A Novel Multi-scale Simulation Strategy for Turbulent Reacting Flows

A stochastic modeling approach, the so‐called One‐Dimensional Turbulence (ODT), is used to study passive scalar transport in incompressible, fully‐developed, turbulent channel flows up to very high Schmidt numbers Sc = ν/Γ ∼ 104 (kinematic viscosity ν, scalar diffusivity Γ). Good agreement is obtained between ODT and Direct Numerical Simulation (DNS) results with respect to the mean, the fluctuation statistics, and the dimensionless mass transfer coefficient K+. ODT yields the mass transfer coefficient to become independent of the Reynolds number at high Schmidt numbers, which is similar to reference laboratory measurements and DNS. The present ODT results exhibit the power law K+ ∝ Sc−0.65 with a scaling exponent that is only slightly larger than in the reference laboratory measurements and DNS. The results obtained suggests that ODT can be a versatile tool for turbulent transport modeling in a wide range of physical parameters. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

ABSTRACTThe incompressible temporally developing turbulent boundary layer (TBL) is analysed using the map-based stochastic one-dimensional turbulence (ODT) model. The TBL is a canonical flow problem, which is, in the present study, formed by a planar moving wall and a free stream at rest. An understanding of this idealised flow is of fundamental relevance for the numerical analysis of turbulent boundary-layer-type flows. In the present ODT simulations, the flow variables are resolved on all scales along a wall-normal, one-dimensional domain. These variables are evolved by a deterministic and a stochastic process. The latter models the effect of turbulent advection and pressure fluctuations, whereas the former represents molecular diffusion. The model is appropriate for high Reynolds numbers for which the turbulence field exhibits a broad range of scales and is notionally featureless. We show that ODT is able to capture salient features of the TBL by comparing the various statistics with available reference direct numerical simulation (DNS) results for different bulk Reynolds numbers in the range using fixed model parameters. The influence of the model parameters is analysed for and optimal parameter values are provided. The results discussed in this paper suggest that ODT is an economical and reasonably accurate approach for the simulation of transient turbulent boundary-layer-type flows.

A parameterization of the composition space based on principal component analysis (PCA) is proposed to represent the transport equations with the one-dimensional turbulence (ODT) solutions of a hybrid large-eddy simulation (LES) and ODT scheme. The 1D ODT solutions are embedded in the 3D LES domain and solve for thermo-chemical scalars; while, the LES governing equations solve for the flow. An a priori validation of the proposed approach is implemented based on stand-alone ODT solutions of the Sandia Flame F, which is characterized by different regimes of combustion starting with pilot stabilization, to extinction and reignition and self-stabilized combustion. The PCA analysis is carried out with a full set of the thermo-chemical scalars’ vector as well as a subset of this vector. The subset is made up primarily of major species and temperature. The results show that the different regimes are reproduced using only three principal components for the thermo-chemical scalars based on the full and a subset of the thermo-chemical scalars’ vector. Reproduction of the source term of the principal components represents a challenge, because of the inherent non-linearity of reaction rates’ expressions. It is found that using the subset of the thermo-chemical scalars’ vector both minor species and the first three principal components source terms are reasonably well predicted.

A novel principal component analysis-based acceleration scheme for LES–ODT: An a priori study

A novel large-eddy simulation (LES) approach is developed for the study of turbulent non-premixed flames. The approach is based on the embedding of 1D flamelet solutions on the flame surface based the one-dimensional turbulence (ODT) model. LES is used to evolve mass conservation, momentum and a flame capturing scalar, the mixture fraction; while, ODT is used to solve for the momentum and thermo-chemical scalars (species and energy). The two solutions are implemented in parallel and coupled to account for the effects of turbulent on the flame and the effects of heat release on the flow. The ODT model resolution is designed to capture important fine-grained unresolved physics on the LES sub-filter scales, including finite-rate chemistry effects and the sub-filter scale flame wrinkling.

One-dimensional turbulence (ODT) offers an alternative single-column solver for wall-bounded turbulence that sits between traditional 1D boundary-layer parametrisations and fully 3D direct numerical simulation: in fully resolved mode, molecular transport is explicitly resolved along a 1D vertical domain, while turbulent advection is represented by instantaneous spatial mappings ("eddy events"). For high-Reynolds-number, wall-bounded flows relevant to the atmospheric boundary layer (ABL), resolving Kolmogorov scales is prohibitively expensive. This motivates careful implementation of wall models and subgrid scale models in ODT similar to large eddy simulations (LES).Here, we develop an ODT formulation operated in an LES-like mode, in which unresolved eddy events are represented by a Smagorinsky–Lilly subgrid-scale (SGS) model, and surface coupling is provided through standard surface parametrisations for an extended range of resolved scales. We assess the formulation on two benchmark problems: (i) canonical smooth turbulent channel flow, using an algebraic wall model to supply surface stress consistent with resolved inertial-sublayer dynamics; and (ii) the GABLS1 intercomparison case (a weakly stable, shear-driven ABL with prescribed surface cooling rate), using Monin-Obukhov similarity theory to compute surface momentum and heat fluxes.Together, these two cases demonstrate the feasibility of combining ODT's eddy-event transport with LES-style SGS and surface models, thus providing a computationally efficient platform for future studies of ABL regimes, in which turbulence, surface fluxes, entrainment across sharp inversions, and multi-phase physics interact and remain challenging for coarse-resolution weather and climate models.

In this paper, the effect of subgrid-scale (SGS) modelling, grid resolution and anisotropy of the subgrid-scales on large eddy simulation (LES) is investigated. LES of turbulent channel flow is performed at Re τ=934, based on friction velocity and channel half width, for a wide range of resolutions. The dynamic Smagorinsky model (DS), the high-pass filtered dynamic Smagorinsky model (HPF) based on the variational multiscale method and the recent explicit algebraic model (EA), which accounts for the anisotropy of the SGS stresses are considered. The first part of the paper is focused on the resolution effects on LES, where the performances of the three SGS models at different resolutions are compared to direct numerical simulation (DNS) results. The results show that LES using eddy viscosity SGS models is very sensitive to resolution. At coarse resolutions, LES with the DS and the HPF models deviate considerably from DNS, whereas LES with the EA model still gives reasonable results. Further analysis shows that the two former models do not accurately predict the SGS dissipation near the wall, while the latter does, even at coarse resolutions. In the second part, the effect of SGS modelling on LES predictions of near-wall and outer-layer turbulent structures is discussed. It is found that different models predict near-wall turbulent structures of different sizes. Analysis of the spectra shows that although near-wall scales are not resolved at coarse resolutions, large-scale motions can be reasonably captured in LES using all the tested models.

In this contribution, results of a direct particle-fluid simulation (DPFS) are compared with direct numerical simulations and large-eddy simulations (LES) using a popular Euler-Lagrange method (ELM). DPFS facilitates the computation of particulate turbulent flow with particle sizes on the order of the smallest flow scales, which requires advanced numerical methods and parallelization strategies accompanied by considerable computing resources. After recapitulating methods required for DPFS, a setup is proposed where DPFS is used as a benchmark for direct numerical simulations and LES. Therefore, a modified implicit LES scheme is proposed, which shows convincing statistics in comparison to a direct numerical simulation of a single phase flow. Preliminary results of particle-laden flow show good agreement of the LES and the DPFS findings. Further benchmark cases for an appreciable range of parameters are required to draw a rigorous conclusion of the accuracy of the ELM.

Study of numerical errors in direct numerical simulation and large eddy simulation

The dynamics and evolution of the turbulent flow inside an experimentally investigated engine-like geometry consisting of a flat-top cylinder head with a fixed, axis-centered valve and low-speed piston were studied numerically by means of Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), with a particular focus on Cycle-to-Cycle Variability (CCV). DNS was performed by the spectral element code nek5000 on a 58M points grid, whereas LES was carried out by the finite volume software OpenFOAM on a 4.6M hexahedral mesh. Results obtained by DNS and LES are compared with respect to the velocity means and fluctuations, as well with other derived quantities, achieving good agreement between simulations and experiments. The cyclic variability and complex unsteady flow features like the laminar-to-turbulent transition and the evolution of the tumble vortices were studied by time-resolved analysis and Proper Orthogonal Decomposition (POD). Simulations show that during the first half of the intake stroke the flow field is dominated by the dynamics of the incoming jet and the vortex rings it creates. With decreasing piston speed, the large central ring becomes the dominant flow feature until the top dead center. The flow field at the end of the previous cycle is found to have a strong effect on the jet breakup process and the dynamics of the vortex ring below the valve of the subsequent cycle as well as on the observed significant cyclic variations.

