Taylor Microscale Research Articles

Properties of the turbulent/non-turbulent layer of a turbulent Boussinesq plume: A study using direct numerical simulation

The turbulent/non-turbulent layer (TNTL) in a turbulent Boussinesq plume is analyzed using direct numerical simulations. The Reynolds number (Re) used in the simulation, based on the scales defined at the bottom hot patch, is 2000, and the Reynolds number (Reλ) based on the Taylor microscale (λ) is 114.4 in the self-similar region. The flow is sufficiently resolved till the Kolmogorov scale. The outer edge of the TNTL is detected using the vorticity magnitude. Conditional statistics of various quantities are calculated with reference to the outer edge of the TNTL, which is referred to as the irrotational boundary (IB). The profiles of conditional vorticity magnitude are used to identify the TNTL and determine its thickness. The presence of viscous superlayer (VSL) and turbulent sublayer (TSL) within the TNTL is revealed by exploring the conditional profiles of the enstrophy transport equation. The baroclinic torque, which is a source of vorticity, has been shown to be inconsequential in determining the width of the VSL. The widths of the TNTL and the VSL are determined to be δTNTL≈15η and δVSL≈3.12η, respectively, where η is the Kolmogorov length scale. This gives the width of the TSL as δTSL=δTNTL−δVSL≈13.88η. The invariants of the velocity gradient tensor have been analyzed across the TNTL. The joint probability density function of the invariants Q and R shows a teardrop shape within the turbulent core. The teardrop shape is not fully developed within the TNTL. The TNTL and the turbulent core have a mixed tendency for irrotational dissipation, vortex sheets, and vortex tubes. When normalized by Kolmogorov length and velocity scales, the conditional statistics of the TNTL of the plume are similar to other turbulent flow types, and hence, this provides additional evidence for the universality of small-scale motion within/around the TNTL of various turbulent flows.

Experimental study of two side-by-side decaying grid turbulent fields at different mean velocities

A Hot-wire anemometry experiment is conducted to investigate how two turbulent fields decaying with different mean velocities interact at their interface. A grid with different mesh sizes and solidities on either side of the grid centerline is used to generate two turbulent fields. It is found that the resulting turbulent shear layer created at the interface of the two fields evolves in a self-preserving manner. Further, the Taylor microscale Reynolds number, increases linearly while and become constants as the distance x downstream of the grids increases. Off the centerline one observes the classical decay of turbulence, e.g. varies like (n is negative) and decreases. It is observed that the transport equation for is dominated by the production and pressure-velocity correlation in the central region of the turbulent shear layer while production, dissipation, and turbulent diffusion of the transport equation for dominate in the central part of the shear layer. The pressure-velocity correlation term for is negligible on the centreline of the shear layer and important on the edges. The measurements of the scale-by-scale (SBS) energy terms on the shear layer centerline reveal that the energy transfer from large to small scales occurs in a non-trivial manner.

Scale-by-scale analysis of interscale scalar transfer in grid turbulence with mean scalar gradient

Direct numerical simulations were carried out on grid turbulence with a mean scalar gradient to reveal interscale scalar transport. Two-point statistical analysis using the structure function and the scale-by-scale scalar equation was performed. Results show that the third-order structure function becomes negative at large scales in the upstream region (inverse cascade occurs), while such distributions do not appear for turbulence energy. This phenomenon in scalars gradually disappears in the downstream region. Budget analysis of the structure function reveals that this is mainly caused by the non-linear scalar transfer term in the direction of the mean scalar gradient (vertical direction here). When the separation distance is smaller than Taylor's microscale, where the interscale scalar transfer is normal (large to small scales), the direction of the scalar flux is determined by the vertical velocity fluctuation difference between two points. However, when separation is larger than Taylor's microscale and inverse cascading occurs, the direction is determined by derivative of the scalar fluctuation rather than the velocity fluctuation difference. Further analysis reveals that the existence of fluid mass with an unmixed scalar plays an important role in the inverse cascade phenomenon.

A Rational Approach to Meshing Cerebral Venous Geometries for High-Fidelity Computational Fluid Dynamics.

