Supersonic Regime Research Articles

Self-consistent gyrokinetic modeling of turbulent and neoclassical tungsten transport in toroidally rotating plasmas

The effect of toroidal rotation on both turbulent and neoclassical transport of tungsten (W) in tokamaks is investigated using the flux-driven, global, nonlinear 5D gyrokinetic code GYSELA. Nonlinear simulations are carried out with different levels of momentum injection that drive W into the supersonic regime, while the toroidal velocity of the main ions remains in the subsonic regime. The numerical simulations demonstrate that toroidal rotation induces centrifugal forces that cause W to accumulate in the outboard region, generating an in–out poloidal asymmetry. This asymmetry enhances neoclassical inward convection, which can lead to central accumulation of W in cases of strong plasma rotation. The core accumulation of W is mainly driven by inward neoclassical convection. However, as momentum injection continues, roto-diffusion, proportional to the radial gradient of the toroidal velocity, becomes significant and generates outward turbulent flux in the case of ion temperature gradient turbulence. Overall, the numerical results from nonlinear GYSELA simulations are in qualitative agreement with the theoretical predictions for impurity transport.

Ground Vibration Test Based Flutter Prediction for a Combat Aircraft

This paper compares the flutter characteristics of a combat aircraft predicted using experimental modal parameters from ground vibration tests with the results obtained by flight flutter tests. An equivalent finite element model representing the test points in ground vibration tests has been developed and further refined to obtain a finite element model with fine mesh encompassing the entire lifting surface areas. Infinite plate interpolation scheme has been used to extrapolate the eigenvectors for the refined model. A Direct Matrix Abstraction Program (DMAP) written in NASTRAN replaces the generated mass normalized eigenvalues and vectors of the refined model from a dynamic analysis in NASTRAN, with the experimentally obtained eigenvalues and extrapolated eigenvectors. Flutter analysis has been carried out with the replaced experimental modal parameters in subsonic, transonic and supersonic regimes using flutter modules in NASTRAN and ZAERO software. The results obtained using this procedure have been compared with the flight flutter test results. The dispersion in the damping and frequency results obtained from computations and the flight flutter tests were within acceptable limits showing a good correlation.

Nonlinear coherent structures of nucleus-acoustic wave excitations in multi-nuclei quantum plasmas with ultra-relativistically degenerate electrons and positrons

The propagation dynamics of the nucleus-acoustic waves (NAW) in a quantum plasma composed of nondegenerate inertial light nuclei, stationary heavy nuclei, and ultra-relativistically degenerate electrons and positrons has been theoretically investigated within the framework of the Boussinesq equation, which is valid for a bi-directional propagation of a small but finite amplitude limit. The N-soliton solution of the Boussinesq equation is derived using Hirota's method. It is found that positive potential structures exist in the sonic and supersonic regimes, whereas negative potential structures are found to be present in the subsonic regime. Pertinent plasma properties are analyzed for one-, two-, and three-soliton solutions in terms of different parameters. In addition to the typical solitary wave solutions, our findings indicate that the nonlinear NAW has breather structures. The three- and four-soliton solutions are used to construct the elastic interaction solutions of the breather–soliton and breather–breather, respectively. The findings are discussed in the context of ultra-relativistic astrophysical plasmas.

Stationary transport above the critical velocity in a one-dimensional superflow past an obstacle

We consider in this work the different possible stationary flows of a one-dimensional quantum fluid in the mean-field regime. We focus on the supersonic regime where a transition from a time-dependent flow to a stationary diffractive flow occurs at a given critical velocity. We give nonperturbative results for this critical velocity in the presence of a localised obstacle of arbitrary size and strength. In addition, we discuss the existence of superfluid-like solution in the supersonic regime due to resonant transport and provide a complete map of the different regimes of stationary transport of a quantum fluid.

