Half-angle Cone Research Articles

Large-eddy simulations of conical hypersonic turbulent boundary layers over cooled walls via volumetric rescaling method

Large-eddy simulations (LES) of a hypersonic boundary layer on a $7^\circ$ -half-angle cone are performed to investigate the effects of highly cooled walls (wall-to-recovery temperature ratio of $T_w / T_r \sim 0.1$ ) on fully developed turbulence and to validate a newly developed rescaling method based on volumetric flow extraction. Two Reynolds numbers are considered, $Re_m = 4.1 \times 10^6\ \text {m}^{-1}$ and $6.4 \times 10^6\ \text {m}^{-1}$ , at free-stream Mach numbers of $M_\infty = 7.4$ . A comparison with a reference laminar-to-turbulent simulation, capturing the full history of the transitional flow dynamics, reveals that the volumetric rescaling method can generate a synthetic turbulent inflow that preserves the structure of the fluctuations. Equilibrium conditions are recovered after approximately 40 inlet boundary layer thicknesses. Numerical trials show that a longer streamwise extent of the rescaling box increases numerical stability. Analyses of turbulent statistics and flow visualizations reveal strong pressure oscillations, up to $50\,\%$ of local mean pressure near the wall, and two-dimensional longitudinal wave structures resembling second-mode waves, with wavelengths up to 50 % of the boundary layer thickness, and convective Mach numbers of $M_c \simeq 4.5$ . It is shown that their quasi-periodic recurrence in the flow is not an artefact of the rescaling method. Strong and localized temperature fluctuations and spikes in the wall-heat flux are associated with such waves. Very high values of temperature variance near the wall result in oscillations of the wall-heat flux exceeding its average. Instances of near-wall temperature falling below the imposed wall temperature of $T_w=300$ K result in pockets of instantaneous heat flux oriented against the statistical mean direction.

THE EFFECT OF MAGNETIC PARAMETER OVER A VERTICAL WAVY SURFACED RIGHT CIRCULAR CONE IN PRESENCE OF NATURAL CONVECTION

The novelty of this study lies in the combination of wavy cone and magnetic field. The interaction between the velocity decrease and the temperature increase has a various applications. This phenomenon has potential applications in fields such as heat transfer, where there is ability to control temperature profiles. Employing magnetic field can be useful in heat exchangers, cooling systems and other thermal processes. The effects of magnetic fields on fluid flow and heat transfer can be relevant in material processing and manufacturing. This work presents the influence of magnetic field on a vertical wavy cone immersed in viscous fluid, in the presence of natural convection flow with viscosity inversely proportional to linear temperature function. The dominating problem is nonlinear partial differential equations, which is transformed into non-dimensional partial differential equations by using the dimensionless variables, and the wavy surface effect is eliminated from the boundary conditions applying these dimensionless variables. The transformed equations are solved numerically by finite difference (fully implicit method). The numerical results are obtained for magnetic parameter, Prandtl number, surface amplitude, cone half-angle and viscosity variation parameter and their effect on velocity, temperature and Nusselt number. The effect of increasing the magnetic parameter reduces the velocity and increases the temperature. Redundancy of Prandtl number increases the temperature, while the increase of Cone half-angle (CHA) increases the velocity profile. The influence of increasing the viscosity parameter tends to increase the Nusselt number.

Effect of hydrogen mixing on the flame geometry of natural gas-powered equipment

AbstractEnergy strategies at the international level increasingly support the utilization of hydrogen for energy purposes. One way to do this is to mix hydrogen into natural gas, which is delivered by the network to the combustion equipment of consumers. The paper examines the expected changes that will occur if the maximum amount of hydrogen permitted by law is mixed into the natural gas network. According to our results, the inflowing heat quantity in the gas has decreased, which is compensated by the increased flow rate due to the reduced density. The flame image changes spectacularly, the flame becomes lower, the half-cone angle increases in case of hydrogen mixing. Another noteworthy result is that the temperature of the equipment's burner did not change significantly as a result of mixing.

