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.

Turbulent boundary layer at very high Reynolds number and its relation to the initial conditions

2001 ◽  
Author(s):  
Luciano Castillo ◽  
Junghwa Seo ◽  
David Walker ◽  
Gunnar Johansson ◽  
Horia Hangan ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
High Reynolds Number ◽  
Initial Conditions ◽  
High Reynolds ◽  
Very High

A new k-ϵ eddy viscosity model for high reynolds number turbulent flows

1995 ◽  
Vol 24 (3) ◽  
pp. 227-238 ◽  
Author(s):  
Tsan-Hsing Shih ◽  
William W. Liou ◽  
Aamir Shabbir ◽  
Zhigang Yang ◽  
Jiang Zhu
Keyword(s):  
Reynolds Number ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Eddy Viscosity ◽  
Viscosity Model ◽  
Eddy Viscosity Model ◽  
High Reynolds

Eddy viscosity of cellular flows

2001 ◽  
Vol 446 ◽  
pp. 173-198 ◽  
Author(s):  
ALEXEI NOVIKOV ◽  
GEORGE PAPANICOLAOU
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Eddy Viscosity ◽  
Variational Principles ◽  
Stokes Equations ◽  
Stationary Solutions ◽  
Effective Coefficients ◽  
Cellular Flows ◽  
High Reynolds

We analyse modulational (large-scale) perturbations of stationary solutions of the two-dimensional incompressible Navier–Stokes equations. The stationary solutions are cellular flows with stream function ϕ = sin y1 sin y2 + δ cos y1 cos y2, 0 [les ] δ [les ] 1. Using multiscale techniques we derive effective coefficients, including the eddy viscosity tensor, for the (averaged) modulation equations. For cellular flows with closed streamlines we give rigorous asymptotic bounds at high Reynolds number for the tensor of eddy viscosity by means of saddle-point variational principles. These results allow us to compare the linear and nonlinear modulational stability of cellular flows with no channels and of shear flows at high Reynolds number. We find that the geometry of the underlying cellular flows plays an important role in the stability of the modulational perturbations. The predictions of the multiscale analysis are compared with direct numerical simulations.

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.

On drag reduction scaling and sustainability bounds of superhydrophobic surfaces in high Reynolds number turbulent flows

2019 ◽  
Vol 864 ◽  
pp. 327-347 ◽  
Author(s):  
Amirreza Rastegari ◽  
Rayhaneh Akhavan
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Turbulent Flows ◽  
High Reynolds Number ◽  
Scaling Laws ◽  
Base Flow ◽  
Geometrical Parameters ◽  
Pressure Stability ◽  
High Reynolds

The drag reduction characteristics and sustainability bounds of superhydrophobic (SH) surfaces in high Reynolds number turbulent flows are investigated using results from direct numerical simulation (DNS) and scaling-law analysis. The DNS studies were performed, using lattice Boltzmann methods, in turbulent channel flows at bulk Reynolds numbers of $Re_{b}=3600$ ($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 222$) and $Re_{b}=7860$ ($Re_{\unicode[STIX]{x1D70F}_{0}}\approx 442$) with SH longitudinal microgrooves or SH aligned microposts on the walls. Surface microtexture geometrical parameters corresponding to microgroove widths or micropost spacings of $4\lesssim g^{+0}\lesssim 128$ in base flow wall units and solid fractions of $1/64\leqslant \unicode[STIX]{x1D719}_{s}\leqslant 1/2$ were investigated at interface protrusion angles of $\unicode[STIX]{x1D703}_{p}=0^{\circ }$ and $\unicode[STIX]{x1D703}_{p}=-30^{\circ }$. Analysis of the governing equations and DNS results shows that the magnitude of drag reduction is not only a function of the geometry and size of the surface microtexture in wall units, but also the Reynolds number of the base flow. A Reynolds number independent measure of drag reduction can be constructed by parameterizing the magnitude of drag reduction in terms of the friction coefficient of the base flow and the shift, $(B-B_{0})$, in the intercept of a logarithmic law representation of the mean velocity profile in the flow with SH walls compared to the base flow, where $(B-B_{0})$ is Reynolds number independent. The scaling laws for $(B-B_{0})$, in terms of the geometrical parameters of the surface microtexture in wall units, are presented for SH longitudinal microgrooves and aligned microposts. The same scaling laws are found to also apply to liquid-infused (LI) surfaces as long as the viscosity ratios are large, $N\equiv \unicode[STIX]{x1D707}_{o}/\unicode[STIX]{x1D707}_{i}\gtrsim 10$. These scaling laws, in conjunction with the parametrization of drag reduction in terms of $(B-B_{0})$, allow for a priori prediction of the magnitude of drag reduction with SH or LI surfaces in turbulent flow at any Reynolds number. For the most stable of these SH surface microtextures, namely, longitudinal microgrooves, the pressure stability bounds of the SH surface under the pressure loads of turbulent flow are investigated. It is shown that the pressure stability bounds of SH surfaces are also significantly curtailed with increasing Reynolds number of the flow. Using these scaling laws, the narrow range of SH surface geometrical parameters which can yield large drag reduction as well as sustainability in high Reynolds number turbulent flows is identified.

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