Thrust performance of the rocket-based combined-cycle engine under ejector mode

The Rocket-Based Combined-Cycle (RBCC) engine integrates the preponderance of ramjet and rocket engines. It can perform excellently at a lower Mach number than a ramjet while consuming less fuel than the rocket. The higher specific impulse under lower flight Mach conditions guarantees the competitiveness and application prospect of an RBCC engine for reusable space transportation and hypersonic cruise vehicles. With a wide range of Mach numbers, the flow choking between primary and secondary streams in the inner flow passage of the engine becomes complicated. The flow choking not only affects the mass flow ratio between the air stream and rocket plume but also determines the thrust performance of the engine. However, the relationship between flow-choking states and thrust performance has not been revealed. This investigation aimed to provide a better design reference for the RBCC trajectory design and a basis for the RBCC engine geometry design so that the thrust performance under different flow choking states was studied. The findings indicate that the engine is more favorable in the supersonic regime status than others. At the premise of the lower total pressure air stream condition, the thrust of the RBCC engine is attributed to the rocket pressurization effect. On the contrary, its thrust is ascribed to the air stream when the air stream total pressure is higher. Besides, the thrust augmentation of the RBCC engine is essentially due to the larger entrainment ratio. There is a rocket mass flow rate range in different mixer diameters, named region B in this paper, in which the air mass flow rate can be boosted with the rocket mass flow rate and the specific impulse ratio is higher than the rocket specific impulse. Significantly, the RBCC design state should be maintained in region B to meet the operational requirements of engines under the precondition of an insufficient flight Mach number.

Density and velocity correlations in isothermal supersonic turbulence

ABSTRACT In star-forming clouds, high velocity flow gives rise to large fluctuations of density. In this work, we explore the correlation between velocity magnitude (speed) and density. We develop an analytic formula for the joint probability distribution function (PDF) of density and speed, and discuss its properties. In order to develop an accurate model for the joint PDF, we first develop improved models of the marginalized distributions of density and speed. We confront our results with a suite of 12 supersonic isothermal simulations with resolution of $1024^3$ cells in which the turbulence is driven by 3 different forcing modes (solenoidal, mixed, and compressive) and 4 rms Mach numbers (1, 2, 4, 8). We show, that for transsonic turbulence, density and speed are correlated to a considerable degree and the simple assumption of independence fails to accurately describe their statistics. In the supersonic regime, the correlations tend to weaken with growing Mach number. Our new model of the joint and marginalized PDFs are a factor of 3 better than uncorrelated, and provides insight into this important process.

Effect of a modulated acoustic field on the dynamics of a vibrating charged bubble

We investigate the effect of amplitude-modulated acoustic irradiation on the dynamics of a charged bubble vibrating in a liquid. We show that the potential V(x) of the bubble, and the number and stability of its equilibria, depend on the magnitude of the charge it carries. Under high-frequency amplitude-modulation, a modulation threshold, Gth, was found for the onset of increased bubble amplitude oscillations. For some pressure field values, charge can facilitate the control of chaotic dynamics via reversed period-doubling bifurcation sequences. There is evidence for peak-shouldering and shock waves. The Mach number increases rapidly with the drive amplitude G. In the supersonic regime, for G>1.90Pa, the high-frequency modulation raises both Blake’s and the transient cavitation thresholds. We found a decrease in the bubble’s maximum charge threshold, and threshold modulation amplitude for the occurrence Vibrational resonance (VR). VR occurs due to the modulated oscillatory pressure field, and the influence on VR of the electrostatic charge, and other parameters of the system are investigated. In contrast to the cases of VR reported earlier, where the amplitude G of the high-frequency driving is typically much higher than the amplitude of the low-frequency driving (Ps), the VR resonance peaks occur here at relatively low G values (0<G<10Pa) compared to the acoustic driving pressure Ps∼105 Pa. The optimal parameter values for enhanced response could be useful in acoustic cavitation applications.