Dynamic large-eddy simulation of hypersonic transition delay over broadband wall impedance

Three-dimensional numerical simulations of hypersonic boundary layer transition delay due to porosity representative of carbon-fibre-reinforced carbon-matrix ceramics (C/C) were carried out on a 7 $^{\circ {}}$ half-angle cone for unit Reynolds numbers $Re_m=2.43 \times 10^6$ – $6.40\times 10^6\ \text {m}^{-1}$ , at the free-stream Mach number $M_\infty =7.4$ , for both sharp and 2.5 mm nose tip radii. A broadband time-domain impedance boundary condition was used to model the acoustic effects of the porous surface on the flow field. A quasi-spectral sub-filter-scale dynamic closure was adopted to stabilize the computations upon turbulent breakdown under extreme cooling conditions, with wall-to-adiabatic temperature ratio of $T_{w}/ T_{ad} \simeq 0.08 $ , while accurately recovering the growth rates of the unstable modes present in the early transition stages. Good agreement is observed with the reference experimental data, both in terms of the predicted extent of the transition delay and the measured second-mode frequency spectrum. The latter is strongly modulated by the formation of near-wall low-temperature three-dimensional streaks. Pressure disturbances concentrate in corridors of locally thickened boundary layer, with frequencies lower than what predicted by linear theory. Here, trapped wavetrains are formed, which can persist long into the turbulent region. Finally, it is shown that the presence of a porous wall simply shifts the onset of turbulence downstream, without affecting its structure.

Integrating Scientific Visualization in the Assessment of Openfoam Solvers for the Flow Around a Spherically Blunted Cone

This study presents a comprehensive comparative analysis of four OpenFOAM solvers for simulating supersonic flow around a Spherically Blunted Cone. Utilizing the generalized computational experiment technique, we evaluated solver performance across varying Mach numbers and cone half-angles. The research aimed to provide clear recommendations for solver selection in high-speed flow simulations. Results show that rhoCentralFoam exhibited the lowest deviation from the exact solution, followed closely by pisoCentralFoam. The sonicFoam solver demonstrated limitations at higher Mach numbers. The QGDFoam solver, while showing promise, requires further optimization of its smoothing parameter for improved accuracy. This study offers valuable insights for OpenFOAM users, enabling them to make informed decisions when choosing solvers for compressible gas dynamics problems.

Traveling wave vibration characteristics of rotating FGM conical shell

Abstract Conical shell is common structural component in various rotating machinery. The study of traveling wave vibration performance of conical shell is of great significant for the design of rotating machinery. This paper addresses the traveling wave vibration performance of rotating functionally graded material (FGM) conical shells. Artificial springs, uniformly distributed, are employed to simulate the boundary constraints of rotating FGM conical shell. Accounting for the effects of Coriolis and centrifugal forces caused by rotation, the energy equation of rotating FGM conical shell is calculated, and then the dynamical model of the rotating FGM conical shell under elastic supported constraints is established using the Lagrange equation. The influence of key factors on traveling wave frequency and response characteristics of rotating FGM conical shell are investigated including rotational speed, half-cone angle and material components.

Interaction of second-mode instability and distributed roughness elements in the hypersonic boundary layer over a sharp cone

The ablation of the thermal protection system (TPS) on the aircraft surface generates distributed roughness elements (DRE), which is expected to affect the hypersonic boundary-layer instability seriously. This work presents the experimental investigation of hypersonic boundary-layer instability waves on a 7° half-angle sharp cone with DRE allocated downstream of synchronization point at 0° angle of attack using surface flush-mounted pressure sensors, focused laser differential interferometer (FLDI), infrared thermography and schlieren technique. The experimental results showed that when the DRE (lower than the local boundary-layer height) was located downstream of the synchronization point, the Mack second mode still dominate the boundary-layer instability, and the transition onset was not significantly affected by DRE at various Reynolds numbers. Based on further analysis in the region downstream of roughness, the DRE didn't influence the nonlinear interaction among instability waves materially, although it promoted the growth of instability waves compared with the smooth case. However, the nonlinear interactions were decaying adjacent to the DRE, as the Mack second-mode instability waves cannot penetrate into the separation bubble because of the flow separation induced by the DRE. The FLDI measurement along the wall-normal direction revealed the second-mode instability waves were suppressed close to the wall by the complex roughness surface at the DRE region, and also confirmed the existence of second-mode instability waves at these streamwise locations. The evolution of instability waves followed the linear stability theory (LST), despite the existence of complex wall surfaces. This work enriches the understanding of the effect of DRE on hypersonic boundary-layer transition and demonstrates the spatial characteristics of instability waves above the complex surface.

Scattering characteristics of dual counter-propagation high-order circularly symmetric Bessel beam by a multilayer chiral sphere.

