Spectral and hyper eddy viscosity in high-Reynolds-number turbulence

2000 ◽  
Vol 421 ◽  
pp. 307-338 ◽  
Author(s):  
STEFANO CERUTTI ◽  
CHARLES MENEVEAU ◽  
OMAR M. KNIO
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Strain Rate ◽  
High Reynolds Number ◽  
Eddy Viscosity ◽  
Isotropic Turbulence ◽  
Reynolds Numbers ◽  
Local Isotropy ◽  
Viscous Term ◽  
High Reynolds

For the purpose of studying the spectral properties of energy transfer between large and small scales in high-Reynolds-number turbulence, we measure the longitudinal subgrid-scale (SGS) dissipation spectrum, defined as the co-spectrum of the SGS stress and filtered strain-rate tensors. An array of four closely spaced X-wire probes enables us to approximate a two-dimensional box filter by averaging over different probe locations (cross-stream filtering) and in time (streamwise filtering using Taylor's hypothesis). We analyse data taken at the centreline of a cylinder wake at Reynolds numbers up to Rλ ∼ 450. Using the assumption of local isotropy, the longitudinal SGS stress and filtered strain-rate co-spectrum is transformed into a radial co-spectrum, which allows us to evaluate the spectral eddy viscosity, v(k, kΔ). In agreement with classical two-point closure predictions, for graded filters, the spectral eddy viscosity deduced from the box-filtered data decreases near the filter wavenumber kΔ. When using a spectral cutoff filter in the streamwise direction (with a box-filter in the cross-stream direction) a cusp behaviour near the filter scale is observed. In physical space, certain features of a wavenumber-dependent eddy viscosity can be approximated by a combination of a regular and a hyper-viscosity term. A hyper-viscous term is also suggested from considering equilibrium between production and SGS dissipation of resolved enstrophy. Assuming local isotropy, the dimensionless coefficient of the hyper-viscous term can be related to the skewness coefficient of filtered velocity gradients. The skewness is measured from the X-wire array and from direct numerical simulation of isotropic turbulence. The results show that the hyper-viscosity coefficient is negative for graded filters and positive for spectral filters. These trends are in agreement with the spectral eddy viscosity measured directly from the SGS stress–strain rate co-spectrum. The results provide significant support, now at high Reynolds numbers, for the ability of classical two-point closures to predict general trends of mean energy transfer in locally isotropic turbulence.

Spectral energy transfer in high Reynolds number turbulence

1977 ◽  
Vol 79 (2) ◽  
pp. 337-359 ◽  
Author(s):  
K. N. Helland ◽  
C. W. Van Atta ◽  
G. R. Stegen
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Energy Spectrum ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Second Order ◽  
Spectral Energy ◽  
Local Isotropy ◽  
High Reynolds ◽  
Good Agreement

The spectral energy transfer of turbulent velocity fields has been examined over a wide range of Reynolds numbers by experimental and empirical methods. Measurements in a high Reynolds number grid flow were used to calculate the energy transfer by the direct Fourier-transform method of Yeh & Van Atta. Measurements in a free jet were used to calculate energy transfer for a still higher Reynolds number. An empirical energy spectrum was used in conjunction with a local self-preservation approximation to estimate the energy transfer at Reynolds numbers beyond presently achievable experimental conditions.Second-order spectra of the grid measurements are in excellent agreement with local isotropy down to low wavenumbers. For the first time, one-dimensional third-order spectra were used to test for local isotropy, and modest agreement with the theoretical conditions was observed over the range of wavenumbers which appear isotropic according to second-order criteria. Three-dimensional forms of the measured spectra were calculated, and the directly measured energy transfer was compared with the indirectly measured transfer using a local self-preservation model for energy decay. The good agreement between the direct and indirect measurements of energy transfer provides additional support for both the assumption of local isotropy and the assumption of self-preservation in high Reynolds number grid turbulence.An empirical spectrum was constructed from analytical spectral forms of von Kármán and Pao and used to extrapolate energy transfer measurements at lower Reynolds number to Rλ = 105 with the assumption of local self preservation. The transfer spectrum at this Reynolds number has no wavenumber region of zero net spectral transfer despite three decades of $k^{-\frac{5}{3}}$. behaviour in the empirical energy spectrum. A criterion for the inertial subrange suggested by Lumley applied to the empirical transfer spectrum is in good agreement with the $k^{-\frac{5}{3}}$ range of the empirical energy spectrum.