A modal Discontinuous Galerkin (DG) method is assessed for the Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) of freely decaying turbulence. We consider as benchmark test case the TaylorGreen vortex flow. Inviscid computations show the conservation and dissipation properties of the DG scheme in the context of 3D non-linear flow problems. DG DNS computations carried at low and moderate Reynolds numbers (Re = 400 and Re = 1600, respectively) show good agreement with a reference solution generated using a Fourier pseudo-spectral code. LES computations are carried out at larger Reynolds number (Re = 3000), and compared to a reference filtered DNS. The Variational Multiscale Simulation framework, which can be straightforwardly implemented in a modal DG code is compared to the classical Smagorinsky approach for LES.

DNS and LES of turbulent flow in a closed channel featuring a pattern of hemispherical roughness elements

Although the vortex is ubiquitous in nature, its definition is somewhat ambiguous in the field of fluid dynamics. In this absence of a rigorous mathematical definition, considerable confusion appears to exist in visualizing and understanding the coherent vortical structures in turbulence. Cited in the previous studies, a vortex cannot be fully described by vorticity, and vorticity should be further decomposed into a rotational and a non-rotational part to represent the rotation and the shear, respectively. In this paper, we introduce several new concepts, including local fluid rotation at a point and the direction of the local fluid rotation axis. The direction and the strength of local fluid rotation are examined by investigating the kinematics of the fluid element in two- and three-dimensional flows. A new vector quantity, which is called the vortex vector in this paper, is defined to describe the local fluid rotation and it is the rotational part of the vorticity. This can be understood as that the direction of the vortex vector is equivalent to the direction of the local fluid rotation axis, and the magnitude of vortex vector is the strength of the location fluid rotation. With these new revelations, a vortex is defined as a connected region where the vortex vector is not zero. In addition, through direct numerical simulation (DNS) and large eddy simulation (LES) examples, it is demonstrated that the newly defined vortex vector can fully describe the complex vertical structures of turbulence.

The critical review discusses the most accurate methods for description of turbulent flows: the computationally very expensive direct numerical simulation (DNS) and slightly less accurate and slightly less expensive large eddy simulation (LES) methods. Both methods have found their way into nuclear thermal hydraulics as tools for studies of the fundamental mechanisms of turbulence and turbulent heat transfer. In the first section of this critical review, both methods are briefly introduced in parallel with the basic properties of the turbulent flows. The focus is on the DNS method, the so-called quasi-DNS approach, and the coarsest turbulence modeling approach discussed in this work, which is still on the very small-scale, wall-resolved LES. Other, coarser turbulence modeling approaches (such as wall-modeled LES, Reynolds Averaged Navier-Stokes (RANS)/LES hybrids, or RANS) are beyond the scope of the present work. Section II answers the question: “How do the DNS and LES methods work?” A short discussion of the computational requirements, numerical approaches, and computational tools is included. Section III is about the interpretation of the DNS and LES results and statistical uncertainties. Sections IV and V give some examples of the DNS and wall-resolved LES results relevant for nuclear thermal hydraulics. The last section lists the conclusions and some of the challenges that might be tackled with the most accurate techniques like DNS and LES.

Environmental flows are replete with situations where shear and stratification coexist, and many attempts have been made to understand the generation and evolution of turbulence in stratified shear flows. Early studies have been made using laboratory simulations (Webster [32] and Rohr et al. [29]), but with increasing computer power, direct numerical simulations (DNS) and large eddy simulations (LES) have become powerful tools for studies of shear-stratified turbulence. There are many reports with numerical approaches, most of them using DNS (Gerz et al. [12], Holt et al. [14], Jacobitz et al. [16] and Werne et al. [33]) and others using LES (Kaltenbach et al. [17]).