Coherent Fine Scale Eddies Research Articles

Large-scale clustering of coherent fine-scale eddies in a turbulent mixing layer

Clustering of coherent fine-scale eddies in a turbulent mixing layer has been analyzed by using direct numerical simulation (DNS) data at Reλ ≃ 250. The coherent fine-scale eddies are defined based on the second invariant of the velocity gradient tensor and the vorticity vector. The clustering is evaluated by the number density of coherent fine-scale eddies, and the large-scale structures are extracted by low-pass filtered velocity fields. Conditional averaging shows that the large-scale enstrophy increases with the number density, whereas the large-scale strain rate stays around the average in the high number density region. The alignments of the vorticity vector and the eigenvectors of the large-scale strain rate tensor are conditioned by the number density or the strain rate magnitude. The eigenvectors and the vorticity vector indicate strong preferential alignments under the intense large-scale strain rate condition. On the other hand, those alignments become weak in the high number density regions. The inter-scale energy transfer between grid and subgrid scales is significantly correlated with the magnitude of the large-scale strain rate while there is no apparent correlation with the number density.

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.

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.

E124 高レイノルズ数乱流予混合火炎の局所構造とフラクタル特性(OS-9:燃焼の最近の進展(2))

Direct numerical simulation (DNS) of a hydrogen-air turbulent premixed flame propagating in homogeneous isotropic turbulence was conducted to investigate the local flame structure and fractal characteristics in high Reynolds number turbulence. A detail kinetic mechanism including 12 reactive species and 27 elementary reactions was used to represent the hydrogen-air reaction. In high Reynolds number turbulence, very complicated flame structures induced by strong coherent fine scale eddy were generated and strong correlation between the inner cutoff and the ratio of diameter of coherent fine scale eddy to laminar flame thickness was observed.

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.

E111 高レイノルズ数水素・空気乱流予混合火炎の三次元構造とフラクタル特性(OS-12:次世代の燃焼技術(I))

Effects of turbulence characteristics on three-dimensional structure and fractal characteristics of flame front were investigated by direct numerical simulation (DNS) of hydrogen-air turbulent premixed flame in high Reynolds number turbulence. The detail kinetic mechanism including 12 reactive species and 27 elementary reactions was used to represent the hydrogen-air reaction. Flame structure in high Reynolds number was very complicated due to strong coherent fine scale eddy and unburned mixture appeared behind flame front. Fractal characteristics of flame front were also investigated by three-dimensional box counting method. Strong correlation between the inner cutoff and the ratio of diameter of coherent fine scale eddy to laminar flame thickness has been observed.

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.

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity ( u k ), and decreases to 1.2 u k , which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length ( η) and α: β: γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.

A quality control method by ultrasonic vibration energy and diagnosis system at trimming process

To investigate a relation between vortex clusters and large-scale structures in the outer layer of wall turbulence, direct numerical simulations of turbulent channel flows have been conducted up to Re τ = 1270. The vortex clusters in the outer layer consist coherent fine scale eddies (CFSEs) of which diameter and maximum azimuthal velocity are scaled by the Kolmogorov length and the Kolmogorov velocity. The CFSE clusters are inside the large-scale structure, which contributes to the streamwise velocity deficit. The scale of those clusters tends to be enlarged with the increase of a distance from the wall. The CFSE clusters are composed of the relatively strong CFSEs, which play an important role in the production of the Reynolds shear stress and the dissipation rate of the turbulent kinetic energy. The most expected maximum azimuthal velocity of the CFSEs in these low-momentum regions of the outer layer is 30 ~ 70% faster compared with those of the CFSEs in unconditioned regions (i.e. all regions of the outer layer), while the most expected diameter of the CFSEs is not changed greatly.

Dynamics of fine scale eddy clusters in turbulent channel flows*

To investigate dynamics of vortex clusters and large-scale structures in the outer layer of wall turbulence, direct numerical simulations of turbulent channel flows have been conducted up to Re τ = 1270. In the outer layer, the vortex clusters are composed of coherent fine-scale eddies (CFSEs) of which diameter and maximum azimuthal velocity are scaled by the Kolmogorov length and velocity. The large-scale structure in the outer layer is composed of these clusters of the CFSEs, which contributes to the streamwise velocity deficit (i.e.low-momentum region). The CFSE clusters are observed in the low-momentum regions of the outer layer, and the scale of those clusters tends to be enlarged with the increase of a distance from the wall. The dynamics of large-scale structures reveals that the cluster structure generated in the bottom of the logarithmic region moves downstream and its scale increases with the increase of the low-momentum region. The CFSE clusters in the low-momentum regions of u′ ≤ −u rms consist of the relatively strong CFSEs, which play an important role in the production of the Reynolds shear stress and the dissipation rate of the turbulent kinetic energy. The process of destruction of the CFSE cluster is also clarified in the outer layer. *This article was chosen from Selected Proceedings of the Fourth International Symposium on Turbulent and Shear Flow Phenomena (Williamsburg, VA USA, 27–29 June 2005) ed J. A. C. Humphrey et al.

