Deciphering the flow structure of Czochralski melt using Partially Averaged Navier–Stokes (PANS) method

The partially averaged Navier–Stokes (PANS) equations are used to predict the variable-density Rayleigh–Taylor (RT) flow at Atwood number 0.5 and maximum Reynolds number 500. This is a prototypical problem of material mixing, featuring laminar, transitional, and turbulent flow, instabilities and coherent structures, density fluctuations, and production of turbulence kinetic energy by both shear and buoyancy mechanisms. These features pose numerous challenges to modeling and simulation, making the RT flow ideal to develop the validation space of the recently proposed PANS Besnard–Harlow–Rauenzahn-linear eddy viscosity model closure. The numerical simulations are conducted at different levels of physical resolution and test three approaches to set the parameters fϕ defining the range of physically resolved scales. The computations demonstrate the efficiency (accuracy vs cost) of the PANS model predicting the spatiotemporal development of the RT flow. Results comparable to large-eddy simulations and direct numerical simulations are obtained at significantly lower physical resolution without the limitations of the Reynolds-averaged Navier–Stokes equations in these transitional flows. The data also illustrate the importance of appropriate selection of the physical resolution and the resolved fraction of each dependent quantity ϕ of the turbulent closure, fϕ. These two aspects determine the ability of the model to resolve the flow phenomena not amenable to modeling by the closure and, as such, the computations' fidelity.

Superiority of PANS compared to LES in predicting a rudimentary landing gear flow with affordable meshes

This review presents the state of the art of hybrid RANS/LES modeling for the simulation of turbulent flows. After recalling the modeling used in RANS and LES methodologies, we propose in a first step a theoretical formalism developed in the spectral space that allows to unify the RANS and LES methods from a physical standpoint. In a second step, we discuss the principle of the hybrid RANS/LES methods capable of representing a RANS-type behavior in the vicinity of a solid boundary and an LES-type behavior far away from the wall boundary. Then, we analyze the principal hybrid RANS/LES methods usually used to perform numerical simulation of turbulent flows encountered in engineering applications. In particular, we investigate the very large eddy simulation (VLES), the detached eddy simulation (DES), the partially integrated transport modeling (PITM) method, the partially averaged Navier-Stokes (PANS) method, and the scale adaptive simulation (SAS) from a physical point of view. Finally, we establish the connection between these methods and more precisely, the link between PITM and PANS as well as DES and PITM showing that these methods that have been built by different ways, practical or theoretical manners have common points of comparison. It is the opinion of the author to consider that the most appropriate method for a particular application will depend on the expectations of the engineer and the computational resources the user is prepared to expend on the problem.

Study of active flow control for a simplified vehicle model using the PANS method

<p><span>Large-eddy simulation (LES) is an often used technique in the geosciences to simulate turbulent oceanic and atmospheric flows. In LES, the effects of the unresolved turbulence scales on the resolved scales (via the Reynolds stress tensor) have to be parameterized with subgrid models. These subgrid models usually require strong assumptions about the relationship between the resolved flow fields and the Reynolds stress tensor, which are often violated in reality and potentially hamper their accuracy.</span></p><p><span>In this study, using the finite-difference computational fluid dynamics code MicroHH (v2.0) and turbulent channel flow as a test case (friction Reynolds number Re<sub>τ</sub> 590), we incorporated and tested a newly emerging subgrid modelling approach that does not require those assumptions. Instead, it relies on neural networks that are highly non-linear and flexible. Similar to currently used subgrid models, we designed our neural networks such that they can be applied locally in the grid domain: at each grid point the neural networks receive as an input the locally resolved flow fields (u,v,w), rather than the full flow fields. As an output, the neural networks give the Reynolds stress tensor at the considered grid point. This local application integrates well with our simulation code, and is necessary to run our code in parallel within distributed memory systems.</span></p><p><span>To allow our neural networks to learn the relationship between the specified input and output, we created a training dataset that contains ~10.000.000 samples of corresponding inputs and outputs. We derived those samples directly from high-resolution 3D direct numerical simulation (DNS) snapshots of turbulent flow fields. Since the DNS explicitly resolves all the relevant turbulence scales, by downsampling the DNS we were able to derive both the Reynolds stress tensor and the corresponding lower-resolution flow fields typical for LES. In this calculation, we took into account both the discretization and interpolation errors introduced by the finite staggered LES grid. Subsequently, using these samples we optimized the parameters of the neural networks to minimize the difference between the predicted and the ‘true’ output derived from DNS.</span></p><p><span>After that, we tested the performance of our neural networks in two different ways:</span></p><ol><li><span>A priori or offline testing, where we used a withheld part of the training dataset (10%) to test the capability of the neural networks to correctly predict the Reynolds stress tensor for data not used to optimize its parameters. We found that the neural networks were, in general, well able to predict the correct values. </span></li> <li><span>A posteriori or online testing, where we incorporated our neural networks directly into our LES. To keep the total involved computational effort feasible, we strongly enhanced the prediction speed of the neural network by relying on highly optimized matrix-vector libraries. The full successful integration of the neural networks within LES remains challenging though, mainly because the neural networks tend to introduce numerical instability into the LES. We are currently investigating ways to minimize this instability, while maintaining the high accuracy in the a priori test and the high prediction speed.</span></li> </ol>

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.

Purpose – Turbulent air flows within a channel with 45° angled rib turbulators on the top and bottom walls are numerically predicted using the numerical code. For the predictions, a v2-f turbulence model (velocity variance scale and elliptic relaxation factor model) is utilized. The paper aims to discuss these issues. Design/methodology/approach – Three different rib arrangements with or without gap are investigated to present information on the effects of gap size on flow structure and heat transfer characteristics. Three-dimensional turbulent transport, and detailed flow structural characteristics are considered to provide new insight into the mechanisms which result in surface heat transfer augmentations. Findings – Compared to the baseline rib arrangement, the numerically predicted results show that the parallel ribs with gap (where the width of the gap is two times of rib height) shows the highest local Nusselt number ratios. This is a result of locally increased vorticity distributions, as well as augmented local magnitudes of mixing, secondary flows, and turbulent transport. Local transport changes are less pronounced when the gap width of gap is 0.5 times of rib height. As a result, associated local and spatially averaged Nusselt number ratios are also lower for this arrangement. Practical implications – Results will give improved heat transfer augmentation technologies. Originality/value – The present investigation provides new information and insight into flow structural characteristics in a channel with rib turbulators, both with and without gaps, especially the mechanisms which result in surface heat transfer augmentations, which are not available in any other existing numerical or experimental investigation.

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

The numerical large eddy simulation (LES) technique is tested on decaying magnetohydrodynamic (MHD) turbulence. The LES approach allows for a strong reduction in computational cost compared to direct numerical simulations by modeling the effects of the smallest turbulent scales instead of computing them directly. Two small-scale models of eddy-viscosity type are presented for this purpose in combination with a procedure for the self-consistent calculation of the model parameters in the course of the simulation. The method is successfully tested by comparing the obtained results to a high-resolution direct numerical simulation of decaying three-dimensional MHD turbulence.

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.

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]).

Ventilated cavitating flows are investigated via direct numerical simulations, using a coupled level set and volume of fluid method to capture the interface between the air and water phases. A ventilated disk cavitator is used to create the cavity and is modelled by a sharp-interface immersed boundary method. The simulation data provide a comprehensive description of the two-phase flow and the air leakage and vortex shedding processes in the cavitating flow. The mean velocity of the air phase suggests the existence of three characteristic flow structures, namely the shear layer (SL), recirculating area (RA) and jet layer (JL). The turbulent kinetic energy (TKE) is concentrated in the JL in the closure region, and streamwise turbulent fluctuations dominate transverse fluctuations in both SL and JL. Budget analyses of the TKE show that the production term causes the TKE to increase in the SL due to the high velocity gradients, and decrease in the JL due to streamwise stretching effects. Air leakage and vortex shedding occur periodically in the closure region, and the one-to-one correspondence between these two processes is confirmed by the velocity and volume fluid spectra results, and the autocorrelation function of the air volume fraction. Moreover, the coherent flow structures are analysed using the spectral proper orthogonal decomposition method. We identify several fine coherent structures, including $SL_{KH}$ induced by the Kelvin–Helmholtz instability, $SL_{out}$ associated with large-scale vortex shedding, $SL_{in}$ associated with small-scale vortex shedding, and $SL_{r}$ associated with upstream turbulent convection. The present study complements previous research by providing detailed descriptions of the turbulent motions associated with the violent mixing of air and water, and the complex interactions between different characteristic structures in cavitating flows.

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.