High Reynolds Number Turbulence Research Articles

Accurate Method for Estimating Wall-Friction Based on Analytical Wall-Law Model

A novel method is proposed for accurately determining the local wall friction through the near-wall measurement of time-average velocity profile in a Type-A turbulent boundary layer (TBL). The method is based on the newly established analytical wall-law in Type-A TBL. The direct numerical simulations (DNS) data of turbulence on a zero-pressure-gradient flat-plate (ZPGFP) is used to demonstrate the accuracy and the robustness of the approach. To verify the reliability and applicability of the method, a two-dimensional particle image velocimetry (PIV) measurement was performed in a ZPGFP TBL with a low-to-moderate Reynolds number (Re). Via utilizing the algorithm of single-pixel ensemble correlation (SPEC), the velocity profiles in the ZPGFP TBL were resolved at a significantly improved spatial resolution, which greatly enhanced the measurement accuracy and permitted us to accurately capture the near-wall velocity information. The accuracy of the approach is then quantitatively validated for the high Reynolds number turbulence using the ZPGFP TBL data. The research demonstrates that the current method can provide the precise estimation of wall friction with a mean error of less than 2%, which not only possesses the advantage of its insensitivity to the absolute wall-normal distance of the measuring point, but also its capability of providing an accurate prediction of wall shear stress based on fairly sparse experimental data on the velocity profile. The current study demonstrates that the wall shear stress can be accurately estimated by a velocity even at a single-point either measured or calculated in the near-wall region.

A novel attention enhanced deep neural network for hypersonic spatiotemporal turbulence prediction

High Reynolds number turbulent flow of hypersonic vehicles exhibits multi-scale flow structures and non-equilibrium high-frequency characteristics, presenting a significant challenge for accurate prediction. A deep neural network integrated with attention mechanism as a reduced order model for hypersonic turbulent flow is proposed, which is capable of capturing spatiotemporal characteristics from high-dimensional numerical turbulent data directly. The network model leverages encoder–decoder architecture where the encoder captures high-level semantic information of input flow field, Convolutional Long Short-Term Memory network learns low-dimensional characteristic evolution, and the decoder generates pixel-level multi-channel flow field information. Additionally, skip connection structure is introduced at the decoding stage to enhance feature fusion while incorporating Dual-Attention-Block that automatically adjusts weights to capture spatial imbalances in turbulence distribution. Through evaluating the time generalization ability, the neural network effectively learns the evolution of multi-scale high-frequency turbulence characteristics. It enables rapid prediction of high Reynolds number turbulence evolution over time with reasonable accuracy while maintaining excellent computational efficiency.

Forgetfulness of turbulent energy cascade associated with different mechanisms

The small scales of high Reynolds number turbulence exhibit the statistical universality by forgetting about the large scales during the energy cascade. In this study, we revisit this schematic description with an information-theoretic point of view. Our objective is to understand the importance of different cascade mechanisms in this process. To this end, we compute the “information flux”, the information-theoretic measure of causality formulated by one of the authors, of the decomposed inter-scale energy transfer. For the kinetics, the ratio of the inertial-range inter-scale energy transfer between the strain self-amplification (SSA) and the vortex stretching (VS) mechanisms is 5 : 3. However, for the information-flux, the VS contribution is roughly twice as large as the SSA. We also find several deviations between the kinetics and the informatics, highlighting the nontrivial nature of information distributed among different scales and mechanics in turbulence. This result infers that the SSA is a less efficient mechanism than the VS in terms of information transfer, and contributes to losing the large-scale information.

Scaling of Acceleration Statistics in High Reynolds Number Turbulence

The scaling of acceleration statistics in turbulence is examined by combining data from the literature with new data from well-resolved direct numerical simulations of isotropic turbulence, significantly extending the Reynolds number range. The acceleration variance at higher Reynolds numbers departs from previous predictions based on multifractal models, which characterize Lagrangian intermittency as an extension of Eulerian intermittency. The disagreement is even more prominent for higher-order moments of the acceleration. Instead, starting from a known exact relation, we relate the scaling of acceleration variance to that of Eulerian fourth-order velocity gradient and velocity increment statistics. This prediction is in excellent agreement with the variance data. Our Letter highlights the need for models that consider Lagrangian intermittency independent of the Eulerian counterpart.