Numerical calculation of decaying isotropic turbulence using the LET theory

1984 ◽  
Vol 143 ◽  
pp. 95-123 ◽  
Author(s):  
W. D. Mccomb ◽  
V. Shanmugasundaram
Keyword(s):  
Reynolds Number ◽  
Energy Transfer ◽  
Energy Dissipation ◽  
Isotropic Turbulence ◽  
Direct Interaction ◽  
Reynolds Numbers ◽  
Energy Dissipation Rate ◽  
Skewness Factor ◽  
Decaying Turbulence ◽  
High Reynolds

The local-energy-transfer (LET) theory (McComb 1978) was used to calculate freely decaying turbulence for four different initial spectra at low-to-moderate values of microscale Reynolds numbers (Rλ up to about 40). The results for energy, dissipation and energy-transfer spectra and for skewness factor all agreed quite closely with the predictions of the well-known direct-interaction approximation (DIA: Kraichnan 1964). However, LET gave higher values of energy transfer and of evolved skewness factor than DIA. This may be related to the fact that LET yields the k−5/3 law for the energy spectrum at infinite Reynolds number.The LET equations were then integrated numerically for decaying isotropic turbulence at high Reynolds number. Values were obtained for the wavenumber spectra of energy, dissipation rate and inertial-transfer rate, along with the associated integral parameters, at an evolved microscale Reynolds number Rλ of 533. The predictions of LET agreed well with experimental results and with the Lagrangian-history theories (Herring & Kraichnan 1979). In particular, the purely Eulerian LET theory was found to agree rather closely with the strain-based Lagrangian-history approximation; and further comparisons suggested that this agreement extended to low Reynolds numbers as well.

Stability of non-parabolic flow in a flexible tube

1999 ◽  
Vol 395 ◽  
pp. 211-236 ◽  
Author(s):  
V. SHANKAR ◽  
V. KUMARAN
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Flexible Tube ◽  
Developing Flow ◽  
Parabolic Flow ◽  
High Reynolds ◽  
The Stability

Flows with velocity profiles very different from the parabolic velocity profile can occur in the entrance region of a tube as well as in tubes with converging/diverging cross-sections. In this paper, asymptotic and numerical studies are undertaken to analyse the temporal stability of such ‘non-parabolic’ flows in a flexible tube in the limit of high Reynolds numbers. Two specific cases are considered: (i) developing flow in a flexible tube; (ii) flow in a slightly converging flexible tube. Though the mean velocity profile contains both axial and radial components, the flow is assumed to be locally parallel in the stability analysis. The fluid is Newtonian and incompressible, while the flexible wall is modelled as a viscoelastic solid. A high Reynolds number asymptotic analysis shows that the non-parabolic velocity profiles can become unstable in the inviscid limit. This inviscid instability is qualitatively different from that observed in previous studies on the stability of parabolic flow in a flexible tube, and from the instability of developing flow in a rigid tube. The results of the asymptotic analysis are extended numerically to the moderate Reynolds number regime. The numerical results reveal that the developing flow could be unstable at much lower Reynolds numbers than the parabolic flow, and hence this instability can be important in destabilizing the fluid flow through flexible tubes at moderate and high Reynolds number. For flow in a slightly converging tube, even small deviations from the parabolic profile are found to be sufficient for the present instability mechanism to be operative. The dominant non-parallel effects are incorporated using an asymptotic analysis, and this indicates that non-parallel effects do not significantly affect the neutral stability curves. The viscosity of the wall medium is found to have a stabilizing effect on this instability.

scholarly journals Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal

2019 ◽  
Vol 9 (4) ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P. K. Yeung
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Isotropic Turbulence ◽  
High Reynolds

scholarly journals On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high-Reynolds-number flow over an Ahmed body

