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1
Yuan, S. P., et R. M. C. So. « Turbulent rotating flow calculations : An assessment of two-equation anisotropic and Reynolds stress models ». Proceedings of the Institution of Mechanical Engineers, Part G : Journal of Aerospace Engineering 212, no 3 (1 mars 1998) : 193–212. http://dx.doi.org/10.1243/0954410981532270.
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The stress field in a rotating turbulent internal flow is highly anisotropic. This is true irrespective of whether the axis of rotation is aligned with or normal to the mean flow plane. Consequently, turbulent rotating flow is very difficult to model. This paper attempts to assess the relative merits of three different ways to account for stress anisotropies in a rotating flow. One is to assume an anisotropic stress tensor, another is to model the anisotropy of the dissipation rate tensor, while a third is to solve the stress transport equations directly. Two different near-wall two-equation models and one Reynolds stress closure are considered. All the models tested are asymptotically consistent near the wall. The predictions are compared with measurements and direct numerical simulation data. Calculations of turbulent flows with inlet swirl numbers up to 1.3, with and without a central recirculation, reveal that none of the anisotropic two-equation models tested is capable of replicating the mean velocity field at these swirl numbers. This investigation, therefore, indicates that neither the assumption of anisotropic stress tensor nor that of an anisotropic dissipation rate tensor is sufficient to model flows with medium to high rotation correctly. It is further found that, at very high rotation rates, even the Reynolds stress closure fails to predict accurately the extent of the central recirculation zone.
2
Sun, Wei, et Liping Xu. « Improvement of corner separation prediction using an explicit non-linear RANS closure ». Journal of the Global Power and Propulsion Society 5 (7 avril 2021) : 50–65. http://dx.doi.org/10.33737/jgpps/133913.
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In this paper, an investigation into the effect of explicit non-linear turbulence modelling on anisotropic turbulence flows is presented. Such anisotropic turbulence flows are typified in the corner separations in turbomachinery. The commonly used Reynolds-Averaged Navier-Stokes (RANS) turbulence closures, in which the Reynolds stress tensor is modelled by the Boussinesq (linear) constitutive relation with the mean strain-rate tensor, often struggle to predict corner separation with reasonable accuracy. The physical reason for this modelling deficiency is partially attributable to the Boussinesq hypothesis which does not count for the turbulence anisotropy, whilst in a corner separation, the flow is subject to three-dimensional (3D) shear and the effects due to turbulence anisotropy may not be ignored. In light of this, an explicit non-linear Reynolds stress-strain constitutive relation developed by Menter et al. is adopted as a modification of the Reynolds-stress anisotropy. Coupled with the Menter’s hybrid "k-ω" ⁄"k-ε" turbulence model, this non-linear constitutive relation gives significantly improved predictions for the corner separation flows within a compressor cascade, at both the design and off-design flow conditions. The mean vorticity field are studied to further investigate the physical reasons for these improvements, highlighting its potential for the widespread applications in the corner separation prediction.
3
Dey, Subhasish, Prianka Paul, Sk Zeeshan Ali et Ellora Padhi. « Reynolds stress anisotropy in flow over two-dimensional rigid dunes ». Proceedings of the Royal Society A : Mathematical, Physical and Engineering Sciences 476, no 2242 (octobre 2020) : 20200638. http://dx.doi.org/10.1098/rspa.2020.0638.
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Characteristics of turbulence anisotropy in flow over two-dimensional rigid dunes are analysed. The Reynolds stress anisotropy is envisaged from the perspective of the stress ellipsoid shape. The spatial evolutions of the anisotropic invariant map (AIM), anisotropic invariant function, eigenvalues of the scaled Reynolds stress tensor and eccentricities of the stress ellipsoid are investigated at various streamwise distances along the vertical. The data plots reveal that the oblate spheroid axisymmetric turbulence appears near the top of the crest, whereas the prolate spheroid axisymmetric turbulence dominates near the free surface. At the dune trough, the axisymmetric contraction to the oblate spheroid diminishes, as the vertical distance below the crest increases. At the reattachment point and one-third of the stoss-side, the oblate spheroid axisymmetric turbulence formed below the crest appears to be more contracted, as the vertical distance increases. The AIMs suggest that the turbulence anisotropy up to edge of the boundary layer follows a looping pattern. As the streamwise distance increases, the turbulence anisotropy at the edge of the boundary layer approaches the plane-strain limit up to two-thirds of the stoss-side, intersecting the plane-strain limit at the top of the crest and thereafter moving towards the oblate spheroid axisymmetric turbulence.
4
Morrison, G. L., M. C. Johnson et G. B. Tatterson. « Three-Dimensional Laser Anemometer Measurements in an Annular Seal ». Journal of Tribology 113, no 3 (1 juillet 1991) : 421–27. http://dx.doi.org/10.1115/1.2920641.
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The flow field inside an annular seal with a 1.27 mm clearance is investigated using a 3-D laser Doppler anemometer system. Through the use of this system, the mean velocity vector and the entire Reynolds stress tensor distributions are measured for the entire length of the seal (37.3 mm). The seal is operated at a Reynolds number of 18,600 and a Taylor number of 4500. The annular seal is found to produce anisotropic turbulence since the Reynolds stress measurements show the flow entering the seal with isotropic turbulence but exiting the seal with anisotropic turbulence.
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Pinarbasi, A., et M. W. Johnson. « Detailed Stress Tensor Measurements in a Centrifugal Compressor Vaneless Diffuser ». Journal of Turbomachinery 118, no 2 (1 avril 1996) : 394–99. http://dx.doi.org/10.1115/1.2836654.
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Detailed flow measurements have been made in the vaneless diffuser of a large low-speed centrifugal compressor using hot-wire anemometry. The three time mean velocity components and full stress tensor distributions have been determined on eight measurement planes within the diffuser. High levels of Reynolds stress result in the rapid mixing out of the blade wake. Although high levels of turbulent kinetic energy are found in the passage wake, they are not associated with strong Reynolds stresses and hence the passage wake mixes out only slowly. Low-frequency meandering of the wake position is therefore likely to be responsible for the high kinetic energy levels. The anisotropic nature of the turbulence suggests that Reynolds stress turbulence models are required for CFD modeling of diffuser flows.
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Suga, Kazuhiko, Yuki Okazaki, Unde Ho et Yusuke Kuwata. « Anisotropic wall permeability effects on turbulent channel flows ». Journal of Fluid Mechanics 855 (21 septembre 2018) : 983–1016. http://dx.doi.org/10.1017/jfm.2018.666.
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Streamwise–wall-normal ( $x$ – $y$ ) and streamwise–spanwise ( $x$ – $z$ ) plane measurements are carried out by planar particle image velocimetry for turbulent channel flows over anisotropic porous media at the bulk Reynolds number $Re_{b}=900{-}13\,600$ . Three kinds of anisotropic porous media are constructed to form the bottom wall of the channel. Their wall permeability tensor is designed to have a larger wall-normal diagonal component (wall-normal permeability) than the other components. Those porous media are constructed to have three mutually orthogonal principal axes and those principal axes are aligned with the Cartesian coordinate axes of the flow geometry. Correspondingly, the permeability tensor of each porous medium is diagonal. With the $x$ – $y$ plane data, it is found that the turbulence level well accords with the order of the streamwise diagonal component of the permeability tensor (streamwise permeability). This confirms that the turbulence strength depends on the streamwise permeability rather than the wall-normal permeability when the permeability tensor is diagonal and the wall-normal permeability is larger than the streamwise permeability. To generally characterize those phenomena including isotropic porous wall cases, modified permeability Reynolds numbers are discussed. From a quadrant analysis, it is found that the contribution from sweeps and ejections to the Reynolds shear stress near the porous media is influenced by the streamwise permeability. In the $x$ – $z$ plane data, although low- and high-speed streaks are also observed near the anisotropic porous walls, large-scale spanwise patterns appear at a larger Reynolds number. It is confirmed that they are due to the transverse waves induced by the Kelvin–Helmholtz instability. By the two-point correlation analyses of the fluctuating velocities, the spacing of the streaks and the wavelengths of the Kelvin–Helmholtz (K–H) waves are discussed. It is then confirmed that the transition point from the quasi-streak structure to the roll-cell-like structure is characterized by the wall-normal distance including the zero-plane displacement of the log-law velocity which can be characterized by the streamwise permeability. It is also confirmed that the normalized wavelengths of the K–H waves over porous media are in a similar range to that of the turbulent mixing layers irrespective of the anisotropy of the porous media.