An Immersed Boundary Method Based on Parallel Adaptive Cartesian Grids for High Reynolds Number Turbulent Flow

In this paper, a set of parallelised adaptive hierarchical Cartesian-based immersed boundary methodology is developed for high Reynolds number compressible flow. First, a robust and efficient grid generation method based on the separation axis theorem for arbitrary geometry is presented for automatic Cartesian grid generation. Second, an immersed boundary method (IBM) is presented coupling with wall model for high Reynolds number flow. Third, a parallel strategy is implemented and special treatment is proposed to guarantee large-scale computing. Finally, cell-based adaptive mesh refinement (AMR) technology is used to capture fluid phenomena under different regimes including but not limited to shock waves and vortices. The overall performance of the methodology is tested through a wide range of regimes including transonic and supersonic flow with high Reynolds number in both two and three dimensions. Results are in good agreement with reference data and indicate the capability and robustness of the present methodology.

Generation of intense dissipation in high Reynolds number turbulence

Intense fluctuations of energy dissipation rate in turbulent flows result from the self-amplification of strain rate via a quadratic nonlinearity, with contributions from vorticity (via the vortex stretching mechanism) and pressure-Hessian—which are analysed here using direct numerical simulations of isotropic turbulence on up to grid points, and Taylor-scale Reynolds numbers in the range 140–1300. We extract the statistics involved in amplification of strain and condition them on the magnitude of strain. We find that strain is self-amplified by the quadratic nonlinearity, and depleted via vortex stretching, whereas pressure-Hessian acts to redistribute strain fluctuations towards the mean-field and hence depletes intense strain. Analysing the intense fluctuations of strain in terms of its eigenvalues reveals that the net amplification is solely produced by the third eigenvalue, resulting in strong compressive action. By contrast, the self-amplification acts to deplete the other two eigenvalues, whereas vortex stretching acts to amplify them, with both effects cancelling each other almost perfectly. The effect of the pressure-Hessian for each eigenvalue is qualitatively similar to that of vortex stretching, but significantly weaker in magnitude. Our results conform with the familiar notion that intense strain is organized in sheet-like structures, which are in the vicinity of, but never overlap with tube-like regions of intense vorticity due to fundamental differences in their amplifying mechanisms.This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.

Exact Coherent Structures and Phase Space Geometry of Preturbulent 2D Active Nematic Channel Flow.

Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic "active turbulence." Here, we study these phenomena using the framework of exact coherent structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact coherent structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant exact coherent structures and connecting orbits in a preturbulent active nematic channel flow, which enables a fully nonlinear but highly reduced-order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite-dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate- to high-activity regime.

Representation model of wind velocity fluctuations and saltation transport in aeolian sand flow

Since the stream-wise and vertical turbulent fluctuations have an important influence on the movement of sand and dust particles, the accurate quantitative estimation of natural wind fluctuations has an important role in improving the forecast level of wind erosion and dust storm. The high Reynolds number turbulence characteristics of aeolian sand flow and the complexity of sand-laden flows are the main difficulties affecting the accuracy of prediction. In this study, the characteristics of the stream-wise and vertical wind velocity fluctuations in sand-laden flows are studied by analyzing the real-time data of the wind velocity field in the atmospheric surface layer (ASL). Then, a simple empirical model representing the stream-wise and vertical wind velocity fluctuations is proposed. The model not only considers the effects of large-scale and small-scale fluctuations, but also has the advantage of predicting the stream-wise and vertical wind velocity fluctuations at any height. Verification shows the results predicted by the model are in good agreement with the observation results, and the predicted saltation sand flux is closer to the experimental results than that without considering the turbulence effect or the vertical wind velocity fluctuations. Moreover, it is a convenient model for application especially in predicting aeolian sand transport.

