Direct Numerical Simulations Simulations Research Articles

Phase diagram for the onset of circulating waves and flow reversal in inclined falling films

AbstractThe onset of circulating waves, i.e. waves with a circulating eddy in the main wave hump, and the onset of flow reversal, i.e. a vortex in the first capillary minimum, in inclined falling films is investigated as a function of the Reynolds number and inclination number using the weighted integral boundary layer (WIBL) model and direct numerical simulations (DNS). Analytical criteria for the onset of circulating waves and flow reversal based on the wave celerity, the average film thickness and the maximum and minimum film thickness have been approximated using self-similar parabolic velocity profiles. This approximation has been validated by second-order WIBL and DNS simulations. It is shown that the onset of circulating waves in the phase diagram for homoclinic solutions (waves of infinite wavelength) is strongly dependent on the inclination, but independent of the streamwise viscous dissipation effect. On the contrary, the onset of flow reversal shows a clear dependence on the viscous dissipation. Furthermore, simulation results for limit cycles (finite wavelength) reveal a strong increase of the corresponding critical Reynolds number with the excitation frequency. Additionally, a critical ratio between the maximum and substrate film thickness (value of approximately 2.5) was found for the onset of circulating waves, which is independent of wavelength, inclination, viscous dissipation and Reynolds number.

Effect of self-stratification on sediment diffusivity in channel flows and boundary layers: a study using direct numerical simulations

Abstract. Sediment transport in nature comprises of bedload and suspended load, and precise modelling of these processes is essential for accurate sediment flux estimation. Traditionally, non-cohesive suspended sediment has been modelled using the advection–diffusion equation (Garcia, 2008), where the success of the model is largely dependent on accurate approximation of the sediment diffusion coefficients. The current study explores the effect of self-stratification on sediment diffusivity using suspended sediment concentration data from direct numerical simulations (DNS) of flows subjected to different levels of stratification, where the level of stratification is dependent on the particle size (parameterized using particle fall velocity Ṽ and volume-averaged sediment concentration (parameterized using shear Richardson number Riτ. Two distinct configurations were explored, first the channel flow configuration (similar to flow in a pipe or a duct) and second, a boundary-layer configuration (similar to open-channel flow). Self-stratification was found to modulate the turbulence intensity (Cantero et al., 2009b), which in turn was found to reduce vertical sediment diffusivity in portions of the domain exposed to turbulence damping. The effect of particle size on vertical sediment diffusivity has been studied in the past by several authors (Rouse, 1937; Coleman, 1970; Nielsen and Teakle, 2004); so in addition to the effect of particle size, the current study also explores the effect of sediment concentration on vertical sediment diffusivity. The results from the DNS simulations were compared with experiments (Ismail, 1952; Coleman, 1986) and field measurements (Coleman, 1970), and were found to agree qualitatively, especially for the case of channel flows. The aim of the study is to understand the effect of stratification due to suspended sediment on vertical sediment diffusivity for different flow configurations, in order to gain insight of the underlying physics, which will eventually help us to improve the existing models for sediment diffusivity.

Magnetic flux concentrations from dynamo-generated fields

The mean-field theory of magnetized stellar convection gives rise to the two possibility of distinct instabilities: the large-scale dynamo instability, operating in the bulk of the convection zone, and a negative effective magnetic pressure instability (NEMPI) operating in the strongly stratified surface layers. The latter might be important in connection with magnetic spot formation, but the growth rate of NEMPI is suppressed with increasing rotation rates, although recent direct numerical simulations (DNS) have shown a subsequent increase in the growth rate. We examine quantitatively whether this increase in the growth rate of NEMPI can be explained by an alpha squared mean-field dynamo, and whether both NEMPI and the dynamo instability can operate at the same time. We use both DNS and mean-field simulations (MFS) to solve the underlying equations numerically either with or without an imposed horizontal field. We use the test-field method to compute relevant dynamo coefficients. DNS show that magnetic flux concentrations are still possible up to rotation rates above which the large-scale dynamo effect produces mean magnetic fields. The resulting DNS growth rates are quantitatively well reproduced with MFS. As expected, for weak or vanishing rotation, the growth rate of NEMPI increases with increasing gravity, but there is a correction term for strong gravity and large turbulent magnetic diffusivity. Magnetic flux concentrations are still possible for rotation rates above which dynamo action takes over. For the solar rotation rate, the corresponding turbulent turnover time is about 5 hours, with dynamo action commencing in the layers beneath.

