Anisotropic Turbulence Research Articles

Data-driven turbulence anisotropy in film and effusion cooling flows

Film and effusion cooling flows contain complex flow that classical Reynolds-averaged Navier–Stokes (RANS) models struggle to capture. A tensor-basis neural network is employed to provide an anisotropic model that can reproduce the Reynolds stress fields of large-eddy simulations (LES). High-quality LES datasets are used to train, validate, and test a neural network model. A priori results show the model can reproduce the Reynolds stress field on a cooling case not present in the model's training. The neural networks are employed directly into RANS solver, augmenting a k-ω shear stress transport (SST) model, with conditioning applied. The model provided improvements to Reynolds stress, velocity, and temperature fields in cases not used to train the model, including a multi-hole case that differs from the single-hole geometry used to train the case. Underpredictions of the turbulent kinetic energy field, modeled with the SST transport equation, were found to lead to underpredictions in the neural network produced Reynolds stresses. Correcting this with the LES, resolved turbulent kinetic energy provided further agreement. The method found significant improvements to the surface cooling results that advance the current state-of-the-art in RANS modeling of film and effusion cooling flows.

Evolution properties of a radially polarized fractional multi-Gaussian Schell-model beam propagating in anisotropic turbulence

Evolution properties of a radially polarized fractional multi-Gaussian Schell-model beam propagating in anisotropic turbulence

Realizability-preserving time-stepping for the differential Reynolds stress turbulence models

In the context of incompressible turbulence modelling, differential Reynolds stress models allow a better representation of turbulence anisotropy than classical linear eddy viscosity models and are less expensive than large eddy simulations in terms of computational cost. They rely on a modelled transport equation for the Reynolds stress tensor, which is by definition a covariance tensor and must remain symmetric positive semi-definite. However, the solution of the modelled and discretized transport equation may not preserve these mathematical properties. In the present article, a methodology to time-split Reynolds stress R__ terms in the transport equation is proposed using a decomposition theorem which proves the realizability of R__ provided realizable initial conditions. Realizability-preserving time-steppings are designed for several differential Reynolds stress models. The numerical schemes are presented in a finite volume context but may be used with others space discretization schemes. The realizability, precision and robustness of the numerical scheme is verified through the anisotropy time evolution in homogeneous shear-flow simulations with various initial conditions.

Three-dimensional Simulation of Thermodynamics on Confined Turbulence in a Large-scale CME-flare Current Sheet

Turbulence plays a key role in forming the complex geometry of the large-scale current sheet (CS) and fast energy release in a solar eruption. In this paper, we present full 3D high-resolution simulations for the process of a moderate coronal mass ejection (CME) and the thermodynamical evolution of the highly confined CS. Copious elongated blobs are generated owing to tearing and plasmoid instabilities, giving rise to a higher reconnection rate, and undergo the splitting, merging, and kinking processes in a more complex way in 3D. A detailed thermodynamical analysis shows that the CS is mainly heated by adiabatic and numerical viscous terms, and thermal conduction is the dominant factor that balances the energy inside the CS. Accordingly, the temperature of the CS reaches to a maximum of about 20 MK, and the range of temperatures is relatively narrow. From the face-on view in the synthetic Atmospheric Imaging Assembly 131 Å, the downflowing structures with similar morphology to supra-arcade downflows are mainly located between the post-flare loops and loop top, while moving blobs can extend spikes higher above the loop top. The downward-moving plasmoids can keep the twisted magnetic field configuration until the annihilation at the flare loop top, indicating that plasmoid reconnection dominates in the lower CS. Meanwhile, the upward-moving ones turn into turbulent structures before arriving at the bottom of the CME, implying that turbulent reconnection dominates in the upper CS. The spatial distributions of the turbulent energy and anisotropy are addressed, which show a significant variation in the spectra with height.

