Blunt Cone Research Articles

Non-equilibrium plasma distribution in the wake of a slender blunted-nose cone in hypersonic flight and its effect on the radar cross section

This paper presents numerical results in hypersonic aerothermodynamics, a critical field within aerospace engineering, traditionally focusing on reentry capsules and more recently, slender hypersonic vehicles. While capsules typically undergo near-field analysis to assess heat flux and pressure distributions for Thermal Protection System sizing, slender bodies demand additional attention to wake dynamics due to plasma presence. Plasma can significantly affect the Radar Cross Section (RCS) of these vehicles, which require tracking during flight due to their maneuvering and sustained flight capability.Utilizing Computational Fluid Dynamics tools, we explore plasma distribution around a slender blunted cone, considering altitudes and Mach number regimes that may characterize gliding or sustained atmospheric hypersonic flight, emphasizing its impact on RCS. Our study integrates an aerothermodynamic model incorporating non-equilibrium relaxation equations for gas composition and energy. By evaluating characteristic plasma quantities, we underscore the importance of wake plasma for subsequent electromagnetic wave analysis, crucial for understanding RCS. Furthermore, we highlight the necessity for collaborative efforts between Computational Fluid Dynamics (CFD) and Computational Electro-Magnetics (CEM) disciplines to address this challenging interdisciplinary problem.

Application of fuzzy PID control algorithm in hypersonic vehicle transpiration cooling control

As an efficient active cooling method, transpiration cooling is employed for thermal protection of blunt nose cones. However, most current systems utilize open-loop control for coolant supply. This study establishes a dynamic model of a one-dimensional blunt nose cone transpiration cooling system that concurrently considers aerodynamic heating, internal heat transfer in porous media, and the thermal insulation process of the air film layer formed by injected coolant. The findings indicate that the coolant film's thermal insulation effect significantly impacts the nose cone cooling system, with flow in the porous media causing a time-delay in the dynamic insulation effect. After implementing a closed-loop feedback controller, the fuzzy PID control algorithm demonstrates superiority over the conventional PID control algorithm in mitigating positive and negative feedback misalignment issues caused by time-delay, resulting in reduced temperature oscillation time and amplitude. Additionally, the fuzzy PID control algorithm achieves faster response and shorter stabilization time when external interference from varying Mach numbers occurs.

High precision aerodynamic heat prediction method based on data augmentation and transfer learning

Data-driven modeling methods have become one of the main technologies for predicting aerodynamic heat in hypersonic conditions. However, due to the limitations of wind tunnel experimental conditions, the spatial distribution of aerothermal wind tunnel experimental data is often sparse, and the sample size is relatively small. Furthermore, there is a lack of direct correlation in the aerodynamic heat distribution data among different shapes of vehicles, which poses challenges for constructing high-performance data-driven aerodynamic heat prediction models. To address these issues, this paper proposes a high-precision aerodynamic heat modeling and prediction method based on data augmentation and transfer learning. First, integrating the concept of data fusion, we propose to enhance the sparse aerothermal wind tunnel experimental data by using deep neural networks and introducing low-precision numerical computation results. Next, based on the close physical correlation between boundary layer outer edge information and wall surface aerodynamic heat, we construct the aerodynamic heat prediction model ED-ResNet using a double-series residual neural network. Finally, by fine-tuning the ED-ResNet model for transfer learning, high-precision predictions of aerothermal wind tunnel experimental results for different shaped vehicles are achieved under small sample conditions. Verification using hypersonic double-ellipsoid, blunt cone, and blunt bicone shows that after data augmentation, the prediction error of the aerodynamic heat prediction model is significantly reduced to 1/3 of that when data augmentation is not used. Moreover, through transfer learning, the model effectively leverages existing hypersonic double-ellipsoid aerothermal wind tunnel experimental data to achieve high-precision predictions of aerodynamic heat distribution for blunt cone and blunt double cone under different incoming flow conditions, with normalized root mean square error(NRMSE) maintained below 10%.

Accurate Modelling of AFM Force-Indentation Curves with Blunted Indenters at Small Indentation Depths.

