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Experiments were conducted to measure convective velocity of large-scale structures in the shear layer of a Mach 2.0 free jet with a convective Mach number of 0.87 and Reynolds number based on a nozzle diameter of 2.6 10 6 . Real-time flow visualization and planar Doppler velocimetry PDV measurements along with space-time correlation were used. The...
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... results com- pare very well to previously reported results 22 on the same jet but using a different camera system and imaging location. Figure 10 is analogous to Fig. 9, but where velocity rather than gray scale intensity forms the basis for correlation and where the jet core, mixing layer, and coflow are all seeded. This condition represents the best available data set and is based on the analysis of 500 full image sequences of 28 images each. ...Context 2
... Fig. 9, but where velocity rather than gray scale intensity forms the basis for correlation and where the jet core, mixing layer, and coflow are all seeded. This condition represents the best available data set and is based on the analysis of 500 full image sequences of 28 images each. Similar to Fig. 9a, the correlation coeffi- cient maxima in Fig. 10a are seen to decrease in magnitude and shift downstream with increasing time. However, it is clear that there is only a single maximum and, from Fig. 10c, that this ensemble-averaged correlation coefficient maximum translates downstream at a velocity of approxi- mately 276 m / s. Similarly, the histogram shows a Gaussian- like ...Context 3
... This condition represents the best available data set and is based on the analysis of 500 full image sequences of 28 images each. Similar to Fig. 9a, the correlation coeffi- cient maxima in Fig. 10a are seen to decrease in magnitude and shift downstream with increasing time. However, it is clear that there is only a single maximum and, from Fig. 10c, that this ensemble-averaged correlation coefficient maximum translates downstream at a velocity of approxi- mately 276 m / s. Similarly, the histogram shows a Gaussian- like distribution of convective velocities with a mean value of 295 m / s and standard deviation of 64 m / s. Both the ensemble-averaged and histogram-averaged ...Context 4
... discussing these results, we begin with the additional two sets of flow visualization images, which were obtained under different seeding conditions. Figure 11 gives the his- togram of convective velocities for flow visualization image sequences with a the jet core and b the coflow seeded, in addition to naturally occurring seeding of the mixing layer. In both cases, the histogram indicates a relatively high value of convective velocity with respect to theory. ...Context 5
... of convective velocity from time se- quences often pairs of such images. The results presented here illustrate that consideration of the details of the flow visualization method is essential for proper interpretation of the results. This is particularly evident when comparing the data presented in Fig. 9 traditional flow visualization and Fig. 10 fully seed PDV data. Both sets of data were ac- quired from the same flow field but give completely different pictures of the dynamics of large-scale turbulence structures. To better understand how these drastically different pictures can arise, we take a closer look at the correlation procedure used to track structures in these image ...Context 6
... the arguments posed above, only one ex- periment met the conditions necessary to produce reliable convective velocity measurements. Specifically, we focus on the PDV data acquired in a fully seeded flow field, presented in Fig. 10. The most striking result is that the convective velocity determined from these images was very close to the theoretically predicted value given by Eq. 1.2. The convec- tive velocity calculated from the ensemble-averaged space- time cross correlation was 276 m / s, the average convective velocity from the histograms was 295 m / s, and ...Similar publications
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... A combination of experiments and direct numerical simulations (DNS) is applied to study the time-resolved evolution of transitional flow structures. Experimentally, a double-pulsed illumination-imaging system with a repetition rate of 10 Hz, as well as an 8-pulsed ultra-fast image acquisition system with a repetition rate of 100 kHz, is used to capture the flow structure (Thurow et al. 2002(Thurow et al. , 2008. A high-speed schlieren technique is applied (Laurence, Wagner & Hannemann 2016), which for the first time captures the global evolution of unstable modes on a delta flat plate. ...
