Direct Numerical Simulation Data Research Articles

Testing CFD-DEM method with a stochastic drag formulation using particle-resolved direct numerical simulation data as benchmark

Detailed comparison between particle-resolved direct numerical simulations (PR-DNS) and standard CFD-DEM simulations have concluded that the effective interphase drag force was underestimated by currently available drag correlations. Furthermore, PR-DNS have found that the force exerted on a single particle varies significantly even in statistically homogeneous systems, which was unfortunately not considered in standard CFD-DEM simulations. Therefore, it is interesting to test if CFD-DEM simulation with a stochastic drag formulation (stochastic CFD-DEM method) was able to obtain a better agreement with the data of PR-DNS. In this short communication, stochastic CFD-DEM method was assessed using the PR-DNS data of Tang et al. (2016) and Luo et al. (2016) as benchmark. It was found that although a minor improvement can be achieved, stochastic CFD-DEM method was insufficient to fill the gap between PR-DNS and CFD-DEM simulations. Therefore, effort is still needed to develop a better drag model after extensive studies, where the detailed information of particle configuration may need to be properly used.

Assessment of a flamelet approach to evaluating mean species mass fractions in moderately and highly turbulent premixed flames

Complex-chemistry direct numerical simulation (DNS) data obtained from lean methane-air turbulent flames are analyzed to perform a priori assessment of predictive capabilities of the flamelet approach to evaluating mean concentrations of various species in turbulent flames characterized by Karlovitz numbers Ka=6.0, 74.0, and 540. Six definitions of a combustion progress variable c are probed and two types of probability density functions (PDFs) are adapted: (i) actual PDFs extracted directly from the DNS data or (ii) presumed β-function PDFs obtained using the DNS data on the first two moments of the c-field. Results show that the mean density, the mean temperature, and the mean mass fractions of CH4, O2, H2O, CO2, CO, CH2O, CH3, and HCO are very well predicted using the temperature-based combustion progress variable cT and the actual PDF. For other considered species, the quantitative predictions are worse but still appear to be encouraging (with the exception of CH3O at Ka=540). The use of the flamelet library obtained from the equidiffusive laminar flame improves results for H2, HO2, and H2O2 at the highest Karlovitz number. Alternative definitions of the combustion progress variable perform worse and the reasons for this are explored. The use of the β-function PDF yields worse results for intermediate species such as OH, O, H, CH3, and HCO, with this PDF being significantly different from the actual PDF. Application of the flamelet approach to rates of production/consumption of various species is also addressed and implications of obtained results for modeling are discussed.

Improved delayed detached-eddy simulation and proper orthogonal decomposition analysis of turbulent wake behind a wall-mounted square cylinder

The turbulent flow past a wall-mounted square cylinder with an aspect ratio of 4 was investigated with the aid of Spalart–Allmaras improved delayed detached-eddy simulation and proper orthogonal decomposition (POD) analysis. The Reynolds number was equal to 12 000 (based on the free-stream velocity and obstacle width). The boundary layer thickness was ∼0.18 of the obstacle height. This study focused on analyzing the vortical structure of the wake and vortex shedding process along the obstacle height. A quantitative comparison of the first- and second-order flow statistics with the available experimental and direct numerical simulation data was used to validate the numerical results. The numerical model coupled with the vortex method of generating the turbulent inflow conditions could successfully reproduce the flow field around and behind the obstacle with commendable accuracy. The flow structure and vortex shedding characteristics near the wake formation region were discussed in detail using time-averaged and instantaneous flow parameters obtained from the simulation. Dipole type mean streamwise vortices and half-loop hairpin instantaneous vortices with energetic motions were identified. A coherent shedding structure was reported along the obstacle using two-point correlations. Two types of vortex shedding intervals were identified, namely, low amplitude fluctuations (LAFs) and high amplitude fluctuations (HAFs) [P. Sattari et al., Exp. Fluids 52, 1149–1167 (2012)]. The HAFs’ interval exhibits von Kármán-like behavior with a phase difference of ∼180°, while the LAFs’ interval shows less periodic behavior. It was observed that the effect of the LAFs’ interval tends to weaken the alternating shedding along the obstacle height. The POD analysis of the wake showed that for the elevations between 0.25 and 0.5 of the obstacle height, the first two POD modes represent the alternating shedding and contribute to 66.6%–57.6% of the total turbulent kinetic energy. However, at the free end of the obstacle, the first two modes have a symmetrical shedding nature and share 36.5% of the kinetic energy, while the rest of the energy is distributed between the alternating and the random shedding processes. A simple low-order model based on the vortex-shedding phase angle and the spectrum of the time coefficients obtained from POD was developed to predict the wake dynamics at the range of elevations where the alternating shedding is dominated.