Computational Studies of Two-Dimensional Rayleigh-Taylor Driven Mixing for a Tilted-Rig

A time-dependent, incompressible, turbulent mixing problem, referred here to as the “tilted-rig,” is defined, based results from an experiment that involved the introduction of a large-scale overturning motion, with a superposed localized Rayleigh-Taylor (RT) driven mixing. The problem serves to examine the development of RT turbulent mixing while being strained by a large-scale two-dimensional confined motion. Care is taken to define the problem in detail so others might use the definition, and the results, to help develop advanced models of buoyancy driven mixing in complex flows. Aside from a careful definition, the problem has been solved using two different implicit-large-Eddy-simulations (ILES) based codes, and with a direct numerical simulations (DNS) code. Two-dimensional and one-dimensional mix metrics are defined, and then used to examine the development of the mixing region, and the overall evolution of the flow. Comparison of simulations with experiment reveals that large-scale overturning can be well captured in all the simulations, similarly central mix widths, and spike/bubble sidewall penetrations are also in good agreement. A comparison between the different simulation methodologies, ILES and DNS, reveals an overall good agreement between mix metrics such as the amount of molecular mixing. The DNS simulations reveal a dependency on Reynolds number that merits further experimental work.

Mean-field and direct numerical simulations of magnetic flux concentrations from vertical field

Strongly stratified hydromagnetic turbulence has previously been found to produce magnetic flux concentrations if the domain is large enough compared with the size of turbulent eddies. Mean-field simulations (MFS) using parameterizations of the Reynolds and Maxwell stresses show a negative effective magnetic pressure instability and have been able to reproduce many aspects of direct numerical simulations (DNS) regarding the growth rate of this large-scale instability, shape of the resulting magnetic structures, and their height as a function of magnetic field strength. Unlike the case of an imposed horizontal field, for a vertical one, magnetic flux concentrations of equipartition strength with the turbulence can be reached. This results in magnetic spots that are reminiscent of sunspots. Here we want to find out under what conditions magnetic flux concentrations with vertical field occur and what their internal structure is. We use a combination of MFS, DNS, and implicit large-eddy simulations to characterize the resulting magnetic flux concentrations in forced isothermal turbulence with an imposed vertical magnetic field. We confirm earlier results that in the kinematic stage of the large-scale instability the horizontal wavelength of structures is about 10 times the density scale height. At later times, even larger structures are being produced in a fashion similar to inverse spectral transfer in helically driven turbulence. Using turbulence simulations, we find that magnetic flux concentrations occur for different values of the Mach number between 0.1 and 0.7. DNS and MFS show magnetic flux tubes with mean-field energies comparable to the turbulent kinetic energy. The resulting vertical magnetic flux tubes are being confined by downflows along the tubes and corresponding inflow from the sides, which keep the field concentrated.

Direct numerical simulation of top-down and bottom-up diffusion in the convective boundary layer

