Homogeneous Isotropic Turbulent Flow Research Articles

A Comparative Study of the Hydrogen Auto-Ignition Process in Oxygen–Nitrogen and Oxygen–Water Vapor Oxidizer: Numerical Investigations in Mixture Fraction Space and 3D Forced Homogeneous Isotropic Turbulent Flow Field

In this paper, we analyze the auto-ignition process of hydrogen in a hot oxidizer stream composed of oxygen–nitrogen and oxygen–water vapor with nitrogen/water vapor mass fractions in a range of 0.1–0.9. The temperature of the oxidizer varies from 1100 K to 1500 K and the temperature of hydrogen is assumed to be 300 K. The research is performed in 1D mixture fraction space and in a forced homogeneous isotropic turbulent (HIT) flow field. In the latter case, the Large Eddy Simulation (LES) method combined with the Eulerian Stochastic Field (ESF) combustion model is applied. The results obtained in mixture fraction space aim to determine the most reactive mixture fraction, maximum flame temperature, and dependence on the scalar dissipation rate. Among others, we found that the ignition in H2-O2-H2O mixtures occurs later than in H2-O2-N2 mixtures, especially at low oxidizer temperatures. On the other hand, for a high oxidizer temperature, the ignitability of H2-O2-H2O mixtures is extended, i.e., the ignition occurs for a larger content of H2O and takes place faster. The 3D LES-ESF results show that the ignition time is virtually independent of initial conditions, e.g., randomness of an initial flow field and turbulence intensity. The latter parameter, however, strongly affects the flame evolution. It is shown that the presence of water vapor decreases ignitability and makes flames more prone to extinction.

Benchmarking Data Assimilation Algorithms For 3D Lagrangian Particle Tracking

This paper reports a comparison of three state-of-the-art data assimilation (DA) algorithms for 3D Lagrangian particle tracking (LPT): Vortex-In-Cell sharp (VIC#), FlowFit3, and neural-implicit particle advection (NIPA). Particle trajectories, termed “tracks,” are spatially sparse, and a reconstruction algorithm is commonly employed to estimate dense Eulerian fields using position, velocity, and/or acceleration data from the tracks. DA algorithms for LPT combine the tracks with a set of governing equations (or constraints) to enhance the accuracy of the velocity field, relative to interpolation methods, and infer additional quantities like pressure. We compare the performance of VIC#, FlowFit3, and NIPA with respect to their accuracy and computational cost. Accuracy is assessed in terms of the mean inter-particle distance, frame rate, and magnitude of tracking errors, and costs are reported in wall time. Synthetic and experimental data sets for homogeneous isotropic turbulence and turbulent boundary layer flows are evaluated; direct numerical simulations are used for the synthetic tests, and realistic localization errors are added to the simulated tracks. All three DA methods perform well in cases with the highest spatio-temporal sampling of the flow, and all three methods are relatively robust to the frame rate and magnitude of localization errors. NIPA is more resilient to sparse seeding than FlowFit or VIC#, which exhibit similar performance, but NIPA is also the most expensive technique by some margin. DA reconstructions are superior to interpolation across the board, with a reduction of error up to 80% in the experimental demonstration.

Spectral energy transfer analysis of a forced homogeneous isotropic turbulence using triple decomposition of velocity gradient tensor

Triple decomposition of the velocity gradient tensor is exploited to investigate the role of the simple-shear, normal-strain, and rigid-body rotation, in the turbulent kinetic energy transfer of a forced, high-Reynolds-number homogeneous isotropic turbulent flow. Splitting the total energy flux into three elementary partial fluxes shows that the rigid-body rotation has a secondary contribution to turbulent kinetic energy transfer, while within 80% of the total energy flux is produced through the simple-shear and normal-strain processes. Energy is dominantly extracted through the shearing process from larger motion scales and injected into smaller scales by the normal-straining process. In addition, each partial energy flux contains a strong conservative part and a weak non-conservative part. Besides the total kinetic energy transfer, all partial energy fluxes also show scale-invariance behaviour over the inertial subrange. Statistically, total energy flux shows a strong correlation with the simple-shear and normal-strain processes. However, the relatively poor correlation between these two dominant processes, implies a fairly low efficiency for turbulent kinetic energy transfer. These results can provide new insights into sub-grid scale turbulence modelling based on the physical mechanism of simple-shear and normal-strain processes.