Computational fluid dynamics (CFD) of cerebral venous flows has become popular owing to the possibility of using local hemodynamics and hemoacoustics to help diagnose and plan treatments for venous diseases of the brain. Lumen geometries in low-pressure cerebral veins are different from those in cerebral arteries, often exhibiting fenestrations and flattened or triangular cross section, in addition to constrictions and expansions. These can challenge conventional size-based volume meshing strategies, and the ability to resolve nonlaminar flows. Here we present a novel strategy leveraging estimation of length scales that could be present if flow were to become transitional or turbulent. Starting from the lumen geometry and flow rate boundary conditions, centerlines are used to determine local hydraulic diameters and cross-sectional mean velocities, from which flow length scales are approximated using conventional definitions of local Kolmogorov and Taylor microscales. By inspection of these scales, a user specifies minimum and maximum mesh edge lengths, which are then distributed along the model in proportion to the approximated local Taylor length scales. We demonstrate in three representative cases that this strategy avoids some of the pitfalls of conventional size-based strategies. An exemplary CFD mesh-refinement study shows convergence of high-frequency flow instabilities even starting from relatively coarse edge lengths near the lower bounds of the approximated Taylor length scales. Rational consideration of the length scales in a possibly nonlaminar flow may thus provide a useful and replicable baseline for denovo meshing of complicated or unfamiliar venous lumen geometries.

Investigation of peak wind loading on a high-rise building in the atmospheric boundary layer using large-eddy simulations

Significant negative peak pressures have been observed in two recent wind tunnel experiments of a high-rise building for certain wind directions. This peak wind loading is crucial for the design of cladding systems. However, the governing flow physics is not well understood. In this study, large-eddy simulations with sufficient resolution are performed to capture and analyze these peak pressure phenomena. The atmospheric boundary layer flow is generated using a divergence free synthetic turbulence inflow generator before the high-rise building is placed in the flow at various wind directions. The mean, standard deviation, and peak pressure coefficients are shown to agree well with the experimental measurements. The strongest negative peak pressures near the top trailing corner on the leeward surface are captured by simulations with the resolved scale between the Taylor microscale and Kolmogorov scale. The probability density function of the pressure at the top trailing corner is well approximated using a log-normal distribution, which is a signature of the effect of small-scale turbulence intermittency. Flow visualization indicates that the strong negative peak values result from the interaction between small eddies shed from the separated flow region at the upwind roof edge and larger eddies downstream of the leeward roof edge.

On the structure of the turbulent/non-turbulent interface in a fully developed spatially evolving axisymmetric wake

In this work, we numerically study the structure of the turbulent/nonturbulent (T/NT) interface in a fully developed spatially evolving axisymmetric wake by means of direct numerical simulations. There is a continuous and contorted pure shear layer (PSL) adjacent to the outer edge of the T/NT interface. The local thickness of the PSL δPSL exhibits a wide range of scales (from the Kolmogorov scale to the Taylor microscale) and the conditional mean thickness 〈δPSL〉I/ηc≈6 with ηc being the centerline Kolmogorov scale is the same as the viscous superlayer. In the viscous superlayer, the pure shear motions without rotation are overwhelmingly dominant. It is also demonstrated that the physics of the turbulent sublayer is closely related to the PSL with a large thickness. Another significant finding is that the time averaged area of the rotational region 〈AR〉, and the pure shear region 〈AS〉 at different streamwise locations scale with the square of the wake-width bU2. This study opens an avenue for a better understanding of the structures of the T/NT interface.

