Shock Motion Research Articles

Simulation of transonic buffet with an automated zonal DES approach

A study of transonic buffet on the NASA Common Research Model at flight Reynolds numbers is presented. The ability of two different hybrid RANS/LES models as well as the URANS approach for resolving three-dimensional buffet motion was evaluated by means of spectral analysis. Automated Zonal DES and URANS simulations show similar results in terms of buffet frequency and spanwise propagation of buffet cells, whereas the Delayed Detached Eddy Simulation results indicate a strong interaction between flow separation and shock motion. The extracted characteristic frequencies which are associated with transonic buffet are located in a range of Sr = 0.2–0.65 for URANS and AZDES and are therefore in accordance with findings from related recent research. Furthermore, the simulation time series were investigated and a structure of spanwise moving buffet cells with varying convection speed and wavelength could be observed.

Differences between main shock and aftershock ground motions derived from the Japanese KiK-net database

We considered the large ground motion Japanese database and statistically analyzed the differences between main shock and aftershock ground motions. In particular, we considered the moment magnitude (M), the rupture distance (Rrup), the fault type, and the time-averaged shear-wave velocity for the upper 30 m of soil deposits (VS30) that could have influenced ground motion characteristics. We analyzed the logarithmic ratios of the spectral accelerations (Sa) and the mean periods of the earthquake ground motions, comparing them to those of the main shock motions. In addition, main shock and aftershock ground motion records with those predicted by the ground motion prediction equation developed for Japan. We observed that aftershock ground motions with Rrup ≤ 60 km, M ≤ 5.5, and period <1 s, had smaller Sa than main shock motions; this was particularly true in the case of shallow active crustal events. Moreover, we verified that the VS30 did not influence the characteristics of aftershock and main shock ground motions. Finally, in the case of moderate nearby earthquakes, the aftershock ground motions were found to have longer mean period than the main shock ground motions.

Features of the spatial organization of the body in athletes of various qualifications when hitting the ball in football

The article analyzes the angular characteristics of football players of different qualifications in the extreme phases of the impact of the middle part of the foot on a stationary ball. The angles of the knee, hip, shoulder, elbow joints involved in the impact are considered. Their quantitative values, changes and differences between them are determined. Analyzing the quantitative characteristics of the angles at different moments of the phases when performing a shot on the ball is established. Highly qualified football players have a pronounced coordination of movements in the corners of the lower extremities. In the first phase, the blow is performed due to movement in the hip joint, ending in the knee. In this case, athletes effectively use the movement in the shoulder joint in the initial phase of the impact to increase its strength. Movement in the elbow joint in the final phase to maintain balance. In low-skilled players, the coordination of movements is disturbed, both joints of the legs are equally involved in the first phase of the blow. The movement of the hands does not occur, the shoulder and elbow joints are connected only in the final phase of the movement. It is established that the angular characteristics of the knee, hip and elbow joints in the micro-phase of the support leg of the preparation phase have statistically significant differences. Also in the micro-phase shock motion of the working phase there are statistically significant differences in all four angles analyzed by us.

Unsteady Flow Features Across Different Shock/Boundary-Layer Interaction Configurations

An experimental study has been conducted to investigate unsteady flow phenomena observed within various two-dimensional configurations of shock/boundary-layer interactions. Six configurations have been tested in Mach 2 flow: and 20° compression ramps, and incident shock reflections from , 8, 9, and 10° shock generators; Reynolds numbers in each case are . The flow is assessed using an array of fast-response pressure transducers in conjunction with a high-repetition rate particle image velocimetry system. Development of the mean flow structures early in each interaction is observed to be consistent with the free interaction concept. Unsteady wall-pressure energy content at frequencies above those associated with the characteristic low-frequency shock motion also shows significant similarities in the vicinity of the shock foot. Results confirm that this low-frequency peak is not associated with a narrow-band forcing mechanism from either upstream or downstream, but rather a characteristic frequency that varies with interaction strength, which describes the flow’s dynamic response. These findings support various models published in the literature that have sought to explain the source of low-frequency unsteady shock motion.

