Internal layers in turbulent free-shear flows

The characteristics of the internal layers of intense shear are examined in a mixing layer and in a jet, in the range of Reynolds numbers 134<Reλ<275. Conditionally averaged profiles of streamwise velocity conditioned on the identified internal layers present strong velocity jumps, which account for approximately 10% of the characteristic large-scale velocity of the flow. The thickness ⟨δw⟩ of the internal layers from the combined analysis of both the mixing layer and the jet scales with ⟨δw⟩/λ∼Re−1/2λ, which suggests a scaling with the Kolmogorov length scale (η), analogous to recent observations on the turbulent/nonturbulent interface (TNTI). The thickness of the internal shear layers within the mixing layer is found to be between 9η and 11η. The concentration of a passive scalar across the internal layers is also examined, at the Schmidt number Sc=1.4. The scalar concentration does not show any jumps across the internal layers, which is an important difference between the internal layers and the TNTI. This can be explained from the analysis of the internal layers of intense scalar gradient, where the flow topology node/saddle/saddle dominates, associated with strain, whereas the internal layers of intense shear are characterized by a prevalence of focus/stretching. A topological content analogous to that obtained in layers of intense scalar gradient is found in proximity to the TNTI, at the boundary between the viscous superlayer and the turbulent sublayer. These observations evidence that the TNTI and the internal layers of intense scalar gradient are similar in several respects

Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor ei, with the vorticity vector ω, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors |ei⋅ˆω| are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e1, in contrast to the global tendency for ω to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between ω and nonlocal e1 and that the strongly swirling worms are kinematically significant to this process.Fluid Mechanic

Small-scale motions in turbulent boundary-free shear flows

The present work is an experimental and numerical investigation of the small-scale motions in turbulent free-shear flows. In the far-field turbulence of a jet at high Reynolds number (Re? = 350) hot-wire anemometry (HWA) is applied to measure time series of flow velocity. By filtering these time series, large- and small-scale velocity fluctuations are obtained. Both the amplitude and the frequency of the small-scale signals are locally stronger (weaker) for positive (negative) fluctuations of the large-scale signal, which is refered to as amplitude and frequency modulation. The local amplitude and frequency of the small-scale signals increase monotonically with the strength of the large-scale velocity fluctuations. The same flow is also investigated with long-range ?PIV (microscopic Particle Image Velocimetry). The measurement is validated against the HWA signals by comparison of the turbulence statistics. A validation based on the topological content is also performed. The coherent structures of vorticity and of intense dissipation are adequately resolved, and their characteristic size is assessed. It is found that the size of the vortical structures does not change significantly when conditioned on strongly-positive or strongly-negative large-scale velocity fluctuations. Using the PIV results the amplitude and frequency modulation observed from HWA signals is explained as an inhomogeneous distribution of the small-scale structures within the flow. In particular, the analysis of ?PIV data reveals that the intense vortical and dissipation structures tend to be preferentially located in high-velocity regions, hence they are characterized by convection velocities higher than the mean velocity of the flow. Furthermore, the spatially resolved velocity vector fields allow to quantify amplitude modulation directly in physical space. From this direct estimation in physical space, amplitude modulation is only 25% of the value measured from hot-wire anemometry. The remaining 75% comes from the fixed spectral band filter used to obtain the large- and the small-scale signals, which does not consider the local convection velocity (Taylor hypothesis of frozen turbulence). A very similar overestimation of amplitude modulation when quantified in the time-frame is also confirmed analytically. Based on the experimental analysis on the jet an explanation for amplitude and frequency modulation is developed, which can be extended to other free-shear flows. The validity of this interpretation is assessed based on the analysis of Direct Numerical Simulations of a mixing layer, at the Reynolds number based on the Taylor microscale (Re? =) of 250. The local vorticity rms, taken as a measure of the small-scale activity, is found to be modulated by the large-scale velocity fluctuations depending on the position within the flow. In particular, on the low-speed side of the mixing layer, positive large-scale velocity fluctuations correspond to a stronger vorticity rms, whereas on the high-speed side, they correspond to a weaker vorticity rms. This is consistent with previous studies on a mixing layer. Important differences are found in the strength of the scale interaction from time series and in physical space, consistent with the predictions developed from the analysis of the jet. On the high-speed side of the mixing layer, amplitude modulation from time series largely underestimates the value obtained from spatial series, and overestimates it on the low-speed side. Therefore, the interaction between large-scale velocity fluctuations and small scales is dependent on the flow position within the mixing layer, similar to a turbulent boundary layer. Nonetheless, when the vorticity rms is correlated with the large-scale shear velocity gradients, the correlation coefficient is found to be nearly constant throughout the mixing layer, and close to unity. This reveals that the large and the small scales present a strong interaction independent of the position when the large-scale shear velocity gradients are considered, instead of the large-scale velocity fluctuations, as in the existing literature on amplitude modulation. The strong correlation between the large-scale gradients and the small scales suggests to investigate possible evidence of the so called “scale invariance” (Meneveau and Katz 2000). The alignment between the local vorticity and the large-scale vorticity is examined within the vortical tubes. It is found that the vorticity from unfiltered (representing the small scales) and from low-pass-filtered velocity vector fields (representing the larger scales) tend to be aligned within the vortical tubes. This suggests that the direction of vorticity does not vary significantly across the scales. Therefore, the anisotropy of the large scales is partially preserved at the small-scale level, which is in contrast with the Kolmogorov’s hypothesis of local isotropy.Process and EnergyMechanical, Maritime and Materials Engineerin

