scholarly journals A spectral model for homogeneous shear-driven anisotropic turbulence in terms of spherically averaged descriptors

2015 ◽  
Vol 788 ◽  
pp. 147-182 ◽  
Author(s):  
Vincent Mons ◽  
Claude Cambon ◽  
Pierre Sagaut
Keyword(s):  
Turbulent Flows ◽  
Computational Cost ◽  
Second Order ◽  
Homogeneous Turbulence ◽  
Spectral Model ◽  
Polarization Anisotropy ◽  
Mean Flow ◽  
Correlation Tensor ◽  
Directional Anisotropy ◽  
Flow Gradients

A nonlinear spectral model in terms of spherically averaged descriptors is derived for the prediction of homogeneous turbulence dynamics in the presence of arbitrary mean-velocity gradients. The governing equations for the tensor $\hat{\unicode[STIX]{x1D619}}_{ij}(\boldsymbol{k},t)$, the Fourier transform of the two-point second-order correlation tensor, are first closed by an anisotropic eddy-damped quasinormal Markovian procedure. This closure is restricted to turbulent flows where linear effects induced by mean-flow gradients have no essential qualitative effects on the dynamics of triple correlations compared with the induced production effects in the equations for second-order correlations. Truncation at the first relevant order of spectral angular dependence allows us to derive from these equations in vector $\boldsymbol{k}$ our final model equations in terms of the wavenumber modulus $k$ only. Analytical spherical integration results in a significant decrease in computational cost. Besides, the model remains consistent with the decomposition in terms of directional anisotropy and polarization anisotropy, with a spherically averaged anisotropic spectral tensor for each contribution. Restriction of anisotropy to spherically averaged descriptors, however, entails a loss of information, and realizability conditions are considered to quantify the upper boundary of anisotropy that can be investigated with the proposed model. Several flow configurations are considered to assess the validity of the present model. Satisfactory agreement with experiments on grid-generated turbulence subjected to successive plane strains is observed, which confirms the capability of the model to account for production of anisotropy by mean-flow gradients. The nonlinear transfer terms of the model are further tested by considering the return to isotropy (RTI) of different turbulent flows. Different RTI rates for directional anisotropy and polarization anisotropy allow us to correctly predict the apparent delayed RTI shown after axisymmetric expansion. The last test case deals with homogeneous turbulence subjected to a constant pure plane shear. The interplay between linear and nonlinear effects is reproduced, yielding the eventual exponential growth of the turbulent kinetic energy.

A Low-Dissipation Second-Order Upwind Flux Formulation for Simulation of Complex Turbulent Flows

2015 ◽  
Author(s):  
Nicole M. W. Poe ◽  
D. Keith Walters ◽  
Edward A. Luke ◽  
Christopher I. Morris
Keyword(s):  
Turbulent Flows ◽  
Computational Cost ◽  
Weighted Average ◽  
Second Order ◽  
Least Square ◽  
Test Cases ◽  
Ansys Fluent ◽  
Cartesian Meshes ◽  
Low Dissipation ◽  
Linear Reconstruction

A numerical method is presented for low-dissipation, high-resolution finite-volume CFD simulations of turbulent flow. The convective fluxes in the governing equations are computed using a conventional upwind-biased second order scheme, with a modified linear reconstruction of face states from neighboring cells. The new scheme, dubbed optimization-based gradient reconstruction (OGRE), incorporates two key enhancements to improve performance. The first is an iterative least-square gradient computation procedure which minimizes the second-order dissipative error contribution to the face reconstruction on structured Cartesian meshes. The second is a slope limiting scheme which enforces local monotonicity near discontinuities without the detrimental effect of limiting in smooth regions of the flowfield. In addition, for density-based methods employing flux-difference splitting for the convective terms, a recently proposed weighted-average for obtaining the reconstructed face variable values is used, which improves accuracy in subsonic flow regions and eliminates the need for preconditioning. The new method has been implemented into the Ansys FLUENT and Loci-CHEM flow solvers, and is validated for several test cases by comparison to a conventional linear reconstruction implementation. Results clearly show the advantage of the new scheme over conventional upwind-biased second order schemes in terms of accuracy, particularly with regard to LES/DNS simulation. The most significant improvement is obtained for Cartesian meshes and low Mach number flows, but all test cases showed some level of improvement using the new scheme. The method is also quantified in terms of increased computational cost versus traditional methods. Based on results shown here, the method appears to represent a viable alternative to currently used centered and blended schemes in terms of accuracy, robustness, and computational expense.