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Klein, Markus, Theresa Trummler, Noah Urban et Nilanjan Chakraborty. « Multiscale Analysis of Anisotropy of Reynolds Stresses, Subgrid Stresses and Dissipation in Statistically Planar Turbulent Premixed Flames ». Applied Sciences 12, no 5 (22 février 2022) : 2275. http://dx.doi.org/10.3390/app12052275.
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The characterisation of small-scale turbulence has been an active area of research for decades and this includes, particularly, the analysis of small-scale isotropy, as postulated by Kolmogorov. In particular, the question if the dissipation tensor is isotropic or not, and how it is related to the anisotropy of the Reynolds stresses is of particular interest for modelling purposes. While this subject has been extensively studied in the context of isothermal flows, the situation is more complicated in turbulent reacting flows because of heat release. Furthermore, the landscape of Computational Fluid Dynamics is characterised by a multitude of methods ranging from Reynolds-averaged to Large Eddy Simulation techniques, and they address different ranges of scales of the turbulence kinetic energy spectrum. Therefore, a multiscale analysis of the anisotropies of Reynolds stress, dissipation and sub-grid scale tensor has been performed by using a DNS database of statistically planar turbulent premixed flames. Results show that the coupling between dissipation tensor and Reynolds stress tensor is weaker compared to isothermal turbulent boundary layer flows. In particular, for low and moderate turbulence intensities, heat release induces pronounced anisotropies which affect not only fluctuation strengths but also the characteristic size of structures associated with different velocity components.
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Xu, Xihai, et Xiaodong Li. « Anisotropic source modelling for turbulent jet noise prediction ». Philosophical Transactions of the Royal Society A : Mathematical, Physical and Engineering Sciences 377, no 2159 (14 octobre 2019) : 20190075. http://dx.doi.org/10.1098/rsta.2019.0075.
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An anisotropic component of the jet noise source model for the Reynolds-averaged Navier–Stokes equation-based jet noise prediction method is proposed. The modelling is based on Goldstein's generalized acoustic analogy, and both the fine-scale and large-scale turbulent noise sources are considered. To model the anisotropic characteristics of jet noise source, the Reynolds stress tensor is used in place of the turbulent kinetic energy. The Launder–Reece–Rodi model (LRR), combined with Menter's ω -equation for the length scale, with modified coefficients developed by the present authors, is used to calculate the mean flow velocities and Reynolds stresses accurately. Comparison between predicted results and acoustic data has been carried out to verify the accuracy of the new anisotropic source model. This article is part of the theme issue ‘Frontiers of aeroacoustics research: theory, computation and experiment’.
9
Barbi, G., A. Chierici, V. Giovacchini, F. Quarta et S. Manservisi. « Numerical simulation of a low Prandtl number flow over a backward facing step with an anisotropic four-equation turbulence model ». Journal of Physics : Conference Series 2177, no 1 (1 avril 2022) : 012006. http://dx.doi.org/10.1088/1742-6596/2177/1/012006.
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Abstract In recent years the use of liquid metals has become more and more popular for heat transfer applications in many fields ranging from IV generation fast nuclear reactors to solar power plants. Due to their low Prandtl number values, the similarity between dynamical and thermal fields cannot be assumed and sophisticated heat turbulence models are required to take into account the anisotropy of the turbulent heat transfer involving liquid metals. In the present work, we solve an anisotropic four-equation turbulence model coupled with the Reynolds Averaged Navier Stokes system of equations to simulate a turbulent flow of liquid sodium over a vertical backward-facing step. We implement an explicit algebraic model for Reynolds stress tensor and turbulent heat flux that takes into account flow anisotropic behavior. We study forced and mixed convection regimes when a uniform heat flux is applied on the wall behind the step. Linear isotropic approximations for eddy viscosity and eddy thermal diffusivity underestimate the turbulent heat flux components while this anisotropic model shows a better agreement with DNS results.
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Maksoud, T. M. A., et M. W. Johnson. « Stress Tensor Measurements within the Vaneless Diffuser of a Centrifugal Compressor ». Proceedings of the Institution of Mechanical Engineers, Part C : Mechanical Engineering Science 203, no 1 (janvier 1989) : 51–59. http://dx.doi.org/10.1243/pime_proc_1989_203_085_02.
Texte intégralRésumé :
Distributions of normal and shear (Reynolds) stresses inside the vaneless diffuser of a low-speed centrifugal compressor are presented. The measurements were made using a triple hot-wire system and a phase lock loop sampling technique. Results were obtained on cross-sectional planes at eight radial stations between the impeller outlet and the diffuser exit at three different flowrates. The turbulence was highly anisotropic and became more so as the flowrate was increased. The tangential component of turbulent intensity was found to be significantly smaller than either the radial or axial component. The blade wake observed at the diffuser inlet decays very rapidly due to the strong tangential Reynolds stresses generated by the opposed secondary flows on either side of the wake. The passage wake decays very much more slowly and is still identifiable at the diffuser discharge.
11
Nieckele, A. O., R. L. Thompson et G. Mompean. « Anisotropic Reynolds stress tensor representation in shear flows using DNS and experimental data ». Journal of Turbulence 17, no 6 (19 avril 2016) : 602–32. http://dx.doi.org/10.1080/14685248.2016.1153106.
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Fang, Rui, David Sondak, Pavlos Protopapas et Sauro Succi. « Neural network models for the anisotropic Reynolds stress tensor in turbulent channel flow ». Journal of Turbulence 21, no 9-10 (24 décembre 2019) : 525–43. http://dx.doi.org/10.1080/14685248.2019.1706742.
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LEE, SEUNG-HYUN, et HYUNG JIN SUNG. « Direct numerical simulation of the turbulent boundary layer over a rod-roughened wall ». Journal of Fluid Mechanics 584 (25 juillet 2007) : 125–46. http://dx.doi.org/10.1017/s0022112007006465.
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The effects of surface roughness on a spatially developing turbulent boundary layer (TBL) are investigated by performing direct numerical simulations of TBLs over rough and smooth walls. The Reynolds number based on the momentum thickness was varied in the range Reθ = 300 ∼ 1400. The roughness elements were periodically arranged two-dimensional spanwise rods, and the roughness height was k = 1.5θin, where θin is the momentum thickness at the inlet, which corresponds to k/δ = 0.045 ∼ 0.125, δ being the boundary layer thickness. To avoid generating a rough-wall inflow, which is prohibitively difficult, a step change from smooth to rough was placed 80θin downstream from the inlet. The spatially developing characteristics of the rough-wall TBL were examined. Along the streamwise direction, the friction velocity approached a constant value, and self-preserving forms of the turbulent Reynolds stress tensors were obtained. Introduction of the roughness elements affected the turbulent stress not only in the roughness sublayer but also in the outer layer. Despite the roughness-induced increase of the turbulent Reynolds stress tensors in the outer layer, the roughness had only a relatively small effect on the anisotropic Reynolds stress tensor in the outer layer. Inspection of the triple products of the velocity fluctuations revealed that introducing the roughness elements onto the smooth wall had a marked effect on vertical turbulent transport across the whole TBL. By contrast, good surface similarity in the outer layer was obtained for the third-order moments of the velocity fluctuations.
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Ling, Julia, Andrew Kurzawski et Jeremy Templeton. « Reynolds averaged turbulence modelling using deep neural networks with embedded invariance ». Journal of Fluid Mechanics 807 (18 octobre 2016) : 155–66. http://dx.doi.org/10.1017/jfm.2016.615.
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There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.
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Lin, Che-Yu, Bayode E. Owolabi et Chao-An Lin. « Polymer-turbulence interactions in a complex flow and implications for the drag reduction phenomenon ». Physics of Fluids 34, no 4 (avril 2022) : 043106. http://dx.doi.org/10.1063/5.0086686.