Low-frequency unsteadiness of shock-wave/boundary-layer interaction in an isolator with background waves

Low-frequency unsteadiness is investigated through wind tunnel experiments and numerical simulations of the internal flow in a supersonic isolator with background waves generated by a 14° wedge in a freestream with a Mach number of 2.94. The power spectra, coherence, and phase analyses of high-frequency pressure signals and schlieren images provide a local and global description of the unsteadiness. The upstream mechanism exhibits a significant influence on the unthrottled flow field. In the weak interactions of small separation flow, the pressure fluctuation between two adjacent incident points has a strong correlation in a large frequency range, while only large-amplitude shock oscillations are exhibited in the pressure fluctuations at the boundary layer. The downstream mechanism dominates the asymmetric shock motion in the throttled flow field. The profiles of the power spectrum and standard deviation both exhibit two peaks at the upstream and downstream peripheries of the wall separation patterns. Two types of oscillations can be identified through the pressure data, and type III is established from the analysis of schlieren images. The oscillation behavior of the three types is obtained through the power spectral analysis of a series of schlieren snapshots. The frequency of the occurrence and the one-cycle amplitude of different oscillation types are significantly different. By combining the coherence and phase analyses with the corresponding schlieren images and pressure data, the feedback mechanism of the three oscillation types is determined. This study combines the low-frequency unsteadiness in supersonic internal flows with the multiple separation regions caused by complex background waves.

Spatially resolved mean and unsteady surface pressure in swept SBLI using PSP

Strong crossflow and swept separation are key aspects of the flow dynamics of 3-D shock wave/boundary layer interactions. This study explores the global surface pressure field beneath the canonical interaction produced by a sharp fin with deflection angle $$15^\circ$$ with a turbulent incoming boundary in a Mach 2 freestream flow. This corresponds to an interaction of moderate strength, and the unsteady pressure distribution captures pressure fluctuations associated with separation shock motion upstream of the interaction. Details of the PSP calibration are also described where the calibration process combines both a priori (with separately painted test coupon) and in situ calibration (with pressure tap measurements during test). Flow features are identified directly from the quantitative pressure distribution and compared to qualitative surface oil flow visualizations. The technique facilitates measurement of the pressure distribution on surfaces that have been difficult or impossible to instrument, such as the face of the shock-generating fin. The unsteady paint response is captured simultaneously with unsteady pressure transducers on the surface underneath the interaction, and a frequency response function based on this comparison is presented. As the results discussed herein demonstrate, the use of PSP allows one to capture significantly more information about this complex, highly three-dimensional interaction with details that are not easily obtained using traditional sensors, while also providing a more informed global view of the interaction. The utility and limitations of the technique in application to supersonic wind tunnel experiments are discussed.

Aeroelastic Reduced Order Model: Kriging-Corrected Potential Flow

A novel aeroelastic reduced order model is developed for two-dimensional gust interaction modeling in transonic flows. Such conditions exhibit a key nonlinearity: sonic shock motion. The proposed approach comprises an aerodynamics reduced order model coupled to a structural model. The aerodynamics model consists of corrected integrated force coefficients computed by an unsteady potential flow method (incompressible vortex panels). The corrections are obtained from kriging surrogates trained using inviscid compressible computational fluid dynamics data. Two gust lengths (namely, long and short) are simulated for this purpose and serve as the upper and lower bounds of the model. The developed aeroelastic reduced order model is evaluated via modeling untried gust cases, the lengths of which fall between the training cases. Applied to the FFAST Crank and NACA0012 airfoils, the approach accurately reproduces aeroelastic response—with deviations never exceeding 8.0 and 10.5%, respectively. In terms of computational cost, the trained models were more than an order of magnitude faster than the computational fluid dynamics simulations.