When testing biological samples with atomic force microscopy (AFM) nanoindentation using pyramidal indenters, Sneddon's equation is commonly used for data processing, approximating the indenter as a perfect cone. While more accurate models treat the AFM tip as a blunted cone or pyramid, these are complex and lack a direct relationship between applied force and indentation depth, complicating data analysis. This paper proposes a new equation derived from simple mathematical processes and physics-based criteria. It is accurate for small indentation depths and serves as a viable alternative to complex classical approaches. The proposed equation has been validated for ℎ < 3R (where h is the indentation depth and R is the tip radius) and confirmed through simulations with blunted conical and pyramidal indenters, as well as experiments on prostate cancer cells. It is a reliable method for experiments where the tip radius cannot be ignored, such as in shallow indentations on thin samples to avoid substrate effects.

Aero-optical effects of a hypersonic vehicle based on the refractive index step ray tracing method

The aero-optical effect caused by the high-speed flight of aircraft can affect the accuracy of astronomical navigation, so studying the laser transmission characteristics in high-speed flow fields is essential. This study adopts a 3D spherical blunt cone model as the physical aircraft model, incorporates the latest reanalysis data from the National Centers for Environmental Prediction as atmospheric parameters, and uses Fluent software to establish a hypersonic aircraft external flow field model. The ray tracing error is calculated using a method based on the refractive index step size. Results indicate that, under the conditions of flying altitude of 5 km and incident angle of 45°, the proposed ray tracing method has better accuracy than the traditional method. Compared with the Runge–Kutta method and the method based on geometric step size, the proposed ray tracing method reduces the error by 46.4% and 12.5%, respectively, at the flight Mach number of 5.

Nonlinear Nonmodal Analysis of Hypersonic Flow over Blunt Cones

The linear amplification of modal disturbances that lead to boundary-layer transition in two-dimensional/axisymmetric hypersonic configurations is strongly reduced by the presence of a blunt nose tip, and the mechanisms underlying the low Mack’s second-mode N-factor values at the observed onset of transition over the cone frustum are currently unknown. Linear nonmodal analysis has shown that both planar and oblique traveling disturbances that peak within the entropy-layer experience appreciable energy amplification for moderate to large nose-tip bluntness. The present study extends the previous linear analysis by including the nonlinear effects. Specifically, the harmonic Navier–Stokes equations (HNSE) are solved with a fully implicit formulation and the Newton–Raphson method. The increased number of degrees of freedom for the nonlinear system presents difficulties for solution strategies based on direct solution of the linearized system. Such difficulties are overcome by using the generalized minimal residual method (GMRES) iterative method with a preconditioner corresponding to a simplified Jacobian without the cross-derivative terms. The HNSE solver is verified by comparing with nonlinear parabolized stability equation results for the nonlinear evolution of planar waves in an incompressible Blasius boundary layer and in a Mach 6 flow over a blunt cone. Finally, nonlinear nonmodal results are presented for planar traveling disturbances over a blunt cone configuration with reduced transition N factor as measured in wind-tunnel experiments. The nonmodal analysis demonstrates that entropy-layer disturbances generated close to the nose tip can seed the amplification of higher-frequency Mack’s second-mode instabilities farther downstream and hence can lead to a reduction in the transition N factor.

Investigating Intra-Pulse Doppler Frequency Coupled in the Radar Echo Signal of a Plasma Sheath-Enveloped Target

In detecting hypersonic vehicles, the radar echo signal is coupled with an intra-pulse Doppler frequency (I-D frequency) component caused by relative motion of a plasma sheath (PSh) and the vehicle, which can induce the phenomenon of a ghost target in a one-dimensional range profile. In order to investigate the I-D frequency generated by the relative motion of a PSh, this study transforms a linear frequency modulated (LFM) signal into a single carrier frequency signal based on echo signal equivalent time delay-dechirp processing and realizes high resolution and fast extraction of the I-D frequency coupled with the frequency-domain echo signal. Furthermore, by relying on the computation of the surface flow field of the RAMC-II Blunt Cone Reentry Vehicle, the coupled I-D frequency in the radar echo signal of a PSh-enveloped target under circumstances of typical altitudes and carrier frequencies is extracted and further investigated, revealing the variation law of I-D frequency. The key findings of this study provide a novel approach for suppressing anomalies in radar detection of PSh-enveloped targets as well as effective detecting and as robust target tracking.

