Supersonic Regime Research Articles

Experimental and numerical investigation of porous bleed control for supersonic/subsonic flows, and shock-wave/boundary-layer interactions

This paper presents a comprehensive experimental and numerical investigation into the control of boundary layers using porous bleed systems. The study focuses on both supersonic and subsonic flow regimes, as well as on the control of shock-wave/boundary-layer interactions. By simplifying this complex problem into two separate scenarios, the research establishes the necessity of individually characterizing bleed systems for both supersonic and subsonic flow regimes due to variations in the flow topology within the bleed holes. In supersonic conditions, a strong agreement between experimental and numerical results validates the effectiveness of porous bleed in controlling boundary layers. Notably, three-dimensional effects are experimentally demonstrated, and variations of the boundary-layer profiles along the span are the first time experimentally proven. The study extends its scope to subsonic flows, revealing that while boundary-layer bleeding enhances flow momentum near the wall, mass removal induces a decrease in momentum in the outer boundary layer and external flow. The research also explores shock-wave/boundary-layer interaction control, achieving a remarkable alignment between simulations and experiments. The findings endorse the use of Reynolds-Averaged Navier-Stokes simulations for studying porous bleed systems in various flow conditions, providing valuable insights to enhance bleed models, especially in the context of shock-wave/boundary-layer interaction control.

Aeroelasticity analysis of anisogrid lattice sandwich cylindrical shells: Extended potential and piston theories

Based on the extended potential and piston aerodynamics theories, buckling and vibration analysis of sandwich cylindrical shells subjected to external airflow in both subsonic and supersonic regimes is presented. Sandwich cylindrical shells are considered to be made of same homogenous face sheets and an anisogrid composite lattice core with hexagonal cells. An equivalent single layer (ESL) theory in the framework of classical Love’s shell theory is used to formulate the global mechanical behavior of such shells. According to the extended potential and piston aerodynamic theories, aerodynamic pressure distributions are determined for steady, inviscid, irrotational compressible, and external airflow. The closed–form solutions of critical upstream pressure and natural frequency are developed for different boundary conditions using the Galerkin method. Finally, case studies are presented to compare between results of extended potential and piston theories and investigate the effects of upstream speed, geometric ratios, boundary conditions, and lattice specifications on various response quantities. Findings indicate that the differences in results of extended potential and piston theories are less than 3% in the supersonic regime with 2.3 ≤ M ∞ ≤ 2.7 for intermediate-length shells with a wide range of R . The piston theory is inadequate for analyzing aeroelasticity behavior of very long thin sandwich cylindrical shells.

Design considerations for efficient spanwise-inclined air-jet vortex generators for separation control in supersonic and hypersonic flows

Shock-wave/boundary-layer interactions and associated flow separation are frequently occurring phenomena in many high-speed flow applications. Injection of spanwise-inclined air-jets is an efficient means to control shock-induced flow separation in supersonic and transonic flows. Separation-control studies in hypersonic flow are scarce and so far mostly restricted to microramp control. The objectives of the current work are to broaden the scope into hypersonic regime, investigate the influence of crossflow Mach and Reynolds number on the jet-injection flow field, and to find a suitable control parameter that is valid across a wide range of flow conditions. For this purpose, we study injection of a single spanwise-inclined jet in supersonic and hypersonic crossflows using large-eddy simulations. We analyzed the flow topology, induced vortical structures and boundary-layer statistics. The general characteristics of the jet/crossflow interactions are similar in the supersonic and hyperonic regimes: the injection of a spanwise-inclined jet induces an asymmetric flow topology with a complex system of shocks and vortical structures. We identified the ratio of injection-pressure-to-freestream-pressure as a suitable parameter to characterize and compare jet/crossflow interactions in different flow regimes. In addition, we recommend larger boundary-layer-to-jet-diameter ratio for control applications, because it delays the lift-off of major vortices. The present results suggest that rows of spanwise-inclined jets can be efficiently used to control separation also in hypersonic flow. Moreover, low momentum-flux jet injection can be potentially also used for cooling purposes.