Numerical simulation of viscosity/implicit large-eddy steady turbulence with the Reynolds number dependency

This study presents a numerical analysis that models small scale turbulence using numerical viscosity or implicit large-eddy simulation (LES). The motivation for focusing on these models is that the sub-grid scale components of LES are assumed to have a sufficiently high Reynolds number turbulence. The Reynolds number dependence of steady isotropic turbulence is used to validate the present analysis. Here, this dependency ranges from low to high Reynolds numbers. The results of this analysis are validated by comparing them with those of direct numerical simulation. The donor cell method and quick method are used as schemes of the numerical viscosity. Analysis based on the numerical viscosity can give accurate turbulent kinetic energy values at high Reynolds numbers and implicit LES at low Reynolds numbers. However, these models did not accurately predict static pressure fluctuations. These results were discussed by visualizing the large-scale turbulent structures.

Scale-dependent statistics of inertial particle distribution in high Reynolds number turbulence

Multiscale statistical analyses of inertial particle distributions are presented to investigate the statistical signature of clustering and void regions in particle-laden incompressible isotropic turbulence. Three-dimensional direct numerical simulations of homogeneous isotropic turbulence at high Reynolds number ($Re_\lambda \gtrsim 200$) with up to $10^9$ inertial particles are performed for Stokes numbers ranging from $0.05$ to $5.0$. Orthogonal wavelet analysis is then applied to the computed particle number density fields. Scale-dependent skewness and flatness values of the particle number density distributions are calculated and the influence of Reynolds number $Re_\lambda$ and Stokes number $St$ is assessed. For $St \sim 1.0$, both the scale-dependent skewness and flatness values become larger as the scale decreases, suggesting intermittent clustering at small scales. For $St \le 0.2$, the flatness at intermediate scales, i.e. for scales larger than the Kolmogorov scale and smaller than the integral scale of the flow, increases as $St$ increases, and the skewness exhibits negative values at the intermediate scales. The negative values of the skewness are attributed to void regions. These results indicate that void regions at the intermediate sales are pronounced and intermittently distributed for such small Stokes numbers. As $Re_\lambda$ increases, the flatness increases slightly. For $Re_\lambda \ge 328$, the skewness shows negative values at large scales, suggesting that void regions are pronounced at large scales, while clusters are pronounced at small scales.

Multi-level stochastic refinement for complex time series and fields: a data-driven approach

Spatio-temporally extended nonlinear systems often exhibit a remarkable complexity in space and time. In many cases, extensive datasets of such systems are difficult to obtain, yet needed for a range of applications. Here, we present a method to generate synthetic time series or fields that reproduce statistical multi-scale features of complex systems. The method is based on a hierarchical refinement employing transition probability density functions (PDFs) from one scale to another. We address the case in which such PDFs can be obtained from experimental measurements or simulations and then used to generate arbitrarily large synthetic datasets. The validity of our approach is demonstrated at the example of an experimental dataset of high Reynolds number turbulence.

Linear and nonlinear hydromagnetic stability in laminar and turbulent flows.

We consider the evolution of arbitrarily large perturbations of a prescribed pure hydrodynamical flow of an electrically conducting fluid. We study whether the flow perturbations as well as the generated magnetic fields decay or grow with time and constitute a dynamo process. For that purpose we derive a generalized Reynolds-Orr equation for the sum of the kinetic energy of the hydrodynamic perturbation and the magnetic energy. The flow is confined in a finite volume so the normal component of the velocity at the boundary is zero. The tangential component is left arbitrary in contrast with previous works. For the magnetic field we mostly employ the classical boundary conditions where the field extends in the whole space. We establish critical values of hydrodynamic and magnetic Reynolds numbers below which arbitrarily large initial perturbations of the hydrodynamic flow decay. This involves generalization of the Rayleigh-Faber-Krahn inequality for the smallest eigenvalue of an elliptic operator. For high Reynolds number turbulence we provide an estimate of critical magnetic Reynolds number below which arbitrarily large fluctuations of the magnetic field decay.