On local isotropy and scale dependence of pair dispersion in turbulent canopy flows

Canopy flows in the atmospheric surface layer play important economic and ecological roles, governing the dispersion of passive scalars in the environment. The interaction of high-velocity fluid and large-scale surface-mounted obstacles in canopy flows produces drag and causes intense, inhomogeneous and anisotropic turbulence. In this work, we focus on the turbulent dispersion of passive scalars by studying the ‘pair dispersion’ – a statistical measure of relative motion between particles. We analyse the results of a three-dimensional particle tracking velocimetry experiment in a wind-tunnel canopy flow, focusing on small scales. We confirm the existence of local isotropy of pair dispersion at scales smaller than a characteristic shear length scale $L_\varGamma =(\epsilon /\varGamma ^3)^{1/2}$ , where $\epsilon$ and $\varGamma$ are the mean dissipation rate and shear rate, respectively. Furthermore, we show that pair dispersion in this locally isotropic regime is a scale-dependent super-diffusive process, similar to what occurs in homogeneous isotropic turbulent flows. In addition, we measure the pair relative velocity correlation function, showing that its de-correlation occurs in the locally isotropic regime, and discuss the implications of this observation for modelling pair dispersion. Thus, our study extends the fundamental understanding of turbulent pair dispersion to the anisotropic inhomogeneous turbulent canopy flow, bringing valuable information for modelling scalar dispersion in the atmospheric surface layer.

Fast macroscopic forcing method

The macroscopic forcing method (MFM) of Mani and Park [1] and similar methods for obtaining turbulence closure operators, such as the Green's function-based approach of Hamba [2], recover reduced solution operators from repeated direct numerical simulations (DNS). MFM has already been used to successfully quantify Reynolds-averaged Navier–Stokes (RANS)-like operators for homogeneous isotropic turbulence and turbulent channel flows. Standard algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of freedom in the RANS space) and conduct a corresponding fine-scale simulation (i.e., DNS), which is expensive. We combine this method with an approach recently proposed by Schäfer and Owhadi [3] to recover elliptic integral operators from a polylogarithmic number of matrix–vector products. The resulting Fast MFM introduced in this work applies sparse reconstruction to expose local features in the closure operator and reconstructs this coarse-grained differential operator in only a few matrix–vector products and correspondingly, a few MFM simulations. For flows with significant nonlocality, the algorithm first “peels” long-range effects with dense matrix–vector products to expose a more local operator. We demonstrate the algorithm's performance for the eddy diffusivity and eddy viscosity operators, which correspond to the unclosed parts of the ensemble-averaged transport equations, excluding the analytically known, closed parts of such equations. However, the algorithm can also be applied to the full operators. We focus on scalar transport in a laminar channel flow and momentum transport in a turbulent channel flow. For these problems, we recover eddy diffusivity- and eddy viscosity-like operators, respectively, at 1% of the cost of computing the exact operator via a brute-force approach for the laminar channel flow problem and 13% for the turbulent one. Applying these operators to compute the averaged fields of interest has visually indistinguishable behavior from the exact solution. Our results show that a similar number of simulations are required to reconstruct the operators to the same accuracy under grid refinement. Thus, the accuracy corresponds to the physics of the problem, not the numerics, so long as the grid is sufficiently refined. We glean that for problems in which the RANS space is reducible to one dimension, eddy diffusivity, and eddy viscosity operators can be reconstructed with reasonable accuracy using only a few simulations, regardless of simulation resolution or degrees of freedom.

SPARSE–R: A point-cloud tracer with random forcing

A predictive, point-cloud tracer is presented that determines with a quantified uncertainty the Lagrangian motion of a group of point-particles within a finite region. The tracer assumes a random forcing within confidence intervals to account for the empiricism of data-driven force models and stochasticity related to the chaotic nature of the subcloud scale dynamics. It builds on the closed Subgrid Particle-Averaged Reynolds Stress-Equivalent (SPARSE) formulation presented in Domínguez-Vázquez et al. (2023) that assumes a deterministic forcing. SPARSE–R describes the first two moments of particle clouds with moment equations in closed-form, with a theoretical third-order convergence rate with respect to the standard deviations of the cloud variables. The cloud model alleviates computational cost and enhances the convergence rate as compared to Monte Carlo (MC) based point-particle methods. The randomness in the forcing model leads to virtual stresses that correlate random forcing and field fluctuations. These stresses strain and rotate the random cloud as compared to a deterministically forced cloud and thus determine to what extent the random forcing propagates into the confidence intervals of the dispersed solution. In symmetric flows the magnitude of the virtual stress is zero. Tests in analytical carrier fields and in a decaying homogeneous isotropic turbulence flow computed with a discontinuous Galerkin (DG) compressible DNS solver are performed to verify and validate the SPARSE–R method for randomly forced particles.