FLEW: A DNS Solver for Compressible Flows in Generalized Curvilinear Coordinates

We present FLEW, an in-house high-fidelity solver for direct numerical simulation (DNS) of turbulent compressible flows over arbitrary shaped geometries. FLEW solves the Navier–Stokes equations written in a generalized curvilinear coordinate system, in which the surface coordinates are non-orthogonal, whereas the third axis is normal to the surface. Spatial discretization relies on high-order finite-difference schemes. The convective terms are discretized using an hybrid approach, combining the near-zero numerical dissipation provided by central approximations with the robustness of weighted essentially non-oscillatory (WENO) schemes, required to capture shock waves. Central schemes are stabilized using a skew-symmetric-like splitting of convective derivatives, endowing the solver with the energy-preserving property in the inviscid limit. The maximum order of accuracy is eighth for central schemes (also used for viscous terms discretization) and seventh for WENO. The code is oriented to modern high-performance computing (HPC) platforms thanks to message passing interface (MPI) parallelization and the ability to run on graphics processing unit (GPU) architectures. Reliability, accuracy and robustness of the code are assessed in the low-subsonic, transonic and supersonic regimes. We present the results of several benchmarks, namely the inviscid Taylor–Green vortex, turbulent curved channel flow, transonic laminar flow over a NACA 0012 airfoil and turbulent supersonic ramp flow. The results for all configurations proved to be in excellent agreement with previous studies.

Active Flutter Suppression of a Wing Section in the Subsonic, Sonic and Supersonic Regimes by the H∞ Control Method

This paper compares various procedures for determining the optimal control law for a wing section in compressible flow. The flow regime includes subsonic, sonic and supersonic flows. For the evolution of the system in the Laplace plane, the present method makes use of the exact unsteady aerodynamic forces in this plane once the control law is established. This is a great advantage over other results previously published, where the unsteady aerodynamics in the Laplace plane are merely approximations of the curve-fitted values in the frequency domain (imaginary axis). A comparison of different control techniques like pole placement, LQR and H-infinity control demonstrates that the H-infinity controller is the optimal choice, exhibiting an H-infinity norm approximately two orders of magnitude lower than the LQR case. Furthermore, the H-infinity controller demonstrates lower pole values than those of the pole placement and LQR compensator, showing the advantage of the H-infinity controller in terms of economic efficiency.

Orbital evolution of eccentric perturbers under dynamical friction: crossing the sound barrier

ABSTRACT In a gaseous medium, dynamical friction (DF) reaches a maximum when the orbital speed of a (point-like) perturber moving on a circular orbit is close to the sound speed. Therefore, in a quasi-steady state, eccentric orbits of perturbers approaching the sound barrier (from below) should rapidly circularize as they experience the strongest drag at pericentre passage. To investigate this effect, we extend the solution for circular DF in a uniform gaseous medium to eccentric Keplerian orbits. We derive an approximation to the steady-state DF force, which is valid for eccentricities as high as e = 0.9 in a limited range of Mach number around the transition to supersonic regime. We validate our analytical result with 3D simulations of the gas density response. Although gaseous DF generally dissipates orbital energy, we find that it can be directed along the motion of the perturber near pericentre passage when the eccentricity is e ≳ 0.9. We apply our results to compute the long-time evolution of the orbital parameters. Most trajectories tend to circularize as the perturber moves into the supersonic regime. However, orbits with eccentricities e ≳ 0.8 below the sound barrier experience a slight increase in eccentricity as they loose orbital energy. Possible extensions to our analytical approach are also discussed.