Turbulence anisotropy in a wall-wake flow downstream of two horizontal cylinders

In this study, experimental results of flow past two horizontal cylinders — one above the other are discussed. The research was conducted using experimental data collected on a rough-bed with double cylinders of three different sizes. First, fundamental features such as streamwise velocity, Reynolds shear stress (RSS), and turbulence intensity profiles have been explained at various downstream positions with respect to the cylinders; next, some advanced analysis such as correlation coefficient, stress anisotropy, and dissipation anisotropy have been presented and compared location-wise. To demonstrate anisotropy, stress, dissipation tensors along with anisotropic invariant map and function are plotted and thoroughly analyzed. Lastly, A different diagrammatic representation of the level of anisotropy of turbulence is obtained by incorporating the eigenvalues of the Reynolds stress tensor, namely barycentric coordinates.© 2017 ElsevierInc.Allrightsreserved.

Development of an effective two-equation turbulence modeling approach for simulating aerosol deposition across a range of turbulence levels

Pharmaceutical aerosol systems present a significant challenge to computational fluid dynamics (CFD) modeling based on the need to capture multiple levels of turbulence, frequent transition between laminar and turbulent flows, anisotropic turbulent particle dispersion, and near-wall particle transport phenomena often within geometrically complex systems over multiple time scales. Two-equation turbulence models, such as the k−ω family of approximations, offer a computationally efficient solution approach, but are known to require the use of near-wall (NW) corrections and eddy interaction model (EIM) modifications for accurate predictions of aerosol deposition. The objective of this study was to develop an efficient and effective two-equation turbulence modeling approach that enables accurate predictions of pharmaceutical aerosol deposition across a range of turbulence levels. Key systems considered were the traditional aerosol deposition benchmark cases of a 90-degree bend (Re=6,000) and a vertical straight section of pipe (Re=10,000), as well as a highly complex case of direct-to-infant (D2I) nose-to-lung pharmaceutical aerosol delivery from an air-jet dry powder inhaler (DPI) including a patient interface and infant nasal geometry through mid-trachea (500<Re<7,000). Of the k−ω family of models, the low Reynolds number (LRN) shear stress transport (SST) approach was determined to provide the best agreement with experimental aerosol deposition data in the D2I system, based on an improved simulation of turbulent jet flow that frequently occurs in DPIs. Considering NW corrections, a new correlation was developed to quantitatively predict best regional values of the y+limit, within which anisotropic NW turbulence is approximated. Considering EIM modifications, a previously described drift correction approach was implemented in pharmaceutical aerosol simulations for the first time. Considering all model corrections and modifications applied to the D2I system, regional relative errors in deposition fractions between CFD predictions and new experimental data were improved from 19–207% (no modifications) to 2–15% (all modifications) with a notable decrease in computational time (up to ∼15%). In conclusion, the highly efficient two-equation k−ω models with physically realistic corrections and modifications provided a viable, efficient and accurate approach to simulate the transport and deposition of pharmaceutical aerosols in complex airway systems that include laminar, turbulent and transitional flows.

Validation and analyses of QCR correction turbulence model in sub-/super-sonic inner flows

The inlet, isolation section, and other internal flow components are important parts of the aircraft propulsion system. Their performances affect the stability of the entire propulsion system. According to those components, complicated shock wave/boundary layer interaction (SBLI), flow separation, and secondary flow phenomena would occur. The commonly used turbulence models, SA and SST, cannot predict the anisotropy of turbulence. This deficiency makes the calculated results differ significantly from the experimental results and cannot accurately predict their aerodynamic performance. This paper validates the feasibility and effectiveness of the turbulence models based on quadratic constitutive relation (QCR) correction applied to the flow of square duct, compression corners, diffusing 3D S-Duct, and axisymmetric cylindrical isolator. This can support future calculations of complex flow fields with flow separation and secondary flow phenomena in the subsonic or supersonic inlet. The results show that the turbulence model with QCR correction is better than the original turbulence model. Among them, the SA-QCR2020 turbulence model is the best, which is able to predict the presence of secondary flows and large boundary layer separated flows well.

