Supersonic Wake Research Articles

Particle Image Velocimetry Measurements in Accelerated, Transonic Wake Flows

This paper reports on particle image velocimetry (PIV) measurements in compressible accelerated wake flows generated by two different central injector types, which are mounted in a convergent-divergent nozzle. The injectors differ by the extent of their trailing edge located either in the subsonic (injector A) or supersonic flow region (injector B). In addition, the undisturbed nozzle flow without injector is studied as a reference case. The PIV results reveal typical wake flow structures expected in subsonic (injector A) and supersonic (injector B) wake flows. They further show that the Reynolds stresses mathrm {Re_{xx}} and mathrm {Re_{yy}} significantly decay in all three cases due to the strong acceleration throughout the nozzle. Interestingly, in the case of injector A, the flow stays non-isotropic with mathrm {Re_{yy}}>mathrm {Re_{xx}} also far downstream in the supersonic flow region. These measurements were motivated by the lack of velocity data needed to validate numerical simulations. That is why this paper additionally contains results from (unsteady) Reynolds-averaged Navier-Stokes ((U)RANS) simulations of the two wake flows investigated experimentally. The URANS simulation of the injector A case is able to accurately predict the entire flow field and periodic fluctuations at the wake centerline. However, in the case of injector B, the RANS simulation underestimates the far wake centerline velocity by about 4%.

Supersonic cylinder wake dynamics

The supersonic wake of a circular cylinder in Mach 3 flow was studied through high-speed, focussing schlieren photography. The mean and unsteady behaviour of the separated shear layers, the reattachment process, the recompression wave and the early wake are analysed, and discussed in detail. The fluctuations in the wake are stronger and more coherent than those within the approaching shear layers and the recirculation region. The recompression of the shear layers energises the finer scales in the flow which leads to a departure from a $-$ 1 spectral roll-off observed in the schlieren spectra further upstream. The recompression wave exhibits low-frequency unsteadiness and a ripple-type motion which occurs as it is perturbed by shocklets radiating from the coherent structures in the wake. The wake consists of coherent disturbances with the same characteristic frequency as that for an incompressible flow over a cylinder; however, this instability is suppressed as the wake accelerates, presumably due to increasing compressibility. The primary instability of the wake flow has a characteristic frequency nearly twice that of its incompressible counterpart and it is shown to be driven by the presence of aeroacoustic resonance in the wake. It is also shown that the resonance, which leads to the formation of broadband standing waves in the wake, is the result of an interaction between the wake instabilities and upstream propagating acoustic waves in the wake. The acoustic waves originate upstream of the reattachment region and are believed to be generated by the unsteady separation on the cylinder surface.

Effects of Forebody on Supersonic Parachute Aerodynamic Performance

As a typical aerodynamic deceleration device, supersonic parachute is widely used in aerospace return and recovery. The influence of the precursor on the aerodynamic performance of parachute is very important due to operating conditions under the wake of the precursor.In order to study the effects of supersonic forebody wake on parachute performance, numerical simulation of supersonic parachute is carried out, and the calculation results are in good agreement with the results of the wind tunnel test. The flow characteristics and flow field distribution of supersonic parachutes under free flow are analyzed. On this basis, the flow field characteristics and distribution laws of forebody and parachutes under different inflow Mach numbers and the aerodynamic characteristics of parachutes are studied. The results show that the compression wave and expansion wave generated by the forebody are reflected through the wall, and the reflected wave alternately appears in the downstream flow field. Affected by the forebody wake and reflected waves, the inflow velocity of the parachute has been asymmetrically distributed, and the velocity in the upper area has been seriously attenuated.

Hysteresis in Supersonic Flow Past a Plane Cascade of Cylindrical Rods

—The results of numerical simulation of the interaction of supersonic flow with a permeable screen in form of an infinite plane cascade (lattice) of circular cylinders are given. The interaction regime in which the shocks ahead of the cylinders are localized on the scale of the cascade step is considered. The multi-block computational technique in which the viscous boundary layers are resolved by means of local grids using the Navier–Stokes equations, while the effects of inteferrence between the shock-wave structures in supersonic wake are described within the framework of Euler’s equations. The action of shock waves induced by the neighboring elements of lattice to the near-wake region behind the intermediate elements can ambiguously affect the aerodynamic lattice performance as well as generate time-dependent phenomena in the wake. The flow regimes are classified depending on continuous increase and decrease in the free-stream supersonic air flow in the Mach number range from 2.4 to 4.2 with reference to the lattice of the 80% permeability. The sources of the hysteresis behavior of the lattice aerodynamic drag with respect to the Mach number and the mechanisms of the onset of self-oscillating wake flow regimes are discussed.