Cross-flow transition over a delta wing is systematically studied in a Mach 6.5 hypersonic wind tunnel, employing the Rayleigh scattering flow visualisation, high-speed schlieren and fast-response pressure sensors. Direct numerical simulations and analysis based on linear stability theory under the same flow conditions are applied to analyse the transition mechanism. Three unstable modes are identified: the travelling cross-flow instabilities, the second mode and the low-frequency waves. It is shown that the travelling cross-flow vortices first appear in the cross-flow region near the leading edge of the model. These vortices can modulate the mean profile of the flow, which benefits the growth of second mode. A phase-locked interaction mechanism transfers energy from the cross-flow instabilities to the high-frequency second mode, leading to amplification at the expense of the cross-flow instability. As the second mode grows to a critical amplitude, it triggers a $z$ -type secondary instability within a similar frequency range, which introduces secondary finger-like structures connecting to the cross-flow vortex. It is further found that the generation of these finger-like structures is related to the expansion and compression of the second mode. These finger vortices further evolve along the streamwise direction into low-frequency waves and corresponding hairpin-like structures that finally trigger turbulence. An interaction mechanism likely exists between the secondary instability and the low-frequency waves, since their phase speeds are approaching each other. These observations of the interaction mechanism are consistent with those of previous studies on hypersonic boundary layers (Zhang et al. , Phys. Fluids , vol. 32 (7), 2020, 071702; Li et al. , Phys. Fluids , vol. 32 (5), 2020, 051701).
... To this end, an ultrafast image acquisition system, combined with an ultrafast camera and a ultrafast laser, is needed, with a repetition rate above 1000 kHz. [72][73][74] There have only been a few reports on ultrafast PIV measurements. Wernet and Opalski 76 reported a 2D PIV system based on ultrafast imaging technology. ...
Transition in a Mach 6 flared cone boundary layer over a heated wall has been investigated in the Mach 6 wind tunnel at Peking University using visualization, focused laser differential interferometry, infrared imaging, particle image velocimetry (PIV), and direct numerical simulation (DNS). The model's wall-temperature ratio [Formula: see text] (where [Formula: see text] and T 0 are, respectively, the wall temperature and oncoming stream stagnation temperature) can be controlled to vary from 0.66 to 1.77. An ultrafast illumination image system has been used for Rayleigh-scattering visualization and PIV to experimentally capture the dynamics of the transition. Lagrangian flow structures are revealed by both the DNS results and the time-resolved PIV data. The effect of wall temperature on the transition is investigated, and it is found that increasing η initially delays but then promotes the transition to turbulence, with the reversal point being near [Formula: see text]. The turbulence onset mechanism over the heated wall for [Formula: see text], where first-mode-induced oblique breakdown dominates, is then investigated, and it is shown that lifting-up three-dimensional (3D) waves appear around the critical layer owing to the nonlinear development of the oblique first mode. Consequently, a downward sweep motion occurs to compensate for the lifting low-speed fluid, with the formation of a warped wave front. High-shear layers are created around the 3D Lagrangian waves and strengthened to cause the formation of a Λ-vortex. In general, this lifting-up 3D wavepacket has been confirmed to play a determining role in hypersonic turbulence production over a heated wall, which is similar to the findings in incompressible boundary layers.
... Using a pulse-burst laser for time-resolved measurements, single-component velocity was measured in a supersonic jet at a rate of 250 kHz (Thurow et al. 2005). The measurements were limited to a sequence of 28 frames; however, this system was later used to investigate convection velocities of large-scale turbulence (Thurow et al. 2008). FM-DGV has also benefitted by the development of high-speed cameras, measuring single velocity components up to 500 kHz in high-pressure fuel injectors (Schlűßler et al. 2015b;Gűrtler et al. 2017). ...
Large-scale turbulent structures can be correlated over many jet diameters, and thus, a large field of view measurement resolved in time and space is desired to link their evolution to aeroacoustic noise production. This work describes the development and demonstration of a novel time-resolved Doppler global velocimetry system capable of spatially resolving a large field of view of the jet. The technique was applied to image a large axial extent, 8 jet diameters, of the flow field in a heated supersonic jet at 50 kHz. From the single-component measurements, mean velocity and turbulence intensity were measured within a root-mean-square error of 0.02U¯/Uj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\overline{U}}/U_j$$\end{document} and 0.01u¯′/Uj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{u}^{\prime}/U_j$$\end{document}, respectively, to PIV validation measurements. The velocity spectrum measured along the nozzle lip line at x/D=6\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x/D=6$$\end{document} was validated by comparison to the existing literature for free jets. The spatial distribution of energy within the jet was also observed through the velocity spectra, showing energy concentrated along the nozzle lip line for all frequencies. Space–time correlations reveal evidence of wavepacket structures, characterized by their long axial correlations and constant convection velocity. The measurement technique developed in this work shows strong suitability for studies in aeroacoustics of high-speed flows, in which large-scale long-lived turbulent structures dominate radiated noise.
