Synthetic Turbulence Research Articles

Assessing and improving the accuracy of synthetic turbulence generation

Abstract

Flow and Noise Predictions of Coaxial Jets

Flow and noise solutions of the two Large-Eddy Simulation (LES) approaches are evaluated for the jet flow conditions corresponding to a benchmark coaxial jet case from the European Union Computation of Coaxial Jet Noise experiment. The jet is heated and issues for a short-cowl axisymmetric nozzle with a central body at a transonic speed. The first LES method is based on the Compact Accurately Boundary-Adjusting High-Resolution Technique (CABARET) scheme, for which implementation features include asynchronous time stepping at an optimal Courant–Friedrichs–Lewy number, a wall model, and a synthetic turbulence inflow boundary condition. The CABARET LES is implemented on Graphics Processing Units. The second LES approach is based on the hybrid Reynolds-average Navier–Stokes (RANS)/implicit LES method that uses a mixture of a high-order Roe and Monotonicity-Preserving reconstruction of the 9th order (MP9 scheme) and a wall distance model of the improved delayed detached-eddy simulation type. The RANS/implicit LES method is run on a Message Passing Interface (MPI) cluster. Two grid generation approaches are considered: the unstructured grid using OpenFOAM utility snappyHexMesh and the conventional structured multiblock body-fitted curvilinear grid. The LES flow solutions are compared with the experiment and also with solutions obtained from the standard axisymmetric RANS method using the turbulence model. For noise predictions, the LES solutions are coupled with the penetrable surface formation of the Ffowcs Williams–Hawkings method. The results of noise predictions are compared with the experiment, and the effect of different LES grids and acoustic integration surfaces is discussed.

Aeroacoustic design and broadband noise predictions of a fan stage with serrated outlet guide vanes

This work, realized in the framework of the European project TurboNoiseBB, presents an advanced aeroacoustic design methodology of Outlet Guide Vanes (OGVs) with leading edge serrations, including details on their broadband noise and aerodynamic performance. The serrated OGV corresponds to a modified stator from an aeroengine fan stage tested at the AneCom AeroTest’s facility (Germany). Sinusoidal leading edge patterns with varying amplitude and wavelength along the span are designed in collaboration with Safran Aircraft Engines. Serrations are adjusted to account for the turbulence characteristics provided by Reynolds-Averaged Navier–Stokes (RANS) calculations. Optimal parameters are found using simple design rules discussed in this paper. Down selection of serrated OGV designs (patent pending) is conducted through a RANS control of aerodynamic performances and in accordance with industrial specifications, ensuring acceptable penalties on the loss coefficient and isentropic efficiency. Broadband noise simulations are performed using a computational aeroacoustic (CAA) code that solves the linearized Euler equations with a synthetic turbulence model. Additionally, the acoustic response of the serrated leading edge airfoils is also estimated using the most relevant analytical formulation in the literature, based on the Wiener–Hopf technique. Numerical predictions at approach conditions are compared to available experimental measurements (on the untreated baseline case) and analytical Amiet-based and Wiener–Hopf solutions, showing satisfactory agreement in the sound power spectrum in the bypass duct. Finally, the acoustic performances estimated at the design stage are numerically assessed by both the CAA and Wiener–Hopf methods, providing around 2.5 dB and 3.5 dB reduction in the overall power level, respectively.

Analysis of the effect of freestream turbulence on dynamic stall of wind turbine blades

The aerodynamics of a wind turbine blade at various fixed and dynamically changing angles of attack for laminar and turbulent freestream is investigated by large-eddy simulations. The effects of freestream turbulence on the aerodynamic coefficients are analyzed for dynamic stall conditions being generated by prescribing gusts, i.e., periodically changing incoming velocity fields, onto a ClarkY airfoil at a chord based Reynolds number of Re=150,000. A synthetic turbulence generation (STG) method is extended and applied to produce the turbulent gusts in a time varying mean flow with predefined turbulence statistics, such as mean velocity, Reynolds stress tensor components, and velocity spectra. The length scales in the turbulent freestream are smaller than the blade chord length. The reduced frequency of the incoming laminar and turbulent gusts is kred=0.2 based on the freestream velocity, chord length, and gust frequency. Dynamic stall is analyzed for an angle of attack ranging from 10° to 25°. It is shown how much the freestream turbulence level delays stall and increases lift at high angle of attack. The effect of the turbulence is most evident on the aerodynamic forces during the phase of decreasing angle of attack of the dynamic stall process, in which the reattachment of the boundary layer is enhanced by the freestream turbulence. The negative damping from the moment coefficient is also significantly reduced due to the incoming turbulence. The results show that the freestream turbulence in a turbulent flow at a turbulence level of 5% improves the aerodynamic performance of the wind turbine blade.