Influence of swirl on the supersonic wake flow structure behind blunt-based axisymmetric afterbodies

Wind-tunnel experiments have been conducted on cylindrical models with canted fins. The fins introduced a swirling motion into the wake downstream of a blunt-based afterbody aligned with a Mach 2 flow. Measurements of the velocity field downstream of the models and the pressure distribution at the model base show evidence of two wake flow patterns distinctively differing from the classical supersonic wake, depending on the degree of rotation introduced. For a fin-cant angle of 16$^\circ$, a rotating wake flow with a central, downstream-directed vortex tube and a concentric, counter-rotating, toric vortex pair forms. A higher fin-cant angle of 32$^\circ$, in turn, results in a swirling flow surrounding a region of low-momentum flow at the axis. Near the central axis of the flow field an upstream flow establishes, extending from the far wake up to the model base. Numerical simulations have been performed to explain the fluid-dynamic processes and the origins of the experimentally observed structural changes of the rotating wakes. The results of the large-scale-turbulence-resolving simulations agree qualitatively well with the measured flow fields. The numerical results show that the centrifugal forces decrease the base pressure and cause the experimentally observed structural changes in the wake.

Instability of an asymmetric supersonic planar wake

Supersonic planar wake has strong instability characteristics due to its complex flow component, such as wake/shear layer, attachment, and complex shock waves interferences. In this experimental study, an asymmetric supersonic planar wake, with Mach numbers of 1.37 and 2.39 on the upper and lower side, is investigated by Nanoparticle-based Planar Laser Scattering (NPLS) technique. The blending thickness of the re-development mixing layer and the position of the re-attachment point are analyzed. Results show that the flow phenomenon of the re-development mixing layer is unsteady. The flow state of the mixing layer can be small scale structures or large scale coherent structures. The distribution of re-attachment points in the polar map shows the spatial unsteadiness of near-wake. Besides, the streamwise instability is dominant. The streamwise span of the re-attachment points is consistent with the thickness of the plate. By correlation analysis, the flow state of the mixing layer is not sensitive to the position change of the re-attachment point.

Aerodynamic cooling for supersonic wake flow behind a backward-facing step

Aerodynamic cooling for supersonic wake flow behind a backward-facing step

Hybrid passive-active control method of a swept shock wave-supersonic wake interaction

In the present study, a hybrid passive-active flow control method is used to investigate the interaction between a swept shock wave (SSW) generated by a swept compression wall, and a supersonic wake formed by a wake generator (WG), using a three-dimensional finite volume code. In order to detect the turbulence in the flow behavior, the Reynolds stress model (RSM) is used. Furthermore, dynamic mesh adaptation (DMA) and full multigrid (FMG) techniques are used to better predict the flow structure. The numerical simulations are validated with available data and acceptable agreements are found. After ensuring the accuracy of the numerical code, the effects of the variations in the wake generator's height and temperature, as a hybrid passive-active flow control method, on a swept shock wave and a supersonic wake are investigated. The results indicate that any change in the height and temperature of the wake generator affects the Mach number distribution, the static and the stagnation pressures, as well as the shock's position.

Time-Resolved Planar Velocimetry of the Supersonic Wake of a Wall-Mounted Hemisphere

Time-resolved particle image velocimetry was conducted at 40 kHz using a pulse-burst laser in the supersonic wake of a wall-mounted hemisphere. Velocity fields suggest a recirculation region with two lobes, in which flow moves away from the wall near the centerline and recirculates back toward the hemisphere off the centerline, contrary to transonic configurations. Spatio-temporal cross-correlations and conditional ensemble averages relate the characteristic behavior of the unsteady shock motion to the flapping of the shear layer. At Mach 1.5, oblique shocks develop, associated with vortical structures in the shear layer and convect downstream in tandem; a weak periodicity is observed. Shock motion at Mach 2.0 appears somewhat different, wherein multiple weak disturbances propagate from shear-layer turbulent structures to form an oblique shock that ripples as these vortices pass by. Bifurcated shock feet coalesce and break apart without evident periodicity. Power spectra show a preferred frequency of shear-layer flapping and shock motion for Mach 1.5, but at Mach 2.0, a weak preferred frequency at the same Strouhal number of 0.32 is found only for oblique shock motion and not shear-layer unsteadiness.

