Osculating Cone Waverider Research Articles

Development of maximum conical shock angle limit for osculating cone waveriders

Hypersonic waveriders are special shapes with leading edges coincident with the body's shock wave, yielding high lift-to-drag ratios. The waverider geometry results from streamline tracing using the solutions of a basic flow field such as the wedge or the cone for specified shock and base curves. The base and shock curves can be independently prescribed in the osculating cone method enabling a larger design space. Generally, low values of the conical shock angle (9∘−15∘) are used. The lack of any method to limit the maximum cone angle for osculating cone waverider motivates this study. Mathematical expressions are derived for geometrical conditions that result in successful osculating cone waverider generation. A power law curve and a Bézier curve are analyzed. Closed-form expressions for the maximum cone shock angle are obtained for the power law curve. A numerical procedure to solve the same for the Bézier curve is developed. The results, for a typical Mach number of 6.0, evidently show that the maximum cone shock angle for successful waverider generation is significantly lower than the maximum angle for attached shock solutions. The limiting conditions developed will be essential in constraining the waverider sample space for automated multi-objective optimization routines. CFD simulations were conducted on waveriders designed with traditional shock angle of 12∘ and near limiting shock angle of 18∘. The analysis revealed a substantial 50% increase in volumetric efficiency, albeit with a minor decrease in aerodynamic performance. This highlights the critical need for determining the maximum conical shock angle when aiming for specific high volumetric efficiency.

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.

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.

Effect of curvature distribution on customized-planform waverider

In the customized-planform waverider derived from the osculating-cone method, when the design curve Inlet Capture Curve (ICC) is selected or determined, its curvature distribution is possibly irregular, leading to a failure of waverider generation. Moreover, in the osculating-cone method, the curvature distribution of ICC is required to be continuous, restricting the design space significantly. In this paper, the effect of modifying and altering the curvature distribution of ICC on the customized-planform waverider is investigated. Test configurations with different curvature distributions of ICC are generated in the two types of customized-planform waveriders and their aerodynamic performances are calculated using CFD techniques. The results indicate that altering the curvature distribution does not break the ‘wave-riding’ performance of high lift-to-drag ratio for the customized-planform waverider significantly. Therefore, in the customized-planform waverider, infeasible curvature distribution of ICC can be modified locally to make the waverider generation work. Meanwhile, altering the curvature distribution of ICC provides an approach to increase the volume of a waverider. Moreover, in the osculating-cone waverider, the ICC curve can be selected over a wider range, even including the curves with non-continuous second-order derivatives, enlarging its design space dramatically.

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.

Nonlinearity Analysis of Increase in Lift of Double Swept Waverider

The double swept waverider is a classic example of the planform-customized osculating-cone waveriders, delivering satisfactory performances over a wide range of velocities. The nonlinear increase in the lift of double swept waveriders at high angles of attack is of vital interest. In this paper, the aerodynamic performance of the double swept waverider is calculated and compared with single swept waveriders. The results suggest that the nonlinear increase in the lift of the double swept waverider is stronger than that of the equal-planform-area single swept waverider, and it increases with the Mach number. Some scholars have proposed the “vortex lift” to explain the nonlinear increase in lift, but it is controversial because the main lift of the waverider comes from the lower rather than the upper surface. This paper proposes that this nonlinear increase is related to the attachment of the shock wave influenced by the leading-edge sweep angle. The shock wave is more inclined to attach under the lower surface at a smaller sweep angle than a larger one as the angle of attack increases. When the shock wave attaches, the increase in pressure via the angle of attack is nonlinear, leading to a nonlinear increase in lift. When the shock wave detaches, the increase in lift is approximately linear.

Novel osculating flowfield methodology for wide-speed range waverider vehicles across variable Mach number

In order to guarantee the good aerodynamic performance of the waverider vehicle in the wide-speed range, the variable Mach number osculating flowfield waverider design theory based on conical basic flowfield is put forward. The shape and aerodynamic characteristics of the variable Mach number osculating flowfield waverider and osculating cone waverider are compared and analyzed. And the inviscid numerical simulation method is used to verify the correctness of the theory and the validity of the design method. The obtained results show that the osculating flowfield waverider has good waverider properties under the conditions of wide-ranged flight Mach numbers. Furthermore, the comparison of osculating flowfield waverider and osculating cone waveriders indicates that the variable Mach number osculating flowfield waverider has balanced internal loading capacity and aerodynamic performance, which is more suitable for wide-speed flight.

Low speed aerodynamic performance analysis of vortex lift waveriders with a wide-speed range

The wide-speed range characteristics of aerodynamic configuration for aircraft are critical to the design of the hypersonic vehicle, and many novel strategies have been proposed. As one of the valid schemes of aircraft with a wide-speed range, the vortex lift waverider with a wide-speed range has attracted an increasing attention. In the current study, the low speed aerodynamic performance of vortex lift waveriders with a wide-speed range has been investigated numerically by means of the three-dimensional implicit Reynolds-averaged Navier-Stokes (RANS) equations coupled with the SST k-ω turbulence model. At the same time, the numerical approaches employed have been validated against the available experimental data in the open literature. The obtained results show that the low speed lift-to-drag ratio of the cuspidal waverider is higher than that of the general osculating cone waverider, while the low speed lift-to-drag ratio of the delta-winged waverider is lower than that of the general osculating cone waverider except for the small and negative angles of attack. At the same time, the low speed vortex lift characteristics of the three types of osculating cone waveriders have been compares and analyzes, and some valuable conclusions have been obtained.