Hybrid computational aeroacoustics approach based on the synthetic turbulence model in Eulerian description

A low-cost hybrid computational aeroacoustics (CAA) approach based on the synthetic turbulence and acoustic perturbation equations (APE) is established. A statistic model based on Reynolds Averaged Navier-Stokes (RANS) simulation is introduced to generate the unsteady synthetic turbulence. The spatial correlation of the turbulence is realized via the spatial filtering of a white noise field. Instead of using the Lagrangian convective particles of the fast random particle-mesh (fRPM) method, the presented model is entirely established in Eulerian description by introducing a convection-attenuation equation of the synthesized turbulent velocity. Therefore, the same discretization is applied for both synthetic turbulence model and APE solver. Without the requirement of the interpolation between different discretization systems, this modified model is more concise to implement numerically and more accessible to extend to parallel processing. Since the convection-attenuation equation only operates in the sound source domain, additional boundary conditions are established. The recommended parameters for mesh generation are discussed through a validation case. The hybrid CAA approach based on the presented model is applied to the slat noise prediction of a two-dimensional high-lift airfoil. Good agreement is found through the comparison with the reference data, and the computational costs are acceptable.

Evaluation of scale-resolving simulations for a turbulent channel flow

Different variable resolution turbulence modelling approaches (Hybrid, Bridging models and LES) are evaluated for turbulent channel flow at Reτ=395, for cases using either streamwise periodic boundary conditions or a synthetic turbulence generator. The effect of iterative, statistical and discretisation errors is investigated. For LES, little difference between the different sub-filter modelling approaches is found on the finer grids, while on coarser grids ILES deviates from explicit LES approaches. The results for Hybrid models are strongly dependent on their formulation, and the corresponding blending between the RANS and LES regions. The application of PANS with different ratios of modelled-to-total kinetic energy, fk, shows that there is no smooth transition in the results between RANS and DNS. Instead a case-dependent threshold which separates two solution regimes is observed: fk values below 0.2 yield a proper turbulent solution, similar to LES results; higher fk values lead to a laminar flow due to filtering of the smallest scales in the inverse energy cascade. The application of a synthetic turbulence generator is observed to yield similar performance for all models. The reduced computational cost and increased flexibility makes it a suitable approach to enable the usage of SRS for industrial flow cases which depend on the development of a turbulent boundary layer. It ensures that sufficient large-scale structures develop over the full boundary layer height, thereby negating the problem of relying on the inverse energy cascade for the development of turbulence. Both LES and PANS with turbulence generator yield a better match with the reference data than Hybrid models; of these methods PANS is preferable due to the separation of modelling and discretisation errors.

Efficacy of the FDA nozzle benchmark and the lattice Boltzmann method for the analysis of biomedical flows in transitional regime

Flows through medical devices as well as in anatomical vessels despite being at moderate Reynolds number may exhibit transitional or even turbulent character. In order to validate numerical methods and codes used for biomedical flow computations, the US Food and Drug Administration (FDA) established an experimental benchmark, which was a pipe with gradual contraction and sudden expansion representing a nozzle. The experimental results for various Reynolds numbers ranging from 500 to 6500 were publicly released. Previous and recent computational investigations of flow in the FDA nozzle found limitations in various CFD approaches and some even questioned the adequacy of the benchmark itself. This communication reports the results of a lattice Boltzmann method (LBM) – based direct numerical simulation (DNS) approach applied to the FDA nozzle benchmark for transitional cases of Reynolds numbers 2000 and 3500. The goal is to evaluate if a simple off the shelf LBM would predict the experimental results without the use of complex models or synthetic turbulence at the inflow. LBM computations with various spatial and temporal resolutions are performed—in the extremities of 45 million to 2.88 billion lattice cells—executed respectively on 32 CPU cores of a desktop to more than 300,000 cores of a modern supercomputer to explore and characterize miniscule flow details and quantify Kolmogorov scales. The LBM simulations transition to turbulence at a Reynolds number 2000 like the FDA’s experiments and acceptable agreement in jet breakdown locations, average velocity, shear stress, and pressure is found for both the Reynolds numbers.Graphical A bisecting plane showing the FDA nozzle and vorticity magnitude at t = 10 s for throat Reynolds numbers of 2000 and 3500