The interaction between dual counter-propagating high-order circularly symmetric Bessel beams (CSBBs) and multi-layered chiral particles is investigated. Within the framework of generalized Lorenz-Mie theory (GLMT), the distribution characteristics of the superposition of two beams are studied based on the vector superposition theorem. The near-field, internal field, and far-field radar cross section (RCS) of the dual-layered chiral sphere illuminated by dual CSBBs are obtained according to the boundary conditions. By comparing the results of RCS with those from the references for two cases: first, when CSBBs degenerate into plane waves incident on multi-layered chiral sphere, and second, when Bessel beams illuminate isotropic multi-layer sphere degenerated by chiral multi-layered sphere, the effectiveness of the principle and program exhibited here is confirmed. The impact of various parameters on the distribution of the superposed field, the near-field, internal field, and far-field RCS of the particles are analyzed in detail, such as the order, half-cone angle, incidence angle, and polarization angle. The research results in this paper provide theoretical assistance for understanding the interaction between dual CSBBs and non-uniform chiral multi-layered particles and have important value in realizing optical manipulation of complex chiral layered particles.

Spatiotemporal Koopman decomposition of second mode instability from a hypersonic schlieren video

Data-driven modal analysis methods provide a powerful way to decompose data into a sum of modes. The spatiotemporal Koopman decomposition (STKD) enables the computation of modes defined by global frequencies and growth rates in various spatial dimensions and time. The method is an extension of the dynamic mode decomposition (DMD) and higher-order dynamic mode decomposition (HODMD) that represents the data as a sum of standing and traveling, possibly growing or decaying, waves. In this paper, the STKD with HODMD is applied to schlieren video highlighting second mode instability waves traveling down the length of a 3-degree half-angle cone and a 7-degree half-angle cone, both at a freestream Mach number of 6. The HODMD is able to compute dominant modes and frequencies that align with those from associated experimental measurements of unsteady pressure fluctuations, and whose mode shapes clearly show the intensifying wavepacket structure of the waves. The STKD algorithm is used to compute streamwise wavenumbers, spatial growth rates, and wave speeds. The spatial growth rates from the STKD and the magnitudes of the HODMD mode shapes are used to compute the N-factor for waves of several frequencies. Overall, the STKD with HODMD is shown to be a useful tool for extracting spatiotemporal disturbance growth from a schlieren video.

Tunable optical force on a perovskite-coated gold nanosphere by a polarized Bessel beam

The optical force on a perovskite-coated gold nanosphere by a polarized Bessel beam is investigated in the generalized Lorenz-Mie theory (GLMT) framework. The dielectric function of the gold core is described using the Drude-Sommerfeld model, and the cesium silver bismuth bromide (CABB) is considered for the coating. The axial optical forces F z are numerically calculated. The effects of both beam parameters (half-cone angle α0, order l, polarization) and the thickness of the coating are discussed. Numerical results show that the optical force peaks can be adjusted by changing the thickness of the coating. However, the half-cone angle α0 and order l can only change the magnitude of the optical force. The optical force can be tuned by changing beam parameters (α0, l), and the coating thickness of particles. The obtained results demonstrate potential applications for the trapped perovskite gold nanosphere.

Linear Photodiode Arrays For Time-Domain FLEET Velocimetry In Hypersonic Flows

Linear photodiode arrays are applied to Femtosecond Laser Electronic Excitation Tagging (FLEET) to determine the stream-wise velocity of flow at Mach 8 in the Sandia Hypersonic Wind Tunnel (HWT). Incident light emitted by nitrogen gas upon FLEET excitation is collected by intensifying optics that amplify and transmit the light to the photodiode elements as the gas advects downstream. Two photodiode array configurations are considered: one aligned with the flow direction and one that is perpendicular to it. Conventional FLEET using a CMOS image sensor is also performed for quantitative comparison. The configurations are tested for purely free-stream cases as well as the wake of a seven-degree half-angle cone model at various Reynolds number. The influence of the bi-exponential decay of the FLEET line and the transfer function imposed by the intensifying optics are identified as key considerations on the time-domain method accuracy. Overcoming these effects leads to promising application spaces due to the compact nature of photodiodes and low data overhead.

ML for fast assimilation of wall-pressure measurements from hypersonic flow over a cone

Data assimilation (DA) integrates experimental measurements into computational models to enable high-fidelity predictions of dynamical systems. However, the cost associated with solving this inverse problem, from measurements to the state, can be prohibitive for complex systems such as transitional hypersonic flows. We introduce an accurate and efficient deep-learning approach that alleviates this computational burden, and that enables approximately three orders of magnitude computational acceleration relative to variational techniques. Our method pivots on the deployment of a deep operator network (DeepONet) as an accurate, parsimonious and efficient meta-model of the compressible Navier–Stokes equations. The approach involves two main steps, each addressing specific challenges. Firstly, we reduce the computational load by minimizing the number of costly direct numerical simulations to construct a comprehensive dataset for effective supervised learning. This is achieved by optimally sampling the space of possible solutions. Secondly, we expedite the computation of high-dimensional assimilated solutions by deploying the DeepONet. This entails efficiently navigating the DeepONet’s approximation of the cost landscape using a gradient-free technique. We demonstrate the successful application of this method for data assimilation of wind-tunnel measurements of a Mach 6, transitional, boundary-layer flow over a 7-degree half-angle cone.

