Synthetic Turbulence Research Articles

Direct anisotropic filter method of generating synthetic turbulence applied to turbulence-airfoil interaction noise prediction

Synthetic turbulence methods are widely used in computational aeroacoustics to study broadband noise physics. In this work, a direct anisotropic filter (DAF) method is proposed to produce desired velocity spectra of three-dimensional anisotropic turbulence, based on a direct form of anisotropic filter that can be implemented directly to obtain non-Gaussian spectra. It contains fewer model constraints than the existing methods, getting rid of the inconvenience induced by complex hypergeometric functions and Gaussian superposition with Mach number dependent model parameters. In addition, compared with the numerical results given by existing methods, e.g., the advanced digital filter method, this technique offers improvement in accuracy and cost. In this study, the DAF method is combined with the linearised Euler equations in computational aeroacoustics to study the turbulence-airfoil interaction noise, with the results showing good agreement with benchmarking analytical solutions and experimental measurement. The numerical study also investigates the effect of anisotropy on leading edge noise for thick airfoils, revealing that the anisotropic turbulence stretched in the axial direction will suppress the thickness-induced noise reduction. This study also highlights the contribution of streamwise energy spectra to noise generation when considering the effects of anisotropy.

A hyperbolic partial differential equation model for filtering turbulent flows

A two dimensional partial differential equation scheme that uses a second-order hyperbolic diffusion equation for image denoising is developed to a three dimensional model for filtering isotropic turbulence. The mathematical derivation of the model is introduced and a consistent finite difference numerical approximation scheme is proposed. The model is tested against the velocity fields of isotropic turbulence that are simulated by solving the lattice Boltzmann(LB) and the Navier–Stokes(NS) equations, respectively. The D3Q15 LB model and the Fourier spectral method are used to solve the LB equation and the Navier–Stokes vorticity equation at grid points of 2563, respectively. Also the filtering method with the choice of the same filtering parameters is applied against a synthetic turbulent field with the same number of points. The high rotation vortex identification method Q is used to visualize the total, coherent and incoherent fields in all cases of the study. Despite the different nature of the LB and NS direct numerical simulations and the synthetic turbulence, all input parameters for the hyperbolic filtering model are chosen the same in all cases. Comparisons between the LB and NS filtered energy spectra, coherent vortices, incoherent regions, skewness, flatness and the fourth order moments are also considered. The same features are calculated for the non-filtered and filtered synthetic turbulent fields. It is shown that the coherent part preserves all statistical features of turbulence. However, the isotropy is the only feature that has been preserved for the incoherent part and other statistical features are divergent in all cases of the study.

Comparison of synthetic turbulence approaches for blade element momentum theory prediction of tidal turbine performance and loads

Turbulence is a crucial flow phenomenon for tidal energy converters (TECs), as it influences both the peak loads they experience and their fatigue life. To best mitigate its effects we must understand both turbulence itself and how it induces loads on TECs. To that end, this paper presents the results of blade element momentum theory (BEMT) simulations of flume-scale TEC models subjected to synthetic turbulent flows. Synthetic turbulence methods produce three-dimensional flowfields from limited data, without solving the equations governing fluid motion. These flowfields are non-physical, but match key statistical properties of real turbulence and are much quicker and computationally cheaper to produce. This study employs two synthetic turbulence generation methods: the synthetic eddy method and the spectral Sandia method. The response of the TECs to the synthetic turbulence is predicted using a robust BEMT model, modified from the classical formulation of BEMT. We show that, for the cases investigated, TEC load variability is lower in stall operation than at higher tip speed ratios. The variability of turbine loads has a straightforward relationship to the turbulence intensity of the inflow. Spectral properties of the velocity field are not fully reflected in the spectra of TEC loads.

Effects of Path Averaging in a Sonic Anemometer on the Estimation of Turbulence-Kinetic-Energy Dissipation Rates

The turbulence-kinetic-energy dissipation rate is a fundamental property in turbulent flows, but its direct measurement in the atmospheric surface layer is still a challenge. Indirect estimates are often obtained from inertial-subrange laws using turbulence statistics of the longitudinal velocity component. In this study, synthetic turbulence data are used to investigate the impact of path-averaging effects present in sonic anemometer data on the inertial subrange of the second-order structure function. Path averaging reduces the energy levels in the second-order structure function, creating a negative bias in the estimates of the dissipation rate. The effect is dependent on the path-averaging transfer function, mean wind speed and path length. A simple correction for the bias on the basis of existing transfer functions is applied and tested with data obtained from two separate sonic anemometers. Compared to the spectrum, the second-order structure function after the correction becomes the optimum statistical measure for indirect estimation of the dissipation rate, due to its lower random error and insensitivity to aliasing effects.