1406 コヒーレント微細渦に基づく抵抗低減効果及び伝熱特性の予測法(S30-1 複雑流体の流動現象(1),S30 複雑流体の流動現象)

The characteristics of heat transfer and drag reduction of turbulent water flow with surfactant have been investigated based on the coherent fine scale eddy in near-wall turbulence. To analyze the heat transfer and drag reduction, time scale ratio of surfactant to coherent fine scale eddy has been introduced. This time scale ratio characterizes the range of drag and heat transfer reduction, simultaneously. With the modification of time scale of the coherent fine scale eddy, the range of the drag reduction for heat exchanging cases agree with those for no heat exchanging cases.

Elliptic feature of coherent fine scale eddies in turbulent channel flows

Direct numerical simulations (DNS) of turbulent channel flows up to Reτ=1270 are performed to investigate an elliptic feature and strain rate field on cross sections of coherent fine scale eddies (CFSEs) in wall turbulence. From DNS results, the CFSEs are educed and the strain rate field around the eddy is analyzed statistically. The principal strain rates (i.e. eigenvalues of the strain rate tensor) at the CFSE centers are scaled by the Kolmogorov length η and velocity u_k. The most expected maximum (stretching) and minimum (compressing) eigenvalues at the CFSE centers are independent of the Reynolds number in each y+ region (i.e. near-wall, logarithmic and wake regions). The elliptic feature of the CFSE is observed in the distribution of phase-averaged azimuthal velocity on a plane perpendicular to the rotating axis of the CFSE (ω_c). Except near the wall, phase-averaged maximum (γ/γ_c) and minimum (α/α_c) eigenvalues show maxima on the major axis around the CFSE and minima on the minor axis near the CFSE center. This results in high energy dissipation rate around the CFSE.

2324 乱流コヒーレント微細渦に基づく界面活性剤水溶液の伝熱・抵抗特性の解明(S42-5 複雑流体の流動現象(5),S42 複雑流体の流動現象)

The characteristics of heat transfer and drag reduction of turbulent water flow with surfactant have been investigated based on the coherent fine scale eddy in near-wall turbulence. To analyze the heat transfer and drag reduction, time scale ratio of surfactant to coherent fine scale eddy has been introduced. This time scale ratio characterizes the range of drag and heat transfer reduction, simultaneously. As the fluid near the wall is cooled in the heat exchanging process, the drag reduction range is shrunk for the high temperature conditions. Therefore, decrease of the heat transfer can be prevented in heat exchangers.

5002 乱流予混合火炎における階層構造のSGSモデリング(S50-1 乱流燃焼の実験と数値シミュレーション(1),S50 乱流燃焼の実験と数値シミュレーション)

A new SGS combustion model is proposed based on hierarchical structure of turbulent premixed flames. The hierarchical structure is clarified by the detailed analysis of direct numerical simulation (DNS) data of three-dimensional hydrogen-air turbulent premixed flame. SGS flame surface area strongly correlates with GS strain rate of turbulent velocity field, which is related to the cluster of coherent fine scale eddy. As the GS strain rate of the turbulent combustion field includes dilatation effects intrinsically, a physical consideration is introduced to give the lower limit of dilatation effects in GS. To represent the relation between GS flame surface area and GS strain rate, a new SGS combustion model is proposed under assumptions of fractal characteristics of flame fronts and the scale separation of turbulence. The results predicted by the proposed model coincide very well with DNS results.

Drag Reduction with Fiber Suspensions in Water Flows

Drag reducing flows by nylon fibers are investigated to discuss the mechanism of the drag reduction with fiber suspensions and to develop the prediction method of the drag reduction range. For the prediction method, time scale ratio of drag reducing additives like fibers to coherent fine scale eddy is introduced. Since the time scale of a given fiber is considered to be constant, the time scale ratio depends only on the time scale of the coherent fine eddy for a given fiber. The time scale of the coherent fine eddy can characterize the range of drag reduction for pipes of different diameters very well. The drag reduction occurs in specific range for low fiber concentration, while the drag reduction range shift to the small time scale of the coherent fine scale eddies for high fiber concentration. The characteristic time of the fiber as a drag reducer becomes longer in proportion to the second power of the fiber aspect ratio for low concentration.

