A new approach for treating boundaries in the context of LES
was developed to address issues related to the LES of
wall-bounded turbulence. In this approach treat the wall by
`filtering through it', so that in the LES representation,
the wall is not a sharp boundary. A homogeneous (or nearly
homogeneous) spatial filter is applied to an extended
domain, in which the wall is embedded. By treating the wall
in this way, the issue of highly inhomogeneous filtering
near a wall in LES can be avoided. When the filter is
applied to the Navier-Stokes equations, and the filtered
boundaries are accounted for, a boundary term appears in the
equations. The boundary term depends on the unfiltered wall
stress, which needs to be modeled. Thus two modeling
problems need to be addressed for LES of wall-bounded flows
in this context: the usual subgrid-scale modeling and
boundary stress modeling. We propose to use optimal LES
subgrid models, and a wall stress model formulated to
minimize the ``leakage'' of energy and momentum through the
filtered wall. This modeling approach was applied to
turbulent channel flow at Re_\tau=590, using a wall-normal
filter width of 38 + units, which effectively filters out
the near-wall dynamics. None-the-less, the LES yields good
results for both mean and rms velocities. These promising
results suggest that this modeling approach may provide a
solution to the well-known LES wall-modeling problem.
[ME.002] Higher entropy conservation and numerical stability of compressible turbulence simulations.
Albert Honein, Parviz Moin (Center for Turbulence Research, Stanford University)
We present a numerical formulation for the treatment of
nonlinear instabilities in shock-free compressible
turbulence simulations. The formulation is high order and
contains no artificial dissipation. Numerical stability is
enhanced through semi-discrete satisfaction of global
conservation properties stemming from the entropy equation.
The numerical implementation is achieved using a
conservative skew-symmetric splitting of the nonlinear
terms. The robustness of the method is demonstrated by
performing unresolved numerical simulations and large eddy
simulations of compressible isotropic turbulence at a very
high Reynolds number. Results show the scheme is capable of
capturing the statistical equilibrium of low Mach number
compressible turbulent fluctuations at infinite Reynolds
number. Comparisons with the entropy splitting technique [J.
Comput. Phys. 162 (2000) 33; J. Comput. Phys. 178 (2002)
307], staggered method [J. Comput. Phys. 191(2) (2003) 392],
and skew-symmetric like schemes [J. Comput. Phys. 161 (2000)
114] confirm the superiority of the current approach.
[ME.003] A robust, colocated, implicit algorithm for direct numerical simulation of compressible, turbulent flows
Yucheng Hou, Krishnan Mahesh (University of Minnesota)
A non-dissipative, robust, implicit algorithm is proposed
for direct numerical and large--eddy simulation of
compressible turbulent flows. The algorithm colocates
variables in space, but staggers the thermodynamic variables
in time. Also, the Navier--Stokes equations are
non--dimensionalized using an incompressible scaling for
pressure. As a result the incompressible Navier--Stokes
equations are recovered in the limit that the Mach number
tends to zero. A pressure--correction approach is used to
solve the resulting equations. The algorithm is not limited
by the acoustic time--scale at low Mach numbers, and is
discretely energy--conserving in the incompressible limit.
Results are shown for acoustic propagation, the
incompressible Taylor problem, periodic shock tube problem,
and isotropic turbulence.
[ME.004] The alignments of S_ij and \tau_ij in two-dimensional energy cascade
Minping Wan, Zuoli Xiao, Shiyi Chen (Department of Mechanical Engineering, the Johns Hopkins University), Gregory Eyink (Department of Applied Mathematics and Statistics, the Johns Hopkins University)
We study the inverse energy cascade in steady-state,
two-dimensional(2D) turbulence. We have performed numerical
simulations of small-scale forced Navier-Stokes equation at
resolutions up to 2048^2. Kraichnan's prediction of a -5/3
spectrum is verified with constant, negative energy flux.
The energy flux is derived to be the production of S_ij
and \tau_ij. The alignments of S_ij and \tau_ij
are discussed. A ``nonlinear model'' for the local energy flux
is derived with a new ``alpha-omega'' topological term. The
alignments of ``alpha-omega'' gradient are also discussed. The
evolution equation of energy flux is also derived and the
pressure term is found to give a big contribution.
[ME.005] A novel efficient pseudospedtral method for the DNS of turbulent flow in a wavy channel
Luo Wang, Antony Beris (Department of Chemical Engineering, University of Delaware)
A specially preconditioned BCGStab (Biconjugate Gradient)
method has been developed for the psudospectral solution of
nonseparable elliptic equations such as those arising from
the implicit solution of the Stokes component of the Navier
Stokes equations in a wavy channel after the application of
a non-orthogonal mapping to a rectangular domain. Two
different preconditioners have been developed: One using a
fast spectral solver for the unperturbed straight channel
and the other using a second order finite difference
solution to the full problem. Both have been proven
successful in obtaining in a computationally efficient
manner the pseudospectral solution of a general Helmholtz
equation within a wavy-walled channel geometry even in the
presence of significant wall wave undulation. This efficient
conjugate gradient solver has then been used to perform
pseudospectral DNS of a Newtonian turbulent flow in a
wavy-walled channel. The influence of the wave amplitude on
the structure of the turbulence is going to be discussed.
[ME.006] Simulations and Modeling of wall-bounded liquid-metal flows under the influence of a DC magnetic field.