2014 ◽  
Vol 747 ◽  
pp. 518-544 ◽  
Author(s):  
Jan Östh ◽  
Bernd R. Noack ◽  
Siniša Krajnović ◽  
Diogo Barros ◽  
Jacques Borée
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Eddy Viscosity ◽  
Initial Conditions ◽  
Base Flow ◽  
Reduced Order ◽  
State Dependent ◽  
Galerkin Models ◽  
High Reynolds ◽  
Ahmed Body

AbstractWe investigate a hierarchy of eddy-viscosity terms in proper orthogonal decomposition (POD) Galerkin models to account for a large fraction of unresolved fluctuation energy. These Galerkin methods are applied to large eddy simulation (LES) data for a flow around a vehicle-like bluff body called an Ahmed body. This flow has three challenges for any reduced-order model: a high Reynolds number, coherent structures with broadband frequency dynamics, and meta-stable asymmetric base flow states. The Galerkin models are found to be most accurate with modal eddy viscosities as proposed by Rempfer & Fasel (J. Fluid Mech., vol. 260, 1994a, pp. 351–375; J. Fluid Mech. vol. 275, 1994b, pp. 257–283). Robustness of the model solution with respect to initial conditions, eddy-viscosity values and model order is achieved only for state-dependent eddy viscosities as proposed by Noack, Morzyński & Tadmor (Reduced-Order Modelling for Flow Control, CISM Courses and Lectures, vol. 528, 2011). Only the POD system with state-dependent modal eddy viscosities can address all challenges of the flow characteristics. All parameters are analytically derived from the Navier–Stokes-based balance equations with the available data. We arrive at simple general guidelines for robust and accurate POD models which can be expected to hold for a large class of turbulent flows.

An Intermittent High-Reynolds-Number Wind Tunnel

1977 ◽  
Vol 28 (4) ◽  
pp. 259-264 ◽  
Author(s):  
J L Stollery ◽  
A V Murthy
Keyword(s):  
Reynolds Number ◽  
Wind Tunnel ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Simple Method ◽  
High Reynolds Numbers ◽  
Reservoir Conditions ◽  
High Reynolds ◽  
Cryogenic Wind Tunnel ◽  
Performance Estimates

SummaryThe paper suggests a simple method of generating intermittent reservoir conditions for an intermittent, cryogenic wind tunnel. Approximate performance estimates are given and it is recommended that further studies be made because this type of tunnel could be valuable in increasing the opportunities for research at high Reynolds numbers.

scholarly journals Lattice Boltzmann Method Simulations of High Reynolds Number Flows Past Porous Obstacles

2019 ◽  
Vol 11 (03) ◽  
pp. 1950028 ◽  
Author(s):  
N. M. Sangtani Lakhwani ◽  
F. C. G. A. Nicolleau ◽  
W. Brevis
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
High Reynolds Number ◽  
Reynolds Numbers ◽  
Navier Stokes Equation ◽  
High Reynolds ◽  
Boltzmann Method ◽  
Reynolds Number Flows

Lattice Boltzmann Method (LBM) simulations for turbulent flows over fractal and non-fractal obstacles are presented. The wake hydrodynamics are compared and discussed in terms of flow relaxation, Strouhal numbers and wake length for different Reynolds numbers. Three obstacle topologies are studied, Solid (SS), Porous Regular (PR) and Porous Fractal (FR). In particular, we observe that the oscillation present in the case of the solid square can be annihilated or only pushed downstream depending on the topology of the porous obstacle. The LBM is implemented over a range of four Reynolds numbers from 12,352 to 49,410. The suitability of LBM for these high Reynolds number cases is studied. Its results are compared to available experimental data and published literature. Compelling agreements between all three tested obstacles show a significant validation of LBM as a tool to investigate high Reynolds number flows in complex geometries. This is particularly important as the LBM method is much less time consuming than a classical Navier–Stokes equation-based computing method and high Reynolds numbers need to be achieved with enough details (i.e., resolution) to predict for example canopy flows.

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