Overview of Computational Methods to Predict Flutter in Aircraft

Abstract Aeroelastic flutter is a dynamically complex phenomenon that has adverse and unstable effects on elastic structures. It is crucial to better predict the phenomenon of flutter within the scope of aircraft structures to improve the design of their wings. This review aims to establish fundamental guidelines for flutter analysis across subsonic, transonic, supersonic, and hypersonic flow regimes, providing a thorough overview of established analytical, numerical, and reduced-order models as applicable to each flow regime. The review will shed light on the limitations and missing components within the previous literature on these flow regimes by highlighting the challenges involved in simulating flutter. In addition, popular methods that employ the aforementioned analyses for optimizing wing structures under the effects of flutter—a subject currently garnering significant research attention—are also discussed. Our discussion offers new perspectives that encourage collaborative effort in the area of computational methods for flutter prediction and optimization.

General concept for autoignitive reaction wave covering from subsonic to supersonic regimes

We consider a one-dimensional (1D) autoignitive reaction wave in a reactive flow system comprising unburned premixed gas entering from the inlet boundary and burned gas exiting from the outlet boundary. In such a 1D system at given initial temperature, it is generally accepted that steady-state solutions can only exist if the inlet velocity matches either the velocity of deflagration wave, as determined by the burning rate eigenvalue in the subsonic regime, or the velocity of detonation wave as dictated by the Chapman–Jouguet condition in the supersonic regime. Based on our recently published theory that ignition is equivalent to deflagration wave with unity Lewis number, we believe that it is possible to redefine deflagration wave from ignition. Thus, we have developed the general concept of “autoignitive reaction wave” and shown theoretically that there are two distinct regions that can maintain steady-state solutions in both the subsonic and supersonic regimes. Based on this theory, we selected inlet velocities that are predicted to yield either steady-state or flashback solutions and conducted numerical simulations. This novel approach revealed that steady-state solutions are possible not only at the velocity of the deflagration wave in the subsonic regime and the velocity of the detonation wave in the supersonic regime, but also across a broad range of inlet velocities. Furthermore, we identify a highly stable autoignitive reaction wave that emerges when the inlet velocity surpasses the velocity of detonation wave, devoid of the typical shock wave commonly seen in detonation waves. This “supersonic autoignitive reaction wave” lacks the instability-inducing detonation cell structure, suggesting the potential for the development of novel combustor concepts.

Self-similar solutions for the non-equilibrium nonlinear supersonic Marshak wave problem

Similarity solutions to the nonlinear non-equilibrium Marshak wave problem with a time dependent radiation driving source are presented. The radiation transfer model used is the gray, non-equilibrium diffusion approximation in the supersonic regime. These solutions constitute an extension of existing non-equilibrium supersonic Marshak wave solutions, which are linear to the nonlinear regime that prevails in realistic high energy density systems. The generalized solutions assume a material model with power law temperature dependent opacities, a material energy density that is proportional to the radiation energy density, and a surface radiation temperature drive that obeys a temporal power law. The solutions are analyzed in detail, and it is shown that they take various qualitatively different forms according to the values of the opacity exponents. The solutions are used to construct a set of standardized benchmarks for supersonic non-equilibrium radiative heat transfer, which are nontrivial but straightforward to implement. These solutions are compared in detail to implicit Monte Carlo and discrete-ordinate transport simulations as well gray diffusion simulations, showing a good agreement, which demonstrates the usefulness of these solutions as a code verification test problem.

Influence of the hydrogen transverse injection mode in a scramjet combustor performance

