Fine-scale Structure Of Turbulence Research Articles

High-Resolution Two-Phase Velocimetry Of Aspherical Particles Using Wavelet-Based Optical Flow Velocimetry (WOFV) Benchmarked With Fully Resolved Direct Numerical Simulations

Several techniques exist to measure the carrier and dispersed phases in multi-phase flows. Particle image velocimetry (PIV) analyzes the carrier phase by cross-correlating particle images, but its resolution is limited by the size of the interrogation window, making it difficult to resolve fine-scale turbulent structures. Particle tracking algorithms capture translational motion of dispersed particles well, but struggle with rotational motion, especially for irregular and aspherical particles. Currently, there is no method that universally measures both the carrier phase velocity field and the translational and rotational motions of dispersed particles. This study evaluates wavelet-based optical flow velocimetry (wOFV) for motion estimation in multi-phase flows, focusing on dispersed ellipsoidal particles and their surrounding turbulent carrier flow using synthetic image data. The research proceeds in two phases: first, the rigid motion of ellipses, including translational and rotational components, is analyzed using wOFV-generated dense motion fields. The results highlight the critical role of the regularization weighting parameter λ. Higher λ values improve translational motion estimation, while an optimal λ avoids under-regularization and non-physical structures in rotational motion. wOFV maintains accuracy in combined motion scenarios with optimal λ values. In the second phase, wOFV captures the turbulent carrier flow around an aspherical particle, benchmarked against DNS data and compared to PIV. wOFV outperforms PIV in resolving finer structures near the particle surface and in accurately representing the wake region. Error analyses confirm wOFV’s superior performance, with optimal results within a specific λ range. In conclusion, wOFV is a highly effective tool for the analysis of multi-phase flow dynamics, providing greater resolution and accuracy than PIV, especially in complex scenarios involving aspherical particles.

High-Resolution Two-Phase Velocimetry Of Aspherical Particles Using Wavelet-Based Optical Flow Velocimetry (WOFV) Benchmarked With Fully Resolved Direct Numerical Simulations

Several techniques exist to measure the carrier and dispersed phases in multi-phase flows. Particle image velocimetry (PIV) analyzes the carrier phase by cross-correlating particle images, but its resolution is limited by the size of the interrogation window, making it difficult to resolve fine-scale turbulent structures. Particle tracking algorithms capture translational motion of dispersed particles well, but struggle with rotational motion, especially for irregular and aspherical particles. Currently, there is no method that universally measures both the carrier phase velocity field and the translational and rotational motions of dispersed particles. This study evaluates wavelet-based optical flow velocimetry (wOFV) for motion estimation in multi-phase flows, focusing on dispersed ellipsoidal particles and their surrounding turbulent carrier flow using synthetic image data. The research proceeds in two phases: first, the rigid motion of ellipses, including translational and rotational components, is analyzed using wOFV-generated dense motion fields. The results highlight the critical role of the regularization weighting parameter λ. Higher λ values improve translational motion estimation, while an optimal λ avoids under-regularization and non-physical structures in rotational motion. wOFV maintains accuracy in combined motion scenarios with optimal λ values. In the second phase, wOFV captures the turbulent carrier flow around an aspherical particle, benchmarked against DNS data and compared to PIV. wOFV outperforms PIV in resolving finer structures near the particle surface and in accurately representing the wake region. Error analyses confirm wOFV’s superior performance, with optimal results within a specific λ range. In conclusion, wOFV is a highly effective tool for the analysis of multi-phase flow dynamics, providing greater resolution and accuracy than PIV, especially in complex scenarios involving aspherical particles.

Unsteady Structure of Compressor Tip Leakage Flows

Abstract Direct numerical simulations (DNS) are performed of a cantilevered stator blade to identify the unsteady and turbulent flow structure within compressor tip flows. The simulations were performed with clearances of 1.6% and 3.2% of chord. The results show that the flow both within the gap and at the exit on the suction side highly unsteady phenomena controlled by fine-scale turbulent structures. The signature of the classical tip-leakage vortex is a consequence of time-averaging and does not exist in the true unsteady flow. Despite the complexity, we are able to replicate the flow within the tip gap using a validated quasi-three-dimensional (Q3D) model. This enables a wide range of Q3D DNS simulations to study the effects of blade tip corner radius and Reynolds number. Tip corner radius is found to radically alter the unsteady flow in the tip; it affects both separation bubble size and shape, as well as transition mechanisms in the tip flow. These effects can lead to variations in tip mass flow of up to 10% and a factor of 2 variation in dissipation within the tip gap.