Predicting wing-pylon-nacelle configuration flutter characteristics using adaptive continuation method

In this study, the aeroelastic response of a wing-pylon-nacelle system in subsonic and low supersonic flow regimes is analyzed using the continuation method in conjunction with an adaptive step size control algorithm. Idealizing the pylon and nacelle as a point mass, the computed effects of a standard structural analysis of the wing together with the pylon and nacelle are compared with those of a clean wing to build a reduced-order model for analysis. The aerodynamic forces relating to different reduced frequencies are assessed using the Doublet Lattice Method (DLM) in the subsonic flow regime and supersonic lifting surface theory relying on the unsteady linearized small-disturbance potential flow model in the low supersonic flow regime. The Rational Function Approximation (RFA) method is then utilized for the state-space formulation of the system equations, appended with the continuation method for flutter prediction. Thereafter, the linearized aeroelastic equations are resolved using the continuation method with adaptive step size, the results of which are matched with those obtained from the traditional p-k method to emphasize that the continuation method exhibits a distinct advantage in achieving better accuracy in estimating the flutter speed and identifying the “mode switching” phenomenon.

Numerical Investigation of a Pulsed Jet Actuator Having Non-Negligible Switching Time

An internal unsteady compressible flowfield of a pulsed jet actuator (PJA) is simulated by unsteady Reynolds-averaged Navier–Stokes (URANS) and large-eddy simulation (LES) frameworks. The PJA’s feedback loops are short enough to have non-negligible jet switching time compared to the oscillation period. The results show that within a range of inlet pressure (which is the only control parameter) where the jet goes from subsonic to supersonic regime, the oscillation frequencies and the exit velocity waveform predicted by LES are in better agreement with the measured data than those predicted by URANS. Although URANS is able to capture the flowfield inside the feedback loops, it fails to predict the exit jet dynamics, unlike LES. This indicates the importance of a proper resolution of turbulence in the interaction region where jet switching occurs. Using LES data, it is found that the total jet switching time remains constant as the inlet pressure changes. It is also found that only the part of the jet switching period that ends at the first moment when the jet attaches to the opposite wall is involved in the oscillation period. Therefore, a new lumped model is proposed to estimate the oscillation frequency, which also explains the trend observed for the low inlet pressure values.

Numerical model of predicting surge boundaries in high-speed centrifugal compressors

A numerical model of the whole compression system is established in this paper. The introduction of the Laval nozzle and opening boundary methods adaptively simulate the physical fluctuating boundary conditions during the surge without any artificial hypothesis. Based on the model, the steady simulation method has the capacity to well predict the low-order systematical oscillations during the surge by monitoring flow parameters on several representative surfaces. The surge boundaries of a high-speed centrifugal compressor, including the mild surge and the deep surge, are predicted based on the current numerical model in different flow regimes. The discrepancies of the mild surge boundary between experimental data and numerical predictions are within 5% in the transonic regime, but within 0.5% in the subsonic and supersonic regimes. The sensitivities of the mild surge to the throttle opening degree differ much in different flow regimes: the highest is in the transonic regime and the lowest is in the supersonic regime. In the supersonic regime, there exist various mild surges in a wide range of throttle opening degrees and an unstable equilibrium point (UEP) which is the most typical characteristic of the two-regime surge. To the best knowledge of the authors, it is the first time that all the oscillation characteristics of various mild surges and the existence of UEP in the supersonic regime are well predicted by one numerical method.

High-fidelity aeroelastic transonic analysis using higher-order structural models

A novel computational approach for static aeroelastic analysis of metal and composite wings in transonic flows is proposed. Static aeroelastic analysis is often performed coupling beam/plate structural formulations with low-fidelity inviscid and irrotational aerodynamics. When high subsonic, transonic or supersonic regimes are met, low-fidelity aerodynamics is unable to accurately describe flow separation, viscous phenomena, and/or shock waves, unless suitable corrections are considered. This work combines the use of a variable-order kinematics structural model with Computational Fluid Dynamics (CFD), with the aim of developing a flexible computational aeroelastic framework. In particular, the structural model is based on the Carrera Unified Formulation and Equivalent Plate Modelling, whose governing equations are then solved through the Finite Element Method. The CFD analysis is performed using the high-fidelity open-source software SU2. The fluid–structure interaction is captured resorting to an energetic approach based on the Moving Least Squares patch technique. The generality and flexibility of the developed tool is demonstrated considering: the structural analysis of a wing exhibiting taper ratio, sweep angle, spars and ribs; the aeroelastic static analysis of a transonic AGARD 445.6 wing; and a prototype aeroelastic tailoring study on a composite wing. Comparison with available literature results confirms the robustness of the approach.