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We present direct numerical simulation data for turbulent duct flow of a finite-extensibility non-linear elastic dumbbell model with the Peterlin approximation (FENE-P) fluid in the high drag reduction regime. While the secondary flow pattern is qualitatively similar to that in a Newtonian fluid, its magnitude is significantly reduced, resulting in a less uniformly distributed velocity profile and hence smaller gradients at the wall. The Reynolds stress tensor in the polymer-laden flow was found to be increasingly anisotropic with most of the turbulent kinetic energy retained in the streamwise component, [Formula: see text]. We introduce a novel approach for investigating polymer stretching using the anisotropy invariant map of the polymer stress tensor and observe the persistence of both uniaxial and biaxial extension. Analysis of the transport equation for the mean kinetic energy indicates that polymer stretching and relaxation is a highly dissipative process; hence, the introduction of an additional channel for dissipation in a flow is key to drag reduction.
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Jovanovic´, J., I. Otic´ et P. Bradshaw. « On the Anisotropy of Axisymmetric Strained Turbulence in the Dissipation Range ». Journal of Fluids Engineering 125, no 3 (1 mai 2003) : 401–13. http://dx.doi.org/10.1115/1.1568355.
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Partition of the stress dissipation has been studied in an axisymmetric strained flow field to assess the possible existence of local isotropy for turbulence at small scales. This is a simple flow to study because the axes of anisotropy of the Reynolds stresses and of the dissipation tensor are aligned. Using invariant theory, the relationship between the stress and dissipation tensors was derived, satisfying restrictions for the limiting states of turbulence and the assumed behavior for large Reynolds number and small anisotropy. The role of the anisotropy in constraining models for the turbulent dissipation rate and the pressure-strain correlations is discussed. Comparisons of the resulting closure with experimental data for several axisymmetric flows are good within the limitations of the data.
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Busse, Angela, et Thomas O. Jelly. « Influence of Surface Anisotropy on Turbulent Flow Over Irregular Roughness ». Flow, Turbulence and Combustion 104, no 2-3 (20 novembre 2019) : 331–54. http://dx.doi.org/10.1007/s10494-019-00074-4.
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AbstractThe influence of surface anisotropy upon the near-wall region of a rough-wall turbulent channel flow is investigated using direct numerical simulation (DNS). A set of nine irregular rough surfaces with fixed mean peak-to-valley height, near-Gaussian height distributions and specified streamwise and spanwise correlation lengths were synthesised using a surface generation algorithm. By defining the surface anisotropy ratio (SAR) as the ratio of the streamwise and spanwise correlation lengths of the surface, we demonstrate that surfaces with a strong spanwise anisotropy (SAR < 1) can induce an over 200% increase in the roughness function ΔU+, compared to their streamwise anisotropic (SAR > 1) equivalent. Furthermore, we find that the relationship between the roughness function ΔU+ and the SAR parameter approximately follows an exponentially decaying function. The statistical response of the near-wall flow is studied using a “double-averaging” methodology in order to distinguish form-induced “dispersive” stresses from their turbulent counterparts. Outer-layer similarity is recovered for the mean velocity defect profile as well as the Reynolds stresses. The dispersive stresses all attain their maxima within the roughness canopy. Only the streamwise dispersive stress reaches levels that are comparable to the equivalent Reynolds stress, with surfaces of high SAR attaining the highest levels of streamwise dispersive stress. The Reynolds stress anisotropy also shows distinct differences between cases with strong streamwise anisotropy that stay close to an axisymmetric, rod-like state for all wall-normal locations, compared to cases with spanwise anisotropy where an axisymmetric, disk-like state of the Reynolds stress anisotropy tensor is observed around the roughness mean plane. Overall, the results from this study underline that the drag penalty incurred by a rough surface is strongly influenced by the surface topography and highlight its impact upon the mean momentum deficit in the outer flow as well as the Reynolds and dispersive stresses within the roughness layer.
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Mazouz, A., L. Labraga et C. Tournier. « Anisotropy Invariants of Reynolds Stress Tensor in a Duct Flow and Turbulent Boundary Layer ». Journal of Fluids Engineering 120, no 2 (1 juin 1998) : 280–84. http://dx.doi.org/10.1115/1.2820645.
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The present study shows that the Reynolds stress anisotropy tensor for turbulent flow depends both on the nature of the surface and the boundary conditions of the flow. Contrary to the case of turbulent boundary layers with k-type surface roughness, the measured anisotropy invariants of the Reynolds stress tensor over a series of spanwise square bars separated by rectangular cavities (k-type) in duct flows show that roughness increases the anisotropy. There is a similarity between the effect of roughness on channel flow turbulence and that on pipe flow turbulence. The present data show that the effect of introducing a surface roughness significantly perturbs the entire thickness of the turbulent flow.
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Barbi, Giacomo, Valentina Giovacchini et Sandro Manservisi. « A New Anisotropic Four-Parameter Turbulence Model for Low Prandtl Number Fluids ». Fluids 7, no 1 (22 décembre 2021) : 6. http://dx.doi.org/10.3390/fluids7010006.
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Due to their interesting thermal properties, liquid metals are widely studied for heat transfer applications where large heat fluxes occur. In the framework of the Reynolds-Averaged Navier–Stokes (RANS) approach, the Simple Gradient Diffusion Hypothesis (SGDH) and the Reynolds Analogy are almost universally invoked for the closure of the turbulent heat flux. Even though these assumptions can represent a reasonable compromise in a wide range of applications, they are not reliable when considering low Prandtl number fluids and/or buoyant flows. More advanced closure models for the turbulent heat flux are required to improve the accuracy of the RANS models dealing with low Prandtl number fluids. In this work, we propose an anisotropic four-parameter turbulence model. The closure of the Reynolds stress tensor and turbulent heat flux is gained through nonlinear models. Particular attention is given to the modeling of dynamical and thermal time scales. Numerical simulations of low Prandtl number fluids have been performed over the plane channel and backward-facing step configurations.
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Lai, Y. G., et R. M. C. So. « On near-wall turbulent flow modelling ». Journal of Fluid Mechanics 221 (décembre 1990) : 641–73. http://dx.doi.org/10.1017/s0022112090003718.
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The characteristics of near-wall turbulence are examined and the result is used to assess the behaviour of the various terms in the Reynolds-stress transport equations. It is found that all components of the velocity-pressure-gradient correlation vanish at the wall. Conventional splitting of this second-order tensor into a pressure diffusion part and a pressure redistribution part and subsequent neglect of the pressure diffusion term in the modelled Reynolds-stress equations leads to finite near-wall values for two components of the redistribution tensor. This, therefore, suggests that, in near-wall turbulent flow modelling, the velocity-pressure-gradient correlation rather than pressure redistribution should be modelled. Based on this understanding, a methodology to derive an asymptotically correct model for the velocity-pressure-gradient correlation is proposed. A model that has the property of approaching the high-Reynolds-number model for pressure redistribution far away from the wall is derived. A similar analysis is carried out on the viscous dissipation term and asymptotically correct near-wall modifications are proposed. The near-wall closure based on the Reynolds-stress equations and a conventional low-Reynolds-number dissipation-rate equation is used to calculate fully-developed turbulent channel and pipe flows at different Reynolds numbers. A careful parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds-number dependent, and a preliminary expression is proposed for this constant. With this modification, excellent agreement with near-wall turbulence statistics, measured and simulated, is obtained, especially the anisotropic behaviour of the normal stresses. On the other hand, it is found that the dissipation-rate equation has a significant effect on the calculated Reynolds-stress budgets. Possible improvements could be obtained by using available direct simulation data to help formulate a more realistic dissipation-rate equation. When such an equation is available, the present approach can again be used to derive a near-wall closure for the Reynolds-stress equations. The resultant closure could give improved predictions of the turbulence statistics and the Reynolds-stress budgets.
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Kuwata, Y., et K. Suga. « Direct numerical simulation of turbulence over anisotropic porous media ». Journal of Fluid Mechanics 831 (13 octobre 2017) : 41–71. http://dx.doi.org/10.1017/jfm.2017.619.