Graphic abstract
... Particularly, the intermittent bias error is pronounced with the velocity difference between seeded and unseeded streams in the mixing region (Rice et al., 2015). It is important to emphasize that the aforementioned errors due to intermittent sampling are not restricted to PIV, but also affect other seeding-based techniques (Samimy and Wernet, 2000;Li et al., 2007), such as laser Doppler velocimetry (McLaughlin and Tiederman, 1973;Birch and Dodson, 1980;Dibble et al., 1987;Fuchs et al., 1994;Nobach, 2015), Doppler global velocimetry (Smith, 1998;Thurow et al., 2008) and particle tracking velocimetry (Li et al., 2012). Although the intermittency in the particle seeding has been extensively observed, quantitative studies about its consequences in the PIV measurements are hardly found in the literature (Kähler et al., 2012;Rice et al., 2015). ...
In the present work, a standard large eddy simulation is combined with tracer particle seeding simulations to investigate the different PIV bias errors introduced by intermittent particle seeding and particle lag. The intermittency effect is caused by evaluating the velocity from tracer particles with inertia in a region where streams mix with different seeding densities. This effect, which is different from the vastly-discussed particle lag, is frequently observed in the literature but scarcely addressed. Here, bias errors in the velocity are analysed in the framework of a turbulent annular gaseous jet weakly confined by low-momentum co-flowing streams. The errors are computed between the gaseous flow velocity, obtained directly from the simulation, and the velocities estimated from synthetic PIV evaluations. Tracer particles with diameters of 0.037, 0.37 and 3.7 µm are introduced into the simulated flow through the jet only, intermediate co-flowing stream only and through both regions. Results quantify the influence of intermittency in the time-averaged velocities and Reynolds stresses when only one of the streams is seeded, even when tracers fulfil the Stokes-number criterion. Additionally, the present work proposes assessing unbiased velocity statistics from large eddy simulations, after validation of biased seeded simulations with biased PIV measurements. The approach can potentially be applied to a variety of flows and geometries, mitigating the bias errors.
... Laser-based diagnostics are used in a variety of applications to help understand chemical [1], thermodynamic [2], and flow [3] effects. Velocity measurements are particularly important to understand flow-transport phenomena [3][4][5][6][7], especially when combined with additional measurements [8]. Gas velocity measurements often require the seeding of particles or a gas into the mixture to allow flow tracking. ...
... Gas velocity measurements often require the seeding of particles or a gas into the mixture to allow flow tracking. Measurements in low-speed flows typically employ solid particle tracers, either via particle image velocimetry (PIV) [9] or laser Doppler velocimetry (LDV) [5,10,11] approaches. At a certain velocity, however, gasphase tracers are strictly required when tracer particles cannot respond quickly enough to flow fluctuations. ...
Multiphoton-resonance enhancement of a rare-gas-assisted nitrogen femtosecond-laser electronic-excitation-tagging (FLEET) signal is demonstrated. The FLEET signal is ideal for velocimetric tracking of nitrogen gas in flow environments by virtue of its long-lived nature. By tuning to three-photon-resonant transitions of argon, energy can be more efficiently deposited into the mixture, thereby producing a stronger and longer-lived FLEET signal following subsequent efficient energy transfer from excited-state argon to the $ C $ C ( ${^3\Pi}_u$ 3 Π u ) excited state of nitrogen. Such resonant excitation exhibits as much as an order of magnitude increase in this rare-gas-assisted FLEET signal, compared to near-resonance excitation of seeded argon demonstrated in previous work, while reducing the required input excitation-pulse energies by two orders of magnitude compared to traditional FLEET.