Investigation of an overlap of heating peaks in the hypersonic boundary layer over a blunt cone

Investigation of an overlap of heating peaks in the hypersonic boundary layer over a blunt cone

Multi-species modeling in the particle-based ellipsoidal statistical Bhatnagar-Gross-Krook method including internal degrees of freedom

The implementation of the ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) method in the open-source particle code PICLas is extended for multi-species modeling of polyatomic molecules, including internal energies with multiple vibrational degrees of freedom. For this, the models of Mathiaud et al. [1], Pfeiffer [2] and Brull [3,4] are combined. In order to determine the transport coefficients of the gas mixture, Wilke's mixing rules and collision integrals are compared. The implementation is verified with simulation test cases of a supersonic Couette flow as well as a hypersonic flow around a 70° blunted cone. The solutions of the ESBGK method are compared to the Direct Simulation Monte Carlo (DSMC) method to assess the accuracy, where overall good agreement is achieved. In general, collision integrals should be preferred for the determination of the transport coefficients, since the results using Wilke's mixing rules show larger deviations in particular for large mass ratios. Considering the computational efficiency of the methods, a considerable reduction in computational time is possible with the ESBGK model.

Three-dimensional receptivity of hypersonic sharp and blunt cones to free-stream planar waves using hierarchical input-output analysis

Three-dimensional receptivity of hypersonic sharp and blunt cones to free-stream planar waves using hierarchical input-output analysis

Tip shape effects on the axial-flow-induced vibration of a cantilever rod

The influence of tip shape on flow-induced vibration of a cantilever rod subjected to axial water flow is experimentally investigated, through optical tracking of the rod movement and mapping of the instantaneous flow field around the rod tip. The experimental setup consists of a vertical cantilever rod housed within a tube. The rod tip shapes considered in this study include a blunt tip and cones with height-to-diameter ratios of 0.5, 1, and 2. The experiments were conducted across a Reynolds number range between 20k to 100k in both clamped-free and free-clamped configurations, representing opposite flow directions. The rod tip motion was captured using fast video image tracking, whereas the flow field near the rod tip was obtained using particle image velocimetry (PIV). The rod vibration dynamics exhibited a primarily fuzzy period-1 behavior, characterized by a periodic motion with a chaotic component. Flutter-like oscillation and buckling were also observed at higher Reynolds numbers, depending on the flow direction. The mechanisms of fluid-structure interaction involved turbulent buffeting and movement-induced excitations. Unsteady flow separation around the rod tip was identified as a further contributing mechanism to flow excitation. In the clamped-free configuration, unsteady flow separation was more pronounced for the cone tips due to the increased rod surface area in the wake region, leading to larger vibration amplitude. In the free-clamped configuration, flow separation effects were more prominent for the blunt tip, as the streamlined cone shapes were less prone to flow separations. Overall, the rod with a blunt tip resulted in smaller displacement in the clamped-free configuration, while the rods with cone tips led to smaller displacement in the free-clamped configuration.

A new very high-order finite-difference method for linear stability analysis and bi-orthogonal decomposition of hypersonic boundary layer flow