Characterising Momentum Flux Events in High Reynolds Number Turbulent Boundary Layers

The momentum flux in a canonical turbulent boundary layer is known to have a time-series signature that is characterised by a highly intermittent variation, which includes very short periods of intense flux activity. Here, we study the variation in these flux signal characteristics across almost a decade of flow Reynolds number (Reτ) by analysing datasets acquired using miniature cross-wire probes with matched spatial resolution. The analysis is facilitated by conditionally sampling the signal based on the quadrant (Qi; i = 1–4) and magnitude of the flux, revealing fractional cumulative contribution from Q4 to increase at a much faster rate than from Q2 with Reτ. An episodic description of the flux signal is subsequently undertaken, which associates this rapid increase in Q4 contributions with the emergence of extreme and rare flux events with Reτ. The same dataset is also used to test Townsend’s hypothesis on the active and inactive components of the momentum flux, which are obtained for the first time by implementing a spectral linear stochastic estimation-based decomposition methodology. While the active component is found to be the dominant contributor to the mean momentum flux consistent with Townsend’s hypothesis, the inactive component is found to be small but non-zero, owing to the non-linear interactions associated with the modulation phenomenon. Finally, an episodic description of the active and inactive momentum flux signal is undertaken to highlight the starkly different time series characteristics of the two flux components. The inactive flux signal is found to comprise individual statistically significant events associated with all four quadrants, leading to a small net contribution to the total flux.

Large eddy simulations of high Reynolds number turbulence based on interscale energy transfer among resolved scales

We show that the task of subgrid scale (SGS) modeling can be split into computing the total SGS energy transfer and determining its distribution among scales of motion. The former can be computed from energy transfers involving only resolved scales, providing a physical constraint on any proposed SGS model. The latter can be prescribed through classical spectral SGS modeling expressions shown in the figure or computed directly from resolved fields, allowing self-contained large eddy simulations.

Large-scale clustering of light small particles in developed turbulence

Small solid particles, droplets, and bubbles can form clusters in turbulent flows by the action of coherent vortices. This phenomenon, sometimes called the preferential concentration, was often thought to be most conspicuous when the velocity relaxation time τp of particles is comparable with the Kolmogorov time τη. However, since high-Reynolds number turbulence consists of coherent eddies with different timescales, particles can form clusters even when τp≫τη. We demonstrate, by direct numerical simulations, that light particles with different τp values form clusters around axes of coherent vortices with different sizes in developed turbulence.

Aerodynamic performance of three-dimensional wing tip high Reynolds number turbulence with jet control

In this paper, the wing tip jet is proposed to improve the aerodynamic performance of the three-dimensional ONERA M6 wing at high Reynolds numbers. The CFD method is used to perform numerical simulation with the SST k-ω two-equation model. To verify present numerical model, ONERA M6 wing at the attack angle(α) of 2° is selected and the simulation results are in good agreement with the experimental data. The flow around the airfoil at high Reynolds number is simulated at 0°-14° attack angle, and the critical attack angle is 11° without jet. Finally, the influence of the jet on the aerodynamic characteristics of the airfoil at different attack angle are studied and it is found that the lift coefficient and lift-drag ratio of the airfoil increase with jet.

An in-flight investigation of a turbulent boundary layer at Reynolds numbers up to hbox {Re}_{theta }=49,400

The ongoing attempts to gain access to the realm of high Reynolds number turbulence have resulted in the dedicated development of major experimental facilities and novel diagnostic methodologies as well as in the probing of atmospheric surface flows. In contrast to this, the presented study discusses the feasibility of an in-flight laboratory for Reynolds number investigations up to rm {Re}_{theta },le ,49,400. The underpinning velocity data were obtained in flight tests by two moveable differential pressure probes and a stereo Particle Image Velocity (sPIV) system. The region of interest was located far downstream of the aircraft’s nose within the fuselage boundary layer. The pressure probes scanned the full boundary layer while the sPIV system remained fixed at certain wall-normal locations. The velocity data acquired exhibits distinct characteristics within the defect layer that deviate from Coles’ classical description of the wake. Furthermore, the streamwise turbulence intensities show a pronounced ‘outer peak’ further away from the wall at y^{+}=2000-5000 . The measurements were conducted under authentic flight conditions with an increased level of free-stream turbulence. These boundary conditions enabled an analysis of turbulent flows that are of relevance for various aeronautical applications. The manuscript elaborates on the main findings of this experimental study by presenting the velocity profiles captured by the moveable pressure probe system and samples of sPIV data. The capabilities and limitations of a flying laboratory for the investigation of high Reynolds number turbulence are discussed in detail.Graphic