... Despite these diagnostic challenges, velocity measurements are extremely important in these settings to understand flow-structure interactions, such as the laminar-to-turbulent boundary layer transition in hypersonic flows; however, these velocities are difficult to measure with current optical diagnostic techniques, particularly in hypersonic environments. Particle image velocimetry (PIV) [3] or laser Doppler velocimetry (LDV) [4][5][6] are often employed in low-speed-often subsonic-applications by seeding the flow with solid or liquid particles that respond quickly enough to flow fluctuations to allow accurate flow tracking. High-speed flows, however, can create conditions in which the response times of the particles are not sufficiently fast to reliably track the flow. ...
Krypton (Kr)-based tagging velocimetry is demonstrated in a ${\rm Kr}/{\rm N}_2$ K r / N 2 jet at 100 kHz repetition rate using a custom-built burst-mode laser and optical parametric oscillator (OPO) system. At this repetition rate, the wavelength-tunable, narrow linewidth laser platform can generate up to 7 mJ/pulse at resonant Kr two-photon-excitation wavelengths. Following a comprehensive study, we have identified the 212.56 nm two-photon-excitation transition as ideal for efficient Kr-based velocimetry, producing a long-lived ( $\sim\!{40}\;\unicode{x00B5} {\rm s}$ ∼ 40 µ s ) fluorescence signal from single-laser-pulse tagging that is readily amenable to velocity tracking without the need for a second “read” laser pulse. This long-lived fluorescence signal is found to emanate from ${\rm N}_2$ N 2 —rather than from Kr—following efficient energy transfer. Successful flow velocity tracking is demonstrated at multiple locations in a high-speed ${\rm Kr}/{\rm N}_2$ K r / N 2 jet flow. The 100 kHz repetition rate provides the ability to perform time-resolved velocimetry measurements in high-speed and even hypersonic flow environments, where standard velocimetry approaches are insufficient to capture the relevant dynamics.
... However, the convection velocity calculated by the isentropic model is constant (Papamoschou and Roshko, 1988), so it unveils very limited information about the dynamic characteristics of vortical structures. On the other hand, the convection velocity of turbulence structures can also be calculated by using two-point space-time correlations because a vortical structure can be tracked by the locations of correlation-peaks in space-time coordinates, as reviewed by Thurow et al. (2008). An example is the experimental study of compressible round jets (Bridges, 2006), where the space-time correlations along the center and lip lines were measured by a particle image velocimetry (PIV) system, so the convection velocities of coherent structures were solvable. ...
... On the other hand, two-point space-time correlation can be employed to calculate the local Uc, i.e., the convection velocity at each grid point. In the spanwise center plane of the jet, the correlation of the fluctuation of streamwise velocity u ′ can be defined as follows (Thurow et al., 2008): ...
Two-point space–time correlation and Fourier spectrum analysis are applied to large-eddy simulation results of a compressible parallel jet flow at Reynolds number 2000 and Mach number 0.9. Flow properties including instantaneous vortical structures, flow intermittency, convection velocity of vortical structures, and pressure signals in the near flow-field are presented and discussed. The results show multi-scale features of vortical structures after flow transition. High intermittency is found to occur around the outer edges of the shear layer and the region surrounding the potential core, where the motion of vortices is vigorous. In order to analyze the motion of vortices, the convection velocity of vortical structures in the center plane of the jet is calculated by a designed solution procedure. The high convection velocity zone is shown to be a “V” shaped cap covering the potential core. The pressure fluctuation signals in the vortical flow are analyzed so as to study the effects of vortex motion. The signals show the feature of wave-packets and contain multiple dominant frequencies. The distribution of the dominant frequencies is characterized by a terrace shaped zone with stairs descending in both the streamwise and lateral directions. In addition, the phase velocity of the pressure signals shown by the frequency–wavenumber diagram unveils that the pressure fluctuations travel at a stable phase velocity along the lip-line of the jet, while the component with a supersonic phase velocity is salient in the downstream of the flow transition region outside the shear layer.
... Image acquisition or illumination systems with a repetition rate above 1 MHz, which are generally called ultrafast systems, 28 have been used in experimental fluids research for flow visualizations. 29,30 There have only been a few reports on ultrafast PIV measurements, mainly from two research groups. One is Versluis's group at the University of Twente, who have used a "rotating mirror" ultrafast camera and continuous cold-light to measure the high-speed flow field of a microfluidic pipe cleaning root canals. ...
