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The unsteady Reynolds-averaged Navier–Stokes (URANS) equations provide a computationally efficient tool to simulate unsteady turbulent flows for a wide range of applications. To account for the errors introduced by the turbulence closure model, recent works have adopted data assimilation (DA) to enhance their predictive capabilities. Recognizing the challenges posed by the computational cost of four-dimensional variational DA for unsteady flows, we propose a three-dimensional DA framework that incorporates a time-discrete Fourier transform of the URANS equations, facilitating the use of the stationary discrete adjoint method in Fourier space. Central to our methodology is the introduction of a corrective, divergence-free, and unsteady forcing term, derived from a Fourier series expansion, into the URANS equations. This term aims at mitigating discrepancies in the modeled divergence of Reynolds stresses, allowing for the tuning of stationary parameters across different Fourier modes. While designed to accommodate multiple modes in general, the basic capabilities of our framework are demonstrated for a setup that is truncated after the first Fourier mode. The effectiveness of our approach is demonstrated through its application to turbulent flow around a two-dimensional circular cylinder at a Reynolds number of 3900. Our results highlight the method's ability to reconstruct mean flow accurately and improve the vortex shedding frequency (Strouhal number) through the assimilation of zeroth mode data. Additionally, the assimilation of first mode data further enhances the simulation's capability to capture low-frequency dynamics of the flow, and finally, it runs efficiently by leveraging a coarse mesh. [ABSTRACT FROM AUTHOR]

This study continues the exploration of temporal large-eddy simulation, particularly the extension of the temporal direct deconvolution method (TDDM) with a regularization term based on spatial dissipation. Furthermore, we aim to put insight stemming from previous work to test. Specifically, the hypothesis is that the temporal residual-stress leads to a reduction of the required artificial dissipation in under-resolved simulations. Moreover, this work seeks corroborate earlier discoveries with a posteriori results. We perform a numerical examination of two different spatial regularization terms in conjunction with TDDM: a spatial variant of selective frequency damping, functioning as a relaxation term that gradually drifts the velocity toward the filtered velocity, and the dynamic Smagorinsky model incorporating a prefactor. We test various cases, including the Taylor–Green vortex flow with a Reynolds number of Re = 3000, forced homogeneous isotropic turbulence with R e λ = 200 , turbulent channel flow at R e τ = 590 , and the flow over a periodic hill with Re = 10 935. Additionally, we also analyze the various dissipation contributions in TDDM as well as their interrelations. We also discuss grid artifacts and energy budget errors using these to compare the different models. Our results confirm the hypothesis that residual-stress dissipation reduces the necessary artificial dissipation. Because of the numerical ill-conditioning of deconvolution, whether temporal or spatial, there are practical limitations in the size of the filter width. Due to these limitations, the impact remains relatively minor. The a posteriori results of the new spatial regularization term show it to be effective in eliminating energy from the high wavenumber range. [ABSTRACT FROM AUTHOR]

Turbulent reactive flows laden with droplets appear in various energy systems but are difficult to understand and parametrize. Such flows involve interactions of turbulent fluctuations, phase changes, and chemical reactions that give rise to complex phenomena. To improve our knowledge, we performed direct numerical simulations of a canonical shear flow. It is composed of a hot, quiescent outer layer and a cold, turbulent inner layer that is laden with droplets. Due to the turbulent fluctuations, the droplets form clusters. Due to the high temperatures, the droplets evaporate quickly and flames emerge spontaneously at the interface of the two layers. We observed premixed flames that enclose droplet clusters and diffusion flames that enclose vapor pockets or single droplets. To examine these flame structures in more detail, we varied the droplet size, droplet loading, and shear rate. We found that the droplet size and droplet loading have significant effects, whereas the shear rate has only subtle effects. [ABSTRACT FROM AUTHOR]

In this work, a numerical study on molecular beam scattering of a nitrogen molecule from a graphite surface has been performed. The study was carried out using the molecular dynamics method. The focus of the study is mainly placed on investigating the scattering dynamics in the case of strong rotational non-equilibrium, defined here as a state in which rotational temperature of a molecule strongly deviates from the room temperature. To that end, the incident beam velocity and initial rotational energy of nitrogen molecules have been varied greatly in order to capture a broad range of possible initial states. The obtained results provide valuable insight into the nature of energy transfer occurring during collisions and help to quantify the intensity of rotational–translational coupling between inner kinetic modes in gas–surface collisions. Consequently, the collected data can potentially be used for more accurate characterization of the respective phenomena and improve the quality of boundary models used in rarefied gas flow simulations. [ABSTRACT FROM AUTHOR]

