Waverider Geometries Research Articles

Multi-objective optimization of high Mach waverider based on small-sample surrogate model

Advancements have been achieved in the optimization of waverider designs with the aid of machine learning to expedite the design process. However, these approaches are hampered by the need for extensive sample sizes and susceptibility to becoming ensnared in local optima. This study undertakes a parametric design based on the wedge-derived, power-law-shaped waverider, increasing configuration diversity and creating a dataset with limited samples by calculating waverider geometry and aerodynamic parameters. At a Mach number of 10, a multi-objective optimization design is implemented using the Young's double-slit experiment-least squares support vector regression (YDSE-LSSVR) surrogate model in conjunction with improved congestion distance multi-objective particle swarm optimization algorithm, focusing on maximizing the lift-to-drag ratio and volumetric efficiency as much as possible. The results indicated that, under conditions of limited samples, the YDSE-LSSVR model outperforms standard models such as support vector regression, LSSVR, Kriging, and Polynomial Chaos Expansions-Kriging regarding prediction accuracy. The Pareto solutions for both concave and convex waveriders, obtained through multi-objective optimization, improve the lift-to-drag ratio by 17.36% and 21.70%, respectively, and increase the volumetric efficiency by 88.89% and 105.56%, in comparison to baseline configurations. In addition, the research examines the impact of various design parameters on the Pareto solutions. Finally, the study applies the K-means method to conduct a cluster analysis of the Pareto solutions, generating three-dimensional waverider configurations based on distinguished solutions from different clusters.

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.

Deep neural operators as accurate surrogates for shape optimization

Deep neural operators, such as DeepONet, have changed the paradigm in high-dimensional nonlinear regression, paving the way for significant generalization and speed-up in computational engineering applications. Here, we investigate the use of DeepONet to infer flow fields around unseen airfoils with the aim of shape constrained optimization, an important design problem in aerodynamics that typically taxes computational resources heavily. We present results that display little to no degradation in prediction accuracy while reducing the online optimization cost by orders of magnitude. We consider NACA airfoils as a test case for our proposed approach, as the four-digit parameterization can easily define their shape. We successfully optimize the constrained NACA four-digit problem with respect to maximizing the lift-to-drag ratio and validate all results by comparing them to a high-order CFD solver. We find that DeepONets have a low generalization error, making them ideal for generating solutions of unseen shapes. Specifically, pressure, density, and velocity fields are accurately inferred at a fraction of a second, hence enabling the use of general objective functions beyond the maximization of the lift-to-drag ratio considered in the current work. Finally, we validate the ability of DeepONet to handle a complex 3D waverider geometry at hypersonic flight by inferring shear stress and heat flux distributions on its surface at unseen angles of attack. The main contribution of this paper is a modular integrated design framework that uses an over-parametrized neural operator as a surrogate model with good generalizability coupled seamlessly with multiple optimization solvers in a plug-and-play mode.

Aerodynamic Characteristics of Supersonic Rocket-Sled Involving Waverider Geometry

Rocket-sleds belong to a category of large-scale test platforms running on the ground which are mainly used for launching tests of weapon equipment and performance tests of airborne equipment. In the present study, a dynamic grid method was used to simulate the running process of an axisymmetric slender rocket-sled (ASRS) and a reversed waverider rocket-sled (RWRRS). The aerodynamic characteristics were studied and the ability of the waverider to control the shockwave with the ground effect was confirmed. In addition to reducing shockwave oscillation, the RWRRS was also able to increase lift and reduce drag. By means of power spectral density analysis, the characteristic frequencies of shockwave oscillations related to shock-wave/rail-fastener interaction were analyzed and a harmonic phenomenon was observed. Furthermore, the ability of the waverider rocket-sled to reduce pressure oscillation was confirmed by comparing the sound pressure level value.

HALO3D: An All-Mach Approach to Hypersonic Flows Simulation

This paper presents HALO3D, a CFD code simulating the wide range of Mach numbers a hypervelocity vehicle experiences. HALO3D is composed of (a) a RANS edge-based Finite Element (FE) solver modelling high-velocity thermo-chemical non-equilibrium flows, (b) an electromagnetic interactions solver, (c) an ablation module, (d) a Direct Simulation Monte Carlo (DSMC) solver for the rarefied regime, seamlessly linked to the continuum one, and (e) a powerful automatic mesh optimiser finely capturing the many singular hypersonic flow phenomena. Verification and validation simulations for two- and three-dimensional hypersonic flows over a flat plate, a cylinder, a blunt conical body, re-entry capsules, and a waverider geometry demonstrate accurate aerothermodynamic predictions in a wide range of Knudsen numbers, complex geometries and multiphysics.