Interaction of a swept shock wave and a supersonic wake

The interaction of a swept shock wave and a supersonic wake has been studied. The swept shock wave is generated by a swept compression sidewall, and the supersonic wake is generated by a wake generator. The flow field is visualized with the nanoparticle-based planar laser scattering method, and a supplementary numerical simulation is conducted by solving the Reynolds-averaged Navier–Stokes equations. The results show that the pressure rise induced by the swept shock wave can propagate upstream in the wake, which makes the location where vortices are generated move upstream, thickens the laminar section of the wake, and enlarges the generated vortices. The wake is swept away from the swept compression sidewall by the pressure gradient of the swept shock wave. This pressure gradient is not aligned with the density gradient of the supersonic wake, so the baroclinic torque generates streamwise vorticity and changes the distribution of the spanwise vorticity. The wake shock is curved, so the flow downstream of it is non-uniform, leaving the swept shock wave being distorted. A three-dimensional Mach disk structure is generated when the wake shock interacts with the swept shock wave.

Characterization of the supersonic wake of a generic space launcher

The wake flow of a generic axisymmetric space-launcher model is investigated experimentally for flow cases with and without propulsive jet to gain insight into the wake-flow phenomena at a supersonic stage of the flight trajectory which is especially critical with respect to dynamic loads on the structure. Measurements are performed at Mach 2.9 and a Reynolds number Re D = 1.3 × 106 based on model diameter D. The nozzle exit velocity of the jet is at Mach 2.5, and the flow is moderately underexpanded (p e/p ∞ = 5.7). The flow topology is described based on velocity measurements in the wake by means of particle image velocimetry and schlieren visualizations. Mean and fluctuating mass-flux profiles are obtained from hot-wire measurements, and unsteady wall-pressure measurements on the main-body base are performed simultaneously. This way, the evolution of the wake flow and its spectral content can be observed along with the footprint of this highly dynamic flow on the launcher main-body base. For the case without propulsive jet, a large separated zone is forming downstream of the main body shoulder, and the flow is reattaching further downstream on the afterbody. The afterexpanding propulsive jet (air) causes a displacement of the shear layer away from the wall, preventing the reattachment of the flow. In the spectral analysis of the baseline case, a dominant frequency around St D = 0.25 is found in the pressure-fluctuation signal at the main-body base of the launcher. This frequency is related to the shedding of the separation bubble and is less pronounced in the presence of the propulsive jet. In the shear layer itself, the spectra obtained from the hot-wire signal have a more broadband low-frequency content, which also reflects the characteristic frequency of turbulent structures convected in the shear layer, a swinging motion (St D = 0.6), as well as the radial flapping motion of the shear layer (St D = 0.85), respectively. Moving downstream along the shear layer, spectral content at slightly higher frequencies (St D < 4) gets more pronounced and can be related to the shear layer instability process and the signature of smaller turbulent structures that appear in the wake.

ON SHOCKS DRIVEN BY HIGH-MASS PLANETS IN RADIATIVELY INEFFICIENT DISKS. II. THREE-DIMENSIONAL GLOBAL DISK SIMULATIONS

ABSTRACT Recent high-resolution, near-infrared images of protoplanetary disks have shown that these disks often present spiral features. Spiral arms are among the structures predicted by models of disk–planet interaction and thus it is tempting to suspect that planetary perturbers are responsible for these signatures. However, such interpretation is not free of problems. The observed spirals have large pitch angles, and in at least one case (HD 100546) it appears effectively unpolarized, implying thermal emission of the order of 1000 K (465 ± 40 K at closer inspection). We have recently shown in two-dimensional models that shock dissipation in the supersonic wake of high-mass planets can lead to significant heating if the disk is sufficiently adiabatic. Here we extend this analysis to three dimensions in thermodynamically evolving disks. We use the Pencil Code in spherical coordinates for our models, with a prescription for thermal cooling based on the optical depth of the local vertical gas column. We use a 5M J planet, and show that shocks in the region around the planet where the Lindblad resonances occur heat the gas to substantially higher temperatures than the ambient gas. The gas is accelerated vertically away from the midplane to form shock bores, and the gas falling back toward the midplane breaks up into a turbulent surf. This turbulence, although localized, has high α values, reaching 0.05 in the inner Lindblad resonance, and 0.1 in the outer one. We find evidence that the disk regions heated up by the shocks become superadiabatic, generating convection far from the planet’s orbit.