Precisely predicting laminar-turbulence transition locations is essential for improvements in hypersonic vehicle design related to flow control and heat protection. Currently state-of-the-art eN prediction method requires the evaluation of discrete normal modes F and S for the growth rate of instability wave. Meanwhile, in receptivity studies, both the discrete and continuous modes, including acoustic, entropy, and vorticity modes, contribute to the generation of the initial disturbance. The purpose of this paper is to introduce a new very high-order numerical method to accurately compute these normal modes with finite-difference on a non-uniform grid. Currently, numerical methods to obtain these normal modes include two major approaches, the boundary value problem approach and the initial value problem approach. The boundary value approach used by Malik (1990) [17] deploys fourth-order finite difference and spectral collocation methods to solve a boundary value problem for linear stability theory (LST). Nonetheless, Malik's presentation only demonstrated the computation of discrete modes, but not the continuous modes essential for conducting modal analysis on receptivity data. To obtain the continuous spectrum for his multimode decomposition framework, Tumin (2007) [16] relies on an initial value approach based on the Runge Kutta scheme with the Gram-Schmidt orthonormalization. However, the initial value approach is a local method that does not give a global evaluation of the eigenvalue spectra of discrete modes. Furthermore, Gram-Schmidt orthonormalization, which can be error-prone in implementation, is required at every step of the integration to minimize the accumulation of numerical errors. To overcome the drawbacks of these two approaches, this paper improves the boundary value approach by introducing a new general very high-order finite difference method for both discrete and continuous modes eigenfunctions. This general high-order finite difference method is based on a non-uniform grid method proposed by Zhong and Tatineni (2003) [22]. Under the finite difference framework, discrete and continuous modes can be obtained by imposing proper freestream asymptotic boundary conditions based on the freestream fundamental solution behavior. This asymptotic boundary condition is used for obtaining both discrete and continuous modes that have both distinct (acoustic) and similar (vorticity and entropy) eigenvalues. Extensive verification of the new method has been carried out by comparing the computed discrete and continuous modes. Subsequently, the discrete and continuous modes obtained with this finite difference method are essential for the bi-orthogonal decomposition, which holds promising potential in obtaining an accurate evaluation of receptivity coefficients. The result of the bi-orthogonal decomposition for a hypersonic boundary layer flow over a flat plate is verified by comparing with existing results. Ultimately, the bi-orthogonal decomposition using the eigenfunctions has been applied to a case of freestream receptivity simulation for an axis-symmetric hypersonic flow over a blunt nose cone with modal contributions computed as coefficients for receptivity analysis.

Inversion of electron densities in plasma wakes of hypersonic targets

Focusing on the plasma wakes of hypersonic targets (PWHT), this work provides a method for the inversion of electron densities in the PWHT by integrating electromagnetic radiation theory and three-wave coupling theory (TWCT). Utilizing the Computational Fluid Dynamics (CFD) method, taking a blunt cone as an example, the spatial distribution characteristics of electron densities in the plasma wake are simulated and analyzed in detail. The Zakharov system of equations (ZSE) is applied to the PWHT for the discussion about the electromagnetic radiation generated by plasma parametric instability. Combining the wavenumber spectrum of electromagnetic radiation and the TWCT, an inverse method of the electron densities of plasma wakes is proposed and applied to a blunt cone model. The results indicate that the inversion error rate is effectively held below 1.37 %. Furthermore, reasons for errors are elucidated through the utilization of the wavenumber spectrum structure. The proposed method may contribute to the development of hypersonic wake diagnostic techniques, and offer new insights and directions for wind tunnel experiments, shock tube experiments, as well as research on hypersonic target detection.

Time-resolved wave packet development in highly cooled hypersonic boundary layers

Boundary-layer disturbances are analysed on a $5^{\circ }$ half-angle blunted cone in Mach 5, high-enthalpy flow ( $h_0 = 9\ {\rm MJ}\ {\rm kg}^{-1}$ ) with a low wall-to-edge temperature ratio, $T_w/T_e = 0.18$ . Schlieren and focused laser differential interferometry (FLDI) are utilized to assess the structures and frequency content associated with disturbances. Wave packets are identified from bursts of modal content on time-resolved spectrograms. Bandpass filtering, proper orthogonal decomposition (POD) and space–time POD are then applied to the schlieren data. Bandpass filtering suggests the presence of wave packet dispersion and elongation indicative of slow-acoustic-wave synchronization. Modal reconstruction techniques indicate the radiation of content outside the boundary layer and distinct orientation changes within disturbances, potentially the first experimental evidence of the supersonic-mode instability in such a flow field. Cross-bicoherence computations are carried out for discrete time segments of data from both schlieren and FLDI data. They demonstrate that the most dominant nonlinear interactions are the fundamental–first-harmonic and the fundamental–low-frequency interactions.