422 一様等方性乱流における微細渦クラスターの統計的性質(S35-1 乱流渦構造(1),S35 乱流渦構造)

To investigate the statistics of the clusters of coherent fine scale eddies, direct numerical simulation database of homogeneous isotropic turbulence up to Re_λ=256.1 have been analyzed. The cluster of the strong coherent fine scale eddies tends to exist in the region with high local turbulent kinetic energy, which is defined as local average in the cube of integral length scale, and with high strain rate in large scales. Even in the Kolmogorov length unit, the most expected diameter of the coherent fine scale eddies depend on the characteristics of the integral length box. The diameter in each integral length boxes can be scaled by the local Kolmogorov scale (ηl). The most expected diameter is about 10_<ηl>. These characteristics of coherent fine scale eddies are similar to those in the near-wall turbulence. Moreover, the large scale eddies tend to exist in the region around the cluster where the energy transfer from GS to SGS is strong.

Scaling law of fine scale eddies in turbulent channel flows up to Reτ=800

To clarify the scaling law of fine scale eddies in turbulent channel flows, direct numerical simulations are conducted for Re τ =180, 400 and 800. The diameter and the maximum azimuthal velocity of coherent fine scale eddies can be scaled by Kolmogorov microscale ( η) and Kolmogorov velocity ( u k ). The most expected diameter and maximum azimuthal velocity are 8–10 η and 1.2–2.0 u k , respectively. Near the wall, the most expected diameter increases to 10 η from 8 η and the most expected maximum azimuthal velocity increases to 2.0 u k from 1.2 u k . Strain rates at the center of the coherent fine scale eddies are small compared with the mean strain rate of the whole flow field. The strain rates acting on the fine scale eddies away from the wall coincide with those in homogeneous isotropic turbulence and turbulent mixing layer. However, relatively large strain rates are acting on the near-wall coherent fine scale eddies. The most expected angle between the intermediate eigenvector and the rotating axis of the fine scale eddy is about 15–17°, which is independent of the turbulent flow fields. The probability that coherent fine scale eddies exist in low-speed streaks is higher than that in high-speed streaks. Large scale structures of wall turbulence are visualized by showing spatial distributions of central axes of coherent fine scale eddies.

804 自由せん断乱流の混合遷移とコヒーレント微細渦

804 自由せん断乱流の混合遷移とコヒーレント微細渦

Anisotropy of MHD Homogeneous Turbulence. 3rd Report. Magnetic Flux Density Fluctuation due to Coherent Fine Scale Eddies.

The generation and the development of the magnetic flux density fluctuation due to the coherent fine scale eddies are investigated in detail by analyzing DNS data of MHD homogeneous turbulence. With the addition of the magnetic field, two circulations of magnetic flux density fluctuation are generated around the eddy on the plane perpendicular to the axis of coherent fine scale eddy in the early stage, while these circulations disappear with time. The current density shows the maximum and the minimum value on the same plane. The distance between the center of the eddy and the location of the maximum or the minimum is almost same with the radius of the fine scale eddy. If the axis of the fine scale eddy is perpendicular to the direction of the applied magnetic field, the Lorentz force weakens the swirling motion of the eddy and works as shear stress for it. However, the Lorentz force tends to expand the eddy if the axis of the fine scale eddy is parallel to the direction of the applied magnetic field.

Prediction of Drag Reduction Based on Coherent Fine Scale Eddies in Turbulence.

Prediction method of drag reduction is presented based on the coherent fine scale eddy in turbulence. To estimate the drag reduction efficiency, time scale ratio of drag reducers like surfactants to coherent fine scale eddy is introduced for the near wall turbulence. Key point of this prediction method is the utilization of characteristics of the coherent fine scale eddy in full-developed near wall turbulence before the manipulation of drag reduction. From analysis of DNS data, it is shown that the time scale of the coherent fine scale eddy can be approximated to be 20 η/μrms, 20 νρ/τw0 or 80 νρ/Δp0d. Since the time scale of a drag reducer is considered to be constant under a constant condition, the time scale ratio depends on the time scale of the coherent fine scale eddy. Therefore, the range of drag reduction can be estimated from the characteristics of turbulence before the manipulation of drag reduction. The prediction method is applied for the case of drag reduction by surfactants. The ranges of drag reduction are assembled for different mean velocity and pipe diameter. The effective range for each surfactant mixture is derived and estimation of scale-up effects are shown.