in hypersonic states, while the flexibility of design methods must still be improved because of some deficiencies such as unsatisfactory off-design performance and stability. In this paper, a geometric relationship in the osculating-cone method is derived and expressed by a differential equation set including five equations. Then the equation set is simplified into a nonhomogeneous ordinary differential equation set with two variables using the trigonometric identities. Using numerical methods to solve the differential equation set, the planform of a waverider can be predefined, improving the flexibility of waverider design significantly. Two types of configurations aided with cubic polynomials and discrete points were generated to validate the expression. Some novel configurations, such as double swept and with dihedral wings, can be generated. Irregular solutions are also discussed, suggesting that some irregularity of the inlet capture curve is permitted in the osculating-cone method.

Novel Volume-Improved Design Method of Large-Slenderness-Ratio Cone-Derived Waveriders

A novel method is developed to improve the volume performance of large-slenderness-ratio cone-derived waveriders. Under the consideration of space utilization, loading capacity, and upper wall expansion performance, the design method is composed of an improved basic flowfield and a specially designed M-shaped flow capture curve. In addition, an improved evaluation method is proposed to provide a better measurement of volume performance for large-slenderness-ratio waveriders than the conventional method, which can also guide the design of volume-improved waveriders. The volume-improved waveriders and conventional cone-derived waveriders with slenderness ratios of more than nine are designed under the condition of a cruising altitude of 40 km and a Mach number of 12. After investigating their volume and aerodynamic performance, it can be found that the volume-improved waverider can achieve about a 48% volume increment, a 91% effective volume increment, and a four times larger volume growth rate compared to the conventional waverider. Furthermore, the lift-to-drag ratio of the volume-improved waverider is higher than that of the conventional waverider in the inviscid case, whereas it is smaller under the viscous condition. The gap in the viscous lift-to-drag ratio between the two waveriders reduces with the increasing attack of angle and is less than 8% at the design condition.

Design methodology of an osculating cone waverider with adjustable sweep and dihedral angles

When considering the practical engineering application of a waverider, the on-design and off-design aerodynamic characteristics of the design conditions, especially the lift-to-drag ratio and the stability, deserve attention. According to recently studies, the planform and rear sight shape of a waverider are closely related to the above aerodynamic performance. Thus, the planform leading-edge profile curve used to design the planform shape of a vehicle is applied to designing an osculating cone waverider. Two key parameters concerned in planform and rear sight shape, namely the plan view sweep angle of the leading edge and the dihedral angle of the underside are introduced to the waverider design process. Each parameter is inserted in the control curve equation. Especially, a parameterization scheme is put forward for the free adjustment of the sweep angle along the leading edge. Finally, three examples are generated for verification and investigation. After the verification process based on the inviscid flow field of one case, the influences of the sweep and dihedral angles on the lift-to-drag ratio and the lateral static stability are evaluated, and meaningful results are obtained. Based on these results, we can conclude that, considering the maximum lift-to-drag ratio, the sweep angle plays a role on the lift-to-drag ratio only at subsonic and trans/supersonic speed as a negligible effect is observed at hypersonic speeds, whereas the dihedral angle is seem to produce a relevant difference at hypersonic speeds. Considering the lateral static stability, the dihedral angles have more influence on the waverider than the sweep angles.

Alleviation of lateral spillage of two-dimensional hypersonic inlet using waverider-configuration chines

Hypersonic inlet is an important part of the propulsion system of hypersonic air-breathing vehicles. However, the performance of the two-dimensional hypersonic inlet, a major type of hypersonic inlets, is considerably deteriorated for lateral spillage. In this study, waverider-configuration chines mounted on the lateral sides of a two-dimensional three-staged external-compression hypersonic inlet for a Mach number of 6.0 are investigated to determine their ability to alleviate the lateral spillage. The chines are built by using a waverider design method. The numerical results suggest that a severe flow spillage induced by three-dimensional effect shows up near the lateral edge of the inlet without chines, which degrades the mass-flow ratio and flow uniformity. In contrast, the waverider-configuration chines effectively alleviate the lateral spillage. Consequently, the mass-flow ratio and the flow uniformity are both improved significantly.

Local-Turning Osculating Cones Method for Waverider Design

To expand the selection of preassigned shock surfaces, a new inverse design method called the local-turning osculating cones method has been proposed for waverider design. The new method discretizes the three-dimensional preassigned shock surface into a multitude of stream surfaces, which are composed of multiple local osculating planes. The flowfield within each stream surface is computed on the same fictional meridian plane based on a new schematic of method of characteristics. In this way, the constraint of obligating the streamline initiating from the discrete leading edge point to flow within the same osculating plane is removed. Two types of shock waves with distinct three-dimensional characteristics are specified as input to demonstrate the validity of the new proposed method. At the same time, two typical waveriders, which are not easily generated by the past waverider design methods, are derived and validated by the inviscid computational fluid dynamics simulation (Euler code). The results indicate that waveriders based on the new method can successfully reproduce the preassigned shock waves and the original flowfields with errors less than 2%. Thus, the local-turning osculating cones method offers a far-improved capability to design waveriders, and it is favorable for hypersonic airframe propulsion integration.

Multiple Osculating Cones’ Waverider Design Method for Ruled Shock Surfaces

The traditional osculating cones’ (OCs’) waverider design method is widely used in hypersonic waverider airframe design. However, it becomes ineffective when the shock strength in each osculating plane varies and the azimuthal pressure gradients appear to be important. To solve this problem, a method called the multiple osculating cones’ (multiple-OCs’) waverider design method has been developed for ruled shock surfaces. The new method discretizes the ruled shock surface into elements that can be derived from multiple locally conical flows. Multiple locally conical flows indicate that neighboring osculating planes have different shock generators. This feature not only provides a practical way to represent the azimuthal pressure gradients but also extends the variety of waverider designs. Waverider test cases at and are performed by the osculating cones with variable shock angles’ (OC-VSAs’) method and the multiple-OCs’ method, respectively. It has been shown that the multiple-OCs’ method is applicable to more generalized shock surfaces. The comparison results reveal that the waverider derived by the multiple-OCs’ method has a better agreement with the computational fluid dynamics solution than the OC-VSAs’ method. Moreover, the new method ensures a more homogeneous inlet captured flowfield on the bottom side of the waverider, which is favorable for hypersonic airframe propulsion integration.

Design and investigation of equal cone-variable Mach number waverider in hypersonic flow

A new design idea is put forward to adapt the design requirement of wide-speed range vehicle in the paper. The novel points are that the design Mach number and shock flowfield are variable continuously in the design methodology. The design process is introduced about the wide-speed waverider and the repeatability function is achieved systematically by means of the parameterized modeling. In order to validate the advantages of the new approach during the wide-speed range, the flowfield characteristics are investigated numerically in the paper. The numerical method is validated by comparing the simulation results with wind tunnel experiment data. The obtained results show that the wide-speed range waverider could be obtained easily by the parameterized modeling. For the variable Mach number waverider, the pressure drag accounts for the main part of total drag, about 60∼70%. The percentage of viscous drag increases and that of the rear drag decreases with the increase of flow velocity. The viscous L/D of Case 5 does not change obviously during the wide-speed range. The variable Mach number waverider holds the steady aerodynamic performance during the wide-speed range. This shows that the new design method is very useful for the integrated design of wide-speed hypersonic vehicles.

Investigation on a Novel Waverider Design Method

Investigation on a Novel Waverider Design Method