Session F11: Turbulence: Modeling & Simulations III: LES and Stochastic Models

Slow-growth approximation for near-wall patch representation of wall-bounded turbulence

Recent experimental and computational studies have demonstrated that wall-bounded turbulent shear flows

exhibit universal small-scale dynamics that are modulated by large-scale flow structures. Strong pressure gradients,

however, complicate this characterization and can cause significant variation of the mean flow in the streamwise

direction. For such situations, we perform asymptotic analysis of the Navier-Stokes equations valid whenever the

viscous length scale is small relative to the length scale over which the mean flow varies. The asymptotics inform

a model for the effect of mean flow growth on near-wall turbulence in a small domain localized to the boundary whose

size scales in viscous units. To ensure the correct momentum environment, a dynamic procedure is introduced that accounts

for the additional sources of mean momentum flux through the upper domain boundary arising from the asymptotic terms.

Comparisons of the model's low-order, single-point statistics with those from direct numerical simulation and wall-

resolved large eddy simulation of adverse pressure gradient boundary layers indicate the asymptotic model successfully

accounts for the effect of boundary layer growth on the small-scale near-wall turbulence, even in the absence of

large-scale structures.   

Fourier Modes in the SPOD Formalism on Aperiodic Domains

In the current work the effect of the use of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. This approach to turbulence decomposition was introduced in [Lumley, 1967] and has more recently become known as Spectral POD (SPOD), [Towne et al., 2018]. The Fourier decomposition in the SPOD method is conventionally applied in the temporal coordinate direction for stationary flows as well as along any homogeneous directions. We reconsider the derivations underlying the conclusions that the Fourier basis is a solution to the POD integral eigenvalue problem along homogeneous (non-periodic)/stationary coordinate directions. We show theoretically that the POD modes do not reduce to Fourier modes along aperiodic coordinates, meaning that Fourier modes cannot formally be considered as solutions to the POD integral eigenvalue problem in this case. This fact is substantiated by numerical analyses of numerical POD modes related to various operators with displacement invariant kernels on aperiodic domains. Furthermore, we quantify the deviation between the numerical modes and Fourier modes for various kernels of the POD integral operator in order to evaluate the approximation accuracy of the Fourier bases in those cases.

[Lumley, 1967] Lumley, J. L. (1967). The structure of inhomogeneous turbulent flows. In Atmospheric turbulence and radio wave propagation, pages 166–178. Nauka, Moscow.

[Towne et al., 2018] Towne, A., Schmidt, O. T., and Colonius, T. (2018). Spectral proper orthogonal decomposition and its relationship to dynamic mode decomposition and resolvent analysis. Journal of Fluid Mechanics, 847:821–867.   

Turbulent mixing simulation of variable Sc flows using the Hierarchical Parcel Swapping (HiPS) model

The Heirarchical Parcel Swapping (HiPS) model is a minimal reduced-order stochastic model for simulating turbulent mixing. HiPS is structured as a binary tree consisting of nodes that branch to fluid parcels at the base of the tree. The tree levels have a geometric progression of length scales, with timescales corresponding to inertial-range scaling. Simulations consist of swapping subtrees and repairing of fluid parcels that can then be mixed in several ways. HiPS can be used as a mixing model in PDF transport-type fluid simulations. Computational costs are similar to other popular methods, e.g., the Modified Curl's model, but with mixing that contains a range of length scales that reproduces key turbulent scalings, is local in scale space, and maintains plausible "closeness" in state space. We extend the HiPS model to treat mixing with scalars of arbitrary Sc. This is important in applications requiring differential diffusion, such as in metallic flows, combustion, or aerosol mixing. We present scalar energy spectra for mixing in the low and high Sc regimes and show that the HiPS model is able to recover the theoretical scalings. We also present results of the scalar dissipation rate including probability density functions and show that a nominally lognormal profile is recovered, with negative skewness that is consistent with detailed numerical and experimental studies. This is significant given the relative simplicity of the HiPS model, and provides insights that can be difficult to discern in high-fidelity experiments or simulations. We also present results of the Richardson dispersion and show that the model recovers the cubic power law. Discussion of the model and further application to reactive flows are discussed.   

Not Participating

Space-time energy spectra describe the distribution of energy density over space and time scales, which are fundamental to studying dynamic coupling at spatial and temporal scales and turbulence-generated noise. We develop a dynamic autoregressive (DAR) random forcing model for space-time energy spectra in turbulent shear flows. This model includes the two essential mechanisms of statistical decorrelation: the convection proposed by Taylor's model and the random sweeping proposed by the Kraichnan-Tennekes model. The new development is that DAR random forcing is introduced to represent the random sweeping effect. The resulting model can correctly reproduce the convection velocity and spectral bandwidths, while a white-in-time random forcing model makes erroneous predictions on spectral bandwidths. The DAR model is further combined with linear stochastic estimation (LSE) to reconstruct the near-wall velocity fluctuations of the desired space-time energy spectra. Direct numerical simulation (DNS) of turbulent channel flows is used to validate the DAR model and evaluate the Werner-Wengle wall model and the LSE approach. Both the wall model and LSE incorrectly estimate the spectral bandwidths.   

Laminar and Turbulent flow Behaviors in a 3-D Kinetic-based Discrete Dynamical System

A 3-D discrete dynamical system (DDS) has been derived in Fourier space based on the lattice Boltzmann equation (LBE) involving four bifurcation parameters, the relaxation time τ from the LBE, and the three wave-vector components k_x, k_y, and k_z. Numerical experiments employing combinations of these bifurcation parameters have produced laminar and turbulent flow behaviors such as periodic, subharmonic, n-period, quasiperiodic, noisy periodic with harmonics, noisy subharmonic, noisy quasiperiodic, and broadband. We now explore the underlying physics behind the observed flow behaviors in terms of the interactions among scales of motion, energy transport from large scale to small scale, etc. This DDS will be used to generate sub-grid scale (SGS) information in the large-eddy simulation of pulsatile turbulence in the LBE. The kinetic-based DDS, by nature of its construction, carries some large-scale information (as observed) not typically found in other similar DDSs. It is important to account for this when constructing SGS models so as not to count intermediate scales repeatedly.   

Two-Level Simulation of Transition to Turbulence in Wall-Bounded Flows

 

 

The two-level simulation (TLS) model is a multi-scale modeling strategy, which was originally developed for the simulation of high Reynolds number (Re) turbulent flows.  Compared to the large-eddy simulation (LES) strategy, where the effects of the unresolved small-scales of motion on the resolved large-scales of motion are modeled, in the TLS model, both large- and small-scales are explicitly solved. Furthermore, the TLS model does not employ the notion of spatial filtering and eddy viscosity, and therefore, it does not suffer from the limitations associated with the use of these concepts. Past studies have shown unique physics-based modeling capabilities of the TLS model for simulation of high Re fully developed turbulent flows, and recently, its ability to capture features of laminar-to-turbulent transition within the three-dimensional Taylor-Green vortex flow has also been demonstrated. The present study focuses on further evaluation of the TLS model by employing it as a near-wall model while performing LES of transitional wall-bounded flows. The results from the simulation of transition within the periodic channel flow at Re = 8000 are examined to understand the behavior of the large- and small-scale dynamics of the flow field during the temporal transition process.