Near-field coherent structures in circular and fractal orifice jets

To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier proper orthogonal decomposition (Fourier-POD) is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analyzed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wave number m=0, associated to the characteristic Kelvin-Helmholtz vortex rings, in the fractal jet modal structures at the fundamental azimuthal wave number m=4 capture the largest amount of energy. In addition, energy is scattered across a wider range of wave numbers than in the round jet. The radial Fourier-POD profiles, however, are nearly insensitive to the orifice geometry, and collapse to a universal distribution when scaled with a characteristic radial length. A similar collapse was recently observed in POD analysis of turbulent structures in pipe flow. However, unlike in pipe flow, the azimuthal-to-radial aspect ratio of the Fourier-POD structures is not constant and varies greatly with the wave number. The second part of the paper focuses on the relationship between streamwise vorticity and streamwise velocity, to characterize the role of the orifice geometry on the lift-up mechanism recently found to be active in turbulent jets [P. Nogueira, A. Cavalieri, P. Jordan, and V. Jaunet, Large-scale streaky structures in turbulent jets, J. Fluid Mech. 873, 211 (2019)]. The averaging of the streamwise vorticity conditioned on intense positive fluctuations of streamwise velocity reveals a pair of vorticity structures of opposite sign flanking the conditioning point, inducing a radial flow towards the jet periphery. This pair of structures is observed in both jets, even if the azimuthal extent of this pattern is 30% larger in the jet issuing from the circular orifice. The coupling between streamwise vorticity and velocity motions is also examined using Fourier-POD. The analysis reveals that in the jet with a circular orifice lower wave-number modes, corresponding to structures at larger scales, capture a larger fraction of the vorticity-velocity coupling. This evidences that the orifice geometry directly influences the interaction between velocity and vorticity

Jet noise predictions by time marching of single-snapshot tomographic PIV fields

Abstract: This work combines the latest advancements in time marching of 3D vector fields from tomographic particle image velocimetry, with an adapted version of Lighthill’s formulation, for the prediction of far-field jet noise. Three-dimensional velocity vector fields of the jet flow are first reconstructed from a tomographic volume of 4× 3× 9.5 Dj3, with Dj = 5 cm being the jet-exit diameter. (The jet-exit Mach number Mj ranges from 0.10 to 0.20.) The obtained vector fields are then used as input to a recently developed procedure for the time marching of the vorticity field, which relies upon the vortex-in-cell methodology. This yields time series of each three-dimensional velocity field, from which the far-field pressure is computed via Lilley’s acoustic analogy (through evaluation of the Lighthill’s stress tensor). It is shown that the estimate of the far-field noise spectrum compares well with the spectrum measured directly from a far-field microphone in the anechoic A-tunnel facility of TU Delft, in the Strouhal number range from approximately 1 to 12. Graphical Abstract: [Figure not available: see fulltext.]Wind EnergyAerodynamic

Streamwise fences for the reduction of trailing-edge noise in a NACA633018 airfoil

