Taylor Scale Research Articles

Analysis of the turbulent law of the wall through the finite scale Lyapunov theory

This work analyzes the turbulent velocity distribution in proximity of the wall using the finite-scale Lyapunov theory just presented in previous works. This theory is here applied to the steady boundary layer under the hypothesis of moderate pressure gradient and fully developed flow along the streamwise direction. The analysis gives an equation for the velocities correlation and identifies the parameters of the expression of the average velocity through the statistical properties of the velocity correlation functions. In particular, the von Kármán constant, theoretically calculated, is about 0.4, and the dimensionless Prandtl’s length is in function of the Taylor-scale Reynolds number. The study provides the average velocity distribution and gives also the variation laws of the other variables, such as Taylor scale and Reynolds stress. The obtained results show that the finite-scale Lyapunov theory is adequate for studying the turbulence in the proximity of the wall.

About scaling properties of relative velocity between heavy particles in turbulence

We present results obtained from high-resolution direct numerical simulations (DNS) of incompressible, statistically homogeneous and isotropic turbulence, up to a Taylor scale based Reynolds number Reλ ≃ 200 and with millions of heavy particles with different inertia. In our set-up, particles are assumed to be spherical and rigid, they simply move by viscous forces, such as the Stokes drag. The velocity statistics is found to be extremely intermittent, with an almost bi-fractal behavior. Here, we consider also a new data analysis for the stationary distribution of rescaled longitudinal velocity difference and further assess the intermittent character of the heavy particles velocities, characterized by the presence of quasi-algebraic tails.

Conditional analysis near strong shear layers in DNS of isotropic turbulence at high Reynolds number

Data analysis of high resolution DNS of isotropic turbulence with the Taylor scale Reynolds number Rλ = 1131 shows that there are thin shear layers consisting of a cluster of strong vortex tubes with typical diameter of order 10η, where η is the Kolmogorov length scale. The widths of the layers are of the order of the Taylor micro length scale. According to the analysis of one of the layers, coarse grained vorticity in the layer are aligned approximately in the plane of the layer so that there is a net mean shear across the layer with a mean velocity jump of the order of the root-mean-square of the fluctuating velocity, and energy dissipation averaged over the layer is larger than ten times the average over the whole flow. The mean and the standard deviation of the energy transfer T(x, κ) from scales larger than 1/κ to scales smaller than 1/κ at position x are largest within the layers (where the most intense vortices and dissipation occur), but are also large just outside the layers (where viscous stresses are weak), by comparison with the average values of T over the whole region. The DNS data are consistent with exterior fluctuation being damped/filtered at the interface of the layer and then selectively amplified within the layer.

Comparison of Holographic and Tomographic Particle-Image Velocimetry Turbulent Channel Flow Measurements

Based on velocity measurements of a fully developed turbulent channel flow, the methods of holographic and tomographic particle-image velocimetry (PIV) are compared. The emphasis of this comparison is on the measurement of time-dependent three-dimensional small-scale flow structures, i.e., structures at a characteristic length on the order of the Taylor scale since such flow patterns can be hardly captured by any two-dimensional experimental technique. The findings show that the holographic PIV method is useful to measure flow patterns in larger volumes whereas the tomographic PIV should be used to resolve three-dimensional small-scale structures.

Digital filter for hot-wire measurements of small-scale turbulence properties

The experimental work on fine-scale properties of turbulence has so far been based mainly on hot-wire and cold-wire measurements. These measurements often suffer from contamination by electronic (including thermal, shot, flicker, burst, etc) noise or from over-filtering by somewhat arbitrary, inappropriate filter settings. This may be overcome by a fast-convergent iterative scheme of filtration developed recently by Mi et al (2005 Phys. Rev. E 71 066304). The present study is carried out (1) to investigate the effectiveness of the scheme using velocity signals (um) obtained from hot-wire measurements in both circular and plane turbulent jets and (2) to assess the effect of the low-pass-filter cut-off frequency on measurements of various small-scale turbulence properties. The results reveal that the electronic noise in um, if not cleaned, may seriously contaminate the fine-scale properties of turbulence derived from um, consequently yielding wrong estimations of typical scales, such as Kolmogorov and Taylor scales. After removing the noise contribution properly, however, these characteristic scales are all obtained appropriately and follow closely their self-preserving relations which have been well confirmed in the past.

