The structure

Rayleigh–Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II

Rayleigh-Taylor and Richtmyer-Meshkov instabilities: A journey through scales

In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this, we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closure which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical k−3 scaling in Kraichnan turbulence.

Data-driven deconvolution for large eddy simulations of Kraichnan turbulence

In diverse areas of science and technology, including inertial confinement fusion (ICF), astrophysics, geophysics, and engineering processes, turbulent mixing induced by hydrodynamic instabilities is of scientific interest as well as practical significance. Because of the fundamental roles they often play in ICF and other applications, three classes of hydrodynamic instability-induced turbulent flows—those arising from the Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities—have attracted much attention. ICF implosions, supernova explosions, and other applications illustrate that these phases of instability growth do not occur in isolation, but instead are connected so that growth in one phase feeds through to initiate growth in a later phase. Essentially, a description of these flows must encompass both the temporal and spatial evolution of the flows from their inception. Hydrodynamic instability will usually start from potentially infinitesimal spatial perturbations, will eventually transition to a turbulent flow, and then will reach a final state of a true multiscale problem. Indeed, this change in the spatial scales can be vast, with hydrodynamic instability evolving from just a few microns to thousands of kilometers in geophysical or astrophysical problems. These instabilities will evolve through different stages before transitioning to turbulence, experiencing linear, weakly, and highly nonlinear states. The challenges confronted by researchers are enormous. The inherent difficulties include characterizing the initial conditions of such flows and accurately predicting the transitional flows. Of course, fully developed turbulence, a focus of many studies because of its major impact on the mixing process, is a notoriously difficult problem in its own right. In this pedagogical review, we will survey challenges and progress, and also discuss outstanding issues and future directions.In diverse areas of science and technology, including inertial confinement fusion (ICF), astrophysics, geophysics, and engineering processes, turbulent mixing induced by hydrodynamic instabilities is of scientific interest as well as practical significance. Because of the fundamental roles they often play in ICF and other applications, three classes of hydrodynamic instability-induced turbulent flows—those arising from the Rayleigh-Taylor, Richtmyer-Meshkov, and Kelvin-Helmholtz instabilities—have attracted much attention. ICF implosions, supernova explosions, and other applications illustrate that these phases of instability growth do not occur in isolation, but instead are connected so that growth in one phase feeds through to initiate growth in a later phase. Essentially, a description of these flows must encompass both the temporal and spatial evolution of the flows from their inception. Hydrodynamic instability will usually start from potentially infinitesimal spatial perturbations, will eventually t...

Turbulent Mixing and Transition Criteria of Flows Induced by Hydrodynamic Instabilities

Numerical investigations on a supersonic turbulent boundary layer over a longitudinal curved compression ramp are conducted using direct numerical simulation for a free stream Mach number M∞ = 2.9 and Reynolds number Reθ = 2300. The total turning angle is 24°, and the concave curvature radius is 15 times the thickness of the incoming turbulent boundary layer. Under the selected conditions, the shock foot is transferred to a fan of the compression wave because of the weaker adverse pressure gradient. The time-averaged flow-field in the curved ramp is statistically attached where the instantaneous flow-field is close to the intermittent transitory detachment state. Studies on coherent vortex structures have shown that large-scale vortex packets are enhanced significantly when the concave curvature is aligned in the spanwise direction. Consistent with findings of previous experiments, the effect of the concave curvature on the logarithmic region of the mean velocity profiles is found to be small. The intensi...

Direct numerical simulation of supersonic turbulent boundary layer subjected to a curved compression ramp

Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner:Turning angle effects

The proportionality between the subgrid-scale (SGS) drain rate of kinetic energy and the viscous dissipation rate of the resolved motions is studied a priori by filtering a given fully resolved field and evaluating a generic form of the hypothesized energy spectrum. The ratio of the SGS drain to the resolved dissipation, on which a balance condition for the SGS dissipation across an arbitrary grid scale is founded, is shown to be independent of the turbulence Reynolds number, and can be described by a function in terms of the averaged mesh Reynolds number. Such a balance condition can serve as a physical constraint in the SGS modeling to account for the scale effects of the model coefficient(s). Scale-adaptive dynamic Smagorinsky-Lilly model and mixed nonlinear model are formulated for large-eddy simulation of transitional and/or turbulent flows in such a way that the constraint is satisfied. The newly proposed scale-adaptive dynamic SGS models are validated in simulations of homogeneous isotropic turbule...

Scale-adaptive subgrid-scale modelling for large-eddy simulation of turbulent flows

A novel eddy-viscosity closure is proposed for the subgrid-scale (SGS) stress tensor in large-eddy simulation of helical turbulence. The eddy-viscosity is shown to be proportional to the product of the large-scale velocity strain rate tensor and the symmetric part of the large-scale vorticity gradient (or vorticity strain rate tensor) based on a SGS helicity dissipation balance and a spectral relative helicity relation. The new SGS model is first tested and validated in simulation of homogeneous and isotropic helical turbulence. The statistical results demonstrate that the present model can predict both the energy and helicity spectra more precisely than the dynamic Smagorinsky model and a mixed helical model as compared with the results calculated in direct numerical simulation. Then, a compressible version of the new SGS model is parameterized and utilized to simulate the compressible flow past a circular cylinder. It is found that the present eddy-viscosity model can reproduce the skin friction force m...

Subgrid-scale eddy viscosity model for helical turbulence

Helmholtz decomposition is applied to investigate the compressibility effect in hypersonic turbulent boundary layers The dilatational component of flow plays an important role in the near-wall region, while the solenoidal component is dominant far from the wall The cold wall condition significantly enhances the compressibility, and especially enhances compression motions near the wall

Changping Yu

Papers

Direct numerical simulation of supersonic turbulent boundary layer subjected to a curved compression ramp

Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner:Turning angle effects

Scale-adaptive subgrid-scale modelling for large-eddy simulation of turbulent flows

Subgrid-scale eddy viscosity model for helical turbulence

Compressibility effect in hypersonic boundary layer with isothermal wall condition