This paper focuses on the numerical investigation of the transverse hydrogen injection technique in the supersonic airflow on the combustor performance of a scramjet technological demonstrator developed at Universidade Federal do Rio Grande do Norte (UFRN). The UFRN's scramjet vehicle was designed to be fully operational at a hypersonic velocity of 2050 m/s (Mach number 6.8), at 30 km of altitude, which provided a temperature of 1156.95 K and supersonic velocity of 1414.39 m/s (Mach number 2.1), at the combustion chamber entrance. Hydrogen was transversally injected into supersonic airflow at a sonic speed of 1318.46 m/s. A set of 2D-RANS simulations of the reactive flow was performed in combination with a simplified chemical kinetics approach based on the finite-rate chemistry model, defined by a one-step global reaction based on Arrhenius expression to combustion modeling. The turbulence was modeled by the k-kl-ω transition model. Different transverse fuel injections with different dimensions and positioning of injectors were evaluated keeping the same inlet conditions: single-injection versus dual-injection modes. A detailed visualization of several flow phenomena, such as the formation of shock waves, and the performance combustion parameters on the combustor surface were discussed. The analyses indicated hydrogen combustion with a predominantly supersonic flow regime. The transversal injection caused the detachment of the boundary layer as indicated by the recirculation flow structures in the neighboring region next to the injectors. Flow analyses indicate that the purely oblique shock trains were established tending to redirect the airflow over the mixing layer and accelerate the hydrogen burning. Nevertheless, the results showed that this was a local effect since the downstream both mixing and combustion efficiency increased. The dual-injection mode proved to be a promising injection method due to the higher global fuel penetration, elevated from 27,9% to 33,8%, and higher combustion efficiency, increased from 10,33% to 21,99%, with reduced addition of total pressure loss, concerning the single-injection case. Additionally, the growth behavior of performance curves showed that an extension of the combustor downstream length can be indicated to maximize combustor performance.

Numerical study on aerodynamic characteristics of the grid fins with different grid patterns

Grid fins are unconventional control surfaces configured by a grid of cells within an outer frame; this grid acts as multiple lifting surfaces, and the pattern of the cells strongly affects the grid fin's performance. In this study, three-dimensional simulations were performed using a computational fluid dynamic approach with a k–ω shear stress transport turbulence model to investigate the effect of grid patterns on fin aerodynamic characteristics. Three fin models were designed, including square, tri, and hexa grid patterns, to be more independently comparative; other parameters consisting of the outer frame's dimensions, internal web's thickness, chord length, dragging area, and grid cell area were kept similar between the models. The Mach numbers 0.7, 1.2, and 2.5 corresponding to subsonic, transonic, and supersonic regimes were investigated for varying angles of attack from −5° to 15° for each fin model. The aerodynamic efficiency of grid fins is appreciably improved by increasing the normal force coefficient (CN) while reducing the area force coefficient (CA) and hinge moment coefficient (CHM). The results underscore the hexa grid pattern's superiority, with CN increasing by 2.2% and CA decreasing by 1.92% compared to the square model (the original model) at Mach number 0.7. Especially, the hexa model exhibited a substantial decrease in CHM, with the largest difference being 56.8% compared to the square model at Mach 2.5.

Supersonic dusty gas flow past a cylinder in Eulerian–Lagrangian framework

The present study utilizes computational methods to analyze two-dimensional particle-laden flow over a circular cylinder. The effect of seeding of dust particles in the viscous flow of a compressible gas is analyzed. A new solver has been developed for the purpose of studying multi-phase flows in the supersonic regime. Most of the prior research has primarily focused on flows characterized by low Mach numbers and the absence of shock waves, and there have been very few studies dealing with supersonic dusty gas flows. This study considers a supersonic Mach number and investigates the effect of particle size and particle volume fraction on dusty-gas flow over a circular cylinder. The simulation results reveal that the seeding of particles in the flow creates perturbations. The present work also highlights the influence of particles on flow separation and the subsequent increase in the skin friction coefficient and coefficient of drag. The study shows that for supersonic flows, at the same volume fraction, larger particle size creates more instabilities in the flow, while smaller particles are responsible for increased drag on the cylinder, owing to a greater frequency of collisions.