For the first time, a tomographic particle image velocimetry system with a 1 MHz sampling rate is used to investigate the evolution of three-dimensional instabilities in a Mach 6 flat plate boundary layer. The system is combined with three ultrafast cameras, one eight-channel ultrafast laser, and one 36-channel synchronization controller. PCB ® fast response pressure sensors are also applied to detect the instability evolution in the streamwise direction. Two near-wall volumes are investigated, the upstream one (volume 1) being in a laminar state and the downstream one (volume 2) containing evolving instabilities. For the laminar flow in volume 1, increasing the boundary layer thickness reduces distortion compared to the hypersonic Blasius solution; decreasing the streamwise location or increasing the angle of attack from 0 ○ to 2 ○ increases the distortion. For the disturbed flow in volume 2, the time-resolved evolution of a three-dimensional instability wave is captured in three snapshots, with its phase speed, wavelength, and frequency about 732 m/s, 49 mm, and 20 kHz. Because of the superposition effect of oblique waves, the instability travels like a chain of wavepackets in the streamwise direction, which is accompanied by an alternative distribution of high-speed and low-speed streaks in the spanwise direction. Published under license by AIP Publishing. https://doi.
... Tinney et al. (2008) extracted the convection velocity using proper orthogonal decomposition. Blohm et al. (2006) and Thurow et al. (2008) conducted planar Doppler velocimetry measurements and investigated the effect of the seeding particles on the estimation of the convection velocity. They showed that the bias error due to the particles can be nearly eliminated if the entire flow fields are filled by seeded particles. ...
A single-pixel ensemble correlation method was applied to the schlieren and shadowgraph image velocimetry (SIV) and a velocimetry method that can obtain the convection velocity distribution of high spatial resolution without an expensive pulsed laser system being achieved for a laboratory-scale supersonic jet flow. A cold axisymmetric supersonic jet was employed, and the basic characteristics of the convection velocity fields are measured by SIV as well as those of the velocity fields by the particle image velocimetry (PIV) in the single-pixel resolution. The Mach number of a supersonic jet was 2.0, and the Reynolds number based on the diameter of the nozzle exit was 1.0 × 10⁶. A pulsed light-emitting-diode light source was used for SIV as a less expensive light source. The single-pixel ensemble correlation method applied to PIV clearly visualizes the potential core and the shear layer development with the high spatial resolution. The axial velocity of SIV at the jet centerline is approximately 0.7–0.8 times of that of PIV which seems to relate to the convection velocity. The velocity calculated from the shadowgraph images agrees well with the convection velocity estimated from the Mach wave emission angle. The comparison between the scale of the visualized turbulent structure and the length scale of large eddies implied that the quantitative discussion of the SIV measurement requires careful consideration of the scale of the visualized turbulent structure on the SIV image.
Graphic abstract
... A number of methods to estimate the convection velocity in turbulent free shear flows have been used in the past and are summarized by [4]. The most widely used technique in turbulent flows is based on the two-point correlation. ...
... Murray and Lyons [12] have estimated the convection velocity by tracing the Mach wave angles in the high speed images. However, as discussed by [4], the drawback of these methodologies lies in the fact that the convection velocity of the local flow field is obtained rather than the exclusive behavior of the large-scale coherent structures. As the large-scale structures travel with different convection speed than the smaller scales, the estimation using the above methods is likely to be inaccurate. ...
Motivated by the aero-acoustic feedback loop phenomenon in high speed free jets and impinging jets, a thorough examination of a POD (Proper Orthogonal Decomposition)-Galerkin method to determine the average convection velocity of coherent structures in the shear layer is presented in this paper. The technique is shown to be applicable to both time resolved as well as time unresolved data, if the data set meets certain requirements. Using a detailed sensitivity analysis on a synthetic data set, a quantitative estimate on the required time resolution for the technique has been found, which can be useful for both experimental, as well as numerical studies investigating the aero-acoustic feedback loop in high speed flows. Moreover, some innovative ways to apply the technique are also demonstrated using a simulated data set, showing the effectiveness of the technique to any general problem in supersonic jets, heat transfer, combustion or other areas in fluid mechanics, where an advection process can be identified.