Experience in using a synthetic turbulence generator for eddy-resolving simulation of the free convection boundary layer on a vertical plate

The paper presents results of eddy-resolving numerical simulation of the turbulent free convection boundary layer that develops along a vertical isothermally heated plate. The problem of definition of boundary conditions at the computational domain inlet, where a time-varying flow field has to be specified, is considered. Mean characteristics of inflow are defined from results of RANS simulation of a 2D boundary layer, and a synthetic turbulence generator is used to introduce unsteady fluctuations at the inlet. Calculations are performed with an in-house unstructured finite-volume code; results of comparison with known experimental data are presented. The influence of the choice of the turbulence model used for RANS-based calculations of the mean inlet flow profiles is considered.

Full-wave model for the lower hybrid wave electric field vector with synthetic turbulence on Alcator C-Mod

The effects of synthetic turbulence on lower hybrid (LH) wave field magnitude and polarization are studied on Alcator C-Mod. Three synthetic turbulence models are evaluated to assess the impact of filaments, holes, and periodic fluctuations on the LH wave electric fields. For all three cases, the synthetic turbulence can greatly impact the LH wave magnitude and polarization. Back scattering, interference and edge/SOL absorption of the LH wave is observed. This impact is shown to depend on the wavelength and amplitude of the fluctuations. The strongest effect appears for fluctuations at high amplitudes and wavelengths comparable to the LH wavelength. This synthetic turbulence model can be used as inputs into a synthetic diagnostic to calculate the lower hybrid wave field magnitude and direction measured by dynamic Stark effect spectroscopy. It will be shown that fluctuations at these high amplitudes and wavelengths may explain the experimentally measured results. The effect of fluctuations on modifying LH polarization are also shown to be anti-correlated with SOL power losses, similar to recently observed experimental trends on Alcator C-Mod. These SOL losses may have detrimental impact on LHCD efficiency.

Deep unsupervised learning of turbulence for inflow generation at various Reynolds numbers

A realistic inflow boundary condition is essential for successful simulation of the developing turbulent boundary layer or channel flows. In the present work, we applied generative adversarial networks (GANs), a representative of unsupervised learning, to generate an inlet boundary condition of turbulent channel flow. Upon learning the two-dimensional spatial structure of turbulence using data obtained from direct numerical simulation (DNS) of turbulent channel flow, the GAN could generate instantaneous flow fields that are statistically similar to those of DNS. After learning data at only three Reynolds numbers, the GAN could produce fields at various Reynolds numbers within a certain range without additional simulation. Eventually, through a combination of the GAN and a recurrent neural network (RNN), we developed a novel model (RNN-GAN) that could generate time-varying fully developed flow for a long time. The spatiotemporal correlations of the generated flow are in good agreement with those of the DNS. This proves the usefulness of unsupervised learning in the generation of synthetic turbulence fields.

Image Reconstruction of Static and Dynamic Scenes Through Anisoplanatic Turbulence

Ground based long-range passive imaging systems often suffer from degraded image quality due to a turbulent atmosphere. While methods exist for removing such turbulent distortions, many are limited to static sequences which cannot be extended to dynamic scenes. In addition, the physics of the turbulence is often not integrated into the image reconstruction algorithms, making the physics foundations of the methods weak. In this article, we present a unified method for atmospheric turbulence mitigation in both static, and dynamic sequences. We are able to achieve better results compared to existing methods by utilizing (i) a novel space-time non-local averaging method to construct a reliable reference frame, (ii) a geometric consistency, and a sharpness metric to generate the lucky frame, (iii) a physics-constrained prior model of the point spread function for blind deconvolution. Experimental results based on synthetic and real long-range turbulence sequences validate the performance of the proposed method.