A GPU-Accelerated Particle Advection Methodology for 3D Lagrangian Coherent Structures in High-Speed Turbulent Boundary Layers

In this work, we introduce a scalable and efficient GPU-accelerated methodology for volumetric particle advection and finite-time Lyapunov exponent (FTLE) calculation, focusing on the analysis of Lagrangian coherent structures (LCS) in large-scale direct numerical simulation (DNS) datasets across incompressible, supersonic, and hypersonic flow regimes. LCS play a significant role in turbulent boundary layer analysis, and our proposed methodology offers valuable insights into their behavior in various flow conditions. Our novel owning-cell locator method enables efficient constant-time cell search, and the algorithm draws inspiration from classical search algorithms and modern multi-level approaches in numerical linear algebra. The proposed method is implemented for both multi-core CPUs and Nvidia GPUs, demonstrating strong scaling up to 32,768 CPU cores and up to 62 Nvidia V100 GPUs. By decoupling particle advection from other problems, we achieve modularity and extensibility, resulting in consistent parallel efficiency across different architectures. Our methodology was applied to calculate and visualize the FTLE on four turbulent boundary layers at different Reynolds and Mach numbers, revealing that coherent structures grow more isotropic proportional to the Mach number, and their inclination angle varies along the streamwise direction. We also observed increased anisotropy and FTLE organization at lower Reynolds numbers, with structures retaining coherency along both spanwise and streamwise directions. Additionally, we demonstrated the impact of lower temporal frequency sampling by upscaling with an efficient linear upsampler, preserving general trends with only 10% of the required storage. In summary, we present a particle search scheme for particle advection workloads in the context of visualizing LCS via FTLE that exhibits strong scaling performance and efficiency at scale. Our proposed algorithm is applicable across various domains, requiring efficient search algorithms in large, structured domains. While this article focuses on the methodology and its application to LCS, an in-depth study of the physics and compressibility effects in LCS candidates will be explored in a future publication.

Verification of a High-Order FEM-based CFD Code using the Method of Manufactured Solutions

A high-order computational fluid dynamics (CFD) code capable of solving compressible turbulent flow problems was developed. The CFD code employs the Flowfield Dependent Variation (FDV) scheme implemented in a Finite Element Method (FEM) framework. The FDV scheme is basically derived from the Lax-Wendroff Scheme (LWS) involving the replacement of LWS’s explicit time derivatives with a weighted combination of explicit and implicit time derivatives. The code utilizes linear, quadratic and cubic isoparametric quadrilateral and hexahedral Lagrange finite elements with corresponding piecewise shape functions that have formal spatial accuracy of second-order, third-order and fourth-order, respectively. In this paper, the results of observed order-of-accuracy of the implemented FDV FEM-based CFD code involving grid and polynomial order refinements on uniform Cartesian grids are reported. The Method of Manufactured Solutions (MMS) is applied to governing 2-D Euler and Navier-Stokes equations for flow cases spanning both subsonic and supersonic flow regimes. Global discretization error analyses using discrete 𝐿2 norm show that the spatial order-of-accuracy of the FDV FEM-based CFD code converges to the shape function polynomial order plus one, in excellent agreement with theory. Uniquely, this procedure establishes the wider applicability of MMS in verifying the spatial accuracy of a high-order CFD code.