Reconstructing velocity and pressure from noisy sparse particle tracks using constrained cost minimization

Emerging time-resolved volumetric PIV techniques have made simultaneous measurements of velocity and pressure fields possible. Yet, in many experimental setups, satisfying the spatial and temporal resolution requirements is a challenge. To improve the quality of sparse and noisy data, this paper introduces a constrained cost minimization (CCM) technique, which interpolates unstructured particle tracks to obtain the velocity, velocity gradients, material acceleration, hence the pressure, on a Eulerian grid. This technique incorporates physical constraints, such as a divergence-free velocity field and curl-free pressure gradients. The performance is evaluated using synthetic particle tracks for an unsteady double gyre and direct numerical simulations data for a turbulent channel flow, with varying particle concentrations and added errors. The errors in pressure, calculated using omni-directional integration, and correlations with the original data are compared to those obtained using the singular value decomposition (SVD) interpolation technique. The CCM errors are mostly lower, and the correlation is higher and less sensitive to particle sparsity and added errors compared to those of SVD. The synthetic particle traces are also projected onto four planar images to evaluate the performance of the new procedure together with shake-the-box (STB) particle tracking. A comparison of pressure spectra and correlation with the original data show very good agreement for the CCM method. Hence, CCM appears to be an effective method for improving the interpolation of sparse data. Sample experimental data obtained in the shear layer behind a backward-facing step demonstrate the application of STB and CCM to resolve the pressure field in coherent vortex structures.

Properties of turbulent channel flow similarity solutions

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Heat flux in turbulent Rayleigh-Bénard convection: Predictions derived from a boundary layer theory

Using recently developed boundary-layer equations for turbulent Rayleigh-B\'enard convection that take into account fluctuations and buoyancy, we derive analytical results for heat flux scaling dependencies in low- and high-Prandtl-number limits. Our theoretical results are supported by direct numerical simulation data, and further reveal a surprising close resemblance of the heat flux scaling dependencies in turbulent Rayleigh-B\'enard and steady forced convection. This finding resolves the paradox of the apparent applicability of the scaling results in steady forced convection even though the boundary layer theory in that case is not applicable to turbulent Rayleigh-B\'enard convection.

Errors Characterization of a RANS Simulation

Abstract This research uses data from direct numerical simulation (DNS) to characterize the different errors associated with a Reynolds-averaged Navier–Stokes (RANS) simulation. The statistics from DNS (Reynolds stresses, kinetic energy of turbulence, κ, and dissipation of turbulence, ε), are fed into a RANS simulation with the same Reynolds number, geometry, and numerical code used for DNS. Three integral metrics error based on the mean velocity, the moduli of the mean rate-of-strain tensor, and the wall shear stress are used to characterize the errors associated with the RANS technique, with the RANS model, and with the linear eddy viscosity model (LEVM). For developed and perturbed flow, it is found that the mean velocity of the RANS simulations with the DNS statistics is almost the same as the mean velocity from DNS data. This procedure enables the study of the relative importance of the different Reynolds stresses in a particular flow. It is shown that for the bounded perturbed turbulent flows studied here, almost all the necessary effects of turbulence are contained in the Reynolds shear stress.

Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales

PurposeCardiovascular engineering includes flows with fluid-dynamical stresses as a parameter of interest. Mechanical stresses are high-risk factors for blood damage and can be assessed by computational fluid dynamics. By now, it is not described how to calculate an adequate scalar stress out of turbulent flow regimes when the whole share of turbulence is not resolved by the simulation method and how this impacts the stress calculation.MethodsWe conducted direct numerical simulations (DNS) of test cases (a turbulent channel flow and the FDA nozzle) in order to access all scales of flow movement. After validation of both DNS with literature und experimental data using magnetic resonance imaging, the mechanical stress is calculated as a baseline. Afterwards, same flows are calculated using state-of-the-art turbulence models. The stresses are computed for every result using our definition of an equivalent scalar stress, which includes the influence from respective turbulence model, by using the parameter dissipation. Afterwards, the results are compared with the baseline data.ResultsThe results show a good agreement regarding the computed stress. Even when no turbulence is resolved by the simulation method, the results agree well with DNS data. When the influence of non-resolved motion is neglected in the stress calculation, it is underpredicted in all cases.ConclusionWith the used scalar stress formulation, it is possible to include information about the turbulence of the flow into the mechanical stress calculation even when the used simulation method does not resolve any turbulence.

Toward neural-network-based large eddy simulation: application to turbulent channel flow

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Hydrodynamic forces acting on the elliptic cylinder performing high-frequency low-amplitude multi-harmonic oscillations in a viscous fluid

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Effects of body forces on vorticity and enstrophy evolutions in turbulent premixed flames

The effects of body forces (alternatively, the Froude number) on both vorticity and enstrophy evolutions within the flame brush have been analyzed using direct numerical simulation data of freely propagating statistically planar turbulent premixed flames subjected to different turbulence intensities. The turbulence parameters are taken to represent the thin reaction zone regime of premixed turbulent combustion. The enstrophy has been found to decay significantly from the unburned to the burned gas side of the flame brush for high turbulence intensities, and this trend becomes particularly prominent with the strengthening of the body force promoting unstable stratification. However, local instances of enstrophy generation have been observed, and in some cases, the decay of enstrophy is arrested across the flame brush for small turbulence intensities. This trend strengthens with the increasing magnitude of the body force promoting stable stratification. The enstrophy generation due to the baroclinic torque is primarily responsible for this local enstrophy generation for small turbulence intensities especially under the body force promoting stable stratification. This baroclinic torque contribution is also found to be responsible for anisotropic behavior of vorticity components within the flame brush. The vortex stretching and viscous dissipation terms have been found to be the leading order source and sink terms, respectively, in the enstrophy transport for high turbulence intensities especially in the case of body force promoting unstable stratification. However, baroclinic torque and the sink term due to dilatation rate continue to play significant roles even for high turbulence intensity cases considered here, but their relative importance increases with a decreasing turbulence intensity especially under the body force that promotes stable stratification. The surface-weighted entrainment velocity has been found to be mostly unaffected by the body force in this analysis, and a minor influence can be discerned in the case of small turbulence intensities where an unstable stratification tends to promote high negative values of entrainment velocity only toward the unburned gas side of the flame brush.

Reynolds stress anisotropy in shock/isotropic turbulence interactions

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2-D and 3-D measurements of flame stretch and turbulence–flame interactions in turbulent premixed flames using DNS

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Physical invariance in neural networks for subgrid-scale scalar flux modeling

In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data, state-of-the-art neural networks, such as convolutional neural networks, may not preserve well known physical priors, which may in turn question their application to real case-studies. To address this issue, we investigate hard and soft constraints into the model based on classical transformation invariances and symmetries derived from physical laws. From simulation-based experiments, we show that the proposed transformation-invariant NN model outperforms both purely data-driven ones as well as parametric state-of-the-art subgrid-scale models. The considered invariances are regarded as regularizers on physical metrics during the a priori evaluation and constrain the distribution tails of the predicted subgrid-scale term to be closer to the DNS. They also increase the stability and performance of the model when used as a surrogate during a large-eddy simulation. Moreover, the transformation-invariant NN is shown to generalize to regimes that have not been seen during the training phase.