Disturbing effects of a cylinder-form macro-roughness on the turbulent free-convection boundary layer: Large Eddy Simulation

The paper presents results of eddy-resolving numerical simulation of non-isothermal turbulent flow in the vicinity of an adiabatic circular cylinder that disturbs the turbulent free-convection boundary layer developing along a vertical heated plate. The computational domain used includes (i) a relatively long section, where the upstream free-convection boundary layer goes over to its natural state from the model state prescribed at the inlet boundary with a synthetic turbulence generator, (ii) a mid-section covering the disturbing cylinder, mounted normally on the plate, (iii) an outlet section that is much longer than the cylinder diameter. The mathematical model is based on the Navier-Stokes equation written with the Boussinesq approximation. In the case simulated, the height of the cylinder (equal to its diameter) is about two times less than the approaching boundary layer half-width, if estimated from the velocity profile. Characteristic features of unsteady phenomena in the flow disturbed by the macro-roughness are analyzed with a focus on behavior of arising horseshoe-like vortex structures. Quantitative data on heat transfer augmentation near the cylinder is presented.

Pitch-angle diffusion coefficients in test particle simulations and the estimation of the particle parallel mean free path

The transport of energetic charged particles in turbulent magnetic fields is a topic of interest in various astrophysical contexts. In order to estimate the mean free path of a particle in the direction parallel to the mean magnetic field, one can use theoretical expressions that employ pitch-angle diffusion coefficients. In this work we review some of the methods used in estimating pitch-angle diffusion coefficients from test particle computer simulations. We examine if these methods and theoretical approaches are able to provide consistent estimates of the parallel mean free path, that can also be obtained directly from computer simulations. We perform test particle simulations for synthetic turbulence models over a range of turbulence parameters and particle energies. From the trajectories of test particles, pitch-angle distribution functions and statistics of pitch-angle displacements are obtained, which are then used to estimate the pitch-angle diffusion coefficients. We find that a method using the pitch-angle flux and derivative of the pitch-angle distribution is able to provide accurate values for the parallel mean free path over the range of parameters considered. Other methods considered are accurate only for a limited range of the turbulent fluctuation strength, or must be evaluated at a specific time to provide a reasonable estimate.

Influence of Wake and Background Turbulence on Predicted Fan Broadband Noise

Next-generation fan designs featuring large bypass ratios have the potential to reduce rotor–stator interaction noise of fans. However, these designs pose new challenges and long-held beliefs regarding the acoustic benefit of such concepts that need to be evaluated. At off-design operating points, the increase in nozzle area serves to maintain the stall margin by reducing the fan loading. To an extent, this may lower the contribution of wake turbulence to fan broadband noise. Therefore, investigating the relative contribution of other noise sources becomes relevant. In this paper, the authors examine the contribution of wake and ingested turbulence to fan broadband noise levels at approach for the ASPIRE fan, which is a next-generation fan concept. To enable the investigation of background turbulence, a Reynolds stress turbulence model is used. The computational fluid dynamics solution then provides inputs for a two-dimensional cyclostationary synthetic turbulence method. The noise predictions are improved by performing simulations at three spanwise positions and by introducing a correction technique to account for the three-dimensional interstage flow. For the investigated case, it is shown that broadband noise generated at the stator is as high as for conventional concepts. Furthermore, both wake and background turbulence contribute significantly to the overall fan broadband noise.

Simulations of co-axial jet flows on graphics processing units: the flow and noise analysis.

Large-eddy simulations (LES) are performed for a range of perfectly expanded co-axial jet cases corresponding to conditions of the computation of coaxial jet noise (CoJeN) experiment by QinetiQ. In all simulations, the high-resolution Compact Accurately Boundary-Adjusting high-REsolution Technique (CABARET) is used for solving the Navier-Stokes equations on unstructured meshes. The Ffowcs Williams-Hawkings method based on the penetrable integral surfaces is applied for far-field noise predictions. To correctly model the turbulent flow downstream of the complex nozzle that includes a central body, a wall modelled LES approach is implemented together with a turbulent inflow condition based on synthetic turbulence. All models are run on graphics processing units to enable a considerable reduction of the flow solution time in comparison with the conventional LES. The flow and noise solutions are validated against the experimental data available with 1-2 dB accuracy being reported for noise spectra predictions on the fine grid. To analyse the structure of effective noise sources of the jets, the covariance of turbulent fluctuating Reynolds stresses is computed and their characteristic scales are analysed in the context of the generalized acoustic analogy jet noise models. Motivated by self-similarity of single-stream axi-symmetric jet flows, a suitable non-dimensionalization of the effective jet noise sources of the CoJeN jets is tested, and its implications for low-order jet noise models are discussed. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