Numerical simulation of nonlinear aeroelastic behaviors of composite panels in transonic flow

Aiming to better understand how the presence of both structural and aerodynamic nonlinearities affect the aeroelastic behavior of laminated composite panels in transonic flow, we employ fluid-structure coupling algorithm with a midpoint serial staggered procedure to solve nonlinear aeroelastic responses. In this algorithm, the Euler equations are solved by a flux splitting scheme to obtain unsteady aerodynamic pressure in case of shock movement; a finite element co-rotational formulation, as well as stress-strain relations in the laminate coordinate system, is applied to model geometric nonlinear composite structure; the algorithm is validated by aeroelastic response analysis of a flat panel in the transonic and supersonic regime. Then six different thin laminated composite panels, which have two different layer orientations, cross-ply [0°/90°/0°/90°/0°] and angle-ply [45°/-45°/45°/-45°/45°], as well as three different sizes of curvature, H/h = 0, H/h = 5 and H/h = 10, are numerically simulated at Mach 1.01. The results, comprising the static divergence, flutter onset, amplitude, and spectra of the post-flutter responses are determined. They illustrate that with different layer orientation and curvature, the aeroelastic response of the composite panel presents entirely different forms. Especially, due to the development of the multiple-shock structure in the transonic regime, oscillations with very low-frequency are observed for the curved composite panels with ply [45°/-45°/45°/-45°/45°], which have not as yet been found in the work of previous researchers.

A pressure- or velocity-dependent acceleration rate law for the shock-to-detonation transition process in PBX 9502 high explosive

Shock-to-detonation transition profiles of PBX 9502 explosive are analyzed to develop a rate law for shock acceleration. The shock motion profiles are seen to follow a common trend in the shock acceleration–velocity frame, aside from an early time transient that is dependent on the initiating shock strength. The duration of the early time transient is seen to correlate with the initial shock strength. The common shock acceleration profile is seen to be Arrhenius-like with respect to the local particle velocity or pressure. A dual-rate pressure-dependent Arrhenius-type rate law is developed with the duration of the early rate set by the initial shock strength. The rate law is able to predict the shock motion for all tests well in both particle velocity and pressure space. In addition to directly measuring commonalities in the acceleration profiles of the experimental shock motion, this work provides insight into the functional form of the reaction rate laws for this TATB-based high explosive. The rate law also supports the concept that shock-driven reaction in heterogenous high explosives is driven by localized ignition and growth of hotspots.

Modal Analysis of a Laminar-Flow Airfoil under Buffet Conditions at Re = 500,000

An airfoil undergoing transonic buffet exhibits a complex combination of unsteady shock-wave and boundary-layer phenomena, for which prediction models are deficient. Recent approaches applying computational fluid mechanics methods using turbulence models seem promising, but are still unable to answer some fundamental questions on the detailed buffet mechanism. The present contribution is based on direct numerical simulations of a laminar flow airfoil undergoing transonic buffet at Mach number M = 0.7 and a moderate Reynolds number Re = 500, 000. At an angle of attack α = 4∘, a significant change of the boundary layer stability depending on the aerodynamic load of the airfoil is observed. Besides Kelvin Helmholtz instabilities, a global mode, showing the coupled acoustic and flow-separation dynamics, can be identified, in agreement with literature. These modes are also present in a dynamic mode decomposition (DMD) of the unsteady direct numerical solution. Furthermore, DMD picks up the buffet mode at a Strouhal number of St = 0.12 that agrees with experiments. The reconstruction of the flow fluctuations was found to be more complete and robust with the DMD analysis, compared to the global stability analysis of the mean flow. Raising the angle of attack from α = 3∘ to α = 4∘ leads to an increase in strength of DMD modes corresponding to type C shock motion. An important observation is that, in the present example, transonic buffet is not directly coupled with the shock motion.