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To investigate which component of the anisotropic permeability tensor of porous media influences turbulence over porous walls, direct numerical simulation of anisotropic porous-walled channel flows is performed by the D3Q27 multiple-relaxation-time lattice Boltzmann method. The presently considered anisotropic permeable walls have square pore arrays aligned with the Cartesian axes. Vertical, streamwise and spanwise pore arrays are systematically introduced to the walls to impose anisotropic permeability. Simulations are carried out at a friction Reynolds number of 111 and 230, which is based on the averaged friction velocity of the porous bottom and the smooth top walls. It is found that streamwise and spanwise permeabilities enhance turbulence whilst vertical permeability itself does not. In particular, the enhancement of turbulence is remarkable over porous walls with streamwise permeability. Over streamwise permeable walls, development of high- and low-speed streaks is prevented whilst large-scale intermittent patched patterns of ejection motions are induced. It is revealed by two-point correlation analysis that streamwise permeability allows the development of streamwise large-scale perturbations induced by Kelvin–Helmholtz instability. Spectral analysis reveals that this perturbation contributes to the enhancement of the Reynolds shear stress, leading to significant skin friction of the porous interface. Through the comparison between the two different Reynolds-number cases, it is found that, as the Reynolds number increases, the streamwise perturbation becomes larger and more organized. Consequently, owing to the enhancement of the large-scale perturbation, a significant Reynolds-number dependence of the skin friction of the porous interface can be observed over the streamwise permeable wall. It is also implied that the wavelength of the perturbation can be reasonably scaled by the outer-layer length scale.
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Letoufa, Yassine, Salah Mahmoud Boulaaras, Hamid Benseridi, Mourad Dilmi et Asma Alharbi. « A Study of the Anisotropic Static Elasticity System in Thin Domain ». Journal of Function Spaces 2021 (30 juillet 2021) : 1–8. http://dx.doi.org/10.1155/2021/9918243.
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We study the asymptotic behavior of solutions of the anisotropic heterogeneous linearized elasticity system in thin domain of ℝ 3 which has a fixed cross-section in the ℝ 2 plane with Tresca friction condition. The novelty here is that stress tensor has given by the most general form of Hooke’s law for anisotropic materials. We prove the convergence theorems for the transition 3D-2D when one dimension of the domain tends to zero. The necessary mathematical framework and (2D) equation model with a specific weak form of the Reynolds equation are determined. Finally, the properties of solution of the limit problem are given, in which it is confirmed that the limit problem is well defined.
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Johansson, Arne V., et Magnus Hallbäck. « Modelling of rapid pressure—strain in Reynolds-stress closures ». Journal of Fluid Mechanics 269 (25 juin 1994) : 143–68. http://dx.doi.org/10.1017/s0022112094001515.
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The most general form for the rapid pressure—strain rate, within the context of classical Reynolds-stress transport (RST) closures for homogeneous flows, is derived, and truncated forms are obtained with the aid of rapid distortion theory. By a classical RST-closure we here denote a model with transport equations for the Reynolds stress tensor and the total dissipation rate. It is demonstrated that all earlier models for the rapid pressure—strain rate within the class of classical Reynolds-stress closures can be formulated as subsets of the general form derived here. Direct numerical simulations were used to show that the dependence on flow parameters, such as the turbulent Reynolds number, is small, allowing rapid distortion theory to be used for the determination of model parameters. It was shown that such a nonlinear description, of fourth order in the Reynolds-stress anisotropy tensor, is quite sufficient to very accurately model the rapid pressure—strain in all cases of irrotational mean flows, but also to get reasonable predictions in, for example, a rapid homogeneous shear flow. Also, the response of a sudden change in the orientation of the principal axes of a plane strain is investigated for the present model and models proposed in the literature. Inherent restrictions on the predictive capability of Reynolds-stress closures for rotational effects are identified.
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Chakrabarty, A., et S. N. Yakovenko. « Data-driven turbulence modelling using symbolic regression ». Journal of Physics : Conference Series 2099, no 1 (1 novembre 2021) : 012020. http://dx.doi.org/10.1088/1742-6596/2099/1/012020.
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Abstract The study is focused on the performance of machine-learning methods applied to improve the velocity field predictions in canonical turbulent flows by the Reynolds-averaged Navier–Stokes (RANS) equation models. A key issue here is to approximate the unknown term of the Reynolds stress (RS) tensor needed to close the RANS equations. A turbulent channel flow with the curved backward-facing step on the bottom has the high-fidelity LES data set. It is chosen as the test case to examine possibilities of GEP (gene expression programming) of formulating the enhanced RANS approximations. Such a symbolic regression technique allows us to get the new explicit expressions for the RS anisotropy tensor. Results obtained by the new model produced using GEP are compared with those from the LES data (serving as the target benchmark solution during the machine-learning algorithm training) and from the conventional RANS model with the linear gradient Boussinesq hypothesis for the Reynolds stress tensor.
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Ladeinde, Foluso, Wei Liu et Edward E. O’Brien. « Turbulence in Compressible Mixing Layers ». Journal of Fluids Engineering 120, no 1 (1 mars 1998) : 48–53. http://dx.doi.org/10.1115/1.2819659.
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The direct numerical simulation (DNS) of two-dimensional compressible turbulent mixing layers is reported in this paper for convective Mach numbers Mc = 0.5, 0.8 and 1.0. All scales of flow are resolved with a 2562 grid, although results are also obtained for 642, 962 and 1282 grids for the purpose of determining the effective accuracy and grid-independence of our calculations. The effect of Mach number is also reported for all the Reynolds stress tensor components and for the “shear” components of the anisotropy tensor, the dissipation tensor, pressure-strain, and the triple correlation tensor. The short-time behaviors of some of these quantities are similar to those reported by Sarkar (1995) for homogeneous shear flow, in spite of the differences in the problem type and initial and boundary conditions. The relative magnitudes and signs of the unclosed terms in the Reynolds stress equations provide information on those that have to be retained for turbulence modeling as well as the sense of their contribution.
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Jovanovic´, J., et I. Otic´. « On the Constitutive Relation for the Reynolds Stresses and the Prandtl-Kolmogorov Hypothesis of Effective Viscosity in Axisymmetric Strained Turbulence ». Journal of Fluids Engineering 122, no 1 (8 décembre 1999) : 48–50. http://dx.doi.org/10.1115/1.483225.
Texte intégralRésumé :
The constitutive relation for the Reynolds stress tensor is considered for turbulence developing in axisymmetric strain fields. It is confirmed that the Reynolds stress tensor is aligned linearly with the mean strain rate. In contrast to the Prandtl-Kolmogorov, hypothesis, the effective viscosity is found to grow in proportion to the anisotropy of turbulence and the length scale based on the magnitude of the mean strain rate. Using invariant theory the effective viscosity is determined for the limiting states of turbulence. Additional analysis of the constitutive relations is supplemented for the dissipation and pressure-strain correlations. It is shown that analytical derivations are in excellent agreement with the data obtained from direct numerical simulations. [S0098-2202(00)02801-7]
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Modesti, Davide. « A priori tests of eddy viscosity models in square duct flow ». Theoretical and Computational Fluid Dynamics 34, no 5-6 (31 juillet 2020) : 713–34. http://dx.doi.org/10.1007/s00162-020-00545-9.
Texte intégralRésumé :
Abstract We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number $${\text {Re}}_\tau =1055$$ Re τ = 1055 . We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components $$a_{ij}$$ a ij responsible for turbulent secondary flows, namely the normal stress $$a_{22}$$ a 22 and the secondary shear stress $$a_{23}$$ a 23 . A priori tests on constitutive relations for $$a_{ij}$$ a ij are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of $$a_{ij}$$ a ij . We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to DNS data $${\widetilde{C}}_{ij}$$ C ~ ij , which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress $$a_{12}$$ a 12 ($${\widetilde{C}}_{12}>0.99$$ C ~ 12 > 0.99 ), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress ($${\widetilde{C}}_{22}=0.911$$ C ~ 22 = 0.911 , $${\widetilde{C}}_{23}=0.743$$ C ~ 23 = 0.743 ). Unfortunately, RANS models rely on additional assumptions and a priori analysis carried out on popular models, including k–$$\varepsilon $$ ε and $$v^2$$ v 2 –f, reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the $$v^2$$ v 2 –f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models.
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Yang, S. L., B. D. Peschke et K. Hanjalic. « Second-Moment Closure Model for IC Engine Flow Simulation Using Kiva Code1 ». Journal of Engineering for Gas Turbines and Power 122, no 2 (31 août 1999) : 355–63. http://dx.doi.org/10.1115/1.483213.
