Assessment of the gradient jump penalisation in large-eddy simulations of turbulence

The convolutional neural network (CNN) is implemented to enhance a turbulence model which is needed to close the Reynolds-averaged Navier-Stokes (RANS) equations. The machine-learning technique uses the available data sets of high fidelity for canonical flow test cases. These data have been produced from large-eddy simulations or direct numerical simulations, which require huge computing resources. At the first stage, the widely used k-ω model is taken as a baseline RANS model, and computations are performed by means of OpenFOAM for turbulent flows in the plane channel having the periodic hills on the lower wall and in the converging-diverging channel. Then, the CNN algorithm is applied to these cases. The prediction of the Reynolds-stress anisotropy tensor components is shown to be improved after the application of CNN with the mean square error loss function in comparison with that for the baseline RANS model in the investigated canonical turbulent flows in channels with walls of different geometry.

Hydrophobic surface benefits for drag reduction. Min and Kim[1] do the first Direct Numerical Simulation on drag reduction in turbulent channel flow. And Fukagata and Kasagi[2] make some theoretical analysis based on Dean[3]’s formula and some observations in the DNS results. Using their theory, they conclude that drag reduction is possible in large Reynolds number. Both Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are performed in our research. How the LES behaving in the turbulent channel flow with hydrophobic surface is examined. Original Smagorinsky model and its Dynamical model are used in LES. The slip velocities predicted by LES using Dynamical model are in good agreement with DNS as shown in the Figure. Although the percentage of drag reduction predicted by LES shows some discrepancies, it is in the error limit for industrial flow. First order and second order moments of LES are also examined and compared with DNS’s results. The first-order moments is calculated well by LES. But there are some discrepancies of second-order moments between LES and DNS. The slip velocity normalized by the actual shear velocity, L + s is normalized by the no slip shear velocity respectively

This work focuses on the development of efficient computational tools for the simulation of turbulent multiphase polydispersed flows. In terms of methodologies we focus here on the use of Large Eddy Simulation (LES) and Quadrature-Based Methods of Moments (QBMM). In terms of applications the work is finalised, in order to be applied in the future, to particle production processes (precipitation and crystallisation in particular). An important part of the work concerns the study of the flow field in a Confined Impinging Jets Reactor (CIJR), frequently used in particle production processes. The first part is limited to the comparison and analysis of micro Particle Image Velocimetry (μPIV) experiments, carried out in a previous work, and Direct Numerical Simulation (DNS), carried out in this thesis. In particular the effects of boundary and operating conditions are studied and the numerical simulations are used to understand the experimental predictions and demonstrate the importance of unavoidable fluctuations in the experimental inlets. This represents a preparatory work for the LES modelling of the CIJR. Before investigating the accuracy of LES predictions for this particular application, the model and the implementation are studied in a more general context, represented by a well-known test case such as the periodic turbulent channel flow: the LES model implementation in TransAT, the code used in this work, is compared with DNS data and with predictions of other codes. LES simulations for the CIJR, provided with the proper boundary conditions obtained by the previous DNS/μPIV study, are then performed and compared with experiments, validating the model in a more realistic test case. Since particle precipitation and crystallization often result in complex interactions between particles and the continuous phase, in the second part of the work particular attention has been paid in the modelling of the momentum transfer and the resulting velocity of the particles (relative to the fluid). In particular the possibility of describing poly-disperse fluid-solid systems with QBMM together with LES and Equilibrium Eulerian Model (EEM) is assessed. The study is performed by comparing our predictions with DNS Lagrangian data in the turbulent channel flow previously described, seeded with particles corresponding to a realistic Particle Size Distribution (PSD). The last part of the work deals with particle collisions, extending QBMM to the investigation of non-equilibrium flows governed by the Boltzmann Equation with a hard-sphere collision kernel. The evolution of the particle velocity distribution is predicted and compared with other methods for kinetic equations such as Lattice Boltzmann Method (LBM), Discrete Velocity Method (DVM) and Grad's Moment Method (GM). The overall results of this thesis can be extended to a broad range of other applications of single-phase, dispersed multiphase and non-equilibrium flows