Large eddy simulation of pseudo shock structure in a convergent–long divergent duct

In this paper, the Pseudo shock structure in a convergent–long divergent duct is investigated using large eddy simulation on the basis of Smagorinsky–Lilly,​ Wall-Adapting Local Eddy-Viscosity and Algebraic Wall-Modeled LES subgrid models. The first objective of the study is to apply different subgrid models to predict the structure of Lambda form shocks system, while the ultimate aim is to obtain further control of the shock behavior. To achieve these goals, the dynamic grid adaption and hybrid initialization techniques are applied under the 3D investigation to reduce numerical errors and computational costs. The results are compared to the existing experimental data and it is found that the WMLES subgrid model results in more accurate predictions when compared to the other subgrid models. Subsequently, the influences of the divergent section length with the constant ratio of the outlet to throat area and, the effects of discontinuity of the wall temperature on the flow physics are investigated. The results indicate that the structure of compressible flow in the duct is affected by varying these parameters. This is then further discussed to provide a deeper physical understanding of the mechanism of Pseudo shock motion.

Dynamics of separation bubble dilation and collapse in shock wave/turbulent boundary layer interactions

Although several mechanisms have been suggested as explanations for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions, questions remain on causes and effects. In this effort, we examine the observed asymmetry in large-scale shock motions to highlight which of the suggested mechanisms is most consistent with shock-speed observations and accompanying separation dynamics. The analysis is based on a flowfield obtained from a validated large eddy simulation of a fully separated interaction. A statistical analysis is used to determine the speed of bubble collapse relative to dilation. The low-pass filtering required to separate upstream from downstream motions in the presence of higher-frequency jitter is accomplished with a relatively new technique, empirical mode decomposition, that is very appropriate for this purpose. The dynamics of bubble dilation versus collapse are then elaborated with conditional dynamic mode decomposition (DMD) analyses on the respective pressure fields. Bubble breathing is shown to have a different structure during dilation than during collapse—larger structures are observed during collapse when fluid is expelled from the bubble. The nature of the DMD mode associated with Kelvin–Helmholtz (K–H) shedding in the mixing layer also differs between dilation and collapse: When the bubble is dilating, the structures at the dominant K–H frequency are larger than when the bubble is collapsing. Additionally, a link is established between the convecting K–H structures and corrugation observed along the reflected shock. Some aspects of the nature of the asymmetry are linked to the ease of eddy formation (K–H structures), which plays an important role in the collapse of the bubble.

Unsteady Characteristics of a Swept-Shock/Boundary-Layer Interaction at Mach 2

An unswept fin is placed in Mach 2 flow at an angle () of 15 deg, creating a fully separated interaction of strength, . The time-averaged behavior of the interaction is characterized by mean surface pressure measurements inside the inception zone and in the quasi-conical region. The interaction dynamics are explored through unsteady surface pressure measurements, where the highest unsteadiness is observed near the intermittent separation and underneath the open separation bubble. Further insights into the unsteadiness are sought by examining the contributions to the total pressure fluctuations in three spectral regimes: low-frequency (), mid-frequency (), and high-frequency (). Mid-frequency fluctuations dominate the current 3-D SBLI, in contrast to 2-D interactions where low-frequency disturbances are shown to be prominent. Finally, the interaction is visualized using high-frame-rate conical shadowgraphy (24,000 fps), where a shock identification scheme is used. The PDF of the separation shock locations revealed that it travels the farthest compared with the other two shock features. It is inferred that the smaller extent of the -shock is more probable, which is further confirmed by conditionally sampling the shock slope based on the movement of the separation shock.