Basic Numerical Assessments to Perform a Quasi-Complete LES Toward IC-Engine Applications

2010 ◽  
Author(s):  
Federico Brusiani ◽  
Gian Marco Bianchi
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Computational Cost ◽  
Step Test ◽  
Scale Model ◽  
Numerical Representation ◽  
Mean Flow ◽  
Ic Engine ◽  
Simulation Methodology ◽  
Turbulent Scales

Still today, the numerical representation of a fully 3D turbulent flow remains one of the most challenging task. In Computational Fluid Dynamics (CFD), turbulent flows can be numerically solved with different levels of accuracy bounded between Reynolds Averaged Navier Stokes (RANS) and Direct Numerical Simulation (DNS) methods. Today, the RANS is the standard approach to perform turbulent flow simulations. It allows a good reproduction of the mean flow conditions guaranteeing, at the same time, an acceptable computational cost for practical engineering applications. Unlike the RANS, DNS is the most complete approach that can be used to numerically solve a turbulent flow because, in this case, all the turbulent scales are directly solved. However, today the DNS approach remains inapplicable in industrial field because of the prohibitive computational power required. Between RANS and DNS, a third method can be considered for the solution of high Reynolds turbulent flows: Large Eddy Simulation (LES). LES approach allows the direct solution of the largest turbulent scales (anisotropy turbulence) while the smallest scales (isotropy turbulence) are numerically modelled by a sub-grid scale model. For this reason, with respect to RANS, LES is expected to give an improvement about turbulent flow numerical solution when the physical behaviour of the considered fluid domain is dominated by the large scales of motion. At the same time, the computational cost of a LES simulation is quite lower than for DNS simulation. Even if during the last years LES has helped to improve the comprehension of complex turbulent fluid dynamic systems, for its applications in industrial fields further insights are needed. In particular, one of the main problem linked to the LES method regards the definition of a simulation methodology by which to obtain an high solution level (i.e. high level of energy directly solved) at the lowest computational cost. To fulfill this requirement, the authors defined a new LES simulation methodology based on Adaptive Mesh Refinement (AMR). The first results obtained by its application on a backward facing step test case are here presented and discussed in detail.

scholarly journals Voltage rise anemometry in turbulent flows applied to internal combustion engines

2021 ◽  
Vol 62 (6) ◽  
Author(s):  
Michael Wörner ◽  
Gregor Rottenkolber
Keyword(s):  
Turbulent Flows ◽  
Internal Combustion Engines ◽  
Clear Correlation ◽  
Combustion Engines ◽  
Mean Flow ◽  
Voltage Rise ◽  
Mathematical Correlation ◽  
Thermodynamic Conditions ◽  
Secondary Voltage ◽  
Cylinder Flow

AbstractIn an experimental procedure, a voltage rise anemometry is developed as a measurement technique for turbulent flows. Initially, fundamental investigations on a specific wind tunnel were performed for basic understanding and calibration purpose. Thus, a mathematical correlation is derived for calculating flow from measured secondary voltage of an ignition system under different thermodynamic conditions. Subsequently, the derived method was applied on a spark-ignited engine to measure in-cylinder flow. Therefore, no changes on combustion chamber were necessary avoiding any interferences of the examined flow field. Comparing four different engine configurations, a study of mean flow and turbulence was performed. Moreover, the results show a clear correlation between measured turbulence and analysed combustion parameters. Graphic abstract

scholarly journals Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean ◽  
Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

Scale-to-scale anisotropy in homogeneous turbulence

2017 ◽  
Vol 827 ◽  
pp. 250-284 ◽  
Author(s):  
Douglas W. Carter ◽  
Filippo Coletti
Keyword(s):  
Large Scale ◽  
Velocity Structure ◽  
Longitudinal Velocity ◽  
Reynolds Numbers ◽  
Homogeneous Turbulence ◽  
Mean Flow ◽  
Spatially Correlated ◽  
Air Jets ◽  
Image Velocimetry ◽  
Definition Of