Investigation of slanted perforation diameter in tabs for supersonic jet control

PurposeThis study aims to investigate the effect of slanted perforation diameter in tabs for the control of Mach 1.4 underexpanded supersonic jet flow characteristics.Design/methodology/approachNumerical investigation was carried out for NPR 5 to analyze the effect of slanted perforation diameter in tabs to control the Mach 1.4 jet. Four sets of tabs with slanted circular perforation geometries (Φp = 1, 1.5, 2 and 2.5 mm) were considered in this study. The inclination angle of 20° (αP) with reference to the jet axis was maintained constant for all the four tabs considered.FindingsDetermined value indicates there is a 68%, 71%, 73% and 75% drop in supersonic core for the Φp = 1, 1.5, 2.0 and 2.5 mm, respectively. The results show that the tabs with 2.5 mm perforation diameter were found to be efficient in reducing the supersonic jet core in comparison with other tab cases. The reduction in supersonic core length is due to the extent of miniscule vortices exuviating from slanted small and large diameter perforation in the tabs.Practical implicationsThe concept of slanted perforation can be applied in scramjet combustion, which finds its best application in hypersonic vehicles and in noise suppression in fighter aircraft.Originality/valueSlanted perforation and circular shapes with different diameters have not been studied in the supersonic regime. Examining the effect of circular diameter in slanted perforation is an innovation in this research paper.

Effect of plasma actuator-based control on flow-field and acoustics of supersonic rectangular jets

We perform a computational study on the effects of localized arc filament plasma actuator based control on the flow field and acoustics of a supersonic 2:1 aspect ratio rectangular jet. Post validation of the baseline jet, effects of control in the context of noise reduction are studied at experimentally guided forcing parameters, including frequencies $St=0.3, 1.0$ and $St=2.0$ with duty cycles of $20\,\%$ and $50\,\%$ . In general, high-frequency forcing reduces noise in the downstream direction, with the actuator signature appearing mostly in the sideline direction. Here $St=1$ , ${\rm DC}=50\,\%$ yields an optimum balance between peak noise reduction (of ${\sim }1.5$ dB) and actuator tones, with control being most effective on the major axis plane that bisects the shorter edges of the nozzle. Shear layer response to the most effective forcing includes generation of successive arrays of mutually interacting staggered lambda vortices, which eventually energize streamwise vortical elements. Causal mechanisms of noise mitigation are further elucidated as follows. First, the control reduces the energy within the supersonic phase speed regime of peak radiating frequencies by redistributing a part of it into a high-frequency band. Second, it enhances azimuthal percolation of energy into the first and second helical modes at frequencies where noise reduction is seen, thus weakening the radiatively efficient axisymmetric mode. Finally, sound-producing intermittent events in the jet are significantly reduced, thereby minimizing the high-intensity acoustic emissions. This small-perturbation-based control strategy results in only minor variations in the mean flow properties. However, reduced production and enhanced convection attenuate turbulent kinetic energy within the spreading shear layer in the controlled jet.

Half-quantum-vortex generation in a two-component Bose-Einstein condensate by an oscillatory magnetic obstacle

We numerically investigate the dynamics of vortex generation in a two-dimensional, twocomponent Bose-Einstein condensate subjected to an oscillatory magnetic obstacle. The obstacle creates both repulsive and attractive Gaussian potentials for the two symmetric spin-$\uparrow$ and $\downarrow$ components, respectively. We demonstrate that, as the oscillating frequency f increases, two distinct critical dynamics arise in the generation of half-quantum vortices (HQVs) with different spin circulations. Spin-$\uparrow$ vortices are nucleated directly from the moving obstacle at low f, while spin-$\downarrow$ vortices are created at high f by breaking a spin wave pulse in front of the obstacle. We find that vortex generation is suppressed for sufficiently weak obstacles, in agreement with recent experimental results by Kim et al. [Phys. Rev. Lett. 127, 095302 (2021)]. This suppression is caused by the finite sweeping distance of the oscillating obstacle and the reduction in friction in a supersonic regime. Finally, we show that the characteristic length scale of the HQV generation dynamics is determined by the spin healing length of the system.