Continuous cascades in the wavelet space as models for synthetic turbulence.

We introduce a wide family of stochastic processes that are obtained as sums of self-similar localized "wave forms" with multiplicative intensity in the spirit of the Richardson cascade picture of turbulence. We establish the convergence and the minimum regularity of our construction. We show that its continuous wavelet transform is characterized by stochastic self-similarity and multifractal scaling properties. This model constitutes a stationary, "grid free" extension of W cascades introduced in the past by Arneodo, Bacry, and Muzy using a wavelet orthogonal basis. Moreover, our approach generically provides multifractal random functions that are not invariant by time reversal and therefore is able to account for skewed multifractal models and for the so-called "leverage effect." In that respect, it can be well suited to providing synthetic turbulence models or to reproducing the main observed features of asset price fluctuations in financial markets.

A model for solid propellant burning fluctuations using mesoscale simulations

The combustion of composite solid propellants shows velocity fluctuations which are expected to have marked effects on turbulence or aeroacoustic instabilities. In this work, we propose a specific propellant boundary condition that models such fluctuations using a spectral synthetic turbulence approach. In order to feed this model with reliable input data, we consider mesoscale direct simulations of propellant combustion. This new propellant boundary condition is implemented in a CFD flow solver and applied to a real lab-scale motor. Simulations show that burning fluctuations can trigger aeroacoustic instabilities, in better agreement with experiments.

Synthetic Freestream Disturbance for the Numerical Reproduction of Experimental Zero-Pressure-Gradient Bypass Transition Test Cases

The present work introduces a means of forcing bypass transition within a zero-pressure-gradient smooth flat-plate boundary layer (ZPGSFPBL), suitable for DNS or LES computations for reproducing experimental datasets. In this type of bypass transition, one of the means of forcing transition within the boundary layer is via the introduction of a specific disturbance along the inflow boundary. Following this principle, the current method, introduces synthetic turbulence, generated by the method of Klein et al. (J. Comput. Phys. 186(2), 652–665, 2003), at the inflow, a certain height above the boundary layer, thereby confining it within the freestream. The principle parameter which dictates the transition behaviour is the height above the boundary layer at which the freestream turbulence is injected. By adjusting this parameter, as well as the integral length-scale and the intensity (either estimated or known a priori from experiments), ILES computations providing good agreement with experimental data sets can be achieved upon a variety of grids. This procedure has been validated upon the ERCOFTAC T3A experimental test case (freestream turbulent intensity of 3%), where good matching is achieved on streamwise quantities like skin-friction coefficient, shape factor, boundary layer thickness and fluctuating velocity growth rates as well as for profiles of mean velocity and fluctuating velocities in the wall-normal direction.

On the Power-Law Distribution of Pitch-Angle Scattering Times in Solar Wind Turbulence

The propagation of energetic particles in the solar wind depends in a sensitive way on the pitch-angle scattering of particles in the presence of magnetic turbulence. The well-known quasi-linear theory gives an expression for the pitch-angle scattering rate under the assumption of small turbulence levels, but both in the solar wind and in other astrophysical environments the turbulent magnetic field fluctuations can be large. Therefore, a reliable assessment of the pitch-angle scattering requires an investigation that goes beyond the quasi-linear theory. To this end, we employ a recently developed model of synthetic magnetic turbulence, which allows reproduction of a very long spectrum, while varying the turbulence level and the turbulence intermittency. Test particles representing protons with energies in the range $70~\mbox{keV}\,\mbox{--}\,1~\mbox{MeV}$ are injected in the turbulence spectrum plus a background magnetic field, and the pitch-angle scattering rate is determined by following the individual particles. Using turbulence and intermittency levels comparable to those observed in the solar wind, we find a broad power-law distribution of pitch-angle scattering times, which encompasses the quasi-linear value but extends to values both much larger and much smaller. We find that the distribution of pitch-angle scattering times also depends on the intermittency level. This finding shows that a description of parallel transport based on a single value of the pitch-angle scattering time is not sufficient. These numerical results are compared with observations of the distribution of magnetic variances at the particle resonant scale, measured in the solar wind by the Ulysses spacecraft.