Nanosecond Laser Fabrication of Dammann Grating-like Structure on Glass for Bessel-Beam Array Generation

The generation of optical beam arrays with prospective uses within the realms of microscopy, photonics, non-linear optics, and material processing often requires Dammann gratings. Here, we report the direct fabrication of one- and two-dimensional Dammann grating-like structures on soda lime glass using a nanosecond pulsed laser beam with a 1064 nm wavelength. Using the fabricated grating, an axicon lens, and an optical magnification system, we propose a scheme of generation of a diverging array of zero-order Bessel beams with a sub-micron-size central core, extending longitudinally over several hundred microns. Two different grating fabrication strategies are also proposed to control the number of Bessel beams in an array. It was demonstrated that Bessel beams of 12 degrees conical half-angle in an array of up to [5 × 5] dimensions can be generated using a suitable combination of Dammann grating, axicon lens and focusing optics.

Görtler-number-based scaling of boundary-layer transition on rotating cones in axial inflow

This paper reports on the efficacy of the Görtler number in scaling the laminar-turbulent boundary-layer transition on rotating cones facing axial inflow. Depending on the half-cone angle $\psi$ and axial flow strength, the competing centrifugal and cross-flow instabilities dominate the transition. Traditionally, the flow is evaluated by using two parameters: the local meridional Reynolds number $Re_l$ comparing the inertial versus viscous effects and the local rotational speed ratio $S$ accounting for the boundary-layer skew. We focus on the centrifugal effects, and evaluate the flow fields and reported transition points using Görtler number based on the azimuthal momentum thickness of the similarity solution and local cone radius. The results show that Görtler number alone dominates the late stages of transition (maximum amplification and turbulence onset phases) for a wide range of investigated $S$ and half-cone angle ( $15^{\circ } \leq \psi \leq 50^{\circ }$ ), although the early stage (critical phase) seems to be not determined by the Görtler number alone on the broader cones ( $\psi =30^{\circ }$ and $50^{\circ }$ ) where the primary cross-flow instability dominates the flow. Overall, this indicates that the centrifugal effects play an important role in the boundary-layer transition on rotating cones in axial inflow.

Vibration Analysis of Porous Functionally Graded Material Truncated Conical Shells in Axial Motion

In this study, a vibration equation for axially moving truncated conical thin shells made of functionally gradient materials with uniformly and non-uniformly distributed pores has been established based on classical thin shell theory. The free vibration and dynamic response solutions are obtained using the Galerkin method. The effects of axial velocity, half cone angle, ceramic material mass composition, material component index, and internal porosity on the free vibration and dynamic response of mentioned shells were analyzed and discussed. The results show that the increase of axial velocity, half cone angle, and material composition index all decrease the natural frequency of the truncated conical shell but amplify its dynamic response, and the rise of the mass fraction of the ceramic material increases the natural frequency of the truncated conical shell but reduces the dynamic response. The results also demonstrate that compared with non-uniformly distributed pores, the effects of uniformly distributed pores on the shells’ dynamic responses are more evident under axial motion.

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.

Scattering Field Intensity and Orbital Angular Momentum Spectral Distribution of Vortex Electromagnetic Beams Scattered by Electrically Large Targets Comprising Different Materials

In this study, we obtained the intensity and orbital angular momentum (OAM) spectral distribution of the scattering fields of vortex electromagnetic beams illuminating electrically large targets composed of different materials. We used the angular spectral decomposition method to decompose a vortex beam into plane waves in the spectral domain at different elevations and azimuths. We combined this method with the physical optics algorithm to calculate the scattering field distribution. The OAM spectra of the scattering field along different observation radii were analyzed using the spiral spectrum expansion method. The numerical results indicate that for beams with different parameters (such as polarization, topological charge, half-cone angle, and frequency) and targets with different characteristics (such as composition), the scattering field intensity distribution and OAM spectral characteristics varied considerably. When the beam parameters change, the results of scattering from different materials show similar changing trends. Compared with beams scattered by uncoated metal and dielectric targets, the scattering field of the coating target can better maintain the shape and OAM mode of beams from the incident field. The scattering characteristics of metal targets were the most sensitive to beam-parameter changes. The relationship between the beam parameters, target parameters, the scattering field intensity, and the OAM spectra of the scattering field was constructed, confirming that the spiral spectrum of the scattering field carries the target information. These findings can be used in remote sensing engineering to supplement existing radar imaging, laying the foundation for further identification of beam or target parameters.