Vibration of a thin panel exposed to ramp-induced shock-boundary layer interaction at Mach 2

Flight vehicles that operate in the supersonic regime can be subject to adverse fluid–structure interactions due to their lightweight design. The presence of geometric obstructions such as control surfaces or fins can induce shocks that can interact with the boundary layer, leading to flow separation. This work investigates experimentally the interaction between a compliant panel in a Mach 2 flow under a compression ramp-induced shock-wave/boundary-layer interaction (SBLI). Thin brass panels of different thickness are investigated in a wind tunnel. Tests are performed both with and without a 20° compression ramp installed. This direct comparison allows characterization of the effect of the SBLI on the system dynamics. High-speed stereoscopic digital image correlation (DIC) and fast-response pressure sensitive paint (PSP) are used to obtain simultaneous measurements of full field deformation and surface pressure of the panels. The panel vibration is dominated by the first bending mode. Despite the forcing of the separation shock foot, the presence of the SBLI does not significantly modify the operational deflection shape, frequency, and amplitude of the dominant vibration mode, beyond what is observed for the no-SBLI case. On the other hand, analysis of the shock foot motion shows that the shock primarily oscillates at the first natural frequency of the panel. This leads to the conclusion that the shock foot oscillation is driven by the panel vibration in a one-way coupling mechanism. The SBLI does modify the higher modes, which is likely due to localized forcing by the separation shock foot. Full-field surface pressure predictions are made using first order piston theory. Results show that the fluid–structure interaction is dominated by the large region of attached flow upstream of the shock foot.

Parametric aeroelastic modeling, maneuver loads analysis using CFD methods and structural design of a fighter aircraft

The DLR Future Fighter Demonstrator (FFD) is a highly agile, two-seated aircraft with twin-engines equipped, a reheat and a design flight speed extending into the supersonic regime (up to Ma=2.0). Based on a given conceptual design, the presented work focuses on the aeroelastic modeling, including structures, masses and aerodynamics. Using the models, a comprehensive loads analysis with 688 maneuver load cases, covering the whole flight envelope, is performed. Comparing the results obtained from aerodynamic panel methods (VLM and ZONA51) with higher fidelity results obtained from CFD, the necessity of CFD based maneuver loads analysis in preliminary design of such fighter configuration is shown, as it leads to physically different as well as higher loads. The rigorous application of CFD is a heavy burden during the preliminary design, but this work demonstrates that it is doable as of today. Finally, the model is subject to structural optimization, demonstrating that the differences in loads result in a heavier primary structural net mass with ≈3.3t for the approach based on aerodynamic panel methods and ≈4.1t for the CFD based approach. Because all remaining models are unchanged, this difference in mass can be clearly attributed to the physical differences in the flow solutions obtained from the panel methods and CFD.

α-, β-phenomena for the supersonic flow around an impulsively started circular cylinder

The vortex dynamics of a supersonic flow past an impulsively started circular cylinder are studied numerically. A well-developed high-order finite difference method is adopted to solve the two-dimensional Navier–Stokes equations. In particular, Ma = 1.1 and Re = 2.2 × 104 are selected to report the vortex evolution process. The results confirm that the α-, β-, sub-α-, and sub-β-phenomena observed in incompressible flow in the separated region do exist in the supersonic regime. In addition, the influence of Mach number and Reynolds number on the vortex is also studied, and the vortex changes are compared at Ma = 1.1, 1.7 and Re = 1 × 104, 2 × 104, 2.5 × 104, 3 × 104, 5 × 104, and 1 × 105.

Sulfur hexafluoride pulsed jet visualization by the Resonant Schlieren method

Resonant Schlieren technique combines the variation of the refractive index of the medium with the absorption of seeded particles, thus producing high contrast images. It presents low cost and a relatively easy implementation and operation, and allows visualization of low and high-density flows. This paper describes the application of the Resonant Schlieren method to visualize a pulsed free jet of sulfur hexafluoride. A piezoelectric valve with a duty cycle of 10 Hz and pulse width of 2 ms was used to control the flow through a nozzle with 1 mm diameter. Pressures in a vacuum chamber with optical windows were varied from 20 mbar to 1 bar and the flow was seeded with iodine molecules in order to increase the gas refractive index. The Schlieren images of the expanded flows presented a high contrast and the measured pulsed jet front velocities varied from 3 to 166 m/s, from subsonic to supersonic flow regimes. Numerical simulations were performed using the lattice Boltzmann method and the theoretical results showed a good agreement with experimental data.