A novel approach for design and analysis of volume-improved osculating-cone waveriders

A novel design methodology for waverider is proposed based on the conical flow field, named volume-improved osculating-cone waveriders. The new waverider is generated through three given curves, including flow capture curve, inlet capture curve, and curve of the center of exit shock. To meet more design requirements, the curve of the center of exit shock, which can be flexibly designed, is newly introduced to generate configurations with different properties and performances. The feasibility and effectiveness of the method have been verified by computational fluid dynamics (CFD) simulation. The discrepancies between the volume-improved osculating-cone waverider and conventional waveriders are numerically analyzed in detail. The results demonstrate that the new waverider takes the advantage of the volumetric efficiency with little loss of performance compared to the conventional waveriders in design conditions. Furthermore, the results of the off-design conditions show excellent aerodynamic performance as the conventional waverider. Moreover, for bluntness with a radius of 10 mm, the new waverider synthetically owns higher viscous lift-to-drag ratio and greater volumetric efficiency than conventional configurations at 0° angle of attack. Therefore, the novel approach is useful to design the hypersonic waverider vehicle.

Planform-customized waverider design integrating with vortex effect

The global geometric relationship among the inlet capture curve, flow capture tube and planform contour line in the osculating-cone waverider design is deduced by a differential equation set. Planform-customized waverider is enabled to be constructed based on the geometric relationship. Thus the configuration with satisfactory wide-velocity-range performance is proposed, employing vortex effect to improve subsonic performance and shock effect to improve super/hypersonic performance, respectively. To validate the concept, the double swept waveriders are generated as test cases. Compared with flat plate models, the aerodynamic performance and flow mechanics of the double swept waverider are analyzed under subsonic and hypersonic conditions using computational fluid dynamics (CFD) simulation. CFD results show that the performance of the waverider with reasonable planform is favorable under both subsonic and hypersonic conditions, remedying some deficiencies of traditional waverider. The work demonstrates a new thought for wide-velocity-range configuration design.

Design and high speed aerodynamic performance analysis of vortex lift waverider with a wide-speed range

According to the geometrical relationships of osculating cone waveriders, two kinds of design methods for the constant swept waverider are discussed in the current study, and both of them own more flexible design curves. The correctness and effectiveness of the proposed approaches has been verified by means of the CFD approach. The design Mach numbers of the cuspidal waverider and the general osculating cone waverider with the same volumetric efficiency of the delta-winged waverider have been determined by writing a program for calculating the volumetric efficiencies of waveriders. Furthermore, the high speed aerodynamic performance advantages of the cuspidal and delta-winged waveriders have been analyzed in detail, in comparison with the high speed aerodynamic performance of the general osculating cone waverider. The obtained results show that compared with the general osculating cone waverider, the cuspidal waverider has better high speed aerodynamic performance under any flight condition in the high speed range, while the high speed aerodynamic performance of the delta-winged waverider is worse. In addition, at the high flight Mach number, the cuspidal waverider shows the significant non-linear behavior of the vortex generated lift, while the delta-winged waverider and the general osculating cone waverider do not have this property.

Design and analysis osculating general curved cone waverider

PurposeWaverider has high lift to drag ratio and will be an idea aerodynamic configuration for hypersonic vehicles. But a structure permitting aerodynamic like waverider is still difficult to generate under airframe’s geometric constrains using traditional waverider design methods. And furthermore, traditional waverider’s aerodynamic compression ability cannot be easily adjusted to satisfy the inlet entrance requirements for hypersonic air-breathing vehicles. The purpose of this paper is to present a new method named osculating general curved cone (OCC) method aimed to improve the shortcomings of traditional waveriders.Design/methodology/approachA basic curved cone is, first, designed by the method of characteristics. Then the waverider’s inlet captured curve and front captured tube are defined in the waverider’s exit plane. Osculating planes are generated along the inlet captured curve and the designed curved cone is transformed to the osculating planes. Streamlines are traced in the transformed curved cone flow field. Combining all streamlines which have been obtained, OCC waverider’s compression surface is generated. Waverider’s upper surface uses the free stream surface.FindingsIt is found that OCC waverider has good volumetric characteristics and good flow compression abilities compared with the traditional osculating cone (OC) waverider. The volume of OCC waverider is 25 per cent larger than OC waverider at the same design condition. Furthermore, OCC waverider can compress incoming flow to required flow conditions with high total pressure recovery in the waverider’s exit plane. The flow uniformity in the waverider exit plane is quite well.Practical implicationsThe analyzed results show that the OCC waverider can be a practical high performance airframe/forebody for hypersonic vehicles. Furthermore, this novel waverider design method can be used to design a structure permitting aerodynamic like waverider for a practical hypersonic vehicle.Originality/valueThe paper puts forward a novel waverider design method which can improve the waverider’s volumetric characteristics and compression abilities compared with the traditional waverider design methods. This novel design approach can extend the waverider’s applications for designing hypersonic vehicles.

Effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider under different angles of attack

In order to research the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider, thermochemical non-equilibrium flow and perfect gas model are employed to study the aerodynamics of an osculating-cone waverider under different angles of attack. The obtained results show that the slope of the oblique shock wave has little difference when considering the thermochemical non-equilibrium effect under the condition of zero angle of attack. However, under the condition of other attack angles, the slope of the oblique shock wave diminishes when considering the thermochemical non-equilibrium effect. Furthermore, the non-equilibrium effect moves the pressure center of the osculating-cone waverider forward by as much as 1.53% of the whole craft's length, which must be taken into consideration in the balance design of aircraft.

Design and comparative analysis of multistage compression cone-derived waverider and osculating cone waverider

Design and comparative analysis of multistage compression cone-derived waverider and osculating cone waverider

Longitudinal static stability analysis of hypersonic waveriders

The study of hypersonic glider design has great application value. Its longitudinal design has great difference with the airplane design. Because of its high flying altitude, hypersonic velocity and lack of horizontal tail, The traditional flight mechanics do not have specific design rule for such flight condition. Based on osculating cone waverider method, this paper has established an infinitesimal computational model for the analysis of its longitudinal stability, both the first and second derivative are taken into consideration. By combining Newtonian Theory, Piston Theory and Tangent Cone/Wedge Theory, the typical 2D profiles are used to investigate its longitudinal stability under hypersonic and wide angle of attack conditions. The result shows that the convex case could improve its longitudinal stability while the concave case has the contrary effect. This conclusion is verified by both 2D and 3D computational examples. On the basis of the theory above, the physical reason why conical derived waverider do not satisfy longitudinal static stability, and the influence of pitch trim rudder are also illustrated. Further analysis shows that this conclusion could also be applied to a broad Mach number and altitude, and the viciousity has little influence on such law. The conclusions of this paper could be used in the preliminary aerodynamic design of hypersonic vehicles.

Rocket-Based Combined-Cycle Engine Integration on an Osculating Cone Waverider Vehicle

Anaerodynamicmodelforarocket-basedcombined-cycleengine-airframeintegratedvehicleusinganosculating conewaveriderforebody ispresented.Emphasisisplaced onthehypersonicportionofthevehicletrajectory,where scramjet operation occurs. An analytical model for the compression e owe eld in the engine is developed, validated, and incorporatedinto a e nite-ratechemistryenginemodel forhydrogenand air. Issuesofoff-designMach number, angle of attack, and performancethrough a trajectory areaddressed for a nonoptimal example vehicle. Theresults show that the aerodynamic performance of this class of engine-airframe integrated vehicle can be rapidly solved and incorporated into a vehicle design and trajectory code.

Optimization of Waverider-Based Hypersonic Cruise Vehicles with Off-Design Considerations

A waverider-base d hypersonic vehicle is optimized for a Mach 10 cruise mission. Issues related to optimization of a fully integrated hypersonic engine - airframe combination are reviewed. In contrast to previous optimizations presented for waverider-based designs, the current approach takes into account certain aspects of the off-design performance. The design is optimized for maximum range along a 1000psf dynamic pressure trajectory from Mach 6 to Mach 10 under scramjet propulsion. A so-called osculating cone waverider forebody is chosen so that it generates uniform flow for the two-dimensional multiple-ramp inlet design. The flow through the scramjet engine is modeled analytically, including effects of mixing and combustion. The vehicle model is validated with computational fluid dynamics calculations. Both the inlet and the nozzle shapes as well as the overall airframe configuration are optimized for maximum range along the trajectory using the method of sequential quadratic programming. The difference in the range performance of the present design and a design that has been optimized at a fixed Mach 10 cruise condition is less than 1%. This suggests that previous single-point designs will in fact perform well across the hypersonic portion of the flight envelope.

Engineering evaluation of flight testing dive or toss bomb computers

In order to research the effect of thermochemical non-equilibrium on the aerodynamics of an osculating-cone waverider, thermochemical non-equilibrium flow and perfect gas model are employed to study the aerodynamics of an osculating-cone waverider under different angles of attack. The obtained results show that the slope of the oblique shock wave has little difference when considering the thermochemical non-equilibrium effect under the condition of zero angle of attack. However, under the condition of other attack angles, the slope of the oblique shock wave diminishes when considering the thermochemical non-equilibrium effect. Furthermore, the non-equilibrium effect moves the pressure center of the osculating-cone waverider forward by as much as 1.53% of the whole craft's length, which must be taken into consideration in the balance design of aircraft.