Quad-plane stereoscopic PIV for fine-scale structure measurements in turbulence

The fine-scale structure in turbulence is investigated by quad-plane stereoscopic particle image velocimetry (QPSPIV). The quad-plane consists of two each of different polarizations and wavelengths, and it provides three velocity components at four independent parallel planes. Measurements have been undertaken in the developed region of a turbulent round jet with a spatial resolution sufficient to capture the small-scale structures. The advantage of the QPSPIV is presented in terms of the spectral response in the evaluation of the out-of-plane velocity gradient. The full velocity gradient tensor is computed with a fourth-order finite difference scheme in the out-of-plane direction as well as the in-plane directions. The turbulence quantities, such as the vorticity components, the energy dissipation rate and the second and third invariants of the velocity gradient tensor, are computed according to their faithful definitions. The coherent fine-scale eddies are extracted from the present QPSPIV data. The probability density functions of the diameter and the maximum azimuthal velocity of the extracted eddies exhibit their peak at approximately $$8\eta $$ and $$1.5u_k$$ , respectively, where $$\eta $$ and $$u_k$$ are the Kolmogorov length and velocity. These values agree well with the data in the literature. The phase-averaged distributions of turbulence quantities around the coherent fine-scale eddy indicate an apparent elliptic feature around the axis. Furthermore, the state of the strain rate exerting the eddy is quantified from the phase-averaged distributions of eigenvalues of the strain rate tensor and the alignment of the corresponding eigenvectors against the axis. The present study gives a solid experimental support of the coherent fine-scale structures in turbulence, and the technique can be applied to various flow fields and to the higher Reynolds number condition.

New insights into the fine-scale structure of turbulence

In a recent study, Lawson & Dawson (J. Fluid Mech., vol. 780, 2015, pp. 60–98) present experimental results on the fine-scale structure of turbulence, which are obtained with a novel variant of particle image velocimetry, to elucidate the relation between the small-scale structure, dynamics and statistics of turbulence. The results are carefully validated against direct numerical simulation data. Their extensive study focuses on the mean structure of the velocity gradient and the pressure Hessian fields for various small-scale flow topologies. It thereby reveals the dynamical impact of turbulent strain and vorticity structures on the velocity gradient statistics through non-local interactions, and points out ways to improve low-dimensional closure models for the dynamics of small-scale turbulence.

Turbulence–flame interaction and fractal characteristics of H2–air premixed flame under pressure rising condition

Direct numerical simulation (DNS) of turbulent premixed flames in a constant volume vessel is conducted to investigate turbulence–flame interaction and fractal characteristics under pressure rising condition. DNS is conducted for hydrogen–air mixture with decaying homogeneous isotropic turbulence of which the Reynolds number based on Taylor micro scale is 97.1. The detailed kinetic mechanism including 12 reactive species and 27 elementary reactions is used to represent the hydrogen–air flames. Even for the pressure rising process, the local heat release rate, the flame curvature and the tangential strain rate can be scaled by the maximum laminar heat release rate corresponding to instantaneous mean pressure, the Kolmogorov length scale and the ratio of the turbulent intensity to the Taylor micro scale in the unburned mixture. These facts show a rapid response of flame characteristics to the pressure change. In the propagation process, flame displacement speed is very high compared to open flames due to the expansion of the burned gas. The compression of the unburned mixture due to the high displacement speed increases pressure in the vessel and induces slow decaying or increasing in the turbulent Reynolds number even for no mean flow. It is clarified that the fractal dimension of the flame surface does not show any dependence on pressure increase. The inner cutoff obtained in the pressure rising condition is in good agreement with the expression proposed in our previous study (Shim et al., 2011) [6] where the ratio of the diameter of coherent fine scale eddy, which is a universal fine scale structure of turbulence, to the laminar flame thickness is used as an important parameter.