AbstractA direct numerical simulation (DNS) of an unstably stratified convective boundary layer with system rotation was performed to study top-down and bottom-up diffusion processes. In order to better understand near-wall dynamics associated with scalar diffusion in the absence of surface roughness, direct simulation is utilized to numerically integrate the governing equations that model the atmospheric boundary layer. The ratio of the inversion height to Obukhov length scale, ${z}_{i} / L= - 49. 1$, indicates moderately strong heating for the case studied. Two passive scalars were initialized in the flow field: the first with a zero gradient at the wall (${q}_{t} $, top-down diffusion), and the second with a non-zero wall gradient and a close-to-zero gradient at the height of the temperature inversion (${q}_{b} $, bottom-up diffusion). Scalar flux, variance and covariance profiles show good agreement between the DNS and rough-wall large-eddy simulation (LES). The top-down gradient function displays a slight increase in amplitude, indicating reduced mixing efficiency for the smooth-wall, low-Reynolds-number convective boundary layer. For the bottom-up process, the gradient matches other rough-wall simulations. The only notable difference between the smooth-wall DNS data and other rough-wall simulations is an increase in the gradient function near the wall. This indicates that the bottom-up gradient functions for a rough wall and a smooth wall are nearly identical except as the viscous sublayer is approached. Finally, a new empirical model for the scalar variance of a bottom-up scalar is proposed: here, a single function replaces two piecewise relationships to accurately capture the DNS results up to the viscous sublayer. The scalar covariance between top-down and bottom-up processes agrees with rough-wall and tree-canopy LES results; this indicates that the scalar covariance is independent of both Reynolds number and surface friction.

Direct numerical simulations of boundary condition effects on the propagation of density current in wall-bounded and open channels

The propagation of density current under different boundary conditions is investigated using high resolution direct numerical simulations (DNS). A revised Kleiser and Schumann influence-matrix method is used to treat the general Robin type velocity boundary conditions and the related “tau” error corrections in the numerical simulations. Comparison of the simulation results reveals that the boundary conditions change the turbulent flow field and therefore the propagation of the front. This paper mainly focuses on the effects of boundary conditions and initial depth of the dense fluid. The differences in energy dissipation and overall front development in wall-bounded and open channels are examined. Through DNS simulations, it is evident that with the decrease of initial release depth ratio (\(D/H\)), the effect of the top boundary becomes less important. In wall-bounded channels, there are three distinctive layers in the vertical distribution of energy dissipation corresponding to the contributions from bottom wall, interface, and top wall, respectively. In open channels, there are only two layers with the top one missing due to the shear free nature of the boundary. It is found that the energy dissipation distribution in the bottom layer is similar for cases with the same \(D/H\) ratio regardless the top boundary condition. The simulation results also reveal that for low Reynolds number cases, the energy change due to concentration diffusion cannot be neglected in the energy budget. To reflect the real dynamics of density current, the dimensionless Froude number and Reynolds number should be defined using the release depth \(D\) as the length scale.

Complex chemistry DNS of n-heptane spray autoignition at high pressure and intermediate temperature conditions

Direct Numerical Simulations (DNS) of turbulent n-heptane sprays autoigniting at high pressure (P=24bar) and intermediate air temperature (Tair=1000K) have been performed to investigate the physical mechanisms present under conditions where low-temperature chemistry is expected to be important. The initial turbulence in the carrier gas, the global equivalence ratio in the spray region, and the initial droplet size distribution of the spray were varied. Results show that spray ignition exhibits a spotty nature, with several kernels developing independently in those regions where the mixture fraction is close to its most reactive value ξMR (as determined from homogeneous reactor calculations) and the scalar dissipation rate is low. Turbulence reduces the ignition delay time as it promotes mixing between air and the fuel vapor, eventually resulting in lower values of scalar dissipation. High values of the global equivalence ratio are responsible for a larger number of ignition kernels, due to the higher probability of finding regions where ξ=ξMR. Spray polydispersity results in the occurrence of ignition over a wider range of mixture fraction values. This is a consequence of the inhomogeneities in the mixing field that characterize these sprays, where poorly mixed rich spots are seen to alternate with leaner ones which are well-mixed. The DNS simulations presented in this work have also been used to assess the applicability of the Conditional Moment Closure (CMC) method to the simulation of spray combustion. CMC is found to be a valid method for capturing spray autoignition, although care should be taken in the modelling of the unclosed terms appearing in the CMC equations.