Texte intégralRésumé :
The flow and turbulence in an IC engine cylinder were studied using the SSG variant of the Reynolds stress turbulence closure model. In-cylinder turbulence is characterized by strong turbulence anisotropy and flow rotation, which aid in air-fuel mixing. It is argued that solving the differential transport equations for each turbulent stress tensor component, as implied by second-moment closures, can better reproduce stress anisotropy and effects of rotation, than with eddy-viscosity models. Therefore, a Reynolds stress model that can meet the demands of in-cylinder flows was incorporated into an engine flow solver. The solver and SSG turbulence model were first successfully tested with two different validation cases. Finally, simulations were applied to IC-engine like geometries. The results showed that the Reynolds stress model predicted additional flow structures and yielded less diffusive profiles than those predicted by an eddy-viscosity model. [S0742-4795(00)00101-0]
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Sáez de Ocáriz Borde, Haitz, David Sondak et Pavlos Protopapas. « Convolutional neural network models and interpretability for the anisotropic reynolds stress tensor in turbulent one-dimensional flows ». Journal of Turbulence 23, no 1-2 (10 novembre 2021) : 1–28. http://dx.doi.org/10.1080/14685248.2021.1999459.
Texte intégral
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CHOI, KWING-SO, et JOHN L. LUMLEY. « The return to isotropy of homogeneous turbulence ». Journal of Fluid Mechanics 436 (10 juin 2001) : 59–84. http://dx.doi.org/10.1017/s002211200100386x.
Texte intégralRésumé :
Three types of homogeneous anisotropic turbulence were produced by the plane distortion, axisymmetric expansion and axisymmetric contraction of grid-generated turbulence, and their behaviour in returning to isotropy was experimentally studied using hot-wire anemometry. It was found that the turbulence trajectory after the plane distortion was highly nonlinear, and did not follow Rotta's linear model in returning to isotropy. The turbulence wanted to become axisymmetric even more than it wanted to return to isotropy. In order to show the rate of return to isotropy of homogeneous turbulence, a map of the ratio of the characteristic time scale for the decay of turbulent kinetic energy to that of the return to isotropy was constructed. This demonstrated that the rate of return to isotropy was much lower for turbulence with a greater third invariant of the anisotropy tensor. The invariant technique was then applied to the experimental results to develop a new turbulence model for the return-to-isotropy term in the Reynolds stress equation which satisfied the realizability conditions. The effect of the Reynolds number on the rate of return to isotropy was also investigated and the results incorporated in the proposed model.
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Penna, Nadia, Ellora Padhi, Subhasish Dey et Roberto Gaudio. « Structure functions and invariants of the anisotropic Reynolds stress tensor in turbulent flows on water-worked gravel beds ». Physics of Fluids 32, no 5 (1 mai 2020) : 055106. http://dx.doi.org/10.1063/5.0007698.
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MARSTORP, LINUS, GEERT BRETHOUWER, OLOF GRUNDESTAM et ARNE V. JOHANSSON. « Explicit algebraic subgrid stress models with application to rotating channel flow ». Journal of Fluid Mechanics 639 (12 octobre 2009) : 403–32. http://dx.doi.org/10.1017/s0022112009991054.
Texte intégralRésumé :
New explicit subgrid stress models are proposed involving the strain rate and rotation rate tensor, which can account for rotation in a natural way. The new models are based on the same methodology that leads to the explicit algebraic Reynolds stress model formulation for Reynolds-averaged Navier–Stokes simulations. One dynamic model and one non-dynamic model are proposed. The non-dynamic model represents a computationally efficient subgrid scale (SGS) stress model, whereas the dynamic model is the most accurate. The models are validated through large eddy simulations (LESs) of spanwise and streamwise rotating channel flow and are compared with the standard and dynamic Smagorinsky models. The proposed explicit dependence on the system rotation improves the description of the mean velocity profiles and the turbulent kinetic energy at high rotation rates. Comparison with the dynamic Smagorinsky model shows that not using the eddy-viscosity assumption improves the description of both the Reynolds stress anisotropy and the SGS stress anisotropy. LESs of rotating channel flow at Reτ = 950 have been carried out as well. These reveal some significant Reynolds number influences on the turbulence statistics. LESs of non-rotating turbulent channel flow at Reτ = 950 show that the new explicit model especially at coarse resolutions significantly better predicts the mean velocity, wall shear and Reynolds stresses than the dynamic Smagorinsky model, which is probably the result of a better prediction of the anisotropy of the subgrid dissipation.
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Castro, Nicolas D., et Ayodeji O. Demuren. « Large eddy simulation of turbulent axially rotating pipe and swirling jet flows ». Proceedings of the Institution of Mechanical Engineers, Part C : Journal of Mechanical Engineering Science 231, no 9 (2 décembre 2015) : 1749–61. http://dx.doi.org/10.1177/0954406215620823.
Texte intégralRésumé :
Fully-developed, turbulent rotating pipe flow and swirling jet flow, emitted from the pipe, into open quiescent ambient are investigated numerically using large eddy simulation. Simulations are performed at various rotation rates and Reynolds numbers. Time-averaged large eddy simulation results are compared to experimental and simulation data from previous studies. Pipe flow results show deformation of the turbulent mean axial velocity profile towards the laminar-type Poiseuille profile, with increased rotation. The Reynolds stress anisotropy tensor experiences a component-level redistribution due to pipe rotation. Turbulent energy is transferred from the axial component to the tangential component as rotation is increased. The Reynolds stress anisotropy invariant map also shows a movement away from the one-component limit in the buffer layer, with increased rotation. Exit conditions for the pipe flow simulation are utilized as inlet conditions for the jet flow simulation. Jet flow without swirl and at a swirl rate of S = 0.5 are investigated. Swirl is observed to change the characteristics of the jet flow field, leading to increased jet spread and velocity decay, and a corresponding decrease in the length of the jet potential core. The Reynolds stress anisotropy invariant map shows that the turbulent stress field, with or without rotation straddles the axi-symmetric limit.
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Barbi, G., A. Chierici, L. Chirco, V. Giovacchini, S. Manservisi et L. Sirotti. « Numerical simulation of a low Prandtl number flow with a four-parameters turbulence model through an explicit algebraic definition of Reynolds stress and turbulent heat flux ». Journal of Physics : Conference Series 2177, no 1 (1 avril 2022) : 012005. http://dx.doi.org/10.1088/1742-6596/2177/1/012005.
Texte intégralRésumé :
Abstract Computational Fluid Dynamics codes usually adopt the Reynolds analogy in order to simulate dynamic and thermal flow fields for ordinary fluids like water and air. On the other hand, in low Prandtl fluids, such as heavy liquid metals like Lead-Bismuth Eutectic (LBE), the time scales of temperature and velocity fields are rather different and therefore similarity hypothesis cannot be used. Furthermore, to properly predict a complex flow field characterized by anisotropic behavior, it is necessary to overcome eddy-viscosity models and move to more advanced turbulence models. In the present work, we propose a nonlinear method for the computation of the Reynolds stress tensor and of the turbulent heat flux. Explicit algebraic models (EAM) and new time scales have been implemented using a logarithmic four parameters turbulence model (i.e. K-Ω-K θ -Ω θ ). This new model is validated through the simulation of plane channel and cylinder flows and results are compared with DNS data.
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Belt, R. J., A. C. L. M. Daalmans et L. M. Portela. « Experimental study of particle-driven secondary flow in turbulent pipe flows ». Journal of Fluid Mechanics 709 (24 août 2012) : 1–36. http://dx.doi.org/10.1017/jfm.2012.104.