LES investigation into the generation of momentum deficits in the supersonic wake of a micro-ramp

Implicitly implemented large eddy simulation (LES) with a fifth-order WENO scheme was conducted in this study. Based on Navier-Stokes equations, this LES was carried out to explore the origin of momentum deficit caused by a supersonic micro-ramp at flow conditions of Ma = 2.5 and Reθ = 5760. The numerical results were validated through qualitative and quantitative comparisons with existing experimental data. After describing the aerodynamic properties of the supersonic wake, such as the deficit and the streamwise vortices, the momentum deficit was later detected to originate from the lower portion of the upstream boundary layer, while the high momentum fluid originated from close to the wall at the upper portion. Position alternation trigged by the micro-ramp was finally proposed as a revised mechanism.

Decay of the supersonic turbulent wakes from micro-ramps

The wakes resulting from micro-ramps immersed in a supersonic turbulent boundary layer at Ma = 2.0 are investigated by means of particle image velocimetry. Two micro-ramps are investigated with height of 60% and 80% of the undisturbed boundary layer, respectively. The measurement domain is placed at the symmetry plane of the ramp and encompasses the range from 10 to 32 ramp heights downstream of the ramp. The decay of the flow field properties is evaluated in terms of time-averaged and root-mean-square (RMS) statistics. In the time-averaged flow field, the recovery from the imparted momentum deficit and the decay of upwash motion are analyzed. The RMS fluctuations of the velocity components exhibit strong anisotropy at the most upstream location and develop into a more isotropic regime downstream. The self-similarity properties of velocity components and fluctuation components along wall-normal direction are followed. The investigation of the unsteady large scale motion is carried out by means of snapshot analysis and by a statistical approach based on the spatial auto-correlation function. The Kelvin-Helmholtz (K-H) instability at the upper shear layer is observed to develop further with the onset of vortex pairing. The average distance between vortices is statistically estimated using the spatial auto-correlation. A marked transition with the wavelength increase is observed across the pairing regime. The K-H instability, initially observed only at the upper shear layer also begins to appear in the lower shear layer as soon as the wake is elevated sufficiently off the wall. The auto-correlation statistics confirm the coherence of counter-rotating vortices from the upper and lower sides, indicating the formation of vortex rings downstream of the pairing region.

Subsonic to Supersonic Wake Stabilization Using Discrete Porosity

The feasibility of using discrete suction to improve the laser optics environment associated with a hemisphere-and-cylinder turret was investigated using computational fluid dynamics. Simulations were conducted at Mach numbers of 0.5, 0.7, and 1.5. The discrete suction control generates and positions a large-scale counter-rotating vortex pair that induces a strong downwash over the hemispheric beam director. Flow attachment is maintained regardless of the position of the optical window and whether a shock is present. The density fluctuation in the wake is greatly reduced. Consequently, an improvement in the optical environment over the baseline can be expected for the Mach number range studied.

Explicit algebraic Reynolds stress model for compressible flow turbulence

Algebraic Reynolds stress model (ARSM) is often employed in practical turbulent flow simulations. Most of previous works on ARSM have been carried out for incompressible flows. In the present paper, a new ARSM model is suggested for compressible flows. The model adopts a compressibility factor function involving the turbulent Mach number and the gradient Mach number. Compared to incompressible flow, explicit solution for ARSM for compressible flow can hardly be obtained due to dilatation terms. We propose approximate representations for these dilatation-related terms to obtain an explicit procedure for compressible flow turbulence. The model is applied to compressible mixing layer, supersonic flat-plate boundary and planar supersonic wake flow. It is found that the model works very well yielding results that are in good agreement with the DNS and the experimental data.