Kolmogorov similarity scaling for one-particle Lagrangian statistics

We use direct numerical simulation data up to a Taylor scale Reynolds number Rλ = 1000 to investigate Kolmogorov similarity scaling in the inertial sub-range for one-particle Lagrangian statistics. Although similarity scaling is not achieved at these Reynolds numbers for the Lagrangian velocity structure function, we show clearly that it is achieved for the Lagrangian acceleration frequency spectrum and the scaling range becomes wider with increasing Reynolds number. Stochastic and heuristic model calculations suggest that the difference in behavior observed for the structure function and spectrum is simply a consequence of different rates of convergence to scaling behavior with increasing Reynolds number. Our estimate C0 ≈ 6.9 ± 0.2 for the Lagrangian structure function constant is close to earlier estimates based on extrapolation of the peak value of the compensated structure function. The results presented here suggest prospects for studying Kolmogorov similarity for Lagrangian statistics using the latest innovations in simulation, and measurement techniques are more hopeful than previously suggested in the literature.

High-resolution turbulent scalar field measurements in an optically accessible internal combustion engine

High-resolution planar laser-induced fluorescence (PLIF) measurements were performed in an optically accessible internal combustion engine to investigate the evolution of the turbulent mixing process during the intake and compression strokes. The PLIF measurements were used to analyze the important turbulent length scales, scalar energy and dissipation spectra, and mean scalar gradients. The fluorescence images had sufficient spatial resolution and integrity to resolve all of the fine-scale features of the flow, allowing for direct determination of the Batchelor length scale. The integral and Taylor scales were also determined from two-point spatial correlations of the fluctuating scalar field using an appropriately defined mean scalar value. The general morphology of the scalar field and the measured integral, Taylor and Batchelor length scales were found to be largely independent of engine speed and intake pressure, but increased as the engine cycle progressed through the intake and compression strokes. The measured Batchelor scales ranged from 22 to 54 μm; the integral scales ranged from 1.8 to 3.5 mm; and the Taylor microscales ranged from 0.6 to 1.2 mm. The Taylor and integral scale values were comparable to values reported in the literature from in-cylinder velocity measurements. The mean scalar gradient, a measure of the fine-scale mixing rate, monotonically decreased as the engine cycle advanced. High-resolution measurements of this type are important in the development and validation of future engine combustion models used in computer simulations.

Correlation and Taylor scale variability in the interplanetary magnetic field fluctuations as a function of solar wind speed

[1] Simultaneous multiple point measurements of the magnetic field from 11 spacecraft are employed to determine the correlation scale and the magnetic Taylor microscale of the solar wind as functions of the mean magnetic field direction and solar wind speed. We find that the Taylor scale is independent of direction relative to the mean magnetic field in both the slow ( 600 km/s) solar wind, but the Taylor scale is longer along the mean magnetic field direction in the intermediate (600 km/s ≥ speed ≥ 450 km/s) solar wind. The correlation scale, on the other hand, varies with angle from the mean magnetic field direction. In the slow solar wind the ratio of the parallel correlation scale to the perpendicular correlation scale is 2.55 ± 0.76, decreases to 2.15 ± 0.18 in the intermediate solar wind, and becomes 0.71 ± 0.29 in the fast solar wind. Thus, solar wind turbulence is anisotropic, dominated by quasi two‐dimensional turbulence in both the slow and intermediate solar wind, and by slab type turbulence in the fast solar wind. The correlation and Taylor scales may be used to estimate effective magnetic Reynolds numbers separately for each angular channel. To within the uncertainty, no dependence on the solid angle relative to the mean magnetic field could be identified for the Reynolds number. These results may be useful in magnetohydrodynamic modeling of the solar wind and can contribute to our understanding of solar and galactic cosmic ray diffusion in the heliosphere.