Spectral variations near a high-performance military aircraft

Spectral characteristics of jet noise depend upon location relative to the nozzle axis. Studies of the spectral variation in the far field led to a two-source model of jet noise, in which fine-scale turbulent structures are primarily responsible for noise radiation to the nozzle sideline and large-scale turbulent structures produce the broad, dominant radiation lobe farther aft. Detailed noise measurements near an F-22A Raptor shed additional insights into this variation. An initial study [Neilsen et al., J. Acoust. Soc. Am. 133, 2116–2125] was performed with ground-based microphones in the mid-field. The similarity spectra associated with the large and fine-scale turbulent structures [Tam et al., AIAA paper 96–1716 (1996)] provide a reasonable representation of measured spectra at many locations. However, there are additional features that need further investigation. This paper explores the presence of a double peak in the spectra in the maximum radiation direction and a significant change in spectral shape at the farthest aft angles using data from large measurement planes (2 m × 23 m) located 4–6 jet nozzle diameters from the shear layer. The spatial variation of the spectra provides additional insight into ties between the similarity spectra and full-scale jet noise. [Work supported by ONR.]

Development of a digital receiver for range imaging atmospheric radar

In this paper, we describe a new digital receiver developed for a 1.3-GHz range imaging atmospheric radar. The digital receiver comprises a general-purpose software-defined radio receiver referred to as the Universal Software Radio Peripheral 2 (USRP2) and a commercial personal computer (PC). The receiver is designed to collect received signals at an intermediate frequency (IF) of 130MHz with a sample rate of 10MSs−1. The USRP2 digitizes IF received signals, produces IQ time series, and then transfers the IQ time series to the PC through Gigabit Ethernet. The PC receives the IQ time series, performs range sampling, carries out filtering in the range direction, decodes the phase-modulated received signals, integrates the received signals in time, and finally saves the processed data to the hard disk drive (HDD). Because only sequential data transfer from the USRP2 to the PC is available, the range sampling is triggered by transmitted pulses leaked to the receiver. For range imaging, the digital receiver performs real-time signal processing for each of the time series collected at different frequencies. Further, the receiver is able to decode phase-modulated oversampled signals. Because the program code for real-time signal processing is written in a popular programming language (C++) and widely used libraries, the signal processing is easy to implement, reconfigure, and reuse. From radar experiments using a 1-μs subpulse width and 1-MHz frequency span (i.e., 2-MHz frequency bandwidth), we demonstrate that range imaging in combination with oversampling, which was implemented for the first time by the digital receiver, is able to resolve the fine-scale structure of turbulence with a vertical scale as small as 100m or finer.

Similarity spectra analysis of high-performance jet aircraft noise

Noise measured in the vicinity of an F-22A Raptor has been compared to similarity spectra found previously to represent mixing noise from large-scale and fine-scale turbulent structures in laboratory-scale jet plumes. Comparisons have been made for three engine conditions using ground-based sideline microphones, which covered a large angular aperture. Even though the nozzle geometry is complex and the jet is nonideally expanded, the similarity spectra do agree with large portions of the measured spectra. Toward the sideline, the fine-scale similarity spectrum is used, while the large-scale similarity spectrum provides a good fit to the area of maximum radiation. Combinations of the two similarity spectra are shown to match the data in between those regions. Surprisingly, a combination of the two is also shown to match the data at the farthest aft angle. However, at high frequencies the degree of congruity between the similarity and the measured spectra changes with engine condition and angle. At the higher engine conditions, there is a systematically shallower measured high-frequency slope, with the largest discrepancy occurring in the regions of maximum radiation.

Comparison of near‐field military jet aircraft noise with similarity spectra.

The jet mixing noise from high‐performance military aircraft is broadband and, like other jets, appears to have two origins: the fine‐scale turbulent structures (FSSs) close to the nozzle and the large‐scale turbulent structures (LSSs) farther down the plume. The intense LSS noise dominates the radiation at inlet angles greater than 125 deg, and the more omnidirectional FSS noise is the dominant source of noise to the side and aft of the aircraft. An extensive set of measurements was taken of F‐22 Raptor noise at different engine conditions in 2009. The F‐22 noise is compared to the self‐similarity spectra generally applied to describe the contributions of the LSS and FSS in jet noise [Tam and Zaman, AIAA J. 38, 592–599 (2000)]. For large inlet angles, the shapes of the noise spectra fit the LSS self‐similarity spectra at low frequencies, but the self‐similarity spectra roll off more steeply for frequencies above 1 kHz with the engine at military power and afterburner. Closer to the sideline, the FSS self‐similarity spectra do not match the shape of the data spectra very well at high engine power. Possible reasons for these discrepancies are investigated. [Work sponsored by the Air Force Research Laboratory.]