Effect of surface ablation on aerodynamic heating over a blunt cone in hypersonic airflow

The hypersonic airflow around a blunt cone coupled with carbonaceous surface ablation is numerically simulated to analyze the impacts of ablation on aerodynamic heating. Ablative reactions, including oxidation, nitridation, and sublimation, are found to affect aerodynamic heating mainly through the surface thermal effect (STE) and the gas-phase chemistry thermal effect (GCTE). Specifically, the sublimation reactions produce significant STE and GCTE. The STE of the sublimation reactions is not always endothermic. Downstream along the cone surface, the condensation of gas-phase C atoms on the wall leads to heat release. The GCTE is exothermic and increases the boundary layer temperature. The oxidation reaction generates weak GCTE but powerful STE, which is exothermic overall. On the contrary, nitridation reaction only leads to appreciable GCTE, characterized by releasing heat. The STE of nitridation is quite small and can be neglected. Oxidation and nitridation reactions often dominate the downstream region of the cone. In addition, in the head region where the ablation reactions are intense, ablation processes could generate considerable diffusive heat flux, increasing the total incident heat flux. Simultaneously, mass ejection can carry away much heat from the surface.

Numerical study of a composite cooling method for hypersonic aircraft

Thermal protection is a crucial issue for a long-flying hypersonic aircraft. In this work, a composite cooling method is proposed and implemented on a hypersonic blunt cone. The composite cooling method combines impinging and convective cooling at the cone head with transpiration cooling employed downstream to produce an overall cooling effect of the cone. Using computational fluid dynamics, the influences of the cooling gas and different attack angles on the cooling effect are examined. The results indicate that the combined cooling method can effectively reduce the overall outer wall temperature of the cone. In particular, with the combined cooling method, an increase in mass flow rate of the cooling gas has been observed in numerical tests, which results in a decrease in the head temperature. The maximum temperature decrease can reach 77.0% on the wall when the mass flow rate of the cooling stream is 1.1 kg/m2 s. The cooling performance on the leeward side can be better than that on the windward side for a fixed cooling gas mass flow rate. This gap in cooling performance between the two sides can be further amplified by a larger attack angle. Quantitatively, when using the combined cooling method, the temperature difference between the windward and leeward sides increases from 106 to 270 K when the attack angle increases from 4° to 8°. The numerical results in this study could provide theoretical and statistical guidance for the design of novel active thermal protection methods for hypersonic aircraft.

Three-dimensional receptivity of a high-speed blunt cone to different types of freestream disturbances

Receptivity to freestream disturbances is the initial stage of the boundary-layer transition process, which can determine the final path of boundary-layer disturbance triggering transition. At present, researches on the receptivity of two-dimensional boundary layer to disturbances with zero incident angles, are relatively sufficient. In fact, the freestream disturbances often propagate into the boundary layer in the form of non-zero incident angles, resulting in a component of spatial disturbances in the circumferential direction of rotating bodies (such as a cone). It is a receptivity problem with a distinct three-dimensional feature. However, research on this three-dimensional receptivity problem is relatively scarce. The preliminary work only studied the three-dimensional receptivity to low-frequency incident slow acoustic waves. There has not been a systematic study on the three-dimensional receptivity to different types of freestream disturbances. The paper conducts a study on the three-dimensional receptivity of a blunt cone to different freestream disturbances. Firstly, a high-resolution numerical simulation method is used to compute the three-dimensional receptivity process by introduce freestream disturbances with 15 degree incident angles. The freestream disturbances include fast acoustic wave, slow acoustic wave, entropy wave, and vortex wave. Their frequencies are selected as dimensionless 1.1 and 5, corresponding to the frequencies of the first mode and second mode, respectively. Then, the phase velocity and shape function of the boundary-layer disturbances at each circumferential position for the numerical results are obtained by Fourier transform. To interpret the receptivity mechanisms, the corresponding results by linear stability analysis are obtained for comparisons. It is found that, the first and second modes of the boundary layer can be effectively excited by the incident slow acoustic waves; It is difficult for the incident fast acoustic waves to excite unstable modes in the boundary layer; The incident entropy wave and vortex wave are difficult to excite the first mode at low frequency, but can excite the second mode at high frequency. Furthermore, the incident angle of the freestream disturbances can cause the differences in the receptivity at different circumferential positions of the cone, which can be reflected in two ways. One is the difference in the dominant disturbance form at different circumferential positions; The second is the difference in the amplitude of boundary-layer disturbances. Under different disturbance types and frequencies, these differences between different circumferential positions exhibit different results. The strongest receptivity may occur on the incident front, the incident back, and the incident side. These phenomena may be the result of the combined action of the upstream head disturbances and the disturbances on the incident front.