Energy transfer and vortex structures: visualizing the incompressible turbulent energy cascade

The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. However, the correlations between energy transfer and strain are small, and point to complicated dynamics of energy transfer. By imposing a structure at large scales consisting of antiparallel vortex tubes in a statistically steady flow, we observed a picture qualitatively similar to what was observed for the transient flow, but the energy transfer statistics do not reproduce the type of triadic interactions seen in HIT. These results indicate that the specific properties of the large-scale vortical structures affect the way energy is transferred, and may not be fully representative of HIT.

An experimental study on the settling velocity of inertial particles in different homogeneous isotropic turbulent flows

We propose an experimental study on the gravitational settling velocity of dense, sub-Kolmogorov inertial particles under different background turbulent flows. We report phase Doppler particle analyser measurements in a low-speed wind tunnel uniformly seeded with micrometre scale water droplets. Turbulence is generated with three different grids (two consisting of different active-grid protocols while the third is a regular static grid), allowing us to cover a very wide range of turbulence conditions in terms of Taylor-scale-based Reynolds numbers ( $Re_\lambda \in [30\unicode{x2013}520]$ ), Rouse numbers ( $Ro \in [0\unicode{x2013}5]$ ) and volume fractions ( $\phi _v \in [0.5\times 10^{-5}\unicode{x2013}2.0\times 10^{-5}]$ ). We find, in agreement with previous works, that enhancement of the settling velocity occurs at low Rouse number, while hindering of the settling occurs at higher Rouse number for decreasing turbulence energy levels. The wide range of flow parameters explored allowed us to observe that enhancement decreases significantly with the Taylor–Reynolds number and is significantly affected by the volume fraction $\phi _v$ . We also studied the effect of large-scale forcing on settling velocity modification. The possibility of changing the inflow conditions by using different grids allowed us to test cases with fixed $Re_\lambda$ and turbulent intensity but with different integral length scale. Finally, we assess the existence of secondary flows in the wind tunnel and their role on particle settling. This is achieved by characterising the settling velocity at two different positions, the centreline and close to the wall, with the same streamwise coordinate.

A three-dimensional high-order flux reconstruction lattice boltzmann flux solver for incompressible laminar and turbulent flows

A three-dimensional (3D) high-order flux reconstruction lattice Boltzmann flux solver (FR-LBFS) is developed in this paper for accurate and efficient simulations of incompressible laminar and turbulent flows. The original lattice Boltzmann flux solver (LBFS) is a second-order finite volume method (FVM) which combines the advantages of conventional Navier-Stokes (N-S) solvers and lattice Boltzmann equation (LBE) solvers. But it is not convenient to construct high-order FVM, and the compactness is always a bottleneck. The present work separates LBFS from FVM and combines LBFS with high-order FR scheme. Thus, the FR-LBFS inherits the superiority of LBFS and FR and shares the following attractive features: (i) a fully-explicit arbitrary order compact method, (ii) weakly compressible (WC) model for unsteady incompressible flows and (iii) evaluating inviscid and viscous fluxes simultaneously and no particular technique requirement, such as local discontinuous Galerkin method (LDG), for viscous term discretization. To validate the current method, various 3D incompressible laminar isothermal and thermal numerical experiments are presented first. Good agreements are achieved between the current results and the previous experimental and numerical data whilst the present high-order solver adopt coarse meshes. Furthermore, the ability of the proposed method to perform accurate and stable computations of incompressible decaying homogeneous isotropic turbulent flows and turbulent channel flows with different mesh resolutions and accuracy orders are investigated. The results show that the present 3D FR-LBFS is a promising tool for under-resolved or implicit large eddy simulation (ILES) of incompressible turbulent flows.

A Parallel Computational–Statistical Framework for Simulation of Turbulence: Applications to Data-Driven Fractional Modeling

In this work, an open-source computational–statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport is presented. A parallel implementation of the well-known pseudo-spectral method in addition to the comprehensive record of the statistical and small-scale quantities of the turbulent transport are offered for executing on distributed memory CPU-based supercomputers. The user-friendly workflow and easy-to-run design of the developed package are disclosed through an extensive and step-by-step example. The resulting low- and high-order statistical records vividly verify a well-established and fully developed turbulent state as well as the seamless statistical balance of conservation laws. The post-processing tools provided in this platform would allow the user to easily construct multiple important transport quantities from primitive turbulent fields. The programming codes for this tool are accessible through GitHub (see Data Availability Statement).