Direct Numerical Simulations for Flow and Noise Studies

A new high-fidelity multi-block structured curvilinear compressible Navier-Stokes solver purposely developed for exploiting high- performance computing systems (HPC) is introduced. The code has been designed with maximum efficiency in mind to allow cutting- edge high-fidelity turbulence and aeroacoustics simulations on HPC systems. The performance of the code on different HPC architectures is presented, showing very good scaling up to large core counts for realistic test cases, i.e. multi-block configurations. The code was applied to perform large-scale direct numerical simulations, i.e. model free simulations based on first principles, of a variety of flows for the study of transition, turbulence and flow generated noise. Results will be presented for i) turbulent axisymmetric supersonic wakes, focusing on the effect of inflow turbulence on the behavior of the near wake; ii) fully turbulent jets, looking at the jet noise generating mechanisms, iii) tripped airfoils, studying the noise generation of airfoils including wind tunnel installation effects, and possibly other examples.

Numerical investigation of turbulent supersonic axisymmetric wakes

AbstractNumerical experiments are conducted of turbulent supersonic axisymmetric wakes at Mach number $M= 2. 46$ and Reynolds number, based on free-stream velocity and base diameter, ${\mathit{Re}}_{D} = 1\ensuremath{\times} 1{0}^{5} $. Direct numerical simulations (DNS) are used to study the effect of approach flow conditions, and of specific azimuthal modes, on the near-wake behaviour. To that end, DNS are performed with laminar and turbulent approach boundary layers, and additional turbulent approach flow DNS with reduced circumferential size are conducted to deliberately eliminate certain azimuthal/helical modes. DNS with turbulent approach flow show an increased turning angle and increased growth of the separating shear layer, leading to a shorter recirculation region, a stronger recompression shock system, and ultimately good agreement with experimental data at considerably higher Reynolds number. A similar wake structure is found for laminar and turbulent inflow conditions, giving further evidence of the wake structure being a consequence of the global near-wake instabilities and not a result of upstream conditions. Stability analyses of two-dimensional basic states are carried out by computing the temporal pulse response using forced Navier–Stokes simulations to investigate which azimuthal modes are dominant for fully turbulent wakes and how the stability behaviour is influenced by the choice of basic state. Using the time- and azimuthally averaged data from three-dimensional DNS with turbulent inflow as basic state, an absolute instability of the axisymmetric mode was found and helical modes $m= 4, 5, 6$ were found to be linearly most unstable, in contrast to results obtained earlier using an axisymmetric flow solution as the basic state. The addition of a turbulence viscosity in the forced DNS retains most of the stability characteristics but reduces the wavenumber of the linearly most-amplified modes.

Stability analysis of axisymmetric supersonic wakes using various basic states

Two-dimensional stability analyses are conducted of turbulent axisymmetric supersonic wakes at M = 2.46. The aim is to investigate which azimuthal modes are dominant and how the stability behaviour is influenced by the choice of basic state. To that end, axisymmetric (two dimensional) and three dimensional direct numerical simulations (DNS) with either laminar or turbulent inflow conditions were conducted of supersonic wakes to provide the respective basic states for the stability analysis. The global stability analyses were then performed by computing the temporal pulse response using forced Navier-Stokes simulations for each basic state. Using the time- and azimuthally-averaged data from the 3D DNS with turbulent inflow as basic state, an absolute instability of the axisymmetric mode at a Reynolds number, based on wake-generating body diameter and freestream velocity, ReD = 100,000 was found. This is in contrast to results obtained earlier using an axisymmetric flow solution as the basic state. The linear stability analysis for all basic states is presented showing the temporal growth of various azimuthal modes and the respective radial mode shapes. The results are also contrasted to those obtained from nonlinear DNS.

An axis treatment for flow equations in cylindrical coordinates based on parity conditions

A novel axis treatment using parity conditions is presented for flow equations in cylindrical coordinates that are represented in azimuthal Fourier modes. The correct parity states of scalars and the velocity vector are derived such that symmetry conditions for each Fourier mode of the respective variable can be determined. These symmetries are then used to construct finite-difference and filter stencils at and near the axis, and an interpolation scheme for the computation of terms premultiplied by 1/ r. A grid convergence study demonstrates that the axis treatment retains the formal accuracy of the spatial discretization scheme employed. Two further test cases are considered for evaluation of the axis treatment, the propagation of an acoustic pulse and direct numerical simulation of a fully turbulent supersonic axisymmetric wake. The results demonstrate the applicability of the axis treatment for non-axisymmetric flows.