We experimentally investigate scale-to-scale anisotropy from the integral to the dissipative scales in homogeneous turbulence. We employ an apparatus in which two facing arrays of randomly actuated air jets generate turbulence with negligible mean flow and shear, over a volume several times larger than the energy-containing eddy size. The Reynolds number based on the Taylor microscale is varied in the range$Re_{\unicode[STIX]{x1D706}}\approx 300{-}500$, while the axial-to-radial ratio of the root mean square velocity fluctuations ranges between 1.38 and 1.72. Two velocity components are measured by particle image velocimetry at varying resolutions, capturing from the integral to the Kolmogorov scales and yielding statistics up to sixth order. Over the inertial range, the scaling exponents of the velocity structure functions are found to differ not only between the longitudinal and transverse components, but also between the axial and radial directions of separation. At the dissipative scales, the moments of the velocity gradients indicate that departure from isotropy is, at the present Reynolds numbers, significant and more pronounced for stronger large-scale anisotropy. The generalized flatness factors of the longitudinal velocity differences tend towards isotropy as the separation is reduced from the inertial to the near-dissipative scales (down to about$10\unicode[STIX]{x1D702}$,$\unicode[STIX]{x1D702}$being the Kolmogorov length), but become more anisotropic for even smaller scales which are characterized by high intermittency. At the large scales, the direction of turbulence forcing is associated with a larger integral length, defined as the distance over which the velocity component in a given direction is spatially correlated. Because of anisotropy, the definition of the integral length is not trivial and may lead to dissimilar conclusions on the qualitative behaviour of the large scales and on the quantitative values of the normalized dissipation. Alternative definitions of these quantities are proposed to account for the anisotropy. Overall, these results highlight the importance of evaluating both the different velocity components and the different spatial directions across all scales of the flow.

scholarly journals Adjoint-based parametric sensitivity analysis for swirling M-flames

2018 ◽  
Vol 859 ◽  
pp. 516-542 ◽  
Author(s):  
Calum S. Skene ◽  
Peter J. Schmid
Keyword(s):  
Sensitivity Analysis ◽  
Frequency Response ◽  
Stokes Equations ◽  
Numerical Study ◽  
Computational Cost ◽  
Base Flow ◽  
Sensitivity Analyses ◽  
Perturbation Expansions ◽  
Mean Flow ◽  
Adjoint Solutions

A linear numerical study is conducted to quantify the effect of swirl on the response behaviour of premixed lean flames to general harmonic excitation in the inlet, upstream of combustion. This study considers axisymmetric M-flames and is based on the linearised compressible Navier–Stokes equations augmented by a simple one-step irreversible chemical reaction. Optimal frequency response gains for both axisymmetric and non-axisymmetric perturbations are computed via a direct–adjoint methodology and singular value decompositions. The high-dimensional parameter space, containing perturbation and base-flow parameters, is explored by taking advantage of generic sensitivity information gained from the adjoint solutions. This information is then tailored to specific parametric sensitivities by first-order perturbation expansions of the singular triplets about the respective parameters. Valuable flow information, at a negligible computational cost, is gained by simple weighted scalar products between direct and adjoint solutions. We find that for non-swirling flows, a mode with azimuthal wavenumber $m=2$ is the most efficiently driven structure. The structural mechanism underlying the optimal gains is shown to be the Orr mechanism for $m=0$ and a blend of Orr and other mechanisms, such as lift-up, for other azimuthal wavenumbers. Further to this, velocity and pressure perturbations are shown to make up the optimal input and output showing that the thermoacoustic mechanism is crucial in large energy amplifications. For $m=0$ these velocity perturbations are mainly longitudinal, but for higher wavenumbers azimuthal velocity fluctuations become prominent, especially in the non-swirling case. Sensitivity analyses are carried out with respect to the Mach number, Reynolds number and swirl number, and the accuracy of parametric gradients of the frequency response curve is assessed. The sensitivity analysis reveals that increases in Reynolds and Mach numbers yield higher gains, through a decrease in temperature diffusion. A rise in mean-flow swirl is shown to diminish the gain, with increased damping for higher azimuthal wavenumbers. This leads to a reordering of the most effectively amplified mode, with the axisymmetric ($m=0$) mode becoming the dominant structure at moderate swirl numbers.

scholarly journals Markovian inhomogeneous closures for Rossby waves and turbulence over topography

2018 ◽  
Vol 858 ◽  
pp. 45-70
Author(s):  
Jorgen S. Frederiksen ◽  
Terence J. O’Kane
Keyword(s):  
Turbulent Flows ◽  
Rossby Waves ◽  
Time History ◽  
Direct Interaction ◽  
Mean Flow ◽  
Current Time ◽  
Fluctuation Dissipation ◽  
Large Ensembles ◽  
Direct Interaction Approximation ◽  
The Impact