Time Resolved Scanning PIV measurements at fine scales in a turbulent jet

The temporal and spatial complexity of turbulent flows at intermediate and small scales has prevented the acquisition of full three-dimensional experimental data sets for validating classical turbulent theory and Direct Numerical Simulations (DNS). Experimental techniques like Particle Velocimetry, PIV, allow non-intrusive planar measurements of turbulent flows. The present work applied a Time Resolved Scanning PIV system, TRS-PIV, capable of obtaining three-dimensional two-component velocities to measure the small scales of a turbulent jet. When probing the small scales of these flows with PIV, the uncertainty of the measured turbulent properties are determined by the characteristics of the PIV system and specially the thickness of the laser sheet. A measurement of the particle distribution across the thickness of the laser sheet is proposed as a more detailed description of the PIV sheet thickness. The high temporal and spatial resolution of the TRS-PIV system allowed obtaining quasi-instantaneous volumetric vector fields at the far field of a round turbulent jet in water, albeit for a low Reynolds number of 1478 due to the speed limitations of the present camera and scanning system. Six of the nine components of the velocity gradient tensor were calculated from the velocity measurements. This allowed the visualization with near Kolmogorov-scale resolution of the velocity gradient structures in three-dimensional space. In general, these structures had a complex geometry corresponding to elongated shapes in the form of sheets and tubes. An analysis of the probability density function, pdf, of the velocity gradients calculated showed that the on-diagonal (off-diagonal) velocity gradient components were very similar to each other even for events at the tails of the pdfs, as required for homogeneous isotropy. The root mean square of the components of the velocity gradients is also calculated and their ratio of off-diagonal components to on-diagonal components satisfied the 2 factor required for homogeneous isotropic flows. The ratio of the longitudinal Taylor scale to the transverse Taylor scale was also calculated agreeing with the homogeneous isotropic turbulence requirements within 1%.

Dynamics of inertial particles in a turbulent von Kármán flow

We study the dynamics of neutrally buoyant particles with diameters varying in the range [1, 45] in Kolmogorov scale units (η) and Reynolds numbers based on Taylor scale (Reλ) between 590 and 1050. One component of the particle velocity is measured using an extended laser Doppler velocimetry at the centre of a von Kármán flow, and acceleration is derived by differentiation. We find that the particle acceleration variance decreases with increasing diameter with scaling close to (D/η)−2/3, in agreement with previous observations, and with a hint for an intermittent correction as suggested by arguments based on scaling of pressure spatial increments. The characteristic time of acceleration autocorrelation increases more strongly than previously reported in other experiments, and possibly varying linearly with D/η. Further analysis shows that the probability density functions of the acceleration have smaller wings for larger particles; their flatness decreases as well, as expected from the behaviour of pressure increments in turbulence when intermittency corrections are taken into account. We contrast our measurements with previous observations in wind-tunnel turbulent flows and numerical simulations.

Centreline statistics of the small-scale turbulence of a circular jet and their dependence on high frequency noise

This study systematically investigates the statistics of the centreline small-scale turbulence of a circular jet issuing from a smooth contraction nozzle. Detailed velocity measurements were performed for the exit Reynolds number of Re=20100, where Re≡Ujd /ν with Uj being the exit mean velocity, d the nozzle diameter and ν the kinematic viscosity. After effectively filtering out high frequency noises, statistical properties of the small-scale turbulence were obtained appropriately; those properties include turbulence energy dissipation rate, Kolmogorov length scale, Taylor scale, turbulence Reynolds number, skewness and flatness of the velocity derivative. It is observed that these properties satisfy their self-preserving relations in the far field. It is also revealed that the small-scale turbulence reaches the self-preserving state earlier than does the large-scale motion. Besides, the smallest-scale turbulence depends least on the initial and boundary conditions and therefore behaves most universally across different flows.

Leray-α LES of magnetohydrodynamic turbulence at low magnetic Reynolds number

A series of large eddy simulations is performed for decaying homogeneous magnetohydrodynamic (MHD) turbulence at low magnetic Reynolds number (Rem <<1) with different strengths of magnetic field. The initial isotropic turbulence problem has the Taylor scale Reynolds number (Re λ) of 120. The regularization-based Leray-α model is used for sub-grid scale (SGS) closure for the first time and comparisons are made with our own direct numerical simulation (DNS) calculations conducted as part of this study. Analyses of turbulent kinetic energy decay rates, energy spectra, and vorticity fields are made between the varying magnetic field cases. The SGS model assessments are also made between the Leray-α model and the classic non-dynamic Smagorinsky with several model coefficients. Overall, the Leray-α model was unable to capture the anisotropy associated with MHD flows as well as the non-dynamic Smagorinsky model in this study or even the dynamic Smagorinsky model in previous studies.