One-way fluid-structure interaction of a medium-sized heliostat using scale-resolving CFD simulation

Vortex shedding and the resultant transient loadings on a medium-sized heliostat are investigated in this paper. Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) of a simplified version of an operational heliostat, the LH-2, is used as a validation case for mean loads and to define the orientations used for fluid-structure interaction (FSI): maximum drag in the upright position, and maximum torque-tube moment at an elevation of 60° relative to the vertical. Optimized Atmospheric Boundary Layer profiles for mean flow and turbulence intensity were implemented as the inlet flow boundary condition for both the RANS and Stress-Blended Eddy Simulation (SBES) simulations, with the latter using the synthetic turbulence technique, the Vortex Method, at the inlet. The SBES results show a strong likeness to the experimental results of Peterka et al. (1986) with a comparable mean and peak loading distribution. The transient SBES CFD pressure was implemented in a one-way FSI simulation to obtain the structural response of the heliostat to the transient wind loading. The results show that the response of the heliostat conformed to and depended on the mode shapes and frequencies of the heliostat structure more so than the vortex shedding frequencies. For the upright case, the Strouhal number obtained was within 8% of that obtained from an experimental study in literature, with the main vortex-shedding frequency shown to be 0.5 Hz. When excited with this wind, the structure responded with the third modal frequency of 2.7 Hz. The 60° elevation case also responded mainly with the third mode of 2.6 Hz being excited, but the response was significantly influenced by a combination of higher modes located around 6 Hz. The results from the transient structural analysis using the temporal SBES heliostat surface pressure fields as input indicate that the method holds promise in predicting the transient response of heliostats. Importantly it can be concluded that due to the difference in frequencies between the vortex shedding and modal frequencies, the structure is safe from self-excitation.

On the effects of fan wake modelling and vane design on cascade noise

This paper investigates simplified and representative configurations of fan wake-cascade interaction noise, which is a major source of broadband noise in ultra-high bypass ratio turbofan engines. To this end, two-dimensional computational aeroacoustic simulations are performed by using synthetic turbulence and solving the linearised Euler equations. Several fan wake modelling assumptions are investigated, including isotropic turbulence and cyclostationary variations in both turbulent kinetic energy and turbulence length scale. Results indicate that broadband noise mainly depends on the circumferentially-averaged turbulence spectrum that is perceived by the cascade. Furthermore, the turbulence length scale plays a significant role on cascade noise. Variations in the circumferential distribution of the turbulence length scale modify the slope of the noise spectra, and the maximum noise level can vary significantly. A parameter study on cascade noise has also been performed, including variations in the vane count, aerofoil thickness, camber, mean flow Mach number, stagger angle, and inter-vane spacing. It is shown that noise reduction due to vane thickness at high frequencies can be estimated as a linear function of the frequency, thickness, and mean flow speed in the upstream and downstream directions. A modal spectral decomposition has been performed to study the contribution of cut-on circumferential modes to the sound power level. Variations in vane design parameters lead to significant changes in the cut-on modes and modal spectral distributions. However, their effect on the amplitude of the sound power level spectra is normally below 2 dB, which reinforces the suitability of the flat plate assumption for the prediction of cascade noise at an early design stage.

Design optimization of a curved wind turbine blade using neural networks and an aero-elastic vortex method under turbulent inflow

This article describes the application of neural networks for the design optimization of a curved wind turbine blade using an aero-elastic simulator with synthetic inflow turbulence. A vortex particle method where the wind turbine blades are represented by lifting-line theory is used, while the wind turbine structural dynamics are modeled using a finite-element multi-body based approach. A neural network together with a gradient-based optimizer allows to quickly design a new curved wind turbine blade in a complex aero-elastic wind-turbine simulation scenario. The blade design found from the neural network has increased pre-bend and sweep compared to the straight blade design. It produces approximately 1% more power on average with a slight increase of mean thrust on the rotor of 0.02% compared to the straight one. This study demonstrates that neural networks can be effective for designing wind turbine rotor blades involving complex aero-elastic simulation scenarios with turbulent inflow conditions. Further work may improve the performance of the neural network's predictive capabilities as well as the optimized design.

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.