Large eddy simulation models for incompressible magnetohydrodynamics derived from the variational multiscale formulation

Novel large eddy simulation (LES) models are developed for incompressible magnetohydrodynamics (MHD). These models include the application of the variational multiscale formulation of LES to the equations of incompressible MHD. Additionally, a new residual-based eddy viscosity model is introduced for MHD. A mixed LES model that combines the strengths of both of these models is also derived. The new models result in a consistent numerical method that is relatively simple to implement. The need for a dynamic procedure in determining model coefficients is no longer required. The new LES models are tested on a decaying Taylor-Green vortex generalized to MHD and benchmarked against classical LES turbulence models. The LES simulations are run in a periodic box of size [−π, π]3 with 32 modes in each direction and are compared to a direct numerical simulation (DNS) with 512 modes in each direction. The new models are able to account for the essential MHD physics which is demonstrated via comparisons of energy spectra. We also compare the performance of our models to a DNS simulation by Pouquet et al. [“The dynamics of unforced turbulence at high Reynolds number for Taylor–Green vortices generalized to MHD,” Geophys. Astrophys. Fluid Dyn. 104, 115–134 (2010)], for which the ratio of DNS modes to LES modes is 262:144.

A priori testing of a two-dimensional unsteady flamelet model for three-feed combustion systems

A number of interesting combustion applications involve the mixing of multiple fuel or air streams, such as split-injection and dual-fuel internal combustion engines, which are the main focus of this work, or secondary air in gas turbines. In this study, a two-dimensional flamelet formulation for modeling auto-ignition and combustion in multi-stream configurations is presented and validated using two-dimensional direct numerical simulations (DNS). The DNS simulations were carried out for a multi-stream n-heptane mixture in constant volume isotropic turbulence with finite-rate chemistry according to a reduced chemical mechanism which considers 44 species and 185 reactions. The DNS represents two fuel streams and an oxidizer stream, where the second fuel stream is introduced at a time after the first fuel and oxidizer have started to mix. The resulting data are then used to carry out a priori testing of the two-dimensional flamelet model. The flamelet formulation is found to accurately represent the interaction of the multiple stream mixing and chemistry, thus enabling the accurate prediction of the auto-ignition of each fuel stream.

Role of turbulence fluctuations on uncertainties of acoustic Doppler current profiler discharge measurements

This work presents a systematic analysis quantifying the role of the presence of turbulence fluctuations on uncertainties (random errors) of acoustic Doppler current profiler (ADCP) discharge measurements from moving platforms. Data sets of three‐dimensional flow velocities with high temporal and spatial resolution were generated from direct numerical simulation (DNS) of turbulent open channel flow. Dimensionless functions relating parameters quantifying the uncertainty in discharge measurements due to flow turbulence (relative variance and relative maximum random error) to sampling configuration were developed from the DNS simulations and then validated with field‐scale discharge measurements. The validated functions were used to evaluate the role of the presence of flow turbulence fluctuations on uncertainties in ADCP discharge measurements. The results of this work indicate that random errors due to the flow turbulence are significant when: (a) a low number of transects is used for a discharge measurement, and (b) measurements are made in shallow rivers using high boat velocity (short time for the boat to cross a flow turbulence structure).

Direct numerical simulation of the entrainment coefficient and turbulence properties for compressible spatially evolving axisymmetric jets

In order to gain a better insight in the entrainment coefficient and turbulence properties of a spatial evolving round jet flow in the jet development from the near-field region to the far-field region, we performed Direct Numerical Simulation (DNS) of a round jet with Reynolds number equal to 5000. A computational grid consisting of about 500million is used in present DNS simulation, which is the largest grid used in round jet simulation by DNS method. The computational domain extends up to about 100 jet radii in the streamwise direction, which is found to be large enough for the jet to reach a truly self-similar state. Inflow buffer zone is used in our DNS simulation in order to efficiently simulate the fluid entrainment process. The entrainment coefficient, Reynolds stress and turbulent kinetic energy are plotted with a high resolution and sufficient DNS database to understand the evolution of the jet development. The DNS grid resolution is tested by the wave-number spectrum and Kolmogorov length scale. The DNS results are compared explicitly with the experimental data, and some inconsistencies between DNS and experimental data are explained in our research.We found that the inflow buffer region can significantly affect the jet development in the near-field region, but it takes a mild effect on the entrainment process in the transitional and far-field region. By the inspecting of contours of kinetic energy at plane (Z=0), it reveals that main turbulence production takes place in the high-shear regions. After the high-shear regions, the turbulent kinetic energy begins to decrease along the streamwise direction. The strong growth of kinetic energy along the jet axial direction means that inadequate resolution in the steep growth region of kinetic energy will lead to inaccurate results for the DNS of a spatially evolving round jet.

