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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, we focus on a multi-hole pressure-probe-based flow measurement system for wind tunnelmeasurements that provides real-time feedback to a robot probe-manipulator, rendering the system autonomous. The system relies on a novel, computationally efficient flow analysis technique that translates the probe's point measurements of velocity and pressure into an updatable mean flow map that is accompanied by an uncertainty metric. The latter provides guidance to the manipulator when planning the optimal probe path. The probe is then guided by the robot in the flow domain until an available time budget has been exhausted, or until the uncertainty metric falls below a prescribed target threshold in the entire flow domain. We assess the capabilities of our new measurement system using computational fluid dynamics data, for which the ground truth is available in the form of a mean flow field. An application in a real wind tunnel setting is provided as well. [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]

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, 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]

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]

The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient methods are needed. We propose a new method that is based on a decomposition of the unknown distribution in terms of so-called distribution elements (DEs). These elements enable an adaptive and hierarchical discretization of the sample space with small or large elements in regions with smoothly or highly variable densities, respectively. The novel refinement strategy that we propose is based on statistical goodness-of-fit and pairwise (as an approximation to mutual) independence tests that evaluate the local approximation of the distribution in terms of DEs. The capabilities of our new method are inspected based on several examples of different dimensionality and successfully compared with other state-of-the-art density estimators. [ABSTRACT FROM AUTHOR]

We consider two-phase flow and transport in heterogeneous porous media, where the permeability is modeled as a random field. To assess the resulting uncertainty of flow and transport, multilevel Monte Carlo (MLMC) is used. MLMC involves two types of errors: a sampling error and a discretization error, which, under reasonable assumptions, can be conveniently estimated during execution. In this work, we address the question of how to balance the two errors. Furthermore, a simple MLMC parallelization strategy is presented. A numerical comparison of MLMC with standard Monte Carlo (MC) reveals significant gains in computational efficiency at equivalent accuracy. [ABSTRACT FROM AUTHOR]

Highlights: [•] Particle-laden isotropic turbulence is simulated with kinematic simulation (KS). [•] A rigorous validation of KS with direct numerical simulation is presented. [•] KS provides collision frequencies in good agreement with DNS for St around 0 and >2. [Copyright &y& Elsevier]

In subsurface aquifers, dispersion of contaminant, or tracer, is mainly driven by spatial fluctuations in the flow field caused by heterogeneity of the hydraulic conductivity. Measurements of conductivity, however, are usually sparse. To assess the resulting uncertainty in the transport of tracers, Monte Carlo (MC) methods are usually applied, where the transport statistics are sampled over a large number of probable hydraulic conductivity realizations. In this paper, an alternative method is described that provides accurate transport statistics at a computational expense that is 3 orders of magnitude lower than conventional MC. The new method is applicable for conductivity fields with multivariate Gaussian characterization involving conductivity measurements for both small and high log-conductivity variances. The new method is validated against MC for different dispersion scenarios, where the region of interest spans tens of log-conductivity correlation lengths. [ABSTRACT FROM AUTHOR]

Addition of particles or droplets to turbulent liquid flows or addition of droplets to turbulent gas flows can lead to modulation of turbulence characteristics. Corresponding observations have been reported for very small particle or droplet volume loadings ${\Phi }_{v} $ and therefore may be important when simulating such flows. In this work, a modelling framework that accounts for preferential concentration and reproduces isotropic and anisotropic turbulence attenuation effects is presented. The framework is outlined for both Reynolds-averaged Navier–Stokes (RANS) and joint probability density function (p.d.f.) methods. Validations are performed involving a range of particle and flow-field parameters and are based on the direct numerical simulation (DNS) study of Boivin, Simonin & Squires (J. Fluid Mech., vol. 375, 1998, pp. 235–263) dealing with heavy particles suspended in homogeneous isotropic turbulence (Stokes number $\mathit{St}= O(1\text{{\ndash}} 10)$, particle/fluid density ratio ${\rho }_{p} / \rho = 2000$, ${\Phi }_{v} = O(1{0}^{\ensuremath{-} 4} )$) and the experimental investigation of Poelma, Westerweel & Ooms (J. Fluid Mech., vol. 589, 2007, pp. 315–351) involving light particles ($\mathit{St}= O(0. 1)$, ${\rho }_{p} / \rho \gtrsim 1$, ${\Phi }_{v} = O(1{0}^{\ensuremath{-} 3} )$) settling in grid turbulence. The development in this work is restricted to volume loadings where particle or droplet collisions are negligible. [ABSTRACT FROM PUBLISHER]