Anisotropy of the Taylor scale and the correlation scale in plasma sheet magnetic field fluctuations as a function of auroral electrojet activity

Magnetic field data from the Cluster spacecraft in the magnetospheric plasma sheet are employed to determine the correlation scale and the magnetic Taylor microscale from simultaneous multiple‐point measurements for multiple intervals over a range of mean magnetic field directions for three different levels of geomagnetic activity. We have determined that in the plasma sheet the correlation scale along the mean magnetic field direction decreases from 19,500 ± 2200 to 13,100 ± 700 km as the auroral electrojet activity increases from quiet (&lt;80 nT) to active conditions (&gt;200 nT). The reverse occurs for the correlation scale perpendicular to the magnetic field, which increases from 8200 ± 600 km to 13,000 ± 2100 km as the auroral electrojet activity increases from quiet to active conditions. This variation of the correlation scale with geomagnetic activity may mean either a change in the scale size of the turbulence driver or may mean a change in the predominance of one over another type of turbulence driving mechanism. Unlike the correlation scale, the Taylor scale does not show any clear variation with geomagnetic activity. We find that the Taylor scale is longer parallel to the magnetic field than perpendicular to it for all levels of geomagnetic activity. The correlation and Taylor scales may be used to estimate the effective magnetic Reynolds numbers separately for each angular channel. Reynolds numbers were found to be approximately independent of the angle relative to the mean magnetic field. These results may be useful in magnetohydrodynamic modeling of the magnetosphere and can contribute to our understanding of energetic particle diffusion in the magnetosphere.

The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer

Direct numerical simulations at Reynolds numbers ranging from Reλ=30 to 160 show that the thickness δω of the turbulent/nonturbulent (T/NT) interface in planar jets is of the order of the Taylor scale δω∼λ, while in shear free, irrotational/isotropic turbulence is of the order of the Kolmogorov microscale δω∼η. It is shown that δω is equal to the radius of the large vorticity structures (LVSs) in this region, δω≈RLVS. Thus, the mean shear and the Reynolds number affect the T/NT interface thickness insofar as they define the radial dimension of the LVS near the T/NT interface.

Experimental study of highly turbulent isothermal opposed-jet flows

Opposed-jet flows have been shown to provide a valuable means to study a variety of combustion problems, but have been limited to either laminar or modestly turbulent conditions. With the ultimate goal of developing a burner for laboratory flames reaching turbulence regimes of relevance to practical systems, we characterized highly turbulent, strained, isothermal, opposed-jet flows using particle image velocimetry (PIV). The bulk strain rate was kept at 1250 s−1 and specially designed and properly positioned turbulence generation plates in the incoming streams boosted the turbulence intensity to well above 20%, under conditions that are amenable to flame stabilization. The data were analyzed with proper orthogonal decomposition (POD) and a novel statistical analysis conditioned to the instantaneous position of the stagnation surface. Both POD and the conditional analysis were found to be valuable tools allowing for the separation of the truly turbulent fluctuations from potential artifacts introduced by relatively low-frequency, large-scale instabilities that would otherwise partly mask the turbulence. These instabilities cause the stagnation surface to wobble with both an axial oscillation and a precession motion about the system axis of symmetry. Once these artifacts are removed, the longitudinal integral length scales are found to decrease as one approaches the stagnation line, as a consequence of the strained flow field, with the corresponding outer scale turbulent Reynolds number following a similar trend. The Taylor scale Reynolds number is found to be roughly constant throughout the flow field at about 200, with a value virtually independent of the data analysis technique. The novel conditional statistics allowed for the identification of highly convoluted stagnation lines and, in some cases, of strong three-dimensional effects, that can be screened, as they typically yield more than one stagnation line in the flow field. The ability to lock on the instantaneous stagnation line, at the intersection of the stagnation surface with the PIV measurement plane, is particularly useful in the combustion context, since the flame is aerodynamically stabilized in the vicinity of the stagnation surface. Estimates of the ratio of the mean residence time (inverse strain rate) to the vortex turnover time yield values greater than unity. The conditional mean velocity gradient suggests that, in contrast to the existing literature, the highest gradients are around the system centerline, which would result in a higher probability of flame extinction in that region under chemically reacting conditions. The compactness of the domain and the short mean residence time render the system well suited to direct numerical simulation, more so than conventional jet flames.

Relaminarization of Axisymmetric Turbulent Flow With Combined Axial Jet and Side Injection in a Pipe

The effect of side mass injection on turbulent flow with axial entry to a circular duct in the form of centrally confined jet has been investigated. A standard κ-ε model modified for streamline curvature has been used for detailed analysis following a comparison with a κ-ω model for some test cases. Results show that flow stabilization and relaminarization could occur due to the side injection. The predicted recirculation zone, friction factor, total turbulent energy, turbulent shear stress, Taylor scale Reynolds number, and turbulent energy flux show gradual reduction with increase in the side injection velocity.