A mathematical model for the interaction of anisotropic turbulence with a rigid leading edge

This paper investigates the effect of anisotropic turbulence on generating leading-edge aerofoil–turbulence interaction noise. Thin aerofoil theory is used to model an aerofoil as a semi-infinite plate, and the scattering of incoming turbulence is solved via the Wiener–Hopf technique. This theoretical solution encapsulates the diffraction problem for gust–aerofoil interaction and is integrated over a wavenumber–frequency spectrum to account for general incoming anisotropic turbulence. We develop a novel axisymmetric wavenumber–frequency model that captures the wall-normal variation in turbulence characteristics, differing from previous approaches. Then, the method of Gaussian decomposition, in which the generalised spectra are approximated through the weighted sum of individual Gaussian eddy models, is applied to fit the turbulence model to experimental data. Comparisons with experimental data show good agreement for a range of anisotropic ratios.

Influence of Alfvén Ion–Cyclotron Waves on the Anisotropy of Solar Wind Turbulence at Ion Kinetic Scales

The power spectra of the magnetic field at ion kinetic scales have been found to be significantly influenced by Alfvén ion–cyclotron (AIC) waves. Here, we study whether and how this influence of the AIC wave depends on the θVB angle (the angle between the local mean magnetic field and the solar wind velocity direction). The wavelet technique is applied to the high time-resolution (11 vectors per second) magnetic field data from WIND spacecraft measurements in a fast solar wind stream associated with an outward magnetic sector. It is found that around the ion kinetic scales (0.52 Hz–1.21 Hz), the power spectrum in the parallel angular bin 0∘&lt;θVB&lt;10∘ has a slope of −4.80±0.15. When we remove the left-handed polarized AIC waves (with normalized reduced magnetic helicity smaller than −0.9) from the fluctuations, the spectral index becomes −4.09±0.11. However, the power spectrum in the perpendicular angular bin 80∘&lt;θVB&lt;90∘ changes very little during the wave-removal process, and its slope remains −3.22±0.07. These results indicate that the influence of the AIC waves on the magnetic spectral index at the ion kinetic scales is indeed dependent on θVB, which is due to the anisotropic distribution of the waves. Apparently, when the waves are removed from the original data, the spectral anisotropy weakens. This result may help us to better understand the physical nature of the spectral anisotropy around the ion scales.

Anisotropy of Self-Correlation Level Contours in Three-Dimensional Magnetohydrodynamic Turbulence

MHD turbulence is considered to be anisotropic owing to the presence of a magnetic field, and its self-correlation anisotropy has been unveiled by solar wind observations. Here, based on numerical results of compressible MHD turbulence with a global mean magnetic field, we explore variations of the normalized self-correlation function’s (NCF) level contours with the scale as well as their evolution. The analyses reveal that the NCF’s level contours tend to elongate in the direction parallel to the mean magnetic field, and the elongation becomes weak with decreasing intervals. These results are consistent with slow solar wind observations. The less anisotropy of the NCF’s level contours with the shorter intervals can be produced by the fact that coherent structures stretch more along the parallel direction at the long intervals than at the short intervals. The analyses also disclose that as the simulation time builds up, the NCF’s level contours change thinner and thinner, and the anisotropy of the NCF’s level contours grows, which can be caused by the break of large coherent structures into small ones. The increased self-correlation anisotropy with time foretells that the self-correlation anisotropy of solar wind turbulence enlarges with the radial distance, which needs to be tested against observations by using Parker Solar Probe (PSP) measurements.