This paper examines droplets that cluster and evaporate in reactive turbulence with direct numerical simulations. The flows are statistically homogeneous and isotropic with mass loadings of about 0.1, Stokes numbers of about 1, and Taylor-scale Reynolds numbers of about 40. Our simulation results reveal diffusion and premixed flames. When the mass loading is small or the Stokes number is large, clusters contain few droplets such that diffusion flames surround single droplets. However, when the mass loading is large or the Stokes number is small, clusters contain many droplets such that premixed flames propagate through clusters and diffusion flames surround clusters. [ABSTRACT FROM AUTHOR]

In this work, a gas separation approach based on the selective rotational excitation of different species is investigated. The presented method is particularly suitable for separating gases of similar or equal masses, such as isotopes and isomers. The selective rotational excitation is achieved by a targeted application of multiple non-resonant ultrashort laser pulses. Upon collision with a solid surface, a part of the excited rotational energy gets transferred into translational energy. By creating a discernible difference in average thermal velocities between the species of similar masses, an increased diffusivity of the excited species can be utilized for its successful separation. In order to test the validity of the novel separation technique, a comprehensive computational framework was developed. The energy transfer in gas–surface collisions was analyzed in great detail using a state-of-the-art molecular dynamics code, and the obtained data offered invaluable insight into the nature of scattering dynamics. Furthermore, a novel data-driven approach to gas–surface interaction modeling based on the recently introduced distribution element tree method was proposed. Relevant numerical and experimental data on the selective rotational excitation were gathered, and they served as an input for the performed numerical simulations. Using the developed computational framework, the validity of the proposed separation scheme was tested on a mixture of two species with identical mass. The obtained data offer numerical evidence supporting the proposed separation concept. [ABSTRACT FROM AUTHOR]

This paper investigates droplets that evaporate and cluster in shear turbulence with direct numerical simulations. The flows are statistically stationary and homogeneous, which reduces the physical complexity and simplifies the statistical analysis. The mass loadings are about 0.1, the Stokes numbers are about 1, and the Taylor-scale Reynolds numbers are about 60. The simulations show that the clusters are anisotropic and inclined toward the flow direction on large scales, but isotropic on small scales. When the mass loading increases, the clusters contain more droplets, but their size remains unchanged, and the droplets in clusters experience higher vapor mass fractions. When the Stokes number increases, the clusters contain fewer droplets and become larger, and the droplets in clusters experience lower vapor mass fractions. When the Reynolds number increases, the clusters contain more, smaller droplets and become smaller, and the inclination angles of the clusters change. [ABSTRACT FROM AUTHOR]

In this work, we propose an approach for Temporal Large-Eddy Simulation (TLES) with direct deconvolution. In contrast to previous approaches such as the Temporal Approximate Deconvolution Model (TADM) by Pruett et al. ["A temporal approximate deconvolution model for large-eddy simulation," Phys. Fluids 18, 028104 (2006)], the non-filtered velocity field is recovered using the differential form of the filter operation rather than from a truncated series expansion of the inverse filter operator. This direct deconvolution is used to obtain formal closure of an analytic evolution equation of the temporal residual-stress tensor. Thus, the Temporal Direct Deconvolution Model (TDDM) has advantages relative to the TADM in being both more accurate and requiring less computational effort. As for the TADM, a secondary regularization term based on selective frequency damping is employed. The TDDM was implemented in the spectral element code Nek5000 (Argonne National Laboratory, NEK5000 Version 17.0, 2019, https://nek5000.mcs.anl.gov) to simulate two canonical incompressible flows as three test cases: an a priori test case of Homogeneous Isotropic Turbulence (HIT) at Reλ = 50, a greatly coarsened a posteriori HIT case at Reλ = 190, and an a posteriori highly anisotropic turbulent channel flow at Reτ = 180. Analyses of the energy spectrum, the mean flow, the root-mean-square of the velocity fluctuations, and the Reynolds stresses are presented. The results demonstrate a significant improvement compared to no-model solutions regarding the mean flow in the turbulent channel and the energy spectrum in the HIT case, while the computational cost is reduced dramatically compared to the direct numerical simulation. [ABSTRACT FROM AUTHOR]