Simulations of spatially inhomogeneous turbulent mixing in decaying grid turbulence with a joint velocity-concentration probability density function (PDF) method were conducted. The inert mixing scenario involves three streams with different compositions. The mixing model of Meyer ['A new particle interaction mixing model for turbulent dispersion and turbulent reactive flows,' Phys. Fluids 22(3), 035103 (2010)], the interaction by exchange with the mean (IEM) model and its velocity-conditional variant, i.e., the IECM model, were applied. For reference, the direct numerical simulation data provided by Sawford and de Bruyn Kops ['Direct numerical simulation and lagrangian modeling of joint scalar statistics in ternary mixing,' Phys. Fluids 20(9), 095106 (2008)] was used. It was found that velocity conditioning is essential to obtain accurate concentration PDF predictions. Moreover, the model of Meyer provides significantly better results compared to the IECM model at comparable computational expense. [ABSTRACT FROM AUTHOR]

The probability density function (PDF) of the local concentration of a contaminant, or tracer, is an important component of risk assessment in applications that involve flow in heterogeneous subsurface formations. In this paper, a novel joint velocity-concentration PDF method for tracer flow in highly heterogeneous porous media is introduced. The PDF formalism accounts for advective transport, pore-scale dispersion (PSD), and molecular diffusion. Low-order approximations (LOAs), which are usually obtained using a perturbation expansion, typically lead to Gaussian one-point velocity PDFs. Moreover, LOAs provide reasonable approximations for small log conductivity variances (i.e., σ Y2 < 1). For large σ Y2, however, the one-point velocity PDFs deviate significantly from the Gaussian distribution as demonstrated convincingly by several Monte Carlo (MC) simulation studies. Furthermore, the Lagrangian velocity statistics exhibit complex correlations that span a wide range of scales, including long-range correlations due to the formation of preferential flow paths. Both non-Gaussian PDFs and complex long-range correlations are accurately represented using Markovian velocity processes (MVPs) in the proposed joint PDF method. LOA methods can be generalized to some extent by presuming a certain shape for the concentration PDF (e.g., a β PDF fully characterized by the concentration mean and variance). The joint velocity-concentration PDF method proposed here does not require any closure assumptions on the shape of the marginal concentration PDF. The Eulerian joint PDF transport equation is solved numerically using a computationally efficient particle-based approach. The PDF method is validated with high-resolution MC reference data from Caroni and Fiorotto (2005) for saturated transport in velocity fields, which are stationary in space and time, for domains with σ Y2 = 0.05, 1, and 2 and Péclet numbers ranging from 100 to 10,000. PSD is modeled using constant anisotropic dispersion coefficients in both the reference MC computations and our PDF method. [ABSTRACT FROM AUTHOR]

