Physics of fluids

Vol. 29, num. 11, p. 115109-1-115109-15

DOI: 10.1063/1.5012546

Date of publication: 2017-11-29

Abstract:

Direct numerical simulations of the incompressible Navier-Stokes equations are not feasible yet for most practical turbulent flows. Therefore, dynamically less complex mathematical formulations are necessary for coarse-grained simulations. In this regard, eddy-viscosity models for Large-Eddy Simulation (LES) are probably the most popular example thereof. This type of models requires the calculation of a subgrid characteristic length which is usually associated with the local grid size. For isotropic grids, this is equal to the mesh step. However, for anisotropic or unstructured grids, such as the pancake-like meshes that are often used to resolve near-wall turbulence or shear layers, a consensus on defining the subgrid characteristic length has not been reached yet despite the fact that it can strongly affect the performance of LES models. In this context, a new definition of the subgrid characteristic length is presented in this work. This flow-dependent length scale is based on the turbulent, or subgrid stress, tensor and its representations on different grids. The simplicity and mathematical properties suggest that it can be a robust definition that minimizes the effects of mesh anisotropies on simulation results. The performance of the proposed subgrid characteristic length is successfully tested for decaying isotropic turbulence and a turbulent channel flow using artificially refined grids. Finally, a simple extension of the method for unstructured meshes is proposed and tested for a turbulent flow around a square cylinder. Comparisons with existing subgrid characteristic length scales show that the proposed definition is much more robust with respect to mesh anisotropies and has a great potential to be used in complex geometries where highly skewed (unstructured) meshes are present.]]>

Physics of fluids

Vol. 29, num. 10, p. 105103-1-105103-17

DOI: 10.1063/1.5005842

Date of publication: 2017-10-06

Abstract:

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Bénard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and p spanwise open-ended distance are used at two Rayleigh numbers Ra € (108, 1010) [Dabbagh et al., "On the evolution of flowtopology in turbulent Rayleigh-Bénard convection," Phys. Fluids 28, 115105 (2016)]. First, DNS at Ra = 108 is used to assess the performance of eddy-viscosity models such as QR,Wall-Adapting Local Eddy-viscosity (WALE), and the recent S3PQR-models proposed by Trias et al. ["Building proper invariants for eddy-viscosity subgrid-scale models," Phys. Fluids 27, 065103 (2015)]. The outcomes imply that the eddy-viscosity modeling smoothes the coarse-grained viscous straining and retrieves fairly well the effect of the kinetic unfiltered scales in order to reproduce the coherent large scales. However, these models fail to approach the exact evolution of the SGS heat flux and are incapable to reproduce well the further dominant rotational enstrophy pertaining to the buoyant production. Afterwards, the key ingredients of eddy-viscosity, vt, and eddy-diffusivity, kt , are calculated a priori and revealed positive prevalent values to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. The topological analysis suggests that the effective turbulent diffusion paradigm and the hypothesis of a constant turbulent Prandtl number are only applicable in the large-scale strain-dominated areas in the bulk. It is shown that the bulk-dominated rotational structures of vortex-stretching (and its synchronous viscous dissipative structures) hold the highest positive values of vt ; however, the zones of backscatter energy and counter-gradient heat transport are related to the areas of compressed focal vorticity. More arguments have been attained through a priori investigation of the alignment trends imposed by existing parameterizations for the SGS heat flux, tested here inside RBC. It is shown that the parameterizations based linearly on the resolved thermal gradient are invalid in RBC. Alternatively, the tensor-diffusivity approach becomes a crucial choice of modeling the SGS heat flux, in particular, the tensorial diffusivity that includes the SGS stress tensor. This and other crucial scrutinies on a future modeling to the SGS heat flux in RBC are sought.

At the crossroad between flow topology analysis and turbulence modeling, a priori studies are a reliable tool to understand the underlying physics of the subgrid-scale (SGS) motions in turbulent flows. In this paper, properties of the SGS features in the framework of a large-eddy simulation are studied for a turbulent Rayleigh-Bénard convection (RBC). To do so, data from direct numerical simulation (DNS) of a turbulent air-filled RBC in a rectangular cavity of aspect ratio unity and p spanwise open-ended distance are used at two Rayleigh numbers Ra € (108, 1010) [Dabbagh et al.,]]>

Physics of fluids

Vol. 28, num. 11, p. 115105-1-115105-25

DOI: 10.1063/1.4967495

Date of publication: 2016-11-22

Abstract:

Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Benard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 10(8) and 10(10), inside an air-filled rectangular cell of aspect ratio unity and pi span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (Q(G), R-G) has displayed the so-called "teardrop" spiraling shape through the bulk region. Therein, the mean trajectories are swirling inwards revealing a periodic spin around the converging origin of a constant period that is found to be proportional to the plumes lifetime. This suggests that the thermal plumes participate in the coherent large-scale circulation and the turbulent wind created in the bulk. Particularly, it happens when the plumes elongate substantially to contribute to the large-scale eddies at the lower turbulent state. Supplementary small-scale properties, which are widely common in many turbulent flows have been observed in RBC. For example, the strong preferential alignment of vorticity with the intermediate eigenstrain vector, and the asymmetric alignment between vorticity and the vortex-stretching vector. It has been deduced that in a hard turbulent flow regime, local self-amplifications of straining regions aid in contracting the vorticity worms, and enhance the local interactions vorticity/strain to support the linear vortex-stretching contributions. On the other hand, the evolution of invariants pertained to the traceless part of velocity-times-temperature gradient tensor has also been considered in order to determine the role of thermals in the fine-scale dynamics. These new invariants show an incorporation of kinetic and thermal gradient dynamics that indicate directly the evolution and lifetime of thermal plume structures. By applying an identical approach, the rates of the new invariants have shown a symmetric cycling behaviour decaying towards two skew-symmetric converging origins at the lower Ra number. The trajectories near origins address the hot and cold coherent plumes that travel as an average large-scale heat flux in the sidewall vicinities, and denote a periodic spin period close to the plumes lifetime. At the hard turbulent case, the spiraling trajectories travel in shorter tracks to reveal the reduced lifetime of plumes under the dissipative and mixing effects. The turbulent background kinetic derivatives get self-amplified and the trajectories converge to a zero-valued origin indicating that there is no contribution from the plumes to the average coherent large scales of heat flux. These and other peculiar scrutinies on the small-scale motions in RBC have been enlightened, and may have a fruitful consequence on modelling approaches of buoyancy-driven turbulence.

Copyright 2016 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.

Small-scale dynamics is the spirit of turbulence physics. It implicates many attributes of flow topology evolution, coherent structures, hairpin vorticity dynamics, and mechanism of the kinetic energy cascade. In this work, several dynamical aspects of the small-scale motions have been numerically studied in a framework of Rayleigh-Benard convection (RBC). To do so, direct numerical simulations have been carried out at two Rayleigh numbers Ra = 10(8) and 10(10), inside an air-filled rectangular cell of aspect ratio unity and pi span-wise open-ended distance. As a main feature, the average rate of the invariants of the velocity gradient tensor (Q(G), R-G) has displayed the so-called]]>

Physics of fluids

Vol. 27, num. 6, p. 065103-1-065103-17

DOI: 10.1063/1.4921817

Date of publication: 2015-06-23

Abstract:

Direct simulations of the incompressible Navier-Stokes equations are limited to relatively low-Reynolds numbers. Hence, dynamically less complex mathematical formulations are necessary for coarse-grain simulations. Eddy-viscosity models for large-eddy simulation is probably the most popular example thereof: they rely on differential operators that should properly detect different flow configurations (laminar and 2D flows, near-wall behavior, transitional regime, etc.). Most of them are based on the combination of invariants of a symmetric tensor that depends on the gradient of the resolved velocity field, . In this work, models are presented within a framework consisting of a 5D phase space of invariants. In this way, new models can be constructed by imposing appropriate restrictions in this space. For instance, considering the three invariants P GG T , Q GG T , and R GG T of the tensorGG T , and imposing the proper cubic near-wall behavior, i.e., , we deduce that the eddy-viscosity is given by . Moreover, only R GG T -dependent models, i.e., p > - 5/2, switch off for 2D flows. Finally, the model constant may be related with the Vreman’s model constant via ; this guarantees both numerical stability and that the models have less or equal dissipation than Vreman’s model, i.e., . The performance of the proposed models is successfully tested for decaying isotropic turbulence and a turbulent channel flow. The former test-case has revealed that the model constant, C s3pqr , should be higher than 0.458 to obtain the right amount of subgrid-scale dissipation, i.e., C s3pq = 0.572 (p = - 5/2), C s3pr = 0.709 (p = - 1), and C s3qr = 0.762 (p = 0).

