Large Eddy Simulation of Rotating Turbulence

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Large Eddy Simulation of Rotating Turbulence

• Hao Lu, Christopher J. Rutland and Leslie M.
  Smith
• Sponsored by NSF

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Project Summary
Broader Impact Rotating turbulence has a wide
range of application in engineering science, geo-
and astrophysics. It provides a simple setup to
study the characteristic properties of
homogeneous but anisotropic turbulence flows. One
of the most important applications is the
development and design of turbo-machinery. The
detailed understanding of the consequences of
rotation on the flow characteristics is important
for an advanced layout of these machines. The
whole field of geophysics is crucially determined
by our planets rotation, which influences both
atmospheric and oceanic flows, effecting global
climate as well as short-term weather
forecasting. Understanding the fundamental
processes forms the basis for a detailed analysis
of complex phenomena such as the development of
climate anomalies (El Niño), the formation of
hurricanes and tidal waves, the spreading of
pollutants or the oceanic circulation of
nutrients.

• Research Objectives
• Direct numerical simulation (DNS) of rotating
  turbulence We have small scale forced cases,
  large scale forced cases and decaying cases. DNS
  provides data for LES model development.
• Developing sub-grid scale models Model has the
  capability to capture small-scale turbulence
  properties, reverse energy transfer from small to
  large scales, and length scale anisotropy of
  rotating turbulence.

• Approach
• Pseudo-spectral method, Gaussian white noise
  forcing scheme, and various spatial filters are
  used in this work. Fundamental analyses, such as
  the invariance of models, anisotropy of rotating
  turbulence, and correlation/regression studies,
  are employed.
• A-priori test of various models.
• A-posteriori test of various models.

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Forced rotating turbulence
Energy Spectrum
Energy Spectrum
Development of cyclonic two-dimensional coherent
structures appearing in rotating turbulence as
indicated by iso-surfaces of vorticity, contours
of kinetic energy and velocity vectors (a)
initial very low energy level isotropic
turbulence (b) final state (at normalized time
3.88) of large scale forced rotating case (c)
final state (at normalized time 3.68) of small
scale forced rotating case.
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Description of structure models
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Scatter plot of ?11 by SCDSM
Scatter plot analysis, and correlation/regression
analysis. The correlation coefficient can
represent the variance between the modeled and
the exact terms on the scatter plot and on the
PDF diagram. The regression coefficient can
represent the contour level ratio between the
modeled and the exact terms, the slope of the
regression (scatter) line.
Comparison of contour plots of SGS stress ?11
(left) and similarity type consistent dynamic
structure modeled stress ?11SCDSM (right) at z0
layer. Flow is the small scale forced case ( (c)
at slide 2). Cutoff wave-number k11.6.
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A-priori test
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Conclusion

• Models those are not consistent with MFI cannot
  give high correlation and regression level at
  rotation direction.
• The SGS stress tensor predicted by eddy viscosity
  models is uncorrelated with the stress tensor.
• Dynamic structure models yield very close energy
  flux prediction. Also, two new consistent models
  increase regression coefficients at all special
  directions when compared with other models. They
  improve the correlations significantly comparing
  with eddy viscosity models for a wide range of
  filter size. These results demonstrate their
  capabilities in capture of SGS dynamics.

Ongoing work

• Grid resolution effects on LES models.
• A-posteriori test of LES models
• Decaying isotropic and rotating turbulence.
• For one-equation models, reverse energy transfers
  via forcing at sub-grid scales (at SGS kinetic
  energy equation).
• Large scale forced testing.

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