Monte Carlo (MC) studies of flow in heterogeneous porous formations, in which the log-conductivity field is multi-Gaussian, have shown that as the log-conductivity variance σ Y2 increases beyond about 0.5, the one-point velocity probability density functions (PDFs) deviate significantly from Gaussian behavior. The velocity statistics become more complex due to the formation of preferential flow paths, or channels, as σ Y2 increases. Methods that employ low-order approximations (e.g., truncated perturbation expansions) are limited to small σ Y2 and are unable to represent the complex velocity statistics associated with σ Y2 > 1. Here a stochastic transport model for highly heterogeneous domains (i.e., σ Y2 > 1) is proposed. In the model, the Lagrangian velocity components of tracer particles are represented using continuous Markovian stochastic processes in time. The Markovian velocity process (MVP) model is described using a set of first-order ordinary and stochastic differential equations, which are easy to solve using a particle-based method. Once the MVP model is calibrated based on velocity statistics from MC simulations of the flow (hydraulic head and velocity), the MVP-based model can be used to describe the evolution of the tracer concentration field accurately and efficiently. Specifically, the MVP model is validated using MC simulations of longitudinal and transverse tracer spreading due to a point-like injection in the domain. We demonstrate that for σ Y2 > 1, the ensemble-averaged tracer cloud remains markedly non-Gaussian for relatively large travel distances from the point source. The MVP transport model captures this behavior and reproduces the velocity statistics quite accurately. [ABSTRACT FROM AUTHOR]

Probability density function (PDF) methods are an established tool applied for the simulation of turbulent mixing and turbulent reactive flows. Mixing models are required to close the molecular diffusion term in the PDF transport equation. From the nature of molecular diffusion, several requirements or design criteria can be derived for mixing models. All current models have certain shortcomings with respect to these requirements. A new mixing model is presented which fully satisfies almost all requirements. It conserves the mean of an inert scalar, reduces its scalar variance, and relaxes closely to a Gaussian scalar PDF. Multiple inert scalars without differential diffusion effects evolve independently and are kept bounded within their allowable region. Mixing is conditional on the velocity and particle scalar trajectories are continuous in time leading to a model that is local in a weak sense. Validation tests show that the model can reproduce differential diffusion effects and mixing rate dependencies due to variable initial scalar length scales or Reynolds and Schmidt number variations. [ABSTRACT FROM AUTHOR]

Abstract: For the calculation of nonpremixed turbulent flames with thin reaction zones the joint probability density function (PDF) of the mixture fraction and its dissipation rate plays an important role. The corresponding PDF transport equation involves a mixing model for the closure of the molecular mixing term. Here, the parameterized scalar profile (PSP) mixing model is extended to provide the required joint statistics. Model predictions are validated using direct numerical simulation (DNS) data of a passive scalar mixing in a statistically homogeneous turbulent flow. Comparisons between the DNS and the model predictions are provided, which involve different initial scalar-field lengthscales. [Copyright &y& Elsevier]

We devise an efficient methodology to provide a universal statistical description of advection-dominated dispersion (Péclet→∞) in natural porous media including carbonates. First, we investigate the dispersion of tracer particles by direct numerical simulation (DNS). The transverse dispersion is found to be essentially determined by the tortuosity and it approaches a Fickian limit within a dozen characteristic scales. Longitudinal dispersion was found to be Fickian in the limit for bead packs and superdiffusive for all other natural media inspected. We demonstrate that the Lagrangian velocity correlation length is a quantity that characterizes the spatial variability for transport. Finally, a statistical transport model is presented that sheds light on the connection between pore-scale characteristics and the resulting macroscopic transport behavior. Our computationally efficient model accurately reproduces the transport behavior in longitudinal direction and approaches the Fickian limit in transverse direction. [ABSTRACT FROM AUTHOR]

Stochastic Markov processes are used very frequently to model, for example, processes in turbulence and subsurface flow and transport. Based on the weak Chapman-Kolmogorov equation and the strong Markov condition, we present methods to test the Markov hypothesis that is at the heart of these models. We demonstrate the capabilities of our methodology by testing the Markov hypothesis for fluid and inertial particles in turbulence, and fluid particles in the heterogeneous subsurface. In the context of subsurface macrodispersion, we find that depending on the heterogeneity level, Markov models work well above a certain scale of interest for media with different log-conductivity correlation structures. Moreover, we find surprising similarities in the velocity dynamics of the different media considered. [ABSTRACT FROM AUTHOR]