Neural-network-based mixed subgrid-scale model for turbulent flow

An artificial neural-network-based subgrid-scale (SGS) model, which is capable of predicting turbulent flows at untrained Reynolds numbers and on untrained grid resolution is developed. Providing the grid-scale strain-rate tensor alone as an input leads the model to predict a SGS stress tensor that aligns with the strain-rate tensor, and the model performs similarly to the dynamic Smagorinsky model. On the other hand, providing the resolved stress tensor as an input in addition to the strain-rate tensor is found to significantly improve the prediction of the SGS stress and dissipation, and thereby the accuracy and stability of the solution. In an attempt to apply the neural-network-based model trained for turbulent flows with a limited range of the Reynolds number and grid resolution to turbulent flows at untrained conditions on untrained grid resolution, special attention is given to the normalisation of the input and output tensors. It is found that the successful generalization of the model to turbulence for various untrained conditions and resolution is possible if distributions of the normalised inputs and outputs of the neural network remain unchanged as the Reynolds number and grid resolution vary. In a posteriori tests of the forced and the decaying homogeneous isotropic turbulence and turbulent channel flows, the developed neural-network model is found to predict turbulence statistics more accurately, maintain the numerical stability without ad hoc stabilisation such as clipping of the excessive backscatter, and to be computationally more efficient than the algebraic dynamic SGS models.

Higher-order statistics and intermittency of a two-fluid Hall–Vinen–Bekharevich–Khalatnikov quantum turbulent flow

The Hall–Vinen–Bekharevich–Khalatnikov (HVBK) model is widely used to numerically study quantum turbulence in superfluid helium. Based on the two-fluid model of Tisza and Landau, the HVBK model describes the normal (viscous) and superfluid (inviscid) components of the flow using two Navier–Stokes type of equations, coupled through a mutual friction force term. We derive transport equations for the third-order moments for each component of velocity involving the fourth-order moments, which are classical probes for internal intermittency at any scale, and revealing the probability of rare and strong fluctuations. Budget equations are assessed through direct numerical simulations of the HVBK flow. We simulate a forced homogeneous isotropic turbulent flow with Reynolds number of the normal fluid (based on Taylor's microscale) close to 100. Values from 0.1 to 10 are considered for the ratio between the normal and superfluid densities. For these flows, an inertial range is not discernible and the restricted scaling range approach is used to take into account the finite Reynolds number (FRN) effect. We analyse the importance of each term in budget equations and emphasize their role in energy exchange between normal and superfluid components. Some interesting features are observed: (i) transport and pressure-related terms are dominant, similarly to single-fluid turbulence; and (ii) the mathematical signature of the FRN effect is weak despite the low value of the Reynolds number. The flatness of the velocity derivatives is finally studied through the transport equations and their limit for very small scales, and it is shown to gradually increase for lower and lower temperatures, for both normal fluid and superfluid. This similarity highlights the strong locking of the two fluids. The flatness factors are also found in reasonable agreement with classical turbulence.

Floc Size Distributions of Cohesive Sediment in Homogeneous Isotropic Turbulence

Floc size distribution is one of the key parameters to characterize flocculating cohesive sediment. An Eulerian–Lagrangian framework has been implemented to study the flocculation dynamics of cohesive sediments in homogeneous isotropic turbulent flows. Fine cohesive sediment particles are modeled as the dispersed phase by the discrete element method, which tracks the motion of individual particles. An adhesive contact model with rolling friction is applied to simulate the particle–particle interactions. By varying the physicochemical properties (i.e., stickiness and stiffness) of the primary particles, the dependence of the mathematical form of the floc size distribution on sediment properties is investigated. At the equilibrium state, the aggregation and breakup processes reach a dynamic equilibrium, in which construction by aggregation is balanced with destruction by breakup, and construction by breakup is balanced with destruction by aggregation. When the primary particles are less sticky, floc size distribution fits better with the lognormal distribution. When the primary particles are very sticky, both the aggregation of smaller flocs and breakup from larger flocs play an equally important role in the construction of the intermediate-sized flocs, and the equilibrium floc size distribution can be better fitted by the Weibull distribution. When the Weibull distribution develops, a shape parameter around 2.5 has been observed, suggesting a statistically self-similar floc size distribution at the equilibrium state.