Numerical Simulation of Flat Plate Boundary Layer Transition with Synthetic Inlet Turbulence

A large-eddy simulation (LES) of a flat plate boundary layer undergoing transition to turbulence, i.e., ERCOFTAC’s test case T3B, is performed with synthetic inlet turbulent fluctuations. Generated by Billson and Davidson’s method, the isotropic and homogeneous synthetic turbulence is imposed on a uniform flow directly at the inlet of the computational domain without a precursor adaptation region. The issue of the maximum-contained number (MCN) is specified, which aims at the determination of mesh distribution to maintain and strengthen the correlation between neighboring cells. The numerical results are realistic under the original synthetic turbulence if the MCN is suitably set. For further improvement of the prediction, a correction based on the Poisson equation is adopted to make the synthetic turbulence divergence-free, which is the basic requirement of incompressible flow. It is shown that with the divergence correction, the simulation results are better, and in particular, the decay of free stream turbulence near the upper boundary is more reasonable.

Computation of Aerodynamic and Acoustic Characteristics of NACA0012 Airfoil Using the Zonal RANS–IDDES Approach

The presented results of computations of the aerodynamic and acoustic characteristics of an isolated symmetric NACA0012 airfoil with a blunt trailing edge in a subsonic homogeneous viscous perfect gas flow at zero angle of attack are obtained using the MP5 modified finite-difference scheme proposed in this study. The computations are accomplished within the zonal RANS–IDDES approach engaging the basic RANS Spalart–Allmaras model. A synthetic turbulence generator with a three-dimensional source is used to create turbulent content at the entrance to the IDDES domain. A series of model problems are considered, whose solutions allowed tuning the parameters of the proposed difference scheme and solving some methodological problems related to processing the simulation results.

On possibilities to estimate local concentration variations with CFD-LES in real urban environments

Applied studies with Large Eddy Simulation (LES) of hazardous gas dispersion around buildings in cities have become increasingly feasible due to rapid advancements in computing technology. However, there is little extant literature investigating how each model’s results compare with others, as well as their ability to predict near-field dispersion in a real city. In this study, three typical LES sub-grid-scale models are used to simulate gas dispersion, utilizing alternatively constant values and synthetic turbulence at inflow boundaries. The results are compared with data from the Joint Urban 2003 Atmospheric Dispersion Study in Oklahoma City. Flow and turbulence statistics of the simulation is presented at two probe locations, one inside the city-core and one outside. In addition, comparisons with the measured mean concentration and maximum concentration values are conducted. It was found that in the core of the city, simulated turbulence is mainly determined by buildings and their configurations, and is only weakly affected by model type and assumed turbulence at the inflow boundaries. On the other hand, outside and upwind the city center the turbulence set at the inflow boundaries is very important if realistic turbulence statistics is to be achieved. Downstream of the source, all tested models produce similar predictions of maximum concentration values, which in turn are similar to the experimental data. Thus, the results indicate that it could be better to use the LES calculated maximum-concentration instead of the calculated mean-concentration when developing methods for hazard area estimation.

Local Stochastic Vortex Structure Method for Synthetic Turbulence Computation in Flight Simulators

Rapid turbulence approximation on and around a vehicle is necessary for development of improved flight simulators for helicopters and aircraft, used both for pilot training and for video-gaming applications. Predictions of synthetic turbulence methods must have both temporally and spatially accurate statistics compared to actual turbulence for the given turbulence mean velocity and Reynolds stress tensor. The stochastic vortex structure (SVS) method was recently proposed for turbulent flows with interacting particles and was shown to generate accurate statistical measures for homogeneous turbulence and for turbulent shear flows. Because the velocity in flight simulators is required only on target points near the flight vehicle, the current paper modifies the SVS method by 1) moving and rotating the vortex structures via stochastic differential equations, and 2) introducing vortices only in a restricted vortex region surrounding the aircraft. This local stochastic vortex structure (LSVS) method decreases the SVS computational speed by several orders of magnitude, making it feasible for real-time turbulence computation in flight simulators. The proposed method is validated by comparing results for different statistical measures with predictions from direct numerical simulation of homogeneous turbulence. Sensitivity of the different measures with numerical parameters in the LSVS model is examined.