An experiment generates a specified mean strained rate turbulent flow: Dynamics of particles

This study aimed to simulate straining turbulent flow empirically, having direct similarities with vast naturally occurring flows and engineering applications. The flow was generated in 100<Reλ<500 and seeded with passive and inertial particles. Lagrangian particle tracking and particle image velocimetry were employed to extract the dynamics of particle statistics and flow features, respectively. The studies for axisymmetric straining turbulent flow reported that the strain rate, flow geometry, and gravity affect particle statistics. To practically investigate mentioned effects in the literature, we present the behavior of both passive and inertial particles from the novel experiment conducted on initially homogeneous turbulence undergoing a sudden axisymmetric expansion. We represent the result with two different mean strains and Reynolds–Taylor microscales. However, this study, in contrast to the previous studies, considers the fields of inertial particles in the presence of gravity. The result discloses that the novel designed and conducted experiments simulated the flow satisfactorily. Then, the particle behavior in such flow showed the effectiveness of the flow distortion on particle dynamics such as velocity root mean square and Reynolds stress. Straining turbulence flow is subject to many industrial applications and physics studies, such as stagnation points, external flow around an airfoil, internal flow in changeable cross section pipe, expansion in the engine mixing chamber, and leading edge erosion. This study's conclusion could apply constructively to these areas.

Approach towards local isotropy in statistically stationary turbulent shear flows

We analyse the approach towards local isotropy in statistically stationary turbulent shear flows using the transport equations for the fourth-order moments of the velocity derivative. It is found that terms of these equations representing the large-scale contribution associated with the uniform mean velocity gradient gradually decrease as the Taylor microscale Reynolds number $Re_\lambda$ increases, and finally disappear when $Re_\lambda$ is sufficiently large. This gradual weakening of the large-scale effect is accompanied by a gradual approach towards local isotropy of the small-scale motion. The rate at which local isotropy is approached depends on the weakening of the large-scale forcing, which is controlled by the magnitude of the non-dimensional velocity shear parameter $S^*$ ( $\equiv \overline {u_1^2}({{\partial {{\bar U}_1}}}/{{\partial {x_2}}})/{\bar {\varepsilon }_{iso}}$ , where $\bar {\varepsilon }_{iso}$ is the isotropic mean turbulent energy dissipation rate, $\overline {u_1^2}$ is the streamwise velocity variance, and ${\partial {{\bar U}_1}/\partial {x_2}}$ is the uniform mean velocity gradient in the transverse direction). In particular, we show that the approach towards local isotropy can be recast in the form $C\, Re_\lambda ^{-1}$ , where $C$ is the product of $S^*$ and a ratio of transverse-to-streamwise velocity derivative variances. This is consistent with the behaviour of the normalized third-order moments of transverse velocity derivatives. With the further use of the transport equations for the eighth- and twelfth-order velocity derivative moments, it is found that the even moments of transverse velocity derivatives can significantly affect the rate at which local isotropy is approached, especially for higher orders.

Heat Transfer in a Non-Isothermal Collisionless Turbulent Particle-Laden Flow

To better understand the role of particle inertia on the heat transfer in the presence of a thermal inhomogeneity, Eulerian–Lagrangian direct numerical simulations (DNSs) have been carried out by using the point–particle model. By considering particles transported by a homogeneous and isotropic, statistically steady turbulent velocity field with a Taylor microscale Reynolds number from 37 to 124, we have investigated the role of particle inertia and thermal inertia in one- and two-way coupling collisionless regimes on the heat transfer between two regions at uniform temperature. A wide range of Stokes numbers, from 0.1 to 3 with a thermal Stokes-number-to-Stokes-number ratio equal to 0.5 to 4.43 has been simulated. It has been found that all moments always undergo a self-similar evolution in the interfacial region between the two uniform temperature zones, the thickness of which shows diffusive growth. We have determined that the maximum contribution of particles to the heat flux, relative to the convective heat transfer, is achieved at a Stokes number which increases with the ratio between thermal Stokes and Stokes number, approaching 1 for very large ratios. Furthermore, the maximum increases with the thermal Stokes-to-Stokes number ratio whereas it reduces for increasing Reynolds. In the two-way coupling regime, particle feedback tends to smooth temperature gradients by reducing the convective heat flux and to increase the particle turbulent heat flux, in particular at a high Stokes number. The impact of particle inertia reduces at very large Stokes numbers and at larger Reynolds numbers. The dependence of the Nusselt number on the relevant governing parameters is presented. The implications of these findings for turbulence modelling are also briefly discussed.