An efficient and low-divergence method for generating inhomogeneous and anisotropic turbulence with arbitrary spectra

This paper proposes a low-divergence method to generate inhomogeneous and anisotropic turbulence. Based on the idea of correlation reconstruction, the proposed method uses the Cholesky decomposition matrix to re-establish turbulence correlation functions. This is in contrast with the time-consuming procedure used in conventional methods to solve eigenvalues and eigenvectors in each location required by coordinate transformation, thereby reducing the computational complexity and improving the efficiency of synthetic turbulence generation. The proposed method is based on the classical spectrum-based method that is widely used to generate homogeneous and isotropic turbulence. By adjusting the generation strategy of specific random vectors, inhomogeneous and anisotropic turbulence with a relatively low divergence level can be obtained in practice, with almost no additional computational burden. Two versions of the proposed method are presented: the inverter and shifter versions. Both the versions are highly efficient, easy to implement, and compatible with high-performance computing. This method is also suitable for providing high-quality initial or boundary conditions for scale-resolving turbulence simulations with large grid numbers (such as direct numerical simulations or large eddy simulations); it can be rapidly implemented using various open-source computational fluid dynamics codes or common commercial software.

Anisotropy of turbulence at the core of the tip and hub vortices shed by a marine propeller

Large-eddy simulation on a grid consisting of 5 billion points was utilized to study the properties of turbulence at the core of the tip and hub vortices shed by a marine propeller across working conditions. Turbulence at the core of the tip vortices was found to be initially isotropic, moving towards a ‘cigar-shaped’ axisymmetric state as instability grows, dominated by turbulent fluctuations of the velocity component directed in the radial direction of the cylindrical reference frame centred at the wake axis. The break-up of the coherence of the tip vortices is instead characterized by turbulence recovering an isotropic state. This process is accelerated by growing load conditions of the propeller. In contrast, during instability of the hub vortex, turbulence at its core develops a ‘pancake-shaped’ axisymmetric state, dominated by the fluctuations of the radial and azimuthal velocities. However, at higher propeller loads turbulence at the core of the hub vortex keeps close to isotropy, thanks to a faster instability. Within both tip and hub vortices the deviations from Boussinesq's hypothesis were found very significant, providing evidence of the unsuitability of conventional turbulence modelling. At the core of the tip vortices they become especially large at their break-up and for increasing load conditions of the propeller, equivalent to more intense structures. In contrast, at the core of the hub vortex they were verified to be decreasing functions of the propeller load.

Performance of HQAM/XQAM Laser Communication System in Anisotropic Non-Kolmogorov Ground–HAP–Satellite Uplink

Satellite laser communication can achieve high-speed, high-precision, and high-security broadband communication without being constrained by the electromagnetic spectrum, which has attracted attention. So, this paper proposes the use of a high-altitude platform (HAP) under anisotropic non-Kolmogorov turbulence to improve the communication performance of the system. Cross quadrature amplitude modulation (XQAM) and hexagon quadrature amplitude modulation (HQAM) are applied to the ground–HAP–satellite (G-H-S) laser communication system. Considering the combined effects of uplink light intensity scintillation, beam wander, and the angle of arrival fluctuation, the G-H-S system’s bit error rate (BER) closure expression is derived under the EW distribution. Simultaneously, the relationship between the G-H-S system’s signal-to-noise ratio (SNR) and BER under different anisotropic factor u values is simulated and compared with the traditional ground–satellite (G-S) system. The results show that the communication performance of the G-H-S system with HQAM modulation is better. In addition, the effects of the zenith angle, receiving aperture, transmitter beam radius, and beam divergence angle on the BER performance of the system are also studied. Finally, the correctness of the analysis results is verified via Monte Carlo simulation. This research will benefit the design and optimization of satellite laser communication systems.