Large-Eddy Simulation of the unsteady supersonic flow around a Mars entry capsule at different angles of attack

Time-evolving high-fidelity simulations of an entry capsule in a supersonic flight regime have been performed at different angles of attack (0∘,5∘,10∘ and 15∘) in Mars' atmosphere. The aim is to contribute to the understanding of the critical unsteady phenomena that arise during the descent phase, gaining insights on the optimal design choices to ensure a safe atmospheric entry and a successful landing procedure. Turbulent structures effectively solved via Implicit Large-Eddy Simulation technique allow us to evaluate the flow properties and the capsule's response both in space and time, placing special attention to the analysis of the turbulent motions responsible for the oscillatory and unsteady dynamics. Ultimately, Proper Orthogonal Decomposition is employed to provide a low-order model of the wake dynamics.

Numerical investigation of the effect of strut geometries on the flow characteristics in a model combustor

PurposeThe mixing of fuel and air plays a pivotal role in enhancing combustion in supersonic regime. Proper mixing stabilizes the flame and prevents blow-off. Blow-off is due to the shorter residence time of fuel and air in the combustor, as the flow is in supersonic regime. The flame is initiated in the local subsonic region created using a flameholder within the supersonic combustor. This study aims to design an effective flameholder which increases the residence time of fuel in the combustor allowing proper combustion preventing blow-off and other instabilities.Design/methodology/approachThe geometry of the strut-based flameholder is altered in the present study to induce a streamwise motion of the fluid downstream of the strut. The streamwise motion of the fluid is initiated by the ramps and grooves of the strut geometry. The numerical simulations were carried out using ANSYS Fluent and are validated against the available experimental and numerical results of cold flow with hydrogen injection using plain strut as the flameholder. In the present study, numerical investigations are performed to analyse the effect on hydrogen injection in strut-based flameholders with ramps and converging grooves using Reynolds-averaged Navier–Stokes equation coupled with Menter’s shear stress transport k-ω turbulence model. The analysis is done to determine the effect of geometrical parameters and flow parameter on the flow structures near the base of the strut where thorough mixing takes place. The geometrical parameters under consideration include the ramp length, groove convergence angle, depth of the groove, groove compression angle and the Mach number. Two different strut configurations, namely, symmetric and asymmetric struts were also studied.FindingsHigher turbulence and complex flow structures are visible in asymmetric strut configuration which develops better mixing of hydrogen and air compared to symmetric strut configuration. The variation in the geometric parameters develop changes in the fluid motion downstream of the strut. The fluid passing through the converging grooves gets decelerated thereby reducing the Mach number by 20% near the base of the strut compared to the straight grooved strut. The shorter ramps are found to be more effective, as the pressure variation in lateral direction is carried along the strut walls downstream of the strut increasing the streamwise motion of the fluid. The decrease in the depth of the groove increases the recirculation zone downstream of the strut. Moreover, the increase in the groove compression angle also increases the turbulence near the base of the strut where the fuel is injected. Variation in the injection port location increases the mixing performance of the combustor by 25%. The turbulence of the fuel jet stream is considerably changed by the increase in the injection velocity. However, the change in the flow field properties within the flow domain is marginal. The increase in fuel mass flow rate brings about considerable change in the flow field inducing stronger shock structures.Originality/valueThe present study identifies the optimum geometry of the strut-based flameholder with ramps and converging grooves. The reaction flow modelling may be performed on the strut geometry incorporating the design features obtained in the present study.

Direct Numerical Simulation of Boundary Layers over Microramps: Mach Number Effects

Microvortex generators are passive control devices with heights below the boundary-layer thickness that have been proposed to mitigate the detrimental effects of shock-wave/boundary-layer interaction. Despite their demonstrated control effectiveness, several aspects of the flow induced in turbulent boundary layers still need to be characterized thoroughly. In this work, we present a campaign of direct numerical simulations of a turbulent boundary layer on a microramp, to investigate the effect of the Mach number, from subsonic to supersonic regime. We show that the flow topology changes significantly because of compressibility effects, and that typical wake features do not scale linearly with the geometry dimensions but rather depend on the incoming flow conditions. Moreover, we investigate the spectral content in time and space of the wake, which is dominated by the Kelvin–Helmholtz instability developing along the shear layer. For larger Mach numbers, the shedding onset is postponed and exhibits a lower peak frequency that evolves in space. Finally, we extract the spatially coherent structures convected in the wake by means of a dynamic mode decomposition along the characteristics, which represents effectively and efficiently the evolution of the entire field, despite the convective nature of the flow under consideration.