Statistical Mechanics-Based Surrogates for Scalar Transport in Channel Flow

Thermal hydraulics, in certain components of nuclear reactor systems, involve complex flow scenarios, such as flows assisted by free jets and stratified flows leading to turbulent mixing and thermal fluctuations. These complex flow patterns and thermal fluctuations can be extremely critical from a reactor safety standpoint. The component-level lumped approximations (0D) or one-dimensional approximations (1D) models for such components and subsystems in safety analysis codes cannot capture the physics accurately, and may introduce a large degree of modeling uncertainty. On the other hand, high-fidelity computational fluid dynamics codes, which provide numerical solutions to the Navier–Stokes equations, are accurate but computationally intensive, and thus cannot be used for system-wide analysis. An alternate way to improve reactor safety analysis is by building reduced-order emulators from computational fluid dynamics (CFD) codes to improve system scale models. One of the key challenges in developing a reduced-order emulator is to preserve turbulent mixing and thermal fluctuations across different-length scales or time-scales. This paper presents the development of a reduced-order, non-linear, “Markovian” statistical surrogate for turbulent mixing and scalar transport. The method and its implementation are demonstrated on a canonical problem of differentially heated channel flow, and high-resolution direct numerical simulations (DNS) data are used for emulator or surrogate development. This statistical surrogate model relies on Kramers–Moyal expansion and emulates the turbulent velocity signal with a high degree of accuracy.

Convolutional neural network and long short-term memory based reduced order surrogate for minimal turbulent channel flow

We investigate the applicability of the machine learning based reduced order model (ML-ROM) to three-dimensional complex flows. As an example, we consider a turbulent channel flow at the friction Reynolds number of Reτ=110 in a minimum domain, which can maintain coherent structures of turbulence. Training datasets are prepared by direct numerical simulation (DNS). The present ML-ROM is constructed by combining a three-dimensional convolutional neural network autoencoder (CNN-AE) and a long short-term memory (LSTM). The CNN-AE works to map high-dimensional flow fields into a low-dimensional latent space. The LSTM is, then, utilized to predict a temporal evolution of the latent vectors obtained by the CNN-AE. The combination of the CNN-AE and LSTM can represent the spatiotemporal high-dimensional dynamics of flow fields by only integrating the temporal evolution of the low-dimensional latent dynamics. The turbulent flow fields reproduced by the present ML-ROM show statistical agreement with the reference DNS data in time-ensemble sense, which can also be found through an orbit-based analysis. Influences of the population of vortical structures contained in the domain and the time interval used for temporal prediction on the ML-ROM performance are also investigated. The potential and limitation of the present ML-ROM for turbulence analysis are discussed at the end of our presentation.

Reynolds-Averaged Numerical Simulations of Conical Shock-Wave/Boundary-Layer Interactions

We carry out a parametric study of conical shock-wave/turbulent boundary-layer interactions by means of numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations, with the eventual goal of establishing the predictive capabilities of standard turbulence models. Preliminary assessment of several linear-eddy-viscosity models for the case of planar interactions shows that the model and its variants as well as the Spalart–Allmaras model yield accurate prediction of the typical interaction length scale. Numerical simulations of conical interactions at high Reynolds numbers under attached and separated flow conditions generally support good capability of RANS to predict the gross flow features, including conditions of incipiently and fully separated flow. Comparison with direct numerical simulation data at low Reynolds numbers suggests that caution should be made because certain turbulence models may yield unrealistic incoming velocity profiles. With this caveat, we again find that RANS models yield satisfactory prediction of the three-dimensional flow organization and associated length scales. The -wave mean wall pressure signature is quantitatively predicted, and accurate information about the fluctuating pressure variance can be obtained from RANS data in a postprocessing stage by extension of correlations developed for low-speed separation bubbles.