Numerical Investigation of Bed Shear Stress and Roughness Coefficient Distribution in a Sharp Open Channel Bend

The helical flow leads to the redistribution of the bed shear stress and roughness coefficient in open-channel bends, influencing the transport of sediment and riverbed evolution process. To explore the mechanisms underlying this redistribution, a 3D numerical simulation of a 180° sharp bend was performed by solving the Reynolds-averaged Navier–Stokes (RANS) equations using the Reynolds stress equation model (RSM) as the anisotropic turbulence closure approach. The results indicate that the high bed shear stress zone appeared in the inner bank region from the 50° to 110° sections, and the section maximum bed shear stress gradually shifted outwards, owing to the advective momentum transport by the circulation cells. The quantitative analyses of the terms in depth-averaged Navier-Stokes equations indicate that the contributions of the cross-stream circulation and cross-flow to the downstream bed shear stress were of the same order of magnitude, and the overall contribution rate of the cross-stream circulation was 20%. The contribution rates of the cross-flow, cross-stream circulation, turbulence, and pressure gradient to the transverse bed shear stress were approximately 30%, 7%, 3%, and 60%, respectively, indicating that the pressure gradient term arising from the transverse water surface slope played a dominant role. The Chezy resistance coefficient showed an overall decreasing trend along the bend. Therefore, an effective expression considering the streamwise variation along the centreline and transverse variation was successfully established to predict the uneven distribution of the Chezy resistance coefficient.

Spatial coherence length and wave structure function for plane waves transmitted in anisotropic turbulent oceans.

The spatial coherence length and wave phase structure function are two important factors in describing turbulence's effect on light propagation in seawater. This paper derives the wave phase structure function and spatial coherence length of plane waves in moderate to strong turbulent channels by deriving a "modification seawater turbulence power spectrum" and an oceanic-modified Rytov approximation. The evolutions in wave structure function, coherence length with the temperature dissipation rate, energy dissipation rate, anisotropy turbulence factor, signal wavelength, and propagation distance are analyzed by numerical calculation. In the moderate and strong turbulence regions, the phase structure function and spatial coherence length increase and decrease with increasing transmission distance and turbulence strength, respectively, and there is a saturation tendency for both. The fluctuation of seawater salinity has a greater effect on the phase structure function and coherence length than the temperature fluctuation. In addition, the wave structure function decreases with increasing signal wavelength and degree of turbulent anisotropy, but the trend of spatial coherence length is reversed.

Flow patterns and defect dynamics of active nematic liquid crystals under an electric field.

The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematic liquid crystals are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength. Topological defects in the anisotropic active turbulence are localized and show characteristic dynamics with simultaneous creation of two pairs of defects. A laning state characterized by stripe domains with alternating flow directions is found at a larger field strength near the transition to the uniformly aligned state. We obtained periodic oscillations between the laning state and active turbulence, which resembles an experimental observation of active nematics subject to anisotropic friction.

Model and method to predict the turbulent kinetic energy induced by tidal currents, application to the wave-induced turbulence

A prediction model for the turbulent kinetic energy (TKE) induced by tidal-currents is proposed as a function of the barotropic velocity only, along with a robust method evaluating the different parameters involved using Acoustic Doppler Current Profiler (ADCP) measurements from Alderney Race. We find that the model is able to reproduce correctly the TKE profiles with coefficients of correlation on average higher than 0.90 and normalised root-mean-square errors (NRMSE) less than 14%. Different profiles are also tested for the mean velocity, no satisfactory prediction model is found but we are able to have decent estimates of the velocity shear and friction velocity. Two applications are then carried out. First the turbulent budget terms are estimated and discussed. We identify the turbulent production and dissipation of TKE as the most important mechanisms, then we discuss the validity of several theoretical results derived for isotropic turbulence for this application. A strong departure for the estimation of the turbulent dissipation is notably found and explained by the turbulent anisotropy. At last the prediction model for the TKE is used to infer the wave-induced TKE. We show the importance of removing the tidal component, waves can have a strong influence down to mid-depth.

Influence of ground blocking on the acoustic phase variance in a turbulent atmosphere.