An alternative two-way coupled Euler-Lagrange scheme to model the performance of finite-size particle in supersonic flow

In Euler-Lagrange (EL) framework, the Gauss kernel (GK) is usually introduced to avoid Dirac source disturbance of traditional particle-in-cell (PIC) method in subsonic regime. This work investigates the applicability and limitations of PIC-two-way coupling and GK for finite-size particles subjected to supersonic and dilute regime. Results indicate that the source disturbance of GK always peaks at the symmetric center of GK causing a suboptimal shock and ignoring wake in supersonic regime. Meanwhile, classical PIC-interpolation underestimates the drag force on particles due to shock and finite-size effects. To circumvent those issues, a modified coupling method utilizing upstream weighting averaged method and mix-gaussian kernel is proposed to optimize Euler-to-Lagrange coupling and Lagrange-to-Euler coupling, respectively. The modified method not only allows for accurate tracking of arbitrary finite-size particles in supersonic flows but also restores the undisturbed laden flow quantities exerting on particles. Shock and wake zone are reproduced before and after the particle based on recommended parameters. Furthermore, the modified method is validated using a particle-pair exposed to supersonic flow referred from Utkin's experiment(Utkin et al., 2021), and shows excellent agreement.

Investigation of a Near-Field Cylinder Wake in the Subsonic, Transonic, and Supersonic Regimes

The near wake of a circular cylinder in a high-Reynolds-number regime is investigated using the particle image velocimetry technique for an inflow Mach number spanning 0.3 to 2. The mean flow and turbulent kinetic energy field for different Mach number cases are presented. Furthermore, the influence of the Reynolds and Mach number effects is examined based on the mean separation point along the cylinder surface, which is extracted from complementary schlieren visualization measurements, and the literature. The wake width for the supersonic inflow case is found to be an order of magnitude smaller physically than the subsonic case with an identical cylinder diameter. Additionally, the swirl strength criterion is used to identify the eddies present within the wake, and the eddy size and convection velocity are characterized based on the spatiotemporal correlations. The result suggests that the mean wake features for the subsonic and supersonic cases are very different. Moreover, the interaction of eddies generated at the cylinder’s top and bottom shear layers leads to the large-scale features present in the wake, and the differing paths followed by the eddies between the subsonic and supersonic cases are responsible for the variation in the observed wake width.

Recent findings regarding noise from tactical jet engines

This paper reviews the outcomes of several recent investigations into full-scale supersonic jet noise. First, concordance has been shown between a T-7A-installed GE F404 engine’s sound power and classical jet noise theory in both the subsonic and supersonic regimes [M. A. Christian et al., JASA Express Lett. 3, 073601 (2023)]. The results indicate approximate agreement between the “eighth-power” law for subsonic engine conditions and the “third-power” law for supersonic engine conditions, with a radiation efficiency of ∼0.5–0.6% at afterburner. However, a sudden jump in radiation efficiency in the jet’s transonic region is not presently explained. Second, normalized far field-derived sound power spectra for the F404 do not agree well with a curve found in NASA SP-8072 (Eldred, 1971), likely indicating differences between the importance of different Strouhal number regimes in military jet and rocket noise and, possibly, different radiation phenomena. Third, the maximum directivity angle for overall level appears to be primarily driven by the convective Mach number associated with Kelvin–Helmholtz instability waves (M. A. Christian et al., AIAA Paper 2023-3351). Together, these recent findings represent improved understanding of full-scale tactical jet noise phenomena. [Work supported by ONR.]

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.