Calculation of Dynamic Derivatives for High-Speed Vehicles Based on the National Numerical Windtunnel Software

Based on the NNW-HyFLOW high-speed numerical simulation software, the forced-oscillation dynamic derivatives module has been constructed using the unsteady implicit method, dual time stepping and rigid rotary grid deformation. The code has been validated by the calculation of Finner, HBS, blunt cone and OV-102 vehicle in the range of Mach number 1.85∼6.85 and angle of attack 0∼20°. Compared with the results from experiments, engineering methods and other software, all predicted dynamic derivatives have the same sign as experimental values, and the overall error is within 15%, which illustrate the effectiveness of the dynamic derivative module. Due to the difference of numerical and experimental environment and error bands of both, the numerical predictions of the damping derivatives and cross-coupling derivatives are consistent with the experimental values, which means that the proposed module has the capacity to calculate dynamic derivatives for complex engineering vehicles.

New tuberous Araceae from Binh Thuan Province (South Vietnam)

Two species of the Araceae family, Typhonium praelongum (having tuber of blunt cone shape,very long (about 30cm)sterile appendix of the spadix, horizontal yellow-orange staminodes with tops turning upwards and a glossy entirely papillate upper surface of the simple leaf blade) and Amorphophallus opalinus (having narrow rhizome-like tuber with enlarged basal part, staminodes at the base of male zone of the spadix, narrows pathe, large, broadly-conical with rounded apex, opalescent stigmas and white, one-seeded berries), are described as species new to science from South Vietnam. Detailed morphological descriptions, colour plates of the species and their habitats, phenology, distribution map, provisional conservation status, taxonomic comments and overview of the genera Typhonium and Amorphophallus in the Flora of Vietnam are provided.

Numerical simulation of lateral jet interaction with rarefied hypersonic flow over a two-dimensional blunt body

Reaction Control System (RCS) is a direct force control system that successfully adjusts a craft's attitude or orbit using the reaction force created by jet flow. RCS is frequently employed in the management of near-space vehicles due to its properties of fast response time and effective control efficiency. When the near-space vehicle is navigating at high altitude in a low density atmosphere, the Navier–Stokes equation is no longer applicable. The numerical approach utilized in this study is known as the Conserved Discrete Unified Gas Kinetic Scheme, and the governing equation is the Boltzmann equation, which is not constrained by the continuum hypothesis. In velocity space, an unstructured mesh is utilized, which minimizes the amount of discrete velocity points and considerably increases computation efficiency. The numerical results are in good agreement with the direct simulation Monte Carlo code DS2V when modeling large Knudsen number lateral jet flow. The interaction flow field between hypersonic free stream and lateral jet is then simulated at altitudes of 60–90 km using argon as the working gas and a two-dimensional blunt cone with lateral jet as the study object. Under a fixed jet pressure ratio, preliminary research was conducted on the variation of the lateral jet interference flow field characteristics with the freestream Knudsen number and angle of attack. The differences in surface pressure and heat flux caused by jet opening and shutting are compared. Under rarefied atmospheric conditions, the variation of the force/moment amplification coefficient is given. The numerical results show that when the angle of attack is 0°, the separation area in front of the nozzle and a pair of opposite vortices, which are common in the jet interference flow field, gradually disappear with increasing altitude, but the separation vortex reappears when the angle of attack of the freestream is increased. The high-pressure region generated upstream of the nozzle is the primary cause of the extra force/moment. The density of the main flow decreases as altitude increases, various shock wave patterns of the interference flow field gradually dissipate and the force/moment amplification factor changes considerably. The rarefied gas effect has a significant effect on the lateral jet interference flow.