Sound propagation through atmospheric turbulence is important in many applications such as localization of low flying aircraft, sonic boom disturbances, and auralization of aircraft during takeoff and landing. This article extends an isotropic turbulence model in the atmospheric boundary layer to account for ground blocking of buoyancy-produced velocity fluctuations. The extended, anisotropic turbulence model is needed to correctly predict the effect of the largest velocity eddies on the statistical characteristics of sound signals. This model and geometrical acoustics are then employed to derive a closed-form expression for the variance of the phase fluctuations of a spherical sound wave for vertical and slanted propagation, without the use of the Markov approximation. A numerical analysis of this expression indicates significant anisotropy of the phase variance due to the buoyancy-produced velocity fluctuations with ground blocking such that it decreases in the vertical direction and increases in the near-horizontal directions. The newly formulated phase variance is compared with data from an outdoor experiment on vertical and slanted sound propagation. By accounting for ground blocking, much better agreement is obtained between the theoretical predictions and experimental data.

Self-nested large-eddy simulations in PALM model system v21.10 for offshore wind prediction under different atmospheric stability conditions

Abstract. Large-eddy simulation (LES) resolves large-scale turbulence directly and parametrizes small-scale turbulence. Resolving micro-scale turbulence, e.g., in wind turbine wakes, requires both a sufficiently small grid spacing and a domain large enough to develop turbulent flow. Refining a grid locally via a nesting interface effectively decreases the required computational time compared to the global grid refinement. However, interpolating the flow between nested grid boundaries introduces another source of uncertainty. Previous studies reviewed nesting effects for a buoyancy-driven flow and observed a secondary circulation in the two-way nested area. Using a nesting interface with a shear-driven flow in LES, therefore, requires additional verification. We use PALM model system 21.10 to simulate a boundary layer in a cascading self-nested domain under neutral, convective, and stable conditions and verify the results based on the wind speed measurements taken at the FINO1 platform in the North Sea. We show that the feedback between parent and child domains in a two-way nested simulation of a non-neutral boundary layer alters the circulation in the nested area, despite spectral characteristics following the reference measurements. Unlike the pure buoyancy-driven flow, a non-neutral shear-driven flow slows down in a two-way nested area and accelerates after exiting the child domain. We also briefly review the nesting effect on the velocity profiles and turbulence anisotropy.

Effect of d-type rib roughness on the turbulent structure of side wall boundary layer for wave-current combined flow

An experimental study has been carried out in a laboratory flume to characterize the turbulence structure and turbulence anisotropy in the boundary layer over smooth and rough side walls for both current alone and wave-current combined flow situations. The rough side wall of the flume comprises a train of circular ribs (diameter, k) attached vertically maintaining uniform spacing p along the streamwise direction. The experiments are performed for smooth surface and rough (ribbed) surfaces with p/k = 2, 3, and 4 to reproduce different cases of d-type rib roughness. The effect of wave-current interaction has been investigated by superposing waves of two different frequencies. Time series data of three velocity components are obtained using Acoustic Doppler Velocimeter. At the near wall region, roughness with higher p/k value enhances the level of turbulent intensity and Reynolds stress significantly. In a channel with smooth side wall, the wave-current combined flow produces lesser turbulence intensity than the current alone flow near the wall. However, for a ribbed wall case, the effect is completely opposite that is, wave-current interacting flow induces higher intensities compared to the reference current alone flow. Substantial decline in the turbulent length scales at the near wall region are observed for ribbed walls, which reveals the strong effect of roughness elements on the turbulent structure. Superposition of wave reduces the length scales even more for both smooth and rough wall cases. As the spacing between two ribs ( p/ k ratio) increases, the energy dissipation rate increases. The analysis of anisotropy invariant map demonstrates a reduction of anisotropy in the vicinity of ribbed wall compared to that for a smooth wall. For wave-current combined flow, the anisotropy invariant data of Reynolds stress tensor varies dramatically within the boundary of map, reflecting significant changes in the state of turbulence.