Local structure and fractal characteristics of H2–air turbulent premixed flame

Direct numerical simulation of a hydrogen–air turbulent premixed flame propagating in homogeneous turbulence was conducted to investigate the local flame structure and the fractal characteristics of the flame front at different Reynolds number turbulences. A detailed kinetic mechanism including 12 reactive species and 27 elementary reactions was used to represent the hydrogen–air reaction in turbulence. At high Reynolds number turbulence, the multilayer and the multiply folded flame structures were observed. Flame peninsulas toward unburned mixture were also created and they tended to diminish due to the heat conduction to the surrounding unburned mixture at low temperature. The local extinction of hydrogen–air turbulent flames was frequently generated at the leading edge of corrugated flame fronts at high Reynolds number turbulence. Fractal features of the flame surface were also investigated by the three-dimensional box counting method. Fractal dimensions of the flame surface were 2.3–2.5 and were independent of Reynolds number and equivalence ratio. A strong correlation between the inner cutoff in Kolmogorov length units and the ratio of the diameter of the coherent fine scale eddy, which is a universal fine scale structure of turbulence, to the laminar flame thickness (D/δF) was shown, and an inner cutoff scale expression based on D/δF was proposed.

Statistics of Small-Scale Velocity Fluctuations and Internal Intermittency in Marine Stratocumulus Clouds

AbstractClouds are known to be turbulent, but the details of their internal turbulent structure have been largely unexplored. Measurements of turbulent velocities in stratocumulus clouds presented here reveal an intermittent structure consistent with that observed in classic homogeneous isotropic turbulence. The measurements were taken close to cloud top in a 200-m-thick cloud layer over a path of approximately 6 km, using a hot-wire anemometer below a helicopter as part of the Airborne Cloud Turbulence Observation System (ACTOS) measurement system. Hot-wire signal artifacts resulting from droplet impacts are removed without significantly degrading the signal, such that high-order velocity structure functions can be evaluated. The structure function analysis for orders 2–8 show statistically significant departures from the Kolmogorov’s 1941 scaling, yielding scaling exponents consistent with the Kolmogorov–Obukhov refined similarity hypothesis, with an intermittency exponent of 0.25. This is in agreement with the accepted value determined in single-phase flows under carefully controlled conditions, and no evidence is found of any departure from the large body of knowledge obtained from the laboratory on the finescale turbulence structure. This suggests that processes depending on the finescale structure of turbulence that cannot presently be measured in clouds can be explored in the laboratory setting. Since these findings pertain to clouds with relatively low liquid water content and weak turbulence, further work will be required to determine their applicability to other cloud types.

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a timeaveraged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered \((Re_c = 10^4)\), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motioninduced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stalllike vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number \((Re_c = 10^4)\), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For \(Re_c = 4 \times 10^4\), the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For \(Re_c = 4.85 \times 10^4\), it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.

Measurement of fine scale structure in turbulence by time-resolved dual-plane stereoscopic PIV

To investigate fine scale structure of turbulent flows, time-resolved dual-plane stereoscopic particle image velocimetry (TRDPSPIV) has been developed using high-repetition-rate Nd:YAG lasers for industrial processing and high-speed CMOS cameras. This system provides all three velocity components and nine velocity gradients with high spatial and temporal resolution. The number of lasers used in this system is only two by adopting newly-developed parallel beam forming optics. The developed system was applied to velocity measurements of a turbulent jet with the same spatial resolution of general direct numerical simulation (DNS) of turbulence. The velocities obtained in both planes showed very similar pattern, and energy spectra in the both planes coincide very well because of the small distance between the planes. It is shown that probability density functions of the measured nine velocity gradients agree well with those obtained from DNS. From these velocity gradients, various flow properties such as vorticity vectors, second invariant of velocity gradient tensor and energy dissipation rate are obtained exactly. These properties allow an eddy identification, which has been used in the analysis of DNS, to investigate fine scale structure of turbulence. Velocity distributions around the experimentally-detected fine scale eddies have an elliptic feature, and the histograms of the diameter and maximum azimuthal velocity of the detected eddy show peaks at D / η ≈ 10 and u θ ,max / u k ≈ 0.75 . These characteristics of the fine scale eddy coincide with those obtained from DNS. Experimental evidence for the existence of the coherent fine scale eddy in turbulence is given in the present study.