The general characteristics of the energy spectrum for internal gravity waves in the ocean are well known from the large body of recent experimental observations. The theoretical understanding has not developed at the same rate, perhaps due to the limitation of linear or quasi‐linear theories, which can cope only with weak interaction processes and are inadequate for representing the more violent and sporadic wave breaking processes present in nature. A detailed study of energy transfer among two‐dimensional internal gravity modes in a fully nonlinear regime was performed. Wave‐wave interactions and overturning were included in the solutions of a two‐dimensional numerical model, and the results are presented here. A background spectrum of finite amplitude, random internal gravity wave field was generated by a long time integration of a two‐dimensional model with random body forcing. Over this background field, two sets of experiments were performed: spike‐random, where energy at low, medium, and high wave numbers were introduced and integrated in time, and band‐random, where energy was introduced over a band of wave numbers instead of introducing only discrete modes. The results can be summarized as follows. Multiple triad interactions will result in a filling of the energy spectrum when energy is introduced in a particular band of wave numbers. For bands where the energy level is high enough to result in nonlinear time scales of only a few intrinsic periods, wave‐wave interactions (resonant and nonresonant) provide the mechanism for filling the spectrum. The energy transfer becomes more and more rapid with increasing energy, and no universal spectrum appears to result from these processes. As the energy input increases, energy will accumulate in high wave numbers until localized instabilities (over‐turning) occur. From that point on, these high wave numbers will remain at a saturation such that any additional energy input at the saturated band, either directly or via wave‐wave interactions, will result in localized mixing. On the other hand, additional energy input at bands other than the saturated band will result in an increase of low and medium wave band energy (via wave‐wave interactions) until an equilibrium level is achieved. The equilibrium level of any particular band will depend on the high wave number bands being saturated. For instance, any energy above the equilibrium at low wave numbers will produce localized mixing in physical space almost instantaneously. This does not mean that the low wave numbers are saturated, as their energy levels can be much lower than a saturation level. What takes place at or near an equilibrium level is that the contributions from high and low wave numbers result in localized regions in physical space where the criterion for instability is almost met. In fact, this superposition effect means that low and medium wave numbers are far from meeting any breaking criterion when taken individually, yet cannot tolerate any additional input energy when in the presence of a saturated band of high wave numbers. It was found also that the dissipation is approximately constant over the wave numbers and small compared with the large transfer of energy between neighboring waves. However, if bands of waves are considered, very little energy is transferred between neighboring bands above the equilibrium level. Rather, a direct cascade of energy from low to high wave numbers occurs due to localized instabilities which result in overturning, and it is this amount of energy flux which is dissipated by the high wave numbers.

Regularization-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are quantitatively assessed for decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor-Green vortex (TGV) through comparisons to laboratory measurements and direct numerical simulations (DNS). LES predictions using the Leray-α, LANS-α, and Clark-α regularization-based SGS models are compared to the classic nondynamic Smagorinsky model. Regarding the regularization models, this work represents their first application to relatively high-Re decaying turbulence with comparison to the active-grid-generated decaying turbulence measurements of Kang et al. (J. Fluid Mech., 2003) at Re λ ≈ 720 and the Re = 3000 DNS of transition to turbulence in the TGV of Drikakis et al. (J. Turbulence, 2007). For DHT the nondynamic Smagorinsky model is in excellent agreement with measurements for the turbulent kinetic energy and energy spectra but higher-order moments show slight discrepancies. For TGV too, the energy decay rates of Smagorinsky agree reasonably well with DNS. Regarding the regularization models stable results are not obtained as compared to the Smagorinsky model at the same grid resolution for various values of α; and at higher grid resolutions, they are in worse agreement. However, with additional dissipation such as in mixed α-Smagorinsky models, results are acceptable and show only slight deviations from Smagorinsky.