Direct simulation Monte-Carlo (DSMC) is the most established method for rarefied gas flow simulations. It is valid from continuum to near vacuum, but in cases involving small Knudsen numbers (Kn), it suffers from high computational cost. The Fokker-Planck (FP) method, on the other hand, is almost as accurate as DSMC for small to moderate Kn, but it does not have the computational drawback of DSMC, if Kn is small [P. Jenny, M. Torrilhon, and S. Heinz, "A solution algorithm for the fluid dynamic equations based on a stochastic model for molecular motion," J. Comput. Phys. 229, 1077–1098 (2010) and H. Gorji, M. Torrilhon, and P. Jenny, "Fokker–Planck model for computational studies of monatomic rarefied gas flows," J. Fluid Mech. 680, 574–601 (2011)]. Especially attractive is the combination of the two approaches leading to the FP-DSMC method. Opposed to other hybrid methods, e.g., coupled DSMC/Navier-Stokes solvers, it is relatively straightforward to couple DSMC with the FP method since both are based on particle solution algorithms sharing the same data structure and having similar components. Regarding the numerical accuracy of such particle methods, one has to distinguish between spatial truncation errors, time stepping errors, statistical errors and bias errors. In this paper, the bias error of the FP method is analyzed in detail, and it is shown how it can be reduced without increasing the particle number to an exorbitant level. The effectiveness of the discussed bias error reduction scheme is demonstrated for uniform shear flow, for which an analytical reference solution was derived. [ABSTRACT FROM AUTHOR]

In this work, a data-based approach to gas-surface interaction modeling, which employs the recently introduced distribution element tree (DET) method, is proposed. The DET method allows efficient data-driven probability density function (PDF) estimations with the possibility of conditional and unconditional random number resampling from the constructed distributions. As part of our ongoing research on gas-surface interaction, a comprehensive molecular dynamics (MD) study was performed, where the scattering of a nitrogen molecule from a graphite surface was investigated. Our aim here is to demonstrate how the DET method can be used in combination with the obtained MD database for constructing a generalized kernel of gas-surface interaction and for generating postscattered samples directly from the MD data itself. The major benefit of this approach is that it preserves all the relevant physics contained within numerical or experimental data, without the need for new kernel developments or accommodation coefficient calibrations. A direct comparison between the proposed approach and a classical scattering kernel used in rarefied gas flow simulations was carried out in the case of molecular beam scattering of rotationally hot and cold nitrogen from a solid surface. A further comparison between the proposed method and the available experimental data was also performed. Additionally, the ability of the DET-based kernel to satisfy the reciprocity condition, which ensures energy conservation in the case of thermal equilibrium, is demonstrated. [ABSTRACT FROM AUTHOR]

The efficiency of stochastic particle schemes for large scale simulations relies on the ability to preserve a uniform distribution of particles in the whole physical domain. While simple particle split and merge algorithms have been considered previously, this study focuses on particle management based on a kernel density approach. The idea is to estimate the probability density of particles and subsequently draw independent samples from the estimated density. To cope with that, novel methods are devised in this work leading to efficient algorithms for density estimation and sampling. For the density inference, we devise a bandwidth with a bounded bias error. Furthermore, the sampling problem is reduced to drawing realizations from a normal distribution, augmented by stratified sampling. Thus, a convenient and efficient implementation of the proposed scheme is realized. Numerical studies using the devised method for direct simulation Monte-Carlo show encouraging performance. [ABSTRACT FROM AUTHOR]

This letter investigates the clustering of particles in isotropic turbulence sustained by linear and spectral forcing. The Stokes numbers range from 0.1 to 100. The time series of particles are analyzed with autocorrelation functions of the particle velocity and local fluid velocity. The spatial distributions of particles are analyzed with probability density functions of Voronoï volumes. These statistics show significant differences between the clustering of particles in linearly and spectrally forced turbulence. [ABSTRACT FROM AUTHOR]

We study the capability of the One-Dimensional-Turbulence (ODT) model to simulate the turbulent transport and mixing of multiple passive scalars in homogeneous isotropic stationary turbulence. To this end, forcing schemes that have been widely used for stationary three-dimensional direct numerical simulations are adapted to the ODT framework and the effects of the model and input parameters on the steady state properties are discussed. We observe the model's ability to convincingly represent the physical features of single-scalar mixing and variance decay, but also its limited qualitative accuracy in the multiple scalar case, especially concerning the scalar joint probability density function, which is of importance for reactive flow computations. [ABSTRACT FROM AUTHOR]

The present paper investigates droplet laden turbulent gas flows with point droplet direct numerical simulations. A novel flow configuration is presented, which allows us to simulate statistically stationary homogeneous isotropic regions of turbulent sprays. This configuration enables a physical analysis with small statistical errors under controllable conditions. The length scales of clusters are analyzed with spectra of the droplet number density and vapor mass fraction fluctuations. The local conditions in clusters and voids are analyzed with probability density functions of the local droplet number density, local vapor mass fraction, and evaporation rate. Effects of the mass loading and Stokes number on the clustering of droplets and the mixing of vapor are characterized, and the compositions of clusters and voids are examined. As the mass loading increases from 2.5% to 12.5%, the fluctuations in the vapor mass fraction and droplet number density increase almost equally at all length scales. Clusters contain more droplets that together release more vapor, but their characteristic size remains unchanged. As the mean Stokes number increases from 1 to 4, the fluctuations in the vapor mass fraction and droplet number density decrease predominantly at small length scales. Clusters contain fewer droplets that together release less vapor, and their characteristic size increases. At a mass loading of 7.5% and a mean Stokes number of 2, clusters contain considerably more droplets and vapor than voids. Droplets located in clusters therefore evaporate more slowly than droplets located in voids. [ABSTRACT FROM AUTHOR]