Copyright 2015 AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing.]]>

Physics of fluids

Vol. 26, p. 125110-1-125110-22

DOI: 10.1063/1.4904415

Date of publication: 2014-12-23

Abstract:

It is well known that the flow past a circular cylinder at critical Reynolds number combines flow separation, turbulence transition, reattachment of the flow, and further turbulent separation of the boundary layer. The transition to turbulence in the boundary layer causes the delaying of the separation point and an important reduction of the drag force on the cylinder surface known as the drag crisis. In the present work, large-eddy simulations of the flow past a cylinder at Reynolds numbers in the range 2.5 × 105-6.5 × 105 are performed. It is shown how the pressure distribution changes as the Reynolds number increases in an asymmetric manner, occurring first on one side of the cylinder and then on the other side to complete the drop in the drag up to 0.23 at Re = 6.5 × 105. These variations in the pressure profile are accompanied by the presence of a small recirculation bubble, observed as a small plateau in the pressure, and located around ¿ = 105° (measured from the stagnation point). This small recirculation bubble anticipated by the experimental measurements is here well captured by the present computations and its position and size measured at every Reynolds number. The changes in the wake configuration as the Reynolds number increases are also shown and their relation to the increase in the vortex shedding frequency is discussed. The power spectra for the velocity fluctuations are computed. The analysis of the resulting spectrum showed the footprint of Kelvin-Helmholtz instabilities in the whole range. It is found that the ratio of these instabilities frequency to the primary vortex shedding frequency matches quite well the scaling proposed by Prasad and Williamson [“The instability of the separated shear layer from a bluff body,” Phys. Fluids 8, 1347 (1996); “The instability of the shear layer separating from a bluff body,” J. Fluid Mech. 333, 375–492 (1997)] (f KH /fvs ¿ Re 0.67).]]>

Physics of fluids

Vol. 25, num. 8, p. 085109-085109-21

DOI: 10.1063/1.4818641

Date of publication: 2013-08-23

Abstract:

The presence of low-frequency fluctuations in the wake of bluff bodies have been observed in several investigations. Even though the flow past a circular cylinder at Re = 3900 (Re = UrefD/¿) has been the object of several experimental and numerical investigations, there is a large scattering in the average statistics in the near wake. In the present work, the flow dynamics of the near wake region behind a circular cylinder has been investigated by means of direct numerical simulations and statistics have been computed for more than 858 shedding cycles. The analysis of instantaneous velocity signals of several probes located in the vortex formation region, point out the existence of a low-frequency fluctuation at the non-dimensional frequency of fm = 0.0064. This large-scale almost periodic motion seems to be related with the modulation of the recirculation bubble which causes its shrinking and enlargement over the time. Two different configurations have been identified: (i) a high-energy mode with larger fluctuations in the shear-layer and in the vortex formation region (Mode H) and (ii) a low-energy mode with weaker fluctuations in the shear layer (Mode L). The influence of such a low-frequency in the wake topology has been studied not only by means of the phase-average flow field for each mode, but also by the analysis of the time-average first- and second-order statistics of each wake mode. The results are compared with the long-term averaged solution and with results in the existing literature.

Electronic version of an article published as "Physics of fluids", vol. 25, no 8, 2013. DOI: http://dx.doi.org/10.1063/1.4818641.

The presence of low-frequency fluctuations in the wake of bluff bodies have been observed in several investigations. Even though the flow past a circular cylinder at Re = 3900 (Re = U ref D/ν) has been the object of several experimental and numerical investigations, there is a large scattering in the average statistics in the near wake. In the present work, the flow dynamics of the near wake region behind a circular cylinder has been investigated by means of direct numerical simulations and statistics have been computed for more than 858 shedding cycles. The analysis of instantaneous velocity signals of several probes located in the vortex formation region, point out the existence of a low-frequency fluctuation at the non-dimensional frequency of f m = 0.0064. This large-scale almost periodic motion seems to be related with the modulation of the recirculation bubble which causes its shrinking and enlargement over the time. Two different configurations have been identified: (i) a high-energy mode with larger fluctuations in the shear-layer and in the vortex formation region (Mode H) and (ii) a low-energy mode with weaker fluctuations in the shear layer (Mode L). The influence of such a low-frequency in the wake topology has been studied not only by means of the phase-average flow field for each mode, but also by the analysis of the time-average first- and second-order statistics of each wake mode. The results are compared with the long-term averaged solution and with results in the existing literature.]]>