Deep Learning Forecasts a Strained Turbulent Flow Velocity Field in Temporal Lagrangian Framework: Comparison of LSTM and GRU

The subject of this study presents an employed method in deep learning to create a model and predict the following period of turbulent flow velocity. The applied data in this study are extracted datasets from simulated turbulent flow in the laboratory with the Taylor microscale Reynolds numbers in the range of 90 < Rλ< 110. The flow has been seeded with tracer particles. The turbulent intensity of the flow is created and controlled by eight impellers placed in a turbulence facility. The flow deformation has been conducted via two circular flat plates moving toward each other in the center of the tank. The Lagrangian particle-tracking method has been applied to measure the flow features. The data have been processed to extract the flow properties. Since the dataset is sequential, it is used to train long short-term memory and gated recurrent unit model. The parallel computing machine DEEP-DAM module from Juelich supercomputer center has been applied to accelerate the model. The predicted output was assessed and validated by the rest of the data from the experiment for the following period. The results from this approach display accurate prediction outcomes that could be developed further for more extensive data documentation and used to assist in similar applications. The mean average error and R2 score range from 0.001–0.002 and 0.9839–0.9873, respectively, for both models with two distinct training data ratios. Using GPUs increases the LSTM performance speed more than applications with no GPUs.

Characteristics of the intense vorticity structures in isotropic turbulence at high Reynolds numbers

Intense vorticity structures (IVS) are known to exist in virtually all turbulent flows, and consist of regions with particularly intense vorticity with (typically) a tubelike shape that keeps its coherence for a relatively long time. We investigated these structures at high Reynolds numbers (Re) using direct numerical simulations (DNS) of isotropic turbulence. The IVS aspect ratio (length to radius) is found to be the same for simulations with very different Re. Since the IVS radius scales with the Kolmogorov microscale, independent of Re, the IVS length at high Re also scales that way, and not with the integral scale or Taylor microscale, as has been suggested in the past.

An open source package to perform basic and advanced statistical analysis of turbulence data and other complex systems

We present an open-source package that helps the user to perform a basic statistical analysis of a given turbulence dataset. We believe that this package is useful to the entire turbulence community. It can be used to estimate statistical quantities of turbulence such as the spectral density, turbulence intensity, integral length scale, Taylor microscale, Kolmogorov scale, and dissipation rate as well as velocity increments, structure functions, and their scaling exponents. Different well-known methods available in the literature were selected so that they can be compared. This package also performs an advanced analysis that includes the scale-dependent statistical description of turbulent cascade using the Fokker–Planck equation, consequently leading to the assessment of integral fluctuation theorems. As a precondition for the stochastic process approach, Markovian properties of the turbulent cascade in scale are tested. This is utilized to estimate the drift and diffusion coefficients of the Fokker–Planck equation. The total entropy production for each independent cascade trajectory can be determined using a Fokker–Planck equation. Estimating total entropy production admits a rigorous law of non-equilibrium stochastic thermodynamics, namely, the integral fluctuation theorem, which must be valid if Markov properties hold and the Fokker–Planck equation is correct. This approach to the turbulent cascade process has the potential for a new way to link the statistical description of turbulence, non-equilibrium stochastic thermodynamics, and local turbulent flow structures. Finally, we emphasize that the presented package can be used for the analysis of other data with turbulent-like complexity as well.

Eigenanalysis and non-modal analysis of collocated discontinuous Galerkin discretizations with the summation-by-parts property

Guided by the von Neumann and non-modal analyses, we investigate the dispersion and diffusion properties of collocated discontinuous Galerkin methods with the summation-by-parts property coupled with the simultaneous approximation technique. We use the linear advection and linear advection-diffusion equations as model problems. The analysis is carried out by varying the order of the spatial discretization, the Péclet number, and looking at the effect of the upwind term. The eigenanalysis is verified to provide insights into the numerical errors based on the behavior of the primary mode. The dispersion and diffusion errors associated with the spatial discretization are shown to behave according to the primary- or physical- mode in the range of low wavenumbers. In this context, the discretization of the model problems is verified to be stable for all flow regimes and independent of the solution polynomial degree. The effect of the upwind term shows that its effect decreases by increasing the accuracy of the discretization. Further, two analyses that includes all modes are used to get better insights into the diffusion and robustness of the scheme. From the non-modal analysis, the short-term diffusion is computed for different flow regimes and solution polynomial degrees. The energy decay or long-term diffusion based on all eigenmodes based on the eigenmodes matrix is analyzed for t > 0 and different spatial discretizations. The results are validated against under-resolved turbulence simulations of the Taylor–Green vortex at two Reynolds numbers, i.e. , Re = 100 and 1600, and a Mach number Ma = 0.1 , and the decaying of compressible homogeneous isotropic turbulence at a Reynolds number based on the Taylor microscale of Re λ = 100 and a turbulent Mach number of Ma t = 0.6 .

Effects of low clay concentrations on nearly isotropic turbulence

Aqueous flows containing clay in suspension are ubiquitous in natural environments and play a pivotal role in many processes. Using a novel approach, we experimentally quantified the effect of low clay concentrations in water-clay flows under nearly isotropic turbulence. The results demonstrate the significant impact of clay on the multiscale dynamics of turbulence even at low clay concentrations, including the turbulent kinetic energy, the mean dissipation rate, the Taylor microscale, and the inertial subrange of the velocity spectrum.

Taylor Microscale and Effective Reynolds Number near the Sun from PSP

The Taylor microscale is a fundamental length scale in turbulent fluids, representing the end of fluid properties and onset of dissipative processes. The Taylor microscale can also be used to evaluate the Reynolds number in classical turbulence theory. Although the solar wind is weakly collisional, it approximately behaves as a magnetohydrodynamic (MHD) fluid at scales larger than the kinetic scale. As a result, classical fluid turbulence theory and formalisms are often used to study turbulence in the MHD range. Therefore, a Taylor microscale can be used to estimate an effective Reynolds number in the solar wind. NASA’s Parker Solar Probe (PSP) has reached progressively closer to the Sun than any other spacecraft before. The collected data have revealed many new findings in the near-Sun solar wind. Here, we use the PSP data to estimate the Taylor microscale and effective Reynolds number near the Sun. We find that the Taylor microscale and Reynolds number are small compared to the corresponding near-Earth values, indicating a solar wind that has been less processed by turbulence, with very small-scale dissipative processes near the Sun.

Effects of Boundary Layer and Local Volumetric Cells Refinements on Compressor Direct Noise Computation

<div class="section abstract"><div class="htmlview paragraph">The use of turbochargers with downsized internal combustion engines improves road vehicles’ energy efficiency but introduces additional sound sources of strong acoustic annoyance on the turbocharger’s compressor side. In the present study, direct noise computations (DNC) are carried out on a passenger vehicle turbocharger compressor. The work focuses on assessing the influence of grid parameters on the acoustic predictions, to further advance the maturity of the acoustic modelling of such machines with complex three-dimensional features. The effect of the boundary layer mesh structure, and of the spatial resolution of the mesh, on the simulated acoustic signatures is investigated on detached eddy simulations (DES). Refinements in the core mesh are applied in areas of major acoustic production, to generate cells with sizes proportional to the local Taylor microscale values. Such an educated guess allows for quality enhancement with a smaller increase in computational costs as compared to more general overall refinements. The reflection-free simulation results are validated against experiments. The experimental data were post-processed with methods from the two-port theory to represent pure acoustic source power density for the acoustic modes, cleaned from test-domain-specific reflections. A detailed comparison between experiments and numerical simulations is carried out. As a result of this study, the most critical parameters for the numerical prediction of turbocharger noise are presented. The results can, furthermore, be used to improve the understanding of grid construction when predicting noise signature for compressor flows.</div></div>

Synchronization of turbulence in channel flow

Synchronization of turbulence in channel flow is investigated using continuous data assimilation. The flow is unknown within a region of the channel. Beyond this region the velocity field is provided, and is directly prescribed in the simulation, while the pressure is unknown throughout the entire domain. Synchronization takes place when the simulation recovers the full true state of the flow, or in other words when the missing region is accurately re-established, spontaneously. Successful synchronization depends on the orientation, location and size of the missing layer. For friction Reynolds numbers up to one thousand, wall-attached horizontal layers can synchronize as long as their thickness is less than approximately thirty wall units. When the horizontal layer is detached from the wall, the critical thickness increases with height and is proportional to the local wall-normal Taylor microscale. A flow-parallel, vertical layer that spans the height of the channel synchronizes when its spanwise width is of the order of the near-wall Taylor microscale, while the criterion for a crossflow vertical layer is set by the advection distance within a Lyapunov time scale. Finally, we demonstrate that synchronization is possible when only planar velocity data are available, rather than the full outer state, as long as the unknown region satisfies the condition for synchronization in one direction. These numerical experiments demonstrate the capacity of accurately reconstructing, or synchronizing, the missing scales of turbulence from observations, using continuous data assimilation.

Diffusion of turbulence following both stable and unstable step stratification perturbations

The evolution of a two-phase, air and unsaturated water vapor, time-decaying, shearless, and turbulent layer has been studied in the presence of both stable and unstable perturbations of the normal temperature lapse rate. The top interface between a warm vapor cloud and clear air in the absence of water droplets was considered as the reference dynamics. Direct, three-dimensional, and numerical simulations were performed within a 6 × 6-m-wide and 12-m-high domain, which was hypothesized to be located close to an interface between the warm cloud and clear air. The Taylor microscale Reynolds number was 250 inside the cloud portion. The squared Froude's number varied over intervals of [0.4; 981.6] and [−4.0; −19.6]. A sufficiently intense stratification was observed to change the mixing dynamics. The formation of a sublayer inside the shearless layer was observed. The sublayer, under a stable thermal stratification condition, behaved like a pit of kinetic energy. However, it was observed that kinetic energy transient growth took place under unstable conditions, which led to the formation of an energy peak just below the center of the shearless layer. The scaling law of the energy time-variation inside the interface region was quantified: this is an algebraic law with an exponent that depends on the perturbation stratification intensity. The presence of an unstable stratification increased the differences in statistical behavior among the longitudinal velocity derivatives, compared with the unstratified case. Since the mixing process is suppressed in stable cases, small-scale anisotropy is also suppressed.

Fractal dimensions of hydraulic parameters in sand mined alluvial channel

Abstract Long-term extraction of sand from a river causes large mining pit on the river bed, and these pits change their fluvial processes. In this paper, an experimental study is executed to interpret the turbulence flow structure in a mining pit. This research mainly focuses on the fractal dimension of velocity fluctuations and Reynolds shear stress (RSS) of flow in the longitudinal and vertical plane for a mining pit region. The results show that the magnitude of fractal dimension for velocity fluctuation and RSS is smaller in the mining pit than the upstream and downstream of the pit. The large values of fractal dimensions at the pit downstream show an increase in flow roughness. It is found that the Taylor microscale decreases towards the channel bed, and this is because of increasing turbulence dissipation near the bed region. We have observed a significantly lower value of Taylor microscale in the mining pit. The higher value of the Taylor microscale is found far downstream of the pit. Nondimensional turbulence mixing length shows a decrease in the traversing length of an eddy at the far downstream of the pit.

Hot-Wire Investigation of Turbulence Topology behind Blades at Different Shape Qualities

The scope of this paper is to perform a detailed experimental investigation of the shape error effect on the turbulence evolution behind NACA 64-618 airfoil. This airfoil is 3D-printed with predefined typical shape inaccuracies. A high-precision optical 3D scanner was used to assess the shape and surface quality of the manufactured models. The turbulent flow was studied using hot-wire anemometry. The developed force balance device was provided to measure the aerodynamic characteristics of the airfoil. Experimental studies were carried out for three angles of attack, +10∘, 0∘, −10∘, and different chord-based Reynolds numbers from 5.3×104 to 2.1×105. The obtained results show that the blunt trailing edge and rough surface decline the aerodynamic performance of the blades. In addition, the experimental results revealed a strong sensitivity of the Taylor microscale Reynolds number to the type of shape inaccuracy, especially at Re≈1.7×105. We also discuss the evolution of the Reynolds stress components, the degree of flow anisotropy, and the power spectrum distributions depending on the airfoil inaccuracies.