Non-equilibrium wall functions for large Eddy simulations of complex turbulent flows and heat transfer

In this paper novel unified wall function formulations for large eddy simulation of complex turbulent flows and heat transfer are presented. In contrast to existing wall functions, the proposed analytical expressions for velocity and temperature are: (1) valid over the whole range of dimensionless wall distance y+, (2) applicable to complex flow situations that include local non-equilibrium effects, (3) suitable for a wide range of molecular Prandtl numbers, (4) thermodynamically consistent with the second law of thermodynamics, and (5) easily extendable to account for contributions of additional source term e.g. gravity, radiation, chemical reactions. Such an universal and consistent wall function formulation is particularly useful for computational fluid dynamics applications in providing appropriate wall boundary conditions for complex high Reynolds number flows. The accuracy and thermodynamic consistency of the proposed wall treatment is first testified by comparison with experimental and direct numerical simulation data. Second, in order to highlight the applicability and performance of the proposed wall functions for computational fluid dynamics, results of large eddy simulations of various complex turbulent flows including heat transfer relevant to internal combustion engine applications are presented and evaluated. It turns out that the suggested wall function approach features a superior physics modeling accuracy in terms of well-known key parameters in near-wall bounded flows in comparison to state-of-the-art wall functions.

On skin friction in wall-bounded turbulence

In this paper, we derive mathematical formulas for the skin friction coefficient in wall-bounded turbulence based on the Reynolds averaged streamwise momentum equation and the total stress. Specifically, with a theoretical or empirical relation of the total stress, the skin friction coefficient is expressed in terms of the mean velocity and the Reynolds shear stress in an arbitrary wall-normal region $$[h_0, h_1]$$ . The formulas are validated using direct numerical simulation data of turbulent channel and boundary layer flows, and the results show that our formulas estimate the skin friction coefficient very accurately with an error less than $$2\%$$ . The present integral formula can be used to determine the skin friction in turbulent channel and boundary layer flows at high Reynolds numbers where the near-wall statistics are very difficult to measure accurately.

Development of a mechanism-dynamic-selection turbulent premixed combustion model with application to gasoline engine combustion and emissions simulation

In order to overcome the drawback (tuning reaction rate coefficients) of using a single mechanism in the chemical-kinetics-based turbulent premixed combustion modelling approach, a mechanism-dynamic-selection turbulent premixed combustion model has been developed, validated, and successfully applied to the combustion and emissions simulation of spark ignition gasoline engines. In this new model, based on the local thermal and turbulent conditions of any preheat cell, a certain chemical kinetic mechanism which can achieve the target ratio of turbulent flame speed to laminar flame speed is selected. To realise this goal, based on the laminar flame speed sensitivity analysis of an improved eTRF (ethanol toluene reference fuel) base chemical kinetic mechanism, a derived mechanism library has been generated. Based on enough experimental and DNS (direct numerical simulation) data of S T/S L, a mechanism selection database (mechanism as a function of Borghi-Peters coordinates) has been constructed and implemented into a CFD (computational fluid dynamics) code, also a classification scheme for identifying unburned, preheat, flame front, and burned zones of a combustion domain has been developed and implemented into the CFD code. The developed mechanism-dynamic-selection turbulent premixed combustion model has been validated using the combustion in a spherical constant volume and applied to the prediction of combustion and emissions of a spark ignition gasoline engine under transient cold start process. Validation results show that, without tuning any model parameters, the base mechanism, the derived mechanism library, the mechanism selection function, the classification scheme, as well as a simulation setup strategy for modelling engine transient cold start process, have good prediction performances and are practical for engine combustion and emissions simulation.