Streamwise fences for the reduction of the trailing-edge noise are experimentally investigated on a NACA633018 airfoil. Interchangeable trailing-edge inserts with streamwise fences of different spacing and height are tested in an anechoic wind tunnel. Far-field trailing-edge noise was measured by an array of microphone and the airfoil drag was calculated from the wake profiles acquired by a wake rake. The transversal spacing between the fences has a much stronger impact on noise reduction than the fences height. A maximum noise reduction of 5-6dB is obtained from fences having a spacing of 2 mm, and it is achieved in the range of Strouhal numbers based on the chord of 15-40, equivalent to frequencies 1-3 kHz. When increasing the spacing between the fences from 2 mm to 4 mm, a different aeroacoustic behavior is observed, with a lower noise reduction at high frequencies, and a higher noise reduction and low frequencies. Increasing the angle of attack from α=0° to α=6° does not lead to any significant deterioration of the noise reduction performance. From a wake survey, the coefficient of drag was found to increase of only 6-7%when installing trailing-edge inserts with fences

On near-field coherent structures in circular and fractal orifice jets

To investigate the influence of the orifice geometry on near-field coherent structures in a jet, Fourier-POD is applied. Velocity and vorticity snapshots obtained from tomographic particle image velocimetry at the downstream distance of two equivalent orifice diameters are analysed. Jets issuing from a circular orifice and from a fractal orifice are examined, where the fractal geometry is obtained from a repeating fractal pattern applied to a base square shape. While in the round jet energy is mostly contained at wavenumber m=0, associated to the characteristic Kelvin-Helmholtz vortex rings, in the fractal jet modal structures at the fundamental azimuthal wavenumber m=4 capture the largest amount of energy. The second part of the study focuses on the relationship between streamwise vorticity and streamwise velocity, to characterise the role of the orifice geometry on the lift-up mechanism recently found to be active in turbulent jets. The averaging of the streamwise vorticity conditioned on intense positive fluctuations of streamwise velocity reveals a pair of vorticity structures of opposite sign flanking the conditioning point, inducing a radial flow towards the jet periphery. This pair of structures is observed in both jets, even if the azimuthal extent of this pattern is 30% larger in the jet issuing from the circular orifice. This evidences that the orifice geometry directly influences the interaction between velocity and vorticity

固体壁チェンバーを用いた高速点火方式レーザー核融合炉設計研究

University of Tokyo (東京大学

Spatial-spectral characteristics of momentum transport in a turbulent boundary layer

Spectral content and spatial organization of momentum transport events are investigated in a turbulent boundary layer at the Reynolds number (Re_{\unicode[STIX]{x1D70F}})=2700, with time-resolved planar particle image velocimetry. The spectral content of the Reynolds-shear-stress fluctuations reveals that the largest range of time and length scales can be observed in proximity to the wall, while this range becomes progressively more narrow when the wall distance increases. Farther from the wall, longer time and larger length scales exhibit an increasing spectral content. Wave velocities of transport events are estimated from wavenumber–frequency power spectra at different wall-normal locations. Wave velocities associated with ejection events (Q2) are lower than the local average streamwise velocity, while sweep events (Q4) are characterized by wave velocities larger than the local average velocity. These velocity deficits are almost insensitive to the wall distance, which is also confirmed from time tracking the intense transport events. The vertical advection velocities of the intense ejection and sweep events are on average a small fraction of the friction velocity U_{\unicode[STIX]{x1D70F}}, different from previous observations in a channel flow. In the range of wall-normal locations 60<y^{+}<600, sweeps are considerably larger than ejections, which could be because the ejections are preferentially located in between the legs of hairpin packets. Finally, it is observed that negative quadrant events of the same type tend to appear in groups over a large spatial streamwise extent.</jats:p

Experimental Analysis of Unsteady Natural Convection Around a Horizontal Heater in a Water-Filled Enclosure

Particle Image Velocimetry (PIV) measurements are carried out to analyse the buoyancy-induced flows originating from a horizontal heated cylinder enclosed in a square-sectioned cavity, filled with distilled water. A description of the experimental setup is provided, alongside with a discussion of critical issues in the measurement process and thermal conditioning of the system. Repeatability of the tests is assessed in both steady-state and unsteady conditions. Results are provided for four different values of the leading parameter, the modified Rayleigh number Raq, ranging from 1:48 104 to 8:62 104. The system is witnessed to undergo a transition from steady-state, laminar flow to unsteady oscillatory flow. The evolution of the flow throughout the bifurcation is described by velocity profile plots and 2D field visualizations. The suitability of the technique for the analysis of transitional natural convection regimes is confirmed by the quality of the experimental data, and the agreement with comparative numerical computations