In this work, the energy transfer in gas-surface collisions is investigated using the molecular dynamics method. The numerical setup consists of a nitrogen molecule scattering from a graphite surface. The main focus is put on the energy redistribution between different molecular kinetic modes and the surface for the case of strong thermal non-equilibrium. The thermal non-equilibrium is defined as the state when either translational or rotational temperature of impinging molecules differs significantly from that of the surface. Accordingly, two different scenarios have been examined, including rotational and translational excitation of the initial molecular state. In contrast to the molecular beam method, the initial molecular velocities are sampled from the equilibrium Maxwellian distribution, ensuring isotropic incidence angles and energies. The obtained results are expressed in the form of energy transfer coefficients, which are used to quantify the normalized energy loss or gain in a specific mode. Furthermore, the velocity distributions of reflected molecules are analyzed and compared with some of the available wall kernels, providing further insight into the nature of the energy transfer dynamics and scattering process. Additionally, the numerical setup is tested against the available molecular beam experimental data and the obtained results were used to select a suitable numerical force field. [ABSTRACT FROM AUTHOR]

This work presents a kinetic wall boundary model for diatomic gas molecules. The model is derived by generalizing the Cercignani-Lampis-Lord gas-surface interaction kernel in order to account for the gas internal degrees of freedom. Here, opposed to the extensions by Lord ["Some extensions to the Cercignani-Lampis gas-surface scattering kernel," Phys. Fluids 3, 706-710 (1991)], energy exchange between different molecular modes is honored and thus, different physical phenomena arising from inelastic gas-surface collisions can be described. For practical implementations of the model, a Monte-Carlo algorithm was devised, which significantly reduces the computational cost associated with sampling. Comparisons of model predictions with experimental and molecular dynamics data exhibit good agreement. Moreover, simulation studies are performed to demonstrate how energy transfers between different modes due to wall collisions can be exploited for gas separation. [ABSTRACT FROM AUTHOR]

A Fokker-Planck based kinetic model is presented here, which also accounts for internal energy modes characteristic for diatomic gas molecules. The model is based on a Fokker-Planck approximation of the Boltzmann equation for monatomic molecules, whereas phenomenological principles were employed for the derivation. It is shown that the model honors the equipartition theorem in equilibrium and fulfills the Landau-Teller relaxation equations for internal degrees of freedom. The objective behind this approximate kinetic model is accuracy at reasonably low computational cost. This can be achieved due to the fact that the resulting stochastic differential equations are continuous in time; therefore, no collisions between the simulated particles have to be calculated. Besides, because of the devised energy conserving time integration scheme, it is not required to resolve the collisional scales, i.e., the mean collision time and the mean free path of molecules. This, of course, gives rise to much more efficient simulations with respect to other particle methods, especially the conventional direct simulation Monte Carlo (DSMC), for small and moderate Knudsen numbers. To examine the new approach, first the computational cost of the model was compared with respect to DSMC, where significant speed up could be obtained for small Knudsen numbers. Second, the structure of a high Mach shock (in nitrogen) was studied, and the good performance of the model for such out of equilibrium conditions could be demonstrated. At last, a hypersonic flow of nitrogen over a wedge was studied, where good agreement with respect to DSMC (with level to level transition model) for vibrational and translational temperatures is shown. [ABSTRACT FROM AUTHOR]

In the present study, a unified probability density function formulation for capturing the phenomena of turbulence modification of the continuous phase due to the dispersed phase turbulence is presented. A stochastic model based on dispersed phase turbulence length scale has been proposed for the purpose. The model has been validated with experimental data [Poelma et al., “Particle fluid interactions in grid-generated turbulence,” J. Fluid Mech. 589, 315 (2007)] on the decay of turbulence of the flow seeded with ceramic particles in a vertical recirculating water channel. The obtained simulation results are in good agreement with the experimental data. Numerical experiments have been performed to investigate the influence of gravity on the decay of the continuous phase Reynolds stresses. For comparison, the influence of dispersed phase turbulence on the continuous phase turbulence without taking gravity into consideration has also been studied. [ABSTRACT FROM AUTHOR]