Flow separation unsteadiness in an over-expanded single expansion ramp nozzle

Combined with the focusing schlieren and dynamic pressure measurement technology, the flow field and nozzle wall pressure were experimentally measured, under the different nozzle pressure ratios (NPR) of the single expansion ramp nozzle (SERN). Time and frequency domain analysis provide unsteady flow characteristics within the nozzle. The results show that the flow field structure inside SERN is asymmetry. The flow separation mode on the upper wall of the nozzle is restricted shock separation (RSS), while on the lower wall is free shock separation (FSS); in RSS mode, the pressure on the wall near the outlet sharply oscillated relative to FSS mode. Near separation point, the shock motion exhibits obvious low-frequency characteristics, and the separated shear layer has an influence on the wall pressure near the nozzle exit.

Shock Motion and Flow Structure of an Underexpanded Jet in the Helical Mode

A large-eddy simulation is performed to study the shock motions and flow structures of an underexpanded free jet. The jet is characterized by a nozzle pressure ratio of 3.4 and a fully expanded Mach number of 1.45. At this condition, the dominant instability mode of the jet is the helical (C) mode. The numerical results of mean velocity fields, shock structures, and the screech frequency are in good agreement with the experimental results. A single helical vortex appears in the jet shear layer, which coincides with the helical mode. At the fourth shock cell, the dominant acoustic source location for the screech tone, the shock interacts with vortices and oscillates periodically. The flow structures associated with the generations of the screech tone and the second harmonic are analyzed by the proper orthogonal decomposition. The coherent structures with the azimuthal wave number and 2 are related to the screech tone and its second harmonic, respectively.

Two-dimensional unsteadiness map of oblique shock wave/boundary layer interaction with sidewalls

The low-frequency unsteadiness of oblique shock wave/boundary layer interactions (SBLIs) has been investigated using large-eddy simulation (LES) and high-frequency pressure measurements from experiments. Particular attention has been paid to off-centreline behaviour: the LES dataset was generated including sidewalls, and experimental pressure measurements were acquired across the entire span of the reflected shock foot. The datasets constitute the first maps of low-frequency unsteadiness in both streamwise and spanwise directions. The results reveal that significant low-frequency shock motion (with $St\approx 0.03$) occurs away from the centreline, along most of the central separation shock and in the corner regions. The most powerful low-frequency unsteadiness occurs off-centre, likely due to the separation shock being strengthened by shocks arising from the swept interactions on the sidewalls. Both simulation and experimental results exhibit asymmetry about the spanwise centre. In simulations, this may be attributed to a lack of statistical convergence; however, the fact that this is also seen in experiments is indicative that some SBLIs may exhibit some inherent asymmetry across the two spanwise halves of the separation bubble. There is also significant low-frequency power in the corner separations. The relation of the unsteadiness in the corner regions to that in the centre is investigated by means of two-point correlations: a key observation is that significant correlation does not extend across the attached flow channel between the central and corner separations.

Experimental investigation of shock-induced separation and flow control in a transonic compressor cascade

The influence of transition control on shock-induced flow separation was investigated in a highly loaded transonic compressor cascade at an inlet Mach number of 1.21 and a chord-based Reynolds number of $$1.4 \times 10^6$$ . Transition was influenced by raising the free-stream turbulence from 0.5 to 2.5%. Two further cases employed either air-jet vortex generators (AJVG) or a surface roughness patch as transition control devices. Velocity fields in the vicinity of the unsteady transonic separation were captured by particle image velocimetry (PIV). Blade flexure induced by the unsteady aerodynamic loading was tracked for each image and compensated individually prior to PIV processing. The captured flow fields indicate shape variations of the separation region, while the shock foot moves within a range of up to 20% of chord. The frequency of separation for each investigated case was assessed on the number of vectors with negative velocity in each PIV sample. To further quantify the size of the separation region, the statistically independent PIV samples were conditionally averaged for various passage shock positions at a resolution of 1% chord length. Insight to the dynamics and frequency of the passage shock motion was further provided by high-speed shadowgraphy. Large bubble separation occurs if the turbulence of the incoming flow is low. The size of separation region decreases when AJVGs are applied but still exhibits bubble separation as the passage shock moves downstream. The size of the separation region is significantly reduced either if a roughness patch is applied or if the turbulence level of the incoming flow is high. The flow conditions showing bubble separation in the mean flow also exhibit distinct spectral peaks indicating periodic shock oscillations.