Bernard Knaepen (Université Libre de Bruxelles, Brussels (Belgium)), Yves Dubief (Stanford University, Stanford (USA)), René Moreau (Institut National Polytechnique de Grenoble, Grenoble (France))
Conductive flows in wall-bounded geometries under the
influence of a strong applied external magnetic field are
encountered in many industrial applications such as steel
casting and coolant blankets in nuclear fusion devices
(tokamaks). These flows are characterized by the development
of very thin Hartmann layers on the walls perpendicular to
the magnetic field and a strong tendency towards
bi-dimensionalization of the core flow. To study the
dynamics of such flows, we perform a set of numerical
simulations in a cubic periodic domain. The effect of the
Hartmann layers is modelled by adding to the traditional
Joule dissipation some extra damping terms derived from the
dominant time scales of the flow and MHD. Using this model,
this simplified geometry allows the investigation of the 2D
nature of the core flow. The formalism of Large Eddy
Simulation is then applied to a more realistic geometry to
reproduce a MATUR cell in which the flow is contained in a
(flat) cylindrical container and rotationally driven by an
imposed electrical current. In this case, the Hartmann
layers are explicitly simulated.
[ME.007] Scaling and domain size effects in simulations of rotating turbulence
D.A. Donzis, P.K. Yeung (Georgia Tech), K.R. Sreenivasan (ICTP, Italy amp; U. Maryland)
Turbulence subjected to solid-body rotation is an important
non-equilibrium turbulent flow where substantial changes in
the flow structure arise but are not well understood. It is
well-known that rotation reduces spectral transfer and leads
to quasi-two-dimensionality with longer length scales along
the axis of rotation --- which raises questions about the
effects of periodic boundary conditions in direct numerical
simulations carried out on a finite-sized domain. We present
new results using a larger-than-usual domain size which
through improved sampling of the large scales also leads to
results of better statistical quality. We confirm and extend
several conclusions reached in recent work, including marked
anisotropy at the small scales, reduced intermittency in the
velocity gradients, and changes in alignment between
vorticity and strain rate giving reduced vortex stretching
and enstrophy production. The new results are up to 1024^3
in resolution and cover initial Taylor-scale Reynolds
numbers from 38 to about 240, with microscale Rossby numbers
from 1/4 to 4.
[ME.008] Simulation of Turbulent Flow over a Complex Geometry Using the Immersed Boundary Method and k-\varepsilon-v^2-f Model
Hyunchul Jang, Haecheon Choi (Seoul National University), Seokhyun Lim (Samsung Electronics)
An algorithm for combining the immersed boundary method with
the k-\varepsilon-v^2-f turbulence model is proposed in
the present study, in order to predict turbulent flow
over/inside a complex geometry. In this procedure, source
terms are provided to the u_i-, k-, \varepsilon- and
øverlinev^2-equations, respectively, to satisfy the
proper conditions at the immersed boundary, and mass
source/sink is applied to the continuity equation to satisfy
the local mass conservation. On the other hand, a
modification of matrix from a discretized f-equation is
performed to satisfy the boundary condition at the solid
surface. The present numerical method is applied to four
different separating flows: flows over a backward-facing
step, square cylinder, plane diffuser, and triangular
cylinder. For all the flows considered, the present results
show good agreements with the previous experimental and
numerical ones.
[ME.009] Computational Study of Aero-Optical Distortion by Turbulent Wake
Ali Mani (Stanford University), Meng Wang (Center for Turbulence Research, NASA Ames Res. Ctr./ Stanford Univ.), Parviz Moin (Stanford University)
Spatial variations of refractive index due to density fluctuations in a compressible turbulent flow may cause serious problems for optical systems. In general, distortion by turbulence results in coherence degradation of the optical beam, and leads to loss of intensity at distant locations. The objective of this study is to develop computational capability for aero-optical distortion caused by turbulent boundary layers and wakes around moving objects. In particular, we consider the compressible flow over a circular cylinder at Re_D=3900 and M=0.4. The flow solutions obtained by large-eddy simulation have been validated against previous experimental and numerical results. Ray tracing combined with Fourier optics is chosen as an efficient and accurate tool to simulate optical wave propagation. Statistics of optical aberration and it's correlation to flow motion will be presented. Our results indicate that for short wavelength beams, the far-field intensity pattern is seriously affected by the small scales of the flow, which places a more stringent grid-resolution requirement than that needed to capture the low order flow statistics.
Supported by AFOSR.
[ME.010] Dynamic backscatter for wall-layer models.
Anthony Keating, Ugo Piomelli (University of Maryland)
Early results in channel flow indicated that Detached-Eddy Simulations (DES) showed promise when used as a wall-layer model. However, a transition was observed where unresolved eddies in the URANS region are converted to the resolved eddies in the LES region, which causes a shift in the logarithmic layer, and skin-friction coefficient values too low by 15%. The inclusion of a backscatter model was found to improve the mean velocity profile and skin-friction coefficient; however, the backscatter was not based on a physical argument and trial-and-error was required to calculate its magnitude. Here we present a dynamic method of calculating the amplitude of the backscatter, based on the relative contribution of resolved and modeled shear stresses in the transition region where the model switches from URANS to LES. A controller is used to adjust dynamically the magnitude of the backscatter. The associated level of backscatter removes the shift in the log-layer, and improves the skin-friction coefficient, as well as the turbulence intensities. The method was found to be robust, performing well over a range of backscatter envelopes, Reynolds numbers and grids.