Efficient Parameterization of Waverider Geometries

This paper summarizes the results of investigations into the development of parametric waverider geometry models, with emphasis on their efficiency, in terms of their ability to cover a large feasible design space with a sufficiently small number of design variables to avoid the “curse of dimensionality.” The work presented here is focused on the parameterization of idealized waverider forebody geometries that provide the baseline shapes upon which more sophisticated and realistic hypersonic aircraft geometries can be built. Three different aspects of rationalizing the decisions behind the parametric geometry models developed using the osculating cones method are considered. Initially, three different approaches to the design method itself are discussed. Each approach provides direct control over different aspects of the geometry for which very specific shapes would be more complex to obtain indirectly, thus enabling the geometry to more efficiently meet any related design constraints. Then, a number of requirements and limitations are investigated that affect the available options for the parametric design-driving curves of the inverse design method. Finally, the performance advantages that open up with increasing flexibility of the design-driving curves in the context of a design optimization study are estimated. This allows one to reduce the risk of overparameterizing the geometry model, while still enabling a variety of meaningful shapes. Although the osculating cones method has mainly been used here, most of the findings also apply to other similar inverse design algorithms.

A parameterized geometry design method for inward turning inlet compatible waverider

Intensive studies have been carried out on generations of waverider geometry and hypersonic inlet geometry. However, integration efforts of waverider and related air-intake system are restricted majorly around the X43A-like or conical flow field induced configuration, which adopts mainly the two-dimensional air-breathing technology and limits the judicious visions of developing new aerodynamic profiles for hypersonic designers. A novel design approach for integrating the inward turning inlet with the traditional parameterized waverider is proposed. The proposed method is an alternative means to produce a compatible configuration by linking the off-the-shelf results on both traditional waverider techniques and inward turning inlet techniques. A series of geometry generations and optimization solutions is proposed to enhance the lift-to-drag ratio. A quantitative but efficient aerodynamic performance evaluation approach (the hypersonic flow panel method) with lower computational cost is employed to play the role of objective function for optimization purpose. The produced geometry compatibility with a computational fluid dynamics (CFD) solver is also verified for detailed flow field investigation. Optimization results and other numerical validations are obtained for the feasibility demonstration of the proposed method.

Numerical investigation of off-design regimes of flow past waveriders on the basis of axisymmetric conical flows

Off-design flow past waveriders is studied on the M∞ = 4 to 12 freestream Mach number range. Configurations based on the flows behind axisymmetric conical shocks are considered. The waverider geometry is determined by preassigning the transverse contour of the undersurfaces in the base section using power-law functions. The results are obtained by finite-volume solution of the Euler equations using higher-order Runge-Kutta TVD schemes.

WAVERIDERの形状の違いによる揚抗比の数値解析(一般セッション2 車両と航空宇宙機)

WAVERIDERの形状の違いによる揚抗比の数値解析(一般セッション2 車両と航空宇宙機)

Flight simulation of a waverider-based hypersonic vehicle

This work presents three-dimensional, hypersonic flow computations for a waverider-based hypersonic vehicle with finlets. The waverider geometry, as composed of an airframe and a reflexed trailing-edge, is derived from a perturbed hypersonic flow past a cone with combined transverse and small longitudinal curvature. The flowfield simulations associated with the design and off-design flight conditions are performed by solving the three-dimensional compressible Navier-Stokes equations that are incorporated with an implicit upwind-biased finite volume algorithm. Also, the lift, drag, skin friction, lift-to-drag ratio, and static margin are calculated. In the on-design conditions ( M ∞ = 4.0), the inviscid and viscous numerical results correlate well with the estimates of the hypersonic small-disturbance theory. In addition, the influence on aerodynamic performance and stability of adding finlets is discussed here. Furthermore, the variations of aerodynamic performance caused by altering the angle-of-attack from −10 to +10 ° are investigated.

Numerical simulations of high-speed flows about waveriders with sharp leading edges

A procedure is developed for the numerical simulation of stagnation-free inviscid supersonic and hypersonic flows about waveriders with sharp leading edges. The numerical approach involves the development of a specialized grid generator (named HYGRID), an algebraic solution-adaptive grid scheme, and a modified flow solving method. A comparison of the results obtained for several waverider geometries with exact solutions, other numerical solutions, and experimental results demonstrated the ability of the new procedure to produce stagnation-free Euler solutions about sharp-edged configurations and to describe the physics of the flow in these regions.

Supersonic Flow Past Conical Bodies with Nearly Circular Cross Sections

Abstract : Inviscid, supersonic conical flows past bodies whose cross-section deviates slightly from that of a right circular cone are studied by means of a perturbation technique. The effects of small angles of attack and yaw are included. Using the hypersonic small disturbances theory approximations, we have developed explicity results for the flow field velocity components, pressure, entropy, and shock shape for cases n, m = 1, 2, 3, 4. Comparisons of theory with experiment for n = 1, 2 are favorable. The streamsurfaces of the velocity field are calculated and possible waverider geometries that can be developed therefrom are discussed.