Texte intégralRésumé :
AbstractIn fully developed single-phase turbulent flow in straight pipes, it is known that mean motions can occur in the plane of the pipe cross-section, when the cross-section is non-circular, or when the wall roughness is non-uniform around the circumference of a circular pipe. This phenomenon is known as secondary flow of the second kind and is associated with the anisotropy in the Reynolds stress tensor in the pipe cross-section. In this work, we show, using careful laser Doppler anemometry experiments, that secondary flow of the second kind can also be promoted by a non-uniform non-axisymmetric particle-forcing, in a fully developed turbulent flow in a smooth circular pipe. In order to isolate the particle-forcing from other phenomena, and to prevent the occurrence of mean particle-forcing in the pipe cross-section, which could promote a different type of secondary flow (secondary flow of the first kind), we consider a simplified well-defined situation: a non-uniform distribution of particles, kept at fixed positions in the ‘bottom’ part of the pipe, mimicking, in a way, the particle or droplet distribution in horizontal pipe flows. Our results show that the particles modify the turbulence through ‘direct’ effects (associated with the wake of the particles) and ‘indirect’ effects (associated with the global balance of momentum and the turbulence dynamics). The resulting anisotropy in the Reynolds stress tensor is shown to promote four secondary flow cells in the pipe cross-section. We show that the secondary flow is determined by the projection of the Reynolds stress tensor onto the pipe cross-section. In particular, we show that the direction of the secondary flow is dictated by the gradients of the normal Reynolds stresses in the pipe cross-section, $\partial {\tau }_{rr} / \partial r$ and $\partial {\tau }_{\theta \theta } / \partial \theta $. Finally, a scaling law is proposed, showing that the particle-driven secondary flow scales with the root of the mean particle-forcing in the axial direction, allowing us to estimate the magnitude of the secondary flow.
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Schmelzer, Martin, Richard P. Dwight et Paola Cinnella. « Discovery of Algebraic Reynolds-Stress Models Using Sparse Symbolic Regression ». Flow, Turbulence and Combustion 104, no 2-3 (17 décembre 2019) : 579–603. http://dx.doi.org/10.1007/s10494-019-00089-x.
Texte intégralRésumé :
AbstractA novel deterministic symbolic regression method SpaRTA (Sparse Regression of Turbulent Stress Anisotropy) is introduced to infer algebraic stress models for the closure of RANS equations directly from high-fidelity LES or DNS data. The models are written as tensor polynomials and are built from a library of candidate functions. The machine-learning method is based on elastic net regularisation which promotes sparsity of the inferred models. By being data-driven the method relaxes assumptions commonly made in the process of model development. Model-discovery and cross-validation is performed for three cases of separating flows, i.e. periodic hills (Re=10595), converging-diverging channel (Re=12600) and curved backward-facing step (Re=13700). The predictions of the discovered models are significantly improved over the k-ω SST also for a true prediction of the flow over periodic hills at Re=37000. This study shows a systematic assessment of SpaRTA for rapid machine-learning of robust corrections for standard RANS turbulence models.
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Andersson, Magnus, et Matts Karlsson. « Model Verification and Error Sensitivity of Turbulence-Related Tensor Characteristics in Pulsatile Blood Flow Simulations ». Fluids 6, no 1 (30 décembre 2020) : 11. http://dx.doi.org/10.3390/fluids6010011.
Texte intégralRésumé :
Model verification, validation, and uncertainty quantification are essential procedures to estimate errors within cardiovascular flow modeling, where acceptable confidence levels are needed for clinical reliability. While more turbulent-like studies are frequently observed within the biofluid community, practical modeling guidelines are scarce. Verification procedures determine the agreement between the conceptual model and its numerical solution by comparing for example, discretization and phase-averaging-related errors of specific output parameters. This computational fluid dynamics (CFD) study presents a comprehensive and practical verification approach for pulsatile turbulent-like blood flow predictions by considering the amplitude and shape of the turbulence-related tensor field using anisotropic invariant mapping. These procedures were demonstrated by investigating the Reynolds stress tensor characteristics in a patient-specific aortic coarctation model, focusing on modeling-related errors associated with the spatiotemporal resolution and phase-averaging sampling size. Findings in this work suggest that attention should also be put on reducing phase-averaging related errors, as these could easily outweigh the errors associated with the spatiotemporal resolution when including too few cardiac cycles. Also, substantially more cycles are likely needed than typically reported for these flow regimes to sufficiently converge the phase-instant tensor characteristics. Here, higher degrees of active fluctuating directions, especially of lower amplitudes, appeared to be the most sensitive turbulence characteristics.
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Tamarin, Talia, James R. Maddison, Eyal Heifetz et David P. Marshall. « A Geometric Interpretation of Eddy Reynolds Stresses in Barotropic Ocean Jets ». Journal of Physical Oceanography 46, no 8 (août 2016) : 2285–307. http://dx.doi.org/10.1175/jpo-d-15-0139.1.
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AbstractBarotropic eddy fluxes are analyzed through a geometric decomposition of the eddy stress tensor. Specifically, the geometry of the eddy variance ellipse, a two-dimensional visualization of the stress tensor describing the mean eddy shape and tilt, is used to elucidate eddy propagation and eddy feedback on the mean flow. Linear shear and jet profiles are analyzed and theoretical results are compared against fully nonlinear simulations. For flows with zero planetary vorticity gradient, analytic solutions for the eddy ellipse tilt and anisotropy are obtained that provide a direct relationship between the eddy tilt and the phase difference of a normal-mode solution. This allows a straightforward interpretation of the eddy–mean flow interaction in terms of classical stability theory: the initially unstable jet gives rise to eddies that are tilted “against the shear” and extract energy from the mean flow; once the jet stabilizes, eddies become tilted “with the shear” and return their energy to the mean flow. For a nonzero planetary vorticity gradient, ray-tracing theory is used to predict ellipse geometry and its impact on eddy propagation within a jet. An analytic solution for the eddy tilt is found for a Rossby wave on a constant background shear. The ray-tracing results broadly agree with the eddy tilt diagnosed from a fully nonlinear simulation.
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JONGEN, T., et T. B. GATSKI. « A unified analysis of planar homogeneous turbulence using single-point closure equations ». Journal of Fluid Mechanics 399 (25 novembre 1999) : 117–50. http://dx.doi.org/10.1017/s002211209900631x.
Texte intégralRésumé :
A unified approach for assessing and characterizing both the non-equilibrium and equilibrium states of planar homogeneous flows is analysed within the framework of single-point turbulence closure equations. The underlying methodology is based on the replacement of the modelled evolution equation for the Reynolds stress anisotropy tensor by an equivalent set of three equations for characteristic scalar invariants or state variables. For stress anisotropy evolution equations which use modelled pressure–strain rate correlations that are quasi-linear, this equivalence then leads to an analytic solution for the time evolution of the Reynolds stress anisotropy. With this analysis, the transient system characteristics can be studied, including the dependence on initial states, the occurrence of limit-cycle behaviour, and the system global stability. In the fixed-point asymptotic limit, these results are consistent with and unify previous equilibrium studies, and provide additional information allowing the resolution of some questions that could not be answered in the framework of previous developments. A new result on constraints applicable to the development of realizable pressure–strain rate models is obtained from a re-examination of the stress anisotropy invariant map. With the analytic solution for the transient behaviour, some recent non-equilibrium models, which incorporate relaxation effects, are evaluated in a variety of homogeneous flows in inertial and non-inertial frames.
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KOSOVIĆ, BRANKO. « Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers ». Journal of Fluid Mechanics 336 (10 avril 1997) : 151–82. http://dx.doi.org/10.1017/s0022112096004697.
Texte intégralRésumé :
It has been recognized that the subgrid-scale (SGS) parameterization represents a critical component of a successful large-eddy simulation (LES). Commonly used linear SGS models produce erroneous mean velocity profiles in LES of high-Reynolds-number boundary layer flows. Although recently proposed approaches to solving this problem have resulted in significant improvements, questions about the true nature of the SGS problem in shear-driven high-Reynolds-number flows remain open.We argue that the SGS models must capture inertial transfer effects including backscatter of energy as well as its redistribution among the normal SGS stress components. These effects are the consequence of nonlinear interactions and anisotropy. In our modelling procedure we adopt a phenomenological approach whereby the SGS stresses are related to the resolved velocity gradients. We show that since the SGS stress tensor is not frame indifferent a more general nonlinear model can be applied to the SGS parameterization. We develop a nonlinear SGS model capable of reproducing the effects of SGS anisotropy characteristic for shear-driven boundary layers. The results obtained using the nonlinear model for the LES of a neutral shear-driven atmospheric boundary layer show a significant improvement in prediction of the non-dimensional shear and low-order statistics compared to the linear Smagorinsky-type models. These results also demonstrate a profound effect of the SGS model on the flow structures.