Generic Energy Function To Predict Particle Positions In 4D-PTV

Recent developments in time-resolved Particle Tracking Velocimetry (4D-PTV) consistently improved tracking accuracy and robustness by introducing predictive algorithms such as Shake-The-Box (STB). We propose a generic nondimensional energy function to predict particle positions by leveraging additional information from coherent neighbour motions. The proposed energy function is a combination of position history, neighbour velocity and acceleration terms. Coherent neighbours are quantified by locally utilising Finite Time Lyapunov Exponent (FTLE) as an objective Lagrangian Coherent Structure (LCS) diagnostic method. Synthetic analysis of the wake behind a smooth cylinder at Reynolds number equal to 3900 showed that the optimal solution of the minimised energy function could be modelled as a function of the measurement uncertainties. The model was assessed with the 2D homogeneous isotropic turbulent flow (HIT) as well and was found to be case and Reynolds independent. Results of the 4D-PTV experimental study of the same wake flow configurations are reported. We compared predicted positions with the optimised final positions of STB. It was found that the generic energy function succeeded in estimating particle positions with minimum deviation to the optimised positions in comparison with other techniques.

Effect of electrostatic forces on the dispersion of like-charged solid particles transported by homogeneous isotropic turbulence

The effect of electrostatic forces on the dispersion of small like-charged inertial particles transported by a homogeneous isotropic turbulent flow is analysed by means of direct numerical simulations coupled with the Lagrangian tracking of charged particles. The results show that particle dispersion decreases for increasing charge. Since turbulent particle dispersion is related to the intensity of particle agitation and to the Lagrangian particle integral time scale, we analyse the effects of electrostatic forces on these two quantities. Particle agitation decreases for increasing particle charge. In fact, particle kinetic energy is not directly modified by electrostatic forces, which are conservative, it is rather the particle entrainment by fluid turbulence that is modified. To support this claim, one shows that the fluid–particle velocity covariance is destructed by electrostatic forces, a destruction can be predicted by drawing an analogy between inter-particle collisions and Coulomb collisions. As expected, electrostatic forces decorrelate particle velocities leading to a decrease of the Lagrangian particle integral time scale. Finally, one shows that the analogy with inter-particle collisions allows us to predict the reduction of particle dispersion.

A sub-grid scale cavitation inception model

Unresolved pressure fluctuations at the sub-grid scale (SGS) level of large eddy simulation (LES) or Reynolds-averaged Navier–Stokes computations affect cavitation inception predictions, as SGS low pressures are simply ignored. We present a framework to take the unresolved SGS flow into account. Representing the SGS flow as canonical turbulence, in this paper, homogeneous isotropic turbulence (HIT), the pressure fluctuations, and transport and cavitating behavior of nuclei in such turbulence can be evaluated from direct numerical simulations (DNS) and used to create a model of cavitation inception that accounts for SGS fluctuations. To accomplish this, nuclei of different sizes were transported in DNS of HIT using their pressure history to drive the Rayleigh–Plesset equation that simulates bubble dynamics. In this way, expected average cavitation frequencies were tabulated for a range of SGS Taylor scale Reynolds numbers (Reλ), nucleus size, turbulent kinetic energy dissipation rate, and mean pressure. The model uses this table to estimate the cavitation event rate in each cell of a computational fluid dynamics solution. Inception can then be predicted by comparing the total cavitation rate with the detection criterion. The model is first assessed on two cases of HIT (at Reλ = 240 and 324) by comparing the pressure statistics, which it predicts in LES runs using the SGS cavitation model against the statistics of DNS. Then, a high Reλ (1660–1880) HIT flow is simulated using LES, and cavitation events are compared against experimental data. The inception model successfully predicts the inception pressure and the cavitation rates in the flow.

A data-driven dynamic nonlocal subgrid-scale model for turbulent flows

We developed a novel autonomously dynamic nonlocal turbulence model for the large and very large eddy simulation (LES, VLES) of homogeneous isotropic turbulent flows. The model is based on a generalized (integer-to-noninteger)-order Laplacian of the filtered velocity field, and a novel dynamic model has been formulated to avoid the need for tuning the model constant. Three data-driven approaches were introduced for the determination of the fractional-order to have a model that is totally free of any tuning parameter. Our analysis includes both the a priori and the a posteriori tests. In the former test, using a high-fidelity and well-resolved dataset from direct numerical simulations (DNSs), we computed the correlation coefficients for the stress components of the subgrid-scale (SGS) stress tensor and the one we get directly from the DNS results. Moreover, we compared the probability density function of the ensemble-averaged SGS forces for different filter sizes. In the latter, we employed our new model along with other conventional models including the static and dynamic Smagorinsky models into our pseudo-spectral solver and tested the final predicted quantities. The results of the newly developed model exhibit an expressive agreement with the ground-truth DNS results in all components of the SGS stress and forces. Also, the model exhibits promising results in the VLES region as well as the LES region, which could be remarkably important for cost-efficient nonlocal turbulence modeling, e.g., in meteorological and environmental applications.

Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows.

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-fluid density ratios respond to the turbulence. Overall particle dynamics in the homogeneous isotropic turbulence such as the Lagrangian statistics of single particle and the preferential concentration of particles are investigated. Results show that particle acceleration and angular acceleration are more intermittent than velocity and angular velocity for finite-size particles with different particle-fluid density ratios. The preferential concentration of particles is investigated using radial distribution function and Voronoï tessellation, and the preferential concentration is more profound for particles with two intermediate particle-fluid density ratios. The Voronoï analysis indicates that the distribution of Voronoï cells satisfy the log-normal distribution better than the gamma distribution. The mechanism of preferential concentration is analyzed using the sweep-stick mechanism and drift mechanism. Results show that although a higher probability of having particles located near the sticky points is found, the sticky mechanism is very weak for large density ratios. The particle clustering is then found to be better qualitatively described by the drift mechanism.

Favre-filtered LES-VOF of two-phase flows with eddy viscosity-based subgrid closure models: An a-posteriori analysis

Developing functional closure models for all the subgrid scale (SGS) physics in the large eddy simulation (LES) of turbulent two-phase flows is yet a challenging task due to the complicated turbulence-interface interactions. Our recent study (Saeedipour and Schneiderbauer, 2019) has revisited the classical eddy viscosity concept for the two-phase flows and proposed a new approach to include surface tension into the subgrid eddy viscosity. It has revealed an a-priori competence for the accurate simulation of the interfacial turbulence using the volume of fluid (VOF) method. The present study aims to exploit the potentials of this approach in an a-posteriori manner, which could be an important step towards the fully-functional LES models for two-phase flows. On the basis of the Favre-filtered governing equations, the corrected eddy viscosity model is adopted to close the convective, surface tension, and continuity SGS terms and establishes a functional LES-VOF approach. The models are implemented into an OpenFOAM-based geometric VOF solver. To perform the a-posteriori analysis two benchmark problems are considered: (i) a 2D turbulent phase inversion as also used for a-priori analysis, and (ii) a 3D freely-decaying, homogeneous isotropic turbulent flow in the presence of an initially-flat interface. The results reveal that compared to the conventional Smagorinsky model, the proposed LES-VOF method reveals a better performance in predicting the local turbulence characteristics as well as the energy spectra, particularly at flows with density contrasts. Also, the size distribution of the droplets shows a better agreement with the fully-resolved data. The a-posteriori analysis further unveils the importance of subgrid surface tension and the SGS residual term in the continuity equation in the development of the interfacial characteristics. The original contribution of this study lies in proposing a full LES approach for the two-phase flows with functional SGS models based on the revisited eddy viscosity concept. This method can be used for more accurate coarse-grid simulation of industrial problems with dispersed droplet regimes.

A priori analysis of subgrid-scale terms in compressible transcritical real gas flows

Of interest to the research community dealing with real gas flows, this study analyzes the influence of the physical complexity of real gases on the amplitude of subgrid-scale (SGS) terms present in the filtered Navier–Stokes equations to be solved in large eddy simulations. The direct numerical simulation results of three academic configurations (homogeneous isotropic turbulence, mixing layer, and channel flow) are filtered from the largest scale in the domain down to the Kolmogorov length scale. The analysis of the filtered flow variables consistently shows that the SGS turbulent stress and the SGS pressure cannot be neglected in the momentum equation. In the total energy equation, SGS pressure work and SGS internal and kinetic fluxes are found to be significant in the inertial zone of the turbulent kinetic energy spectrum. Since in the inertial zone, which corresponds to large filter sizes, specific models have not yet been designed for some of these terms, this study calls for such a modeling effort that will benefit the real gas and organic Rankine cycles research communities.