Experimental investigation of the throttling process and oscillation mechanism in a supersonic cascade

The structure and oscillation characteristics of the shock train during steady and oscillatory flows in a supersonic cascade was experimentally studied. The study was based on the SAV21 supersonic cascade designed by the German Aerospace Centre operating under incoming Mach number equal to 2.27 and flow turning angle of 45 degrees. Before the onset of stall, the expansion waves generated on the curved configuration of the suction surface (stage III) and the separation bubble (stage IV) suppresses the movement of the shock train. A striking feature of stage 1 of the oscillatory flows is that as the throttling ratio increases, the dominant frequency of the pressure fluctuation keeps decreasing and the high-energy oscillations take up more time and a wider frequency range. Then stage 2 (which is composed of large-amplitude oscillations and secondary oscillations) appears. With the enhancement of the throttling ratio, the occurrence probability of large-amplitude oscillations rises in stage 3. The shock train propagates into the upstream passage in stage 4, the final stage. Through cross-wavelet transform, it was discovered that the immediate change of the entrance local conditions leads to the in-phase fluctuation of pressure in the entire flowfield during the oscillatory flows, which is consistent with the observation of Dailey. Further analysis indicates that all the oscillation stages except stage 4, are triggered by the suction-surface flow separation, which belongs to the Dailey criterion. Furthermore, the feedback loop established by the communicating ways (acoustic wave propagation, shock movement, spillage, and separation bubble deformation) is brought forward.

Experimental study of the coherent vorticity in slightly under-expanded supersonic screeching jets

The noise generation mechanism of screech tone by shock leakage in underexpended round jets is experimentally investigated by means of phase-averaged velocity fields. Two jet flows at Mach numbers 1.10 and 1.15 are measured by a particle image velocimetry apparatus simultaneously with their near acoustic fields and sorted according to their phase with respect to a screech period. The coherent vorticity fields are then computed and analyzed. They depict two distinct regions of high level of vorticity fluctuations. Thanks to the knowledge about shock leakage gathered in previous studies, the role of both regions in the acoustic generation process is identified and a region of the flow is recognized as suitable for emitting acoustic waves. Phase-averaged schlieren visualizations are also computed and used to determine the motion of the first five shocks over a screech period. For both jets, the peak shock motion is found at the fourth shock tip. This shock is also located in the region recognized as favorable for the shock leakage to be observed.

Wavenumber-Frequency Spectra on a Launch Vehicle Model Measured via Unsteady Pressure-Sensitive Paint

Time histories of pressure fluctuations on a generic, “hammerhead” launch vehicle model were measured using unsteady pressure-sensitive paint over a Mach number range of . The calibration process, using a set of unsteady pressure sensors, was found to overcome some of the inherent problems of the fast-response paint, such as rapid photodegradation, nonlinearity in pressure response, and significant temperature sensitivity. The large data set exposed various critical transonic flow physics such as a coupling of the shock motion on the payload fairing (PF) with the separated flow region downstream, and an upstream convection of pressure fluctuations on the PF at certain Mach numbers. Area-weighted integration of the pressure fluctuation data provided a measure of the unsteady forces on various parts of the model. The unsteady force coefficients on the PF and the upper stage were the highest when transonic shocks were present and found to reduce significantly when supersonic flow set in. Time histories on a dense, regularly spaced, spatial grid points allowed for the calculation of wavenumber–frequency () spectra via Fourier transform. The spectra were dominated by the convected fluctuations; the acoustic domain was not discernible. These data, valuable for the buffet and vibroacoustics analysis of aerospace vehicles, are believed to be the first obtained for the transonic flight regime.