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Poulsen, Mads B., Markus Jochum, James R. Maddison, David P. Marshall et Roman Nuterman. « A Geometric Interpretation of Southern Ocean Eddy Form Stress ». Journal of Physical Oceanography 49, no 10 (octobre 2019) : 2553–70. http://dx.doi.org/10.1175/jpo-d-18-0220.1.
Texte intégralRésumé :
AbstractAn interpretation of eddy form stress via the geometry described by the Eliassen–Palm flux tensor is explored. Complimentary to previous works on eddy Reynolds stress geometry, this study shows that eddy form stress is fully described by a vertical ellipse, whose size, shape, and orientation with respect to the mean flow shear determine the strength and direction of vertical momentum transfers. Following a recent proposal, this geometric framework is here used to form a Gent–McWilliams eddy transfer coefficient that depends on eddy energy and a nondimensional geometric parameter α, bounded in magnitude by unity. The parameter α expresses the efficiency by which eddies exchange energy with baroclinic mean flow via along-gradient eddy buoyancy flux—a flux equivalent to eddy form stress along mean buoyancy contours. An eddy-resolving ocean general circulation model is used to estimate the spatial structure of α in the Southern Ocean and assess its potential to form a basis for parameterization. The eddy efficiency α averages to a low but positive value of 0.043 within the Antarctic Circumpolar Current, consistent with an inefficient eddy field extracting energy from the mean flow. It is found that the low eddy efficiency is mainly the result of that eddy buoyancy fluxes are weakly anisotropic on average. The eddy efficiency is subject to pronounced vertical structure and is maximum at ~3-km depth, where eddy buoyancy fluxes tend to be directed most downgradient. Since α partly sets the eddy form stress in the Southern Ocean, a parameterization for α must reproduce its vertical structure to provide a faithful representation of vertical stress divergence and eddy forcing.
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Lazeroms, W. M. J., G. Brethouwer, S. Wallin et A. V. Johansson. « An explicit algebraic Reynolds-stress and scalar-flux model for stably stratified flows ». Journal of Fluid Mechanics 723 (16 avril 2013) : 91–125. http://dx.doi.org/10.1017/jfm.2013.116.
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AbstractThis work describes the derivation of an algebraic model for the Reynolds stresses and turbulent heat flux in stably stratified turbulent flows, which are mutually coupled for this type of flow. For general two-dimensional mean flows, we present a correct way of expressing the Reynolds-stress anisotropy and the (normalized) turbulent heat flux as tensorial combinations of the mean strain rate, the mean rotation rate, the mean temperature gradient and gravity. A system of linear equations is derived for the coefficients in these expansions, which can easily be solved with computer algebra software for a specific choice of the model constants. The general model is simplified in the case of parallel mean shear flows where the temperature gradient is aligned with gravity. For this case, fully explicit and coupled expressions for the Reynolds-stress tensor and heat-flux vector are given. A self-consistent derivation of this model would, however, require finding a root of a polynomial equation of sixth-order, for which no simple analytical expression exists. Therefore, the nonlinear part of the algebraic equations is modelled through an approximation that is close to the consistent formulation. By using the framework of a$K\text{{\ndash}} \omega $model (where$K$is turbulent kinetic energy and$\omega $an inverse time scale) and, where needed, near-wall corrections, the model is applied to homogeneous shear flow and turbulent channel flow, both with stable stratification. For the case of homogeneous shear flow, the model predicts a critical Richardson number of 0.25 above which the turbulent kinetic energy decays to zero. The channel-flow results agree well with DNS data. Furthermore, the model is shown to be robust and approximately self-consistent. It also fulfils the requirements of realizability.
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Zuo, Feng-Yuan, Antonio Memmolo, Guo-ping Huang et Sergio Pirozzoli. « Direct numerical simulation of conical shock wave–turbulent boundary layer interaction ». Journal of Fluid Mechanics 877 (19 août 2019) : 167–95. http://dx.doi.org/10.1017/jfm.2019.558.
Texte intégralRésumé :
Direct numerical simulation of the Navier–Stokes equations is carried out to investigate the interaction of a conical shock wave with a turbulent boundary layer developing over a flat plate at free-stream Mach number $M_{\infty }=2.05$ and Reynolds number $Re_{\unicode[STIX]{x1D703}}\approx 630$, based on the upstream boundary layer momentum thickness. The shock is generated by a circular cone with half opening angle $\unicode[STIX]{x1D703}_{c}=25^{\circ }$. As found in experiments, the wall pressure exhibits a distinctive N-wave signature, with a sharp peak right past the precursor shock generated at the cone apex, followed by an extended zone with favourable pressure gradient, and terminated by the trailing shock associated with recompression in the wake of the cone. The boundary layer behaviour is strongly affected by the imposed pressure gradient. Streaks are suppressed in adverse pressure gradient (APG) zones, but re-form rapidly in downstream favourable pressure gradient (FPG) zones. Three-dimensional mean flow separation is only observed in the first APG region associated with the formation of a horseshoe vortex, whereas the second APG region features an incipient detachment state, with scattered spots of instantaneous reversed flow. As found in canonical geometrically two-dimensional wedge-generated shock–boundary layer interactions, different amplification of the turbulent stress components is observed through the interacting shock system, with approach to an isotropic state in APG regions, and to a two-component anisotropic state in FPG. The general adequacy of the Boussinesq hypothesis is found to predict the spatial organization of the turbulent shear stresses, although different eddy viscosities should be used for each component, as in tensor eddy-viscosity models, or in full Reynolds stress closures.
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TEJADA-MARTÍNEZ, A. E., et C. E. GROSCH. « Langmuir turbulence in shallow water. Part 2. Large-eddy simulation ». Journal of Fluid Mechanics 576 (28 mars 2007) : 63–108. http://dx.doi.org/10.1017/s0022112006004587.
Texte intégralRésumé :
Results of large-eddy simulation (LES) of Langmuir circulations (LC) in a wind-driven shear current in shallow water are reported. The LC are generated via the well-known Craik–Leibovich vortex force modelling the interaction between the Stokes drift, induced by surface gravity waves, and the shear current. LC in shallow water is defined as a flow in sufficiently shallow water that the interaction between the LC and the bottom boundary layer cannot be ignored, thus requiring resolution of the bottom boundary layer. After the introduction and a description of the governing equations, major differences in the statistical equilibrium dynamics of wind-driven shear flow and the same flow with LC (both with a bottom boundary layer) are highlighted. Three flows with LC will be discussed. In the first flow, the LC were generated by intermediate-depth waves (relative to the wavelength of the waves and the water depth). The amplitude and wavelength of these waves are representative of the conditions reported in the observations of A. E. Gargett & J. R. Wells in Part 1 (J. Fluid Mech. vol .000, 2007, p. 00). In the second flow, the LC were generated by shorter waves. In the third flow, the LC were generated by intermediate waves of greater amplitude than those in the first flow. The comparison between the different flows relies on visualizations and diagnostics including (i) profiles of mean velocity, (ii) profiles of resolved Reynolds stress components, (iii) autocorrelations, (iv) invariants of the resolved Reynolds stress anisotropy tensor and (v) balances of the transport equations for mean resolved turbulent kinetic energy and resolved Reynolds stresses. Additionally, dependencies of LES results on Reynolds number, subgrid-scale closure, size of the domain and grid resolution are addressed.In the shear flow without LC, downwind (streamwise) velocity fluctuations are characterized by streaks highly elongated in the downwind direction and alternating in sign in the crosswind (spanwise) direction. Forcing this flow with the Craik–Leibovich force generating LC leads to streaks with larger characteristic crosswind length scales consistent with those recorded by observations. In the flows with LC, in the mean, positive streaks exhibit strong intensification near the bottom and near the surface leading to intensified downwind velocity ‘jets’ in these regions. In the flow without LC, such intensification is noticeably absent. A revealing diagnostic of the structure of the turbulence is the depth trajectory of the invariants of the resolved Reynolds stress anisotropy tensor, which for a realizable flow must lie within the Lumley triangle. The trajectory for the flow without LC reveals the typical structure of shear-dominated turbulence in which the downwind component of the resolved normal Reynolds stresses is greater than the crosswind and vertical components. In the near bottom and surface regions, the trajectory for the flow with LC driven by wave and wind forcing conditions representative of the field observations reveals a two-component structure in which the downwind and crosswind components are of the same order and both are much greater than the vertical component. The two-component structure of the Langmuir turbulence predicted by LES is consistent with the observations in the bottom third of the water column above the bottom boundary layer.