Aeroelastic analyses of bridges using a Pseudo-3D vortex method and velocity-based synthetic turbulence generation

The accurate representation of aerodynamic forces is essential for a safe, yet reasonable design of long-span bridges subjected to wind effects. In this paper, a novel extension of the Pseudo-three-dimensional Vortex Particle Method (Pseudo-3D VPM) is presented for Computational Fluid Dynamics (CFD) buffeting analysis of line-like structures. This extension entails an introduction of free-stream turbulent fluctuations, based on the velocity-based turbulence generation. The aerodynamic response of a long-span bridge is obtained by subjecting the 3D dynamic representation of the structure to correlated free-stream turbulence in two-dimensional (2D) fluid planes, which are positioned along the bridge deck. The span-wise correlation of the free-stream turbulence between the 2D fluid planes is established based on Taylor’s hypothesis of frozen turbulence. Moreover, the application of the laminar Pseudo-3D VPM is extended to a multimode flutter analysis. Finally, the structural response from the Pseudo-3D flutter and buffeting analyses is verified with the response, computed using the semi-analytical linear unsteady model in the time-domain. Meaningful merits of the turbulent Pseudo-3D VPM with respect to the linear unsteady model are the consideration of the 2D aerodynamic nonlinearity, nonlinear fluid memory, vortex shedding and local non-stationary turbulence effects in the aerodynamic forces. The good agreement of the responses for the two models in the 3D analyses demonstrates the applicability of the Pseudo-3D VPM for aeroelastic analyses of line-like structures under turbulent and laminar free-stream conditions.

Analytical Description of the Time-dependent Perpendicular Transport of Energetic Particles

Abstract A fundamental problem in plasma and astrophysics is the motion of energetic and electrically charged particles through a magnetized plasma, e.g., cosmic rays propagating through the interplanetary or interstellar medium. In particular, the motion of particles across a large-scale or guide field is difficult to describe analytically. Recently, an advanced nonlinear theory for perpendicular transport was developed. The theory shows good agreement with simulations and can be used for a variety of synthetic turbulence models. An interesting feature of the latter theory is that it allows for a full time-dependent description of perpendicular transport, including the initial ballistic motion, sub-diffusion, and the recovery of diffusion as soon as there is transverse complexity of the magnetic field. It is the purpose of the current paper to use this theory to derive analytical forms of the time-dependent perpendicular diffusion parameter for different cases. This is useful for a variety of applications, such as studies of shock acceleration and solar modulation.

Extracting the turbulent flow-field from beam emission spectroscopy images using velocimetry.

The 2D turbulent E × B flow-field is inferred from density fluctuation images obtained with the beam emission spectroscopy diagnostic on DIII-D using the orthogonal dynamic programming velocimetry algorithm. A synthetic turbulence model is used to test the algorithm and optimize it for measuring zonal flows. Zonal flow measurements are found to require a signal-to-noise ratio above ∼10 and a zonal flow wavelength longer than ∼2 cm. Comparison between the velocimetry-estimated flow-field and the E × B flow-field using a nonlinear gyrokinetic GENE simulation finds that the flow-fields have identical spatial structure and differ only by the mean turbulence phase velocity, which is spatially uniform in this flux tube simulation.

Assessment of Turbulence Modelling in the Wake of an Actuator Disk with a Decaying Turbulence Inflow

The characteristics of the turbulence field in the wake produced by a wind turbine model are studied. To this aim, a methodology is developed and applied to replicate wake measurements obtained in a decaying homogeneous turbulence inflow produced by a wind tunnel. In this method, a synthetic turbulence field is generated to be employed as an inflow of Large-Eddy Simulations performed to model the flow development of the decaying turbulence as well as the wake flow behind an actuator disk. The implementation is carried out on the OpenFOAM platform, resembling a well-documented procedure used for wake flow simulations. The proposed methodology is validated by comparing with experimental results, for two levels of turbulence at inflow and disks with two different porosities. It is found that mean velocities and turbulent kinetic energy behind the disk are well estimated. The development of turbulence lengthscales behind the disk resembles what is observed in the free flow, predicting the ambient turbulence lengthscales to dominate across the wake, with little effect of shear from the wake envelope. However, observations of the power spectra confirm that shear yields a boost to the turbulence energy within the wake noticeable only in the low turbulence case. The results obtained show that the present implementation can successfully be used in the modelling and analysis of turbulence in wake flows.

A numerical-experimental investigation on the aerodynamic performance of CAARC building models with geometric modifications

This paper presents the results of a numerical-experimental investigation carried out with the purpose to evaluate the aerodynamic performance of CAARC tall building models with different cross-section configurations. A numerical model based on the Taylor-Galerkin two-step scheme and the Finite Element Method is adopted. Turbulence is described using LES and a synthetic inflow turbulence generator. Experimental tests were performed at the Prof. Joaquim Blessmann Boundary Layer Wind Tunnel considering CAARC tall building models with cross-section modifications based on chamfered and recessed corners. Some of the wind tunnel predictions obtained here are compared with results obtained from the numerical model proposed in this work, where two and three-dimensional meshes are utilized. Comparisons are also performed considering results obtained from other authors in similar studies. From the present investigation, it was observed that the wind action on tall buildings is significantly influenced by the geometric configuration of the building corners, which may lead to important reductions in the aerodynamic forces. Through a direct comparison of results between numerical and experimental simulation, we can see that both reach a convergence of results, thus indicating the potential of use of CFD in the modern aerodynamic investigation of buildings.

Modelling synthetic atmospheric turbulence profiles with temporal variation using Gaussian mixture model

The atmospheric turbulence profile plays a very important role for performance evaluation of wide-field adaptive optic systems. Since the atmospheric turbulence is evolving, the turbulence profile will change with time. To better model the temporal variation of turbulence profile, in this paper, we propose to use the extensive stereo-SCIDAR turbulence profile dataset from one observation site to train a Gaussian mixture model. The trained Gaussian mixture model can describe the structure of the turbulence profile in that particular site with several multidimensional Gaussian distributions. We cluster the turbulence profile data with the Gaussian mixture model and analyse the temporal variation properties of the clusters. We define the characteristic time as the time that the measured turbulence profile remains in a given profile. We find that normally the characteristic time is around 2 to 20 min and will change at different sites and in different seasons. With the statistical results of the characteristic time and the trained Gaussian mixture model, we can generate synthetic artificial turbulence profiles with realistic temporal variation to better test the performance of adaptive optics systems.

Importance of the nozzle-exit boundary-layer state in subsonic turbulent jets

To investigate the effects of the nozzle-exit conditions on jet flow and sound fields, large-eddy simulations of an isothermal Mach 0.9 jet issued from a convergent-straight nozzle are performed at a diameter-based Reynolds number of $1\times 10^{6}$. The simulations feature near-wall adaptive mesh refinement, synthetic turbulence and wall modelling inside the nozzle. This leads to fully turbulent nozzle-exit boundary layers and results in significant improvements for the flow field and sound predictions compared with those obtained from the typical approach based on laminar flow in the nozzle. The far-field pressure spectra for the turbulent jet match companion experimental measurements, which use a boundary-layer trip to ensure a turbulent nozzle-exit boundary layer to within 0.5 dB for all relevant angles and frequencies. By contrast, the initially laminar jet results in greater high-frequency noise. For both initially laminar and turbulent jets, decomposition of the radiated noise into azimuthal Fourier modes is performed, and the results show similar azimuthal characteristics for the two jets. The axisymmetric mode is the dominant source of sound at the peak radiation angles and frequencies. The first three azimuthal modes recover more than 97 % of the total acoustic energy at these angles and more than 65 % (i.e. error less than 2 dB) for all angles. For the main azimuthal modes, linear stability analysis of the near-nozzle mean-velocity profiles is conducted in both jets. The analysis suggests that the differences in radiated noise between the initially laminar and turbulent jets are related to the differences in growth rate of the Kelvin–Helmholtz mode in the near-nozzle region.

A systematic approach to the generation of synthetic turbulence using spectral methods

In this paper, a systematic discussion on the generation of synthetic turbulence using spectral methods is presented. After a brief introduction which reviews existing methodologies, the role played by the fulfilment of the divergence-free condition and Taylor assumption is investigated. Special attention is given to the case in which such random fields are applied as inflow condition for Computational Fluid Dynamics simulations. Subsequently, a new methodology of general applicability for the generation of synthetic turbulence is proposed. The strength of the new approach lies in its generality and conceptual simplicity. The obtained random field fulfils the divergence-free condition as well as Taylor assumption and it is approximately characterised by preselected spectral content in each spatial direction, so also providing direct control over all turbulence integral scales. Synthetic turbulent fields characterised by different spectral content are generated confirming the soundness of the proposed approach and showing its ability to target strongly anisotropic fields. Finally, some remarks on the generation of inhomogeneous fields, obtained by combination of homogeneous ones, are provided so generalising the proposed procedure.