Measurement and analysis of the turbulent length scales in jet flows

The characteristic length and time scales of turbulence are reported in some detail for jet flows. The objective of the work is to determine the frequency dependence of these two-point turbulent properties, which are used to model the sources necessary for noise prediction using the acoustic analogy approach. A range of jet flow conditions for single and co-axial configurations are considered so that the effect of Mach number, temperature ratio and nozzle geometry is examined. The frequency dependence of both the fixed and moving frame length scales and the convection velocities for both the turbulence and the Reynolds stress are derived using a two-point complex coherence function. At higher frequencies, the integral scales are found to be strongly isotropic and inversely proportional to the Strouhal number. A frequency-dependent Taylor scale is derived and shown to agree well with the experimental results at the higher frequencies.

A new simple h-mesh adaptation algorithm for standard Smagorinsky LES: a first step of Taylor scale as a refinement variable

The interaction between discretization error and modeling error has led to some doubts in adopting Solution Adaptive Grid (SAG) strategies with LES. Existing SAG approaches contain undesired aspects making the use of one complicated and less convenient to apply to real engineering applications. In this work, a new refinement algorithm is proposed aiming to enhance the efficiency of SAG methodology in terms of simplicity in defining, less user’s judgment, designed especially for standard Smagorinsky LES and computational affordability. The construction of a new refinement variable as a function of the Taylor scale, corresponding to the kinetic energy balance requirement of the Smagorinsky SGS model is presented. The numerical study has been tested out with a turbulent plane jet in two dimensions. It is found that the result quality can be effectively improved as well as a significant reduction in CPU time compared to fixed grid cases.

The velocity spectra and turbulence length scale distributions in the near to intermediate regions of a round free turbulent jet

Stationary and flying single hot-wire measurements were made to investigate the near to intermediate field in a round free turbulent jet. Measurements were carried out at Reynolds numbers ReD based on the jet exit mean velocity and the nozzle diameter, between 6000 and 100 000. The objective of this study was to investigate the concept of a mixing transition proposed by Dimotakis [“The mixing transition in turbulent flows,” J. Fluid Mech. 409, 69 (2000)]. This was done through the measurement of the velocity spectra and the calculation of Kolmogorov λK, Taylor microscale λT, the Liepmann–Taylor microscale λL, and the viscous length scale λν at different positions in the near to intermediate regions of a round free jet. The present results demonstrate the local nature of mixing transition. It is found that the Kolmogorov, Taylor, and viscous length scales all decrease in magnitude with the local Reynolds number Reδ based on the local center line mean velocity and the local time-averaged diameter of the jet and appear to be only weakly dependent on the radial position, although the ratio ReT∕Reδ1∕2 varies nonlinearly across the jet radius. The ratio of the laminar to viscous length scale exceeds unity beyond the potential core of the jet. Moreover, the skewness of the axial velocity is approximately −0.4 over 30&amp;lt;ReT&amp;lt;400.

Numerical study of turbulent heat and fluid flow in a straight square duct at higher Reynolds numbers

This paper presents the large eddy simulation (LES) results of turbulent heat and fluid flows in a straight square duct (SSD) at higher Reynolds numbers ranged from 10 4 to 10 6 , which are based on the bulk mean velocity and the duct cross-sectional side length. A sub-grid model is proposed, which assumes that the sub-grid stress and heat flux are, respectively, proportional to the temporal increments of the filtered strain rate and temperature gradient, with the proportional coefficient determined by calibrating the friction factor. The temperature was taken as passive due to the neglect of buoyancy effect. The Taylor and Kolmogorov scales in the SSD are predicted and the results show that the LES results are better than c-DNS results. The LES results can explain why the c-DNS is applicable to the problem at a moderate Re, and reveal that the largest relative deviation of the overall mean Nusselt number is less than 10% as compared with existing experimental correlations. With the rise of Reynolds number, the mean secondary vortex pairs move towards the corners and have smaller size, while smaller vortices also occur in the instantaneous secondary flow. Empirical mode decomposition (EMD) was carried out to analyze the fluctuation of the x -averaged cross-sectional origin temperature at Re = 10 5 .