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van den Bos, Nout, Kevin Zwijsen, Alexander H. van Zuijlen, Edo M. A. Frederix et Ferry Roelofs. « Turbulence-induced vibrations prediction through use of an anisotropic pressure fluctuation model ». EPJ Nuclear Sciences & ; Technologies 9 (2023) : 7. http://dx.doi.org/10.1051/epjn/2022050.
Texte intégralRésumé :
In nuclear fuel rod bundles, turbulence-induced pressure fluctuations caused by an axial flow can create small but significant vibrations in the fuel rods, which in turn can cause structural effects such as material fatigue and fretting wear. Fluid-structure interaction simulations can be used to model these vibrations, but for affordable simulations based on the URANS approach, a model for the pressure fluctuations must be utilised. Driven by the goal to improve the current state-of-the-art pressure fluctuation model, AniPFM (Anisotropic Pressure Fluctuation Model) was developed. AniPFM can model velocity fluctuations based on anisotropic Reynolds stress tensors, with temporal correlation through the convection and decorrelation of turbulence. From these velocity fluctuations and the mean flow properties, the pressure fluctuations are calculated. The model was applied to several test cases and shows promising results in terms of reproducing qualitatively similar flow structures, as well as predicting the root-mean-squared pressure fluctuations. While further validation is being performed, the AniPFM has already demonstrated its potential for affordable simulations of turbulence-induced vibrations in industrial nuclear applications.
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Akao, Takumi, Tomoaki Watanabe et Koji Nagata. « Vertical confinement effects on a fully developed turbulent shear layer ». Physics of Fluids 34, no 5 (mai 2022) : 055129. http://dx.doi.org/10.1063/5.0090686.
Texte intégralRésumé :
The effects of vertical confinement on a turbulent shear layer are investigated with large-eddy simulations of a freely developing shear layer (FSL) and a wall-confined shear layer (WSL) that develops between two horizontal walls. In the case of the WSL, the growth of the shear layer is inhibited by the walls. Once the walls prevent the development of the shear layer, highly anisotropic velocity fluctuations become prominent in the flow. These anisotropic velocity fluctuations are recognized as elongated large-scale structures (ELSS), whose streamwise length is much larger than the length scales in the other directions. Spectral analysis confirms that the turbulent kinetic energy is dominated by the ELSS, whose streamwise length grows continuously. A proper orthogonal decomposition can effectively extract a velocity component associated with the ELSS. The isotropy of the Reynolds stress tensor is changed by the presence of the ELSS. These changes in flow characteristics due to the ELSS are not observed in the FSL, where the shear layer thickness increases continuously. These behaviors of the WSL are consistent with those of stably stratified shear layers (SSSLs), where flow structures similar to ELSS also develop when the vertical flow development is confined by the stable stratification. The vertical confinement by the walls or stable stratification strengthens mean shear effects. The flow behavior at large scales in the WSL and SSSL is consistent with rapid distortion theory for turbulence subject to mean shear, suggesting that the development of ELSS is caused by the mean shear.
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Saroha, Sagar, Sawan S. Sinha et Sunil Lakshmipathy. « Evaluation of PANS method in conjunction with non-linear eddy viscosity closure using OpenFOAM ». International Journal of Numerical Methods for Heat & ; Fluid Flow 29, no 3 (4 mars 2019) : 949–80. http://dx.doi.org/10.1108/hff-09-2018-0529.
Texte intégralRésumé :
Purpose In recent years, the partially averaged Navier–Stokes (PANS) methodology has earned acceptability as a viable scale-resolving bridging method of turbulence. To further enhance its capabilities, especially for simulating separated flows past bluff bodies, this paper aims to combine PANS with a non-linear eddy viscosity model (NLEVM). Design/methodology/approach The authors first extract a PANS closure model using the Shih’s quadratic eddy viscosity closure model [originally proposed for Reynolds-averaged Navier–Stokes (RANS) paradigm (Shih et al., 1993)]. Subsequently, they perform an extensive evaluation of the combination (PANS + NLEVM). Findings The NLEVM + PANS combination shows promising result in terms of reduction of the anisotropy tensor when the filter parameter (fk) is reduced. Further, the influence of PANS filter parameter f on the magnitude and orientation of the non-linear part of the stress tensor is closely scrutinized. Evaluation of the NLEVM + PANS combination is subsequently performed for flow past a square cylinder at Reynolds number of 22,000. The results show that for the same level of reduction in fk, the PANS + NLEVM methodology releases significantly more scales of motion and unsteadiness as compared to the traditional linear eddy viscosity model (LEVM) of Boussinesq (PANS + LEVM). The authors further demonstrate that with this enhanced ability the NLEVM + PANS combination shows much-improved predictions of almost all the mean quantities compared to those observed in simulations using LEVM + PANS. Research limitations/implications Based on these results, the authors propose the NLEVM + PANS combination as a more potent methodology for reliable prediction of highly separated flow fields. Originality/value Combination of a quadratic eddy viscosity closure model with PANS framework for simulating flow past bluff bodies.
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DUAN, L., I. BEEKMAN et M. P. MARTÍN. « Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number ». Journal of Fluid Mechanics 672 (2 mars 2011) : 245–67. http://dx.doi.org/10.1017/s0022112010005902.
Texte intégralRésumé :
In this paper, we perform direct numerical simulations (DNS) of turbulent boundary layers with nominal free-stream Mach number ranging from 0.3 to 12. The main objective is to assess the scalings with respect to the mean and turbulence behaviours as well as the possible breakdown of the weak compressibility hypothesis for turbulent boundary layers at high Mach numbers (M > 5). We find that many of the scaling relations, such as the van Driest transformation for mean velocity, Walz's relation, Morkovin's scaling and the strong Reynolds analogy, which are derived based on the weak compressibility hypothesis, remain valid for the range of free-stream Mach numbers considered. The explicit dilatation terms such as pressure dilatation and dilatational dissipation remain small for the present Mach number range, and the pressure–strain correlation and the anisotropy of the Reynolds stress tensor are insensitive to the free-stream Mach number. The possible effects of intrinsic compressibility are reflected by the increase in the fluctuations of thermodynamic quantities (p′rms/pw, ρ′rms/ρ, T′rms/T) and turbulence Mach numbers (Mt, M′rms), the existence of shocklets, the modification of turbulence structures (near-wall streaks and large-scale motions) and the variation in the onset of intermittency.
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Ricardo, Ana M., Dimokratis G. E. Grigoriadis et Rui M. L. Ferreira. « LES modelling of a flow within an infinite array of randomly placed cylinders : Anisotropy characterization ». E3S Web of Conferences 40 (2018) : 02035. http://dx.doi.org/10.1051/e3sconf/20184002035.
Texte intégralRésumé :
The LES approach is employed to model flows within random arrays of emergent cylinders. The model is validated against laboratory data acquired with a 2D-2C Particle Image Velocimetry system. The main goals are: i) discussion of the effect of the numerical domain size and the grid resolution on the predicted flow variables; and ii) spatial characterization of the flow anisotropy. Three domains of different sizes (16 to 36 cylinders) and four grid resolutions were independently tested. A 2D methodology was proposed to characterize the flow anisotropy on the horizontal plane. The results show that the first and second order moments were not significantly affected by the size of the tested numerical domains or by the grid resolution. The comparison with laboratory data showed a fair agreement confirming that the numerical model was able to adequately reproduce all the components of the Reynolds stress tensor. The results show that turbulence is of axisymmetric expansion nature in this type of flow. Relatively to the degree of anisotropy, the highest values were found close to the cylinder, decreasing gradually downstream towards the isotropy state. However, a truly isotropic turbulence state is not reached.
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Mishra, Aashwin A., et Sharath S. Girimaji. « On the realizability of pressure–strain closures ». Journal of Fluid Mechanics 755 (20 août 2014) : 535–60. http://dx.doi.org/10.1017/jfm.2014.446.
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AbstractThe realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined.