Turbulence, Climate and Supercomputers

Turbulence is often referred to as the last mystery of classical physics. Although turbulence is ubiquitous and prominent in our daily lives – from the mixing of milk in a cup of coffee to the perpetual motion of the atmosphere and the resulting weather variation – our understanding of this complex phenomenon is comparatively very limited (e.g., Davidson et al., 2011)

LES of an Inclined Jet into a Supersonic Turbulent Crossflow

This short article describes flow parameters, numerical method, and animations of the fluid dynamics video "LES of an Inclined Jet into a Supersonic Turbulent Crossflow" (http://ecommons.library.cornell.edu/bitstream/1813/14073/3/GFM-2009.mpg [high-resolution] and http://ecommons.library.cornell.edu/bitstream/1813/14073/2/GFM-2009-web.m1v [low-resolution] video). We performed large-eddy simulation with the sub-grid scale (LES-SGS) stretched-vortex model of momentum and scalar transport to study the gas-dynamics interactions of a helium inclined round jet into a supersonic ($M=3.6$) turbulent (\Reth$=13\times10^3$) air flow over a flat surface. The video shows the temporal development of Mach-number and magnitude of density-gradient in the mid-span plane, and isosurface of helium mass-fraction and \lam_2 (vortical structures). The identified vortical structures are sheets, tilted tubes, and discontinuous rings. The vortical structures are shown to be well correlated in space and time with helium mass-fraction isosurface ($Y_{\rm He}=0.25$).Comment: 7 pages, 1 figure, 1 table, article describing fluid dynamics video submitted to Gallery of Fluid Motion, APS-DFD 200

Large-eddy simulation of mixing in a recirculating shear flow

The flow field and mixing in an expansion-ramp geometry is studied using large-eddy simulation (LES) with subgrid scale (SGS) modelling. The expansion-ramp geometry was developed to investigate enhanced mixing and flameholding characteristics while maintaining low total-pressure losses. Passive mixing was considered without taking into account the effects of chemical reactions and heat release, an approximation that is adequate for experiments conducted in parallel. The primary objective of the current work is to validate the LES–SGS closure in the case of passive turbulent mixing in a complex configuration and, if successful, to rely on numerical simulation results for flow details unavailable via experiment. Total (resolved-scale plus subgrid contribution) probability density functions (p.d.f.s) of the mixture fraction are estimated using a presumed beta-distribution model for the subgrid field. Flow and mixing statistics are in good agreement with the experimental measurements, indicating that the mixing on a molecular scale is correctly predicted by the LES– SGS model. Finally, statistics are shown to be resolution-independent by computing the flow for three resolutions, at twice and four times the resolution of the coarsest simulation

Mixing, scalar boundedness, and numerical dissipation in large-eddy simulations

Numerical schemes for scalar transport and mixing in turbulent flows must be high-order accurate, and observe conservation and boundedness constraints. Discretization accuracy can be evaluated from the truncation error, and assessed by its dispersion and dissipation properties. Dispersion errors can cause violation of physical scalar bounds, whereas numerical dissipation is key to mitigating those violations. Numerical dissipation primarily alters the energy at small scales that are critical to turbulent mixing. Influence of additional dissipation on scalar mixing in large-eddy simulations (LES) of incompressible temporally evolving shear flow is examined in terms of the resolved passive-scalar field, z. Scalar fields in flows with different mixing behavior, exhibiting both uniform and non-uniform mixed-fluid composition across a shear layer, are compared for different grid resolutions, subgrid-scale models, and scalar-convection schemes. Scalar mixing is assessed based on resolved passive scalar probability density function (PDF), variance, and spectra. The numerical-dissipation influence on mixing is found to depend on the nature of the flow. Mixing metrics sensitive to numerical dissipation are applied to examine the performance of limiting methods employed to mitigate unphysical scalar excursions. Two approaches, using a linear-scaling limiter for finite-volume schemes and a monotonicity-preserving limiter for finite-difference schemes, are studied. Their performance with respect to accuracy, conservation, and boundedness is discussed

Acceleration-driven variable-density turbulent flow

We discuss turbulent dynamics and mixing of a variable-density flow subject to a uniform-acceleration field. The flow and misalignments of pressure and density gradients are investigated for small to large density ratios, with evidence that the small-density ratio flow is described by the Boussinesq approximation. A new shear-layer growth rate is reported, along with an extension of uniform-density flow vorticity-alignment statistics in the variable-density ow studied. Spectra collapse when properly scaled for variable density

Large-Eddy Simulations of Molecular Mixing in a Recirculating Shear Flow

The flow field and mixing in an expansion-ramp geometry is studied using large-eddy simulation (LES) with subgrid scale (SGS) modeling based on the stretched-vortex model. The expansionramp geometry was developed to provide enhanced mixing and flameholding characteristics while maintaining low total-pressure losses, elements that are important in the design and performance of combustors for hypersonic air-breathing propulsion applications. The mixing was studied by tracking a passive scalar without taking into account the effects of chemical reactions and heat release. In order to verify the solver and the boundary closure implementation, a method utilizing results from linear stability analysis (LSA) theory is developed. LSA can be used to compute unstable perturbations to a flow, subject to certain approximations. The perturbations computed from LSA are used as an inflow condition to the flow computed by the solver been assessed. A projection based metric is constructed that only assumes the shape of the solution and not the growth rate of the perturbations, thus also allowing the latter to be determined as part of the verification. The growth rate of the perturbations for an unbounded (effectively) incompressible shear layer and a confined compressible shear layer is found to be in agreement with the prediction of the LSA. The flow and mixing predictions of the LES are in good agreement with experimental measurements. Total (resolved and subgrid) probability density functions (PDFs) of the passive scalar are estimated using an assumed beta-distribution model for the subgrid scalar field. The improved mixing characteristics of the expansion-ramp geometry compared to free shear layers are illustrated by the shapes of the PDFs. Moreover, the temperature rise and the probability of mixed fluid profiles are in good agreement with the experimental measurements, indicating that the mixing on a molecular scale is correctly predicted by the LES–SGS model. Finally, the predictions of the LES are shown to be resolution-independent. The mean fields and passive scalar PDFs have essentially converged at the two finer grid-resolutions used.</p