We describe a procedure for large eddy simulations of turbulence which uses the subgrid-scale estimation model and truncated Navier–Stokes dynamics. In the procedure the large eddy simulation equations are advanced in time with the subgrid-scale stress tensor calculated from the parallel solution of the truncated Navier–Stokes equations on a mesh two times smaller in each Cartesian direction than the mesh employed for a discretization of the resolved quantities. The truncated Navier–Stokes equations are solved through a sequence of runs, each initialized using the subgrid-scale estimation model. The modeling procedure is evaluated by comparing results of large eddy simulations for isotropic turbulence and turbulent channel flow with the corresponding results of experiments, theory, direct numerical simulations, and other large eddy simulations. Subsequently, simplifications of the general procedure are discussed and evaluated. In particular, it is possible to formulate the procedure entirely in terms of the truncated Navier–Stokes equation and a periodic processing of the small-scale component of its solution.

The log-layer mismatch arises when a Reynolds-averaged Navier-Stokes (RANS) model is blended with a large-eddy simulation (LES) model in a hybrid fashion. Numerous researchers have tackled this problem by simulating a turbulent channel flow. We show that the log-layer mismatch in hybrid RANS-LES can be reduced substantially by splitting the mean pressure gradient term in the wall-normal direction in a manner that keeps the mass flow rate constant. Additionally, an analysis of the wall-normal variation of the friction velocity shows a constant value is recovered in the resolved LES region different than the value at the wall. Second-order turbulence statistics agree very well with direct numerical simulation (DNS) benchmarks when scaled with the friction velocity extracted from the resolved LES region. In light of our findings, we suggest that the current convention to drive a turbulent periodic channel flow with a uniform mean pressure gradient be revisited in testing eddy-viscosity-based hybrid RANS-LES models as it appears to be the culprit behind the log-layer mismatch.

<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>

The e ect of ltering on the sound spectrum in variable density jets is investigated. Prediction of aeroacoustics using large-eddy simulations is becoming increasingly popular. A direct evaluation of the sound eld is, however, often computationally too expensive. The sound in the near far eld of variable density jets was therefore computed using a hybrid method developed by Ewert & Schr oder. The power spectral density (PSD) and overall sound pressure levels (OASPL) of the reference direct numerical simulation (DNS) are compared to ltered DNS and large-eddy simulation (LES) of the variable density jet at a density ratio of s=0.14, relating the jet to the free-stream density. The jet develops under a global instability, which determines the low Strouhal number range of the PSD and results in similar shapes of the spectrum for di erent radiation angles. Unlike the pure LES, the ltered elds show only slightly reduced levels at all Strouhal numbers. Good agreement is found for low radiation angles, but an up to 10dB reduction is observed for sideline and backward radiation. The LES simulation showed higher values at low Strouhal numbers, which could be attributed to a non-universal side-jet phenomenon, which may be encountered in strongly heated jets. A further simulation using a reduced part of the available time series without this event lead to PSD values comparable to that of the DNS.

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

One of the main unresolved issues in large-eddy simulation(LES) of wall-bounded turbulent flows is the requirement of high spatial resolution in the near-wall region, especially in the spanwise direction. Such high resolution required in the near-wall region is generally used throughout the computational domain, making simulations of high Reynolds number, complex-geometry flows prohibitive. A grid-embedding strategy using a nonconforming spectral domain-decomposition method is proposed to address this limitation. This method provides an efficient way of clustering grid points in the near-wall region with spectral accuracy. LES of transitional and turbulent channel flow has been performed to evaluate the proposed grid-embedding technique. The computational domain is divided into three subdomains to resolve the near-wall regions in the spanwise direction. Spectral patching collocation methods are used for the grid-embedding and appropriate conditions are suggested for the interface matching. Results of LES using the grid-embedding strategy are promising compared to LES of global spectral method and direct numerical simulation. Overall, the results show that the spectral domain-decomposition grid-embedding technique provides an efficient method for resolving the near-wall region in LES of complex flows of engineering interest, allowing significant savings in the computational CPU and memory.

Purpose– The purpose of this paper is to numerically study heated channel flow using direct numerical simulation (DNS) and large eddy simulation (LES) method. Using different domain size and different grid resolution it is show that filtering procedure is influenced and may results in very different solutions.Design/methodology/approach– Turbulent non-isothermal fully developed channel flow has been investigated using LES. The filtered Navier-stokes and energy equations were numerically solved with dynamic subgrid scale (SGS) model, standard Smagorinsky model or without additional model for the turbulent SGS stress and heat flux required to close the governing equations.Findings– The numerical LES results in comparison with the DNS data demonstrate that the LES computations may not always offers a reliable prediction of non-isothermal turbulent flow in open channel. It has been found that, even though the models reproduces accurately results for the flow field the thermal field computed using LES do not necessary match the DNS results. Introducing SGS model for scalar do not always show large improvement. One of the reason is thickness of hydrodynamic and thermal boundary layer. In the cases when boundary layers are very different it is not easy optimally set up control volumes in the domain.Originality/value– This is one of the first instance in which a results of numerical computations for different grid resolution, different stretching, SGS model is employed for non-isothermal turbulent channel flow. It shows that in the cases when boundary layers hydrodynamic and thermal are very different it is hardly find optimal grid resolution or stretching

A high-order Navier-Stokes solver based on the flux reconstruction (FR) or the correction procedure via reconstruction (CPR) formulation is employed to perform a direct numerical simulation (DNS) and large eddy simulations (LES) of a well-known benchmark problem – transitional flow over the low-pressure T106C turbine cascade. Hp-refinement studies are carried out to assess the resolution requirement. A 4th order (p3) simulation on the fine mesh is performed with a DNS resolution to establish a "converged" solution, including the mean pressure and skin-friction distributions, and the power spectral density in the wake. Then LES on the coarse and fine meshes with lower order schemes are conducted to assess the mesh and order dependence of the solution. In particular, we study the error in the transition location, the mean skin-friction distribution, and the mean lift and drag coefficients. These h- and p-refinement studies provide a much-needed guideline in h- and p- resolutions to achieve a certain level of accuracy for industrial LES applications.

We investigate the drag reduction effect of the streamwise travelling wave-like wall deformation in a high-Reynolds-number turbulent channel flow by large-eddy simulation (LES). First, we assess the validity of subgrid-scale models in uncontrolled and controlled flows. For friction Reynolds numbers $Re_\tau = 360$ and $720$ , the Smagorinsky and wall-adapting local eddy-viscosity (WALE) models with a damping function can reproduce well the mean velocity profile obtained by direct numerical simulation (DNS) in both the uncontrolled and controlled flows, leading to a small difference in drag reduction rate between LES and DNS. The LES with finer grid resolution can reproduce well the key structures observed in the DNS of the controlled flow. These results show that the high-fidelity LES is valid for appropriately predicting the drag reduction effect. In addition, a small computational domain is sufficient for reproducing the turbulence statistics, key structures and drag reduction rate obtained by DNS. Subsequently, to investigate the trend of drag reduction rate at higher Reynolds numbers, we utilize the WALE model with the damping function to investigate the control effect at higher Reynolds numbers up to $Re_\tau = 3240$ . According to the analyses of turbulence statistics and instantaneous flow fields, the drag reduction at higher Reynolds numbers occurs basically through the same mechanism as that at lower Reynolds numbers. In addition, the drag reduction rate obtained by the present LES approaches that predicted using the semi-empirical formula (Nabae et al., Intl J. Heat Fluid Flow, vol. 82, 2020, 108550) as the friction Reynolds number increases, which supports the high predictability of the semi-empirical formula at significantly high Reynolds numbers.

Comparing LES and URANS results with a reference DNS of the transitional airflow in a patient-specific larynx geometry during exhalation