Modelling of high viscosity oil drop breakage process in intermittent turbulence

A multifractal model of the fine-scale structure of turbulence is applied to describe breakage of viscous drops of immiscible liquid immersed in a fully developed turbulent flow. A population of drops whose diameter falls within the inertial subrange of turbulence is considered here. The population balance equation is used to predict the drop size distributions. Calculations are performed for binary and multiple breakage. Several daughter distribution functions are applied and the results of their application are compared with experimental data. Experimental investigations of drop breakup were carried out in a flat bottom stirred tank having the diameter of T = 0.15 m and equipped with Rushton type agitator and four baffles. Silicone oils with viscosity of 10, 100, 500 and 1000 m Pa s were dispersed in the aqueous continuous phase. Measurements were performed using high resolution digital camera. Experimental results as well as numerical simulations show that after the initial period of multiple breakage, the strongly asymmetric type of binary breakage dominates.

Scale-up effects on the drop size distribution of liquid–liquid dispersions in agitated vessels

A multifractal formalism describing the fine-scale structure of turbulence, including its intermittency, is applied to express the drop breakage and coalescence frequencies for drops whose diameter falls within the inertial subrange of turbulence. The model predicts the transient drop size distributions of dispersions in stirred tanks and is used to test four methods of scaling-up agitated vessels. Fast and slow coalescing dispersions are considered.

Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth- or higher-order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient, and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) switch of Harten. Spatially non-dissipative fourth- or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM switch is used to signal the appropriate amount of second- or third-order total variation diminishing (TVD) or essentially non-oscillatory (ENO) types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex–shock interactions, and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock–turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD, positive, or ENO schemes.

Coherent Fine Scale Structure in Turbulent Channel Flows.

Fine scale structure in near-wall turbulence is investigated by using DNS data bases of turbulent channel flows. Fine scale eddies in turbulent channel flows are educed by a new identification scheme. Characteristics of fine scale vortical structures in turbulent channel flow coincide with those in homogeneous isotropic turbulence and turbulent mixing layers. The most expected diameter and maximum azimuthal velocity of the fine scale eddy are about 10 times of the Kolmogorov microscale and about a half of the r.m.s. velocity fluctuation, respectively. These results show that streamwise vortices and hairpin-type vortices near the wall can be classified into the coherent fine scale structure in turbulence. Near the wall, probability density functions of inclination angles and tilting angles of the coherent fine scale eddy show regularity in their spatial distribution, which corresponds to the anisotophy of the near-wall turbulence.

Anisotropy of MHD Homogeneous Turbulence. 2nd Report. Coherent Fine Scale Eddies and Lorentz Force.

Fine scale structure in MHD homogeneous turbulence is investigated to clarify the relationship between anisotropy and coherent fine scale structure in turbulence. In MHD turbulence, mean diameter of the coherent fine scale eddy is about 10 times of Kolmogorov micro scale and maximum azimuthal velocity is about 0.7 times of umrs, which coincide with those in homogeneous isotropic turbulence, turbulent mixing layer and turbulent channel flows without magnetic field. Effect of magnetic field appears in angle distribution of axis of the coherent fine scale eddy. The coherent fine scale eddy perpendicular to the mean magnetic field decays fast due to strong Lorentz force, which results in anisotropic behaviors of MHD homogeneous turbulence.

Influence of Turbulent Mechanical Stresses on Microorganisms

Many phenomena depend on the features of the fine-scale structure of turbulence, including its intermittency. This article discusses the problem of the turbulent “shear” in biotechnology including the effect of the shear stress on particles (cells, flocs, cells immobilized on microcarriers). Traditionally, the effect of intermittency has not been taken into account in the shear problem and the theory of isotropic turbulence introduced by Kolmogorov (1941) based on average values of the rate of kinetic energy dissipation, velocity fluctuactions, rates of strain, turbulent stresses etc. has been applied. In this paper a multifractal formalism is employed to describe intermittency; the results of multifractal approach are then compared with predictions of other models of intermittent and non-intermittent turbulence. The multifractal model of intermittent turbulence has been used to derive equations describing flow-particle interactions, including: equations describing turbulent stresses acting upon particles in the inertial and viscous subranges of turbulence; mass transfer to small particles suspended in turbulent fluid; turbulent rupture of flocs; particles encounters in turbulent flow including the average number of collisions per unit time in the inertial and viscous subranges of turbulence and the severity of collisions; mechanical stress generated by bubble coalescence. Generally, the article shows how the traditional approach to the shear problem in turbulence, based on the Kolmogorov theory, can be extended by including the influence of intermittency. This review article includes 47 references.