Manifestly Markovian closures for the interaction of two-dimensional inhomogeneous turbulent flows with Rossby waves and topography are formulated and compared with large ensembles of direct numerical simulations (DNS) on a generalized $\unicode[STIX]{x1D6FD}$-plane. Three versions of the Markovian inhomogeneous closure (MIC) are established from the quasi-diagonal direct interaction approximation (QDIA) theory by modifying the response function to a Markovian form and employing respectively the current-time (quasi-stationary) fluctuation dissipation theorem (FDT), the prior-time (non-stationary) FDT and the correlation FDT. Markov equations for the triad relaxation functions are derived that carry similar information to the time-history integrals of the non-Markovian QDIA closure but become relatively more efficient for long integrations. Far from equilibrium processes are studied, where the impact of a westerly mean flow on a conical mountain generates large-amplitude Rossby waves in a turbulent environment, over a period of 10 days. Excellent agreement between the evolved mean streamfunction and mean and transient kinetic energy spectra are found for the three versions of the MIC and two variants of the non-Markovian QDIA compared with an ensemble of 1800 DNS. In all cases mean Rossby wavetrain pattern correlations between the closures and the DNS ensemble are greater than 0.9998.

scholarly journals Accuracy and Reliability in the Simulation of Vibrational Spectra: A Comprehensive Benchmark of Energies and Intensities Issuing From Generalized Vibrational Perturbation Theory to Second Order (GVPT2)

2021 ◽  
Vol 8 ◽  
Author(s):  
Qin Yang ◽  
Marco Mendolicchio ◽  
Vincenzo Barone ◽  
Julien Bloino
Keyword(s):  
Perturbation Theory ◽  
Electronic Structure ◽  
Density Functional ◽  
Computational Cost ◽  
Theoretical Data ◽  
Infrared Region ◽  
Second Order ◽  
Basis Set ◽  
Molecular Systems ◽  
The Impact

Vibrational spectroscopy represents an active frontier for the identification and characterization of molecular species in the context of astrochemistry and astrobiology. As new missions will provide more data over broader ranges and at higher resolution, especially in the infrared region, which could be complemented with new spectrometers in the future, support from laboratory experiments and theory is crucial. In particular, computational spectroscopy is playing an increasing role in deepening our understanding of the origin and nature of the observed bands in extreme conditions characterizing the interstellar medium or some planetary atmospheres, not easily reproducible on Earth. In this connection, the best compromise between reliability, feasibility and ease of interpretation is still a matter of concern due to the interplay of several factors in determining the final spectral outcome, with larger molecular systems and non-covalent complexes further exacerbating the dichotomy between accuracy and computational cost. In this context, second-order vibrational perturbation theory (VPT2) together with density functional theory (DFT) has become particularly appealing. The well-known problem of the reliability of exchange-correlation functionals, coupled with the treatment of resonances in VPT2, represents a challenge for the determination of standardized or “black-box” protocols, despite successful examples in the literature. With the aim of getting a clear picture of the achievable accuracy and reliability of DFT-based VPT2 calculations, a multi-step study will be carried out here. Beyond the definition of the functional, the impact of the basis set and the influence of the resonance treatment in VPT2 will be analyzed. For a better understanding of the computational aspects and the results, a short summary of vibrational perturbation theory and the overall treatment of resonances for both energies and intensities will be given. The first part of the benchmark will focus on small molecules, for which very accurate experimental and theoretical data are available, to investigate electronic structure calculation methods. Beyond the reliability of energies, widely used for such systems, the issue of intensities will also be investigated in detail. The best performing electronic structure methods will then be used to treat larger molecular systems, with more complex topologies and resonance patterns.

The large-scale structure of homogeneous turbulence

1967 ◽  
Vol 27 (3) ◽  
pp. 581-593 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Large Scale ◽  
Isotropic Turbulence ◽  
Homogeneous Turbulence ◽  
Wave Number ◽  
Initial Instant ◽  
Force System ◽  
Correlation Tensor ◽  
Number Magnitude ◽  
Small Wave Number ◽  
Conservation Of Momentum

A field of homogeneous turbulence generated at an initial instant by a distribution of random impulsive forces is considered. The statistical properties of the forces are assumed to be such that the integral moments of the cumulants of the force system all exist. The motion generated has the property that at the initial instant\[ E(\kappa) = C\kappa^2 + o(\kappa^2), \]whereE(k) is the energy spectrum function,kis the wave-number magnitude, andCis a positive number which is not in general zero. The corresponding forms of the velocity covariance spectral tensor and correlation tensor are determined. It is found that the terms in the velocity covarianceRij(r) areO(r−3) for large values of the separation magnituder.An argument based on the conservation of momentum is used to show thatCis a dynamical invariant and that the forms of the velocity covariance at large separation and the spectral tensor at small wave number are likewise invariant. For isotropic turbulence, the Loitsianski integral diverges but the integral\[ \int_0^{\infty} r^2R(r)dr = \frac{1}{2}\pi C \]exists and is invariant.

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