Vortex stretching and enstrophy production in high Reynolds number turbulence

An essential ingredient of turbulent flows is the vortex stretching mechanism, which emanates from the non-linear interaction of vorticity and strain-rate tensor and leads to formation of extreme events. We analyze the statistical correlations between vorticity and strain rate by using a massive database generated from very well resolved direct numerical simulations of forced isotropic turbulence in periodic domains. The grid resolution is up to $12288^3$, and the Taylor-scale Reynolds number is in the range $140-1300$. In order to understand the formation and structure of extreme vorticity fluctuations, we obtain statistics conditioned on enstrophy (vorticity-squared). The magnitude of strain, as well as its eigenvalues, is approximately constant when conditioned on weak enstrophy; whereas they grow approximately as power laws for strong enstrophy, which become steeper with increasing $R_\lambda$. We find that the well-known preferential alignment between vorticity and the intermediate eigenvector of strain tensor is even stronger for large enstrophy, whereas vorticity shows a tendency to be weakly orthogonal to the most extensive eigenvector (for large enstrophy). Yet the dominant contribution to the production of large enstrophy events arises from the most extensive eigendirection, the more so as $R_\lambda$ increases. Nevertheless, the stretching in intense vorticity regions is significantly depleted, consistent with the kinematic properties of weakly-curved tubes in which they are organized. Further analysis reveals that intense enstrophy is primarily depleted via viscous diffusion, though viscous dissipation is also significant. Implications for modeling are nominally addressed as appropriate.

Dissipation range of the energy spectrum in high Reynolds number turbulence

We seek to understand the kinetic energy spectrum in the dissipation range of fully developed turbulence. The data are obtained by direct numerical simulations (DNS) of forced Navier-Stokes equations in a periodic domain, for Taylor-scale Reynolds numbers up to $R_\lambda=650$, with excellent small-scale resolution of $k_{max}\eta \approx 6$ for all cases (and additionally at $R_\lambda=1300$ with $k_{max}\eta\approx3$), where $k_{max}$ is the maximum resolved wavenumber and $\eta$ is the Kolmogorov length scale. We find that, for a limited range of wavenumbers $k$ past the bottleneck in the range $0.1 \lesssim k\eta \lesssim0.5$, the spectra for all $R_\lambda$ display a universal stretched exponential behavior of the form $\exp(-k^{2/3})$, in rough accordance with recent theoretical predictions. The stretched exponential fit in the near dissipation range $1 \lesssim k\eta \lesssim 4$ does not possess a unique exponent, which decreases with increasing $R_\lambda$. This region can be regarded as a crossover between the stretched exponential behavior and the far dissipation range $k\eta > 6$, in which analytical arguments as well as DNS data with superfine resolution (S. Khurshid et al., Phys.~Rev.~Fluids 3, 082601, 2018) suggest a $\exp(-k)$ dependence. We remark on the connection to the multifractal model which hypothesizes a pseudo-algebraic law.

Verification of a CFD-Class Software Tool as Applied to Modeling the Fuel Assemblies of Liquid Metal Cooled Reactors

Methodical approaches to verification of a CFD-class code for modeling fluid dynamics and heat transfer processes within the boundaries of a fuel assembly (FA) used in liquid metal cooled reactors are proposed. For verifying the code, experiments that take into account the specific features pertinent to the flow of and heat transfer in liquid metal coolants in the fast reactor FAs with spacer grids were selected. The experiments cover the following regimes: turbulent flow of and heat transfer in liquid metals in the stabilized and nonstabilized sections in simple and complex shaped channels for which the flow structure in the near-wall region is the determining one; turbulent flow in channels containing elements that cause flow separation and redistribution of the flow rate over the cross section, and flow in channels containing abrupt flow constriction/expansion. Proceeding from the need to save computation resources in solving practical problems, the high Reynolds number turbulence model was used, which does not pose the requirement of fulfilling the y+ ≈ 1 criterion for the dimensionless distance from the first computational node to the wall. The computations were carried out with the use of the high Reynolds number Realizable k–e turbulence model with the standard near-wall function. The local Weigand model for the turbulent Prandtl number Prt, applied in a wide range of Pr number values, including those for liquid metals, was used. The maximum deviations of the calculated values from the experimental data for the practically important parameters are estimated.