Cross-flow instability on a swept-fin cone at Mach 6: characteristics and control

Experiments were performed to document the complex flow field around and over a $70^{\circ }$ swept fin mounted on a $7^{\circ }$ half-angle right-circular cone in a Mach 6 free-stream. Of particular interest is the turbulent transition of the boundary layer over the swept fin, which is expected to be dominated by a cross-flow instability. Stationary features in the surface temperature distribution over the fin are documented using infrared thermal imaging. These were processed further to determine average spatial Stanton number distributions over the fin. Wavelet analysis of the Stanton number distributions revealed stationary patterns with wavelengths near the fin leading edge that were consistent with linear theory predictions of stationary cross-flow modes. Further from the leading edge, the wavelength of the stationary patterns was observed to increase prior to turbulence onset. Based on these observations, specially designed arrays of discrete roughness elements (DREs) were investigated as a means of delaying turbulence transition with the objective of reducing surface heat flux on the swept fin. The DRE designs followed our previous approach used for cross-flow transition control (Corke et al., J. Fluid Mech., vol. 856, issue 10, 2018, pp. 822–849; Arndt et al., J. Fluid Mech., vol. 887, 2020, A30). These focused on either the shorter wavelengths near the leading edge, or the longer wavelengths that developed near turbulence onset. With regard to delaying transition and reducing the surface heat flux, the DREs that focused on the larger wavelengths of stationary modes were most effective. The fin included an array of pressure sensors that were used to document travelling disturbances that could include those associated with travelling cross-flow modes. Phase analysis of the pressure fluctuation time series was used to determine the wavelength, wave angle and phase speed that were consistent with the travelling cross-flow modes. Cross-bicoherence analysis between the stationary and travelling disturbances indicates a nonlinear phase locking that can account for the development of the longer-wavelength stationary features in the surface heat flux, presumed to be due to stationary cross-flow modes, prior to turbulence onset.

Experimental investigation of hypersonic boundary layer instability with wavy wall located downstream of synchronization point

The wavy wall surface has been reported to be effective in suppressing the growth of second mode instability waves in hypersonic boundary layer, while the allocation of wavy wall relative to the synchronization point requires further study. Upon this work experimental investigation of hypersonic boundary layer instability with wavy wall located downstream of synchronization point based on 7° half-angle sharp cone at zero angle of attack was carried out in a hypersonic noisy wind tunnel. The evolution of instability waves with wavy wall surface is measured using both surface-mounted pressure fluctuation sensors and focused laser differential interferometer (FLDI). The results reveal that the growth of instability waves has been enhanced significantly when the wavy wall region is allocated downstream of the synchronization point when the wavy wall height is slightly smaller than the local boundary layer thickness. Additionally, second mode instability waves are observed at both crests and troughs within the wavy wall region based on the FLDI measurement and moreover, the high-frequency instability waves measured in the separation bubbles of troughs are speculated to be the transmission of second mode instability waves from the shear layer, rather than the local generation of second mode instability.

Comparison of force measurement techniques in a short duration hypersonic facility

Force measurement experiments have been conducted within the University of Oxford’s High Density Tunnel with a 7∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$7^{\\circ }$$\\end{document} half-angle cone. The purpose of the study was to provide a direct comparison between two independent force techniques in the same facility at the same free-stream conditions to provide a quantitative and qualitative discussion of the advantages and disadvantages of both techniques. The first force measurement technique used a conventional 4-axis sting-mounted force balance which was calibrated both statically and through the stress wave deconvolution method, whilst the second technique used the less established static free-flight methodology. Experiments were conducted at a Mach 5 test condition which provided sufficient dynamic pressure to generate aerodynamic forces suitable for the measurement range of the force balance. Results for lift, drag and pitching moment coefficients were obtained over a range of angles of attack and compared with predictions from a hypersonic panel method code. Agreement between the independent force techniques and numerical data sets was good over the range of angles of attack. Maximum uncertainties were shown to be 38.46 ± 0.56 N and 22.52 ± 0.44 N for free-flight in lift and drag, respectively, and 38.74 ± 1.59 N and 22.13 ± 1.27 N for the dynamically calibrated force balance which demonstrates the superiority of free-flight.