Hybrid MPI + OpenMP parallelization of an FFT-based 3D Poisson solver with one periodic direction

This work is devoted to the development of efficient parallel algorithms for the direct numerical simulation (DNS) of incompressible flows on modern supercomputers. In doing so, a Poisson equation needs to be solved at each time-step to project the velocity field onto a divergence-free space. Due to the non-local nature of its solution, this elliptic system is the part of the algorithm that is most difficult to parallelize. The Poisson solver presented here is restricted to problems with one uniform periodic direction. It is a combination of a block preconditioned Conjugate Gradient (PCG) and an FFT diagonalization. The latter decomposes the original system into a set of mutually independent 2D systems that are solved by means of the PCG algorithm. For the most ill-conditioned systems, that correspond to the lowest Fourier frequencies, the PCG is replaced by a direct Schur-complement based solver. The previous version of the Poisson solver was conceived for single-core (also dual-core) processors and therefore, the distributed memory model with message-passing interface (MPI) was used. The irruption of multi-core architectures motivated the use of a two-level hybrid MPI + OpenMP parallelization with the shared memory model on the second level. Advantages and implementation details for the additional OpenMP parallelization are presented and discussed in this paper. Numerical experiments show that, within its range of efficient scalability, the previous MPI-only parallelization is slightly outperformed by the MPI + OpenMP approach. But more importantly, the hybrid parallelization has allowed to significantly extend the range of efficient scalability. Here, the solver has been successfully tested up to 12800 CPU cores for meshes with up to 10 9 grid points. However, estimations based on the presented results show that this range can be potentially stretched up until 200,000 cores approximately. Finally, several examples of DNS simulations are briefly presented to illustrate some potential applications of the solver.

A novel multiphase DNS approach for handling solid particles in a rarefied gas

A comprehensive model is proposed for multiphase DNS simulations of gas–solid systems involving particles of size comparable to the mean free path of the gas and to that of the bounding geometry. The model can be implemented into any multiphase Direct Numerical Simulation (DNS) method. In the current work, the Volume of Fluid (VOF) method is used, and it is extended to allow for the incorporation of rarefaction effects. For unbounded flow, the model is in excellent agreement with experimental data from the literature. For flows in closed conduits, the model outperforms the alternate approach of using a slip boundary condition at the particle surface for the most relevant degrees of rarefaction and confinement. The proposed model is also able to correctly handle particle–particle interception. The model is intended for low particle Reynolds number flows, and can be applied to resolve in great detail phenomena in a large number of industrial applications (such as filtration of fine particles in porous media).

LARGE EDDY SIMULATION OF LIQUID JET ATOMIZATION

In the past decade, numerical methods for two-phase flows, which are now capable of fully describing both phases and the interface, have progressed to a state of maturity. At present, direct numerical simulations (DNS) are possible even for complex configurations such as atomization processes. However, the numerical resources necessary to completely compute the atomization up to the formation of the final spray are still out of reach. Therefore, the LES approach is very appealing for two-phase flows. Depending on the assumption concerning the relative size of the LES filter compared to the characteristic scale of interface wrinkles, two classes of LES methods have emerged: the first class of LES method is required close to the injector while the second class is needed far from the injector when the spray is formed. The present work describes a modeling proposal that solves this problem by focusing on the transition between these two classes of method for LES of two phase flows. A postulated transport equation of the surface density is used to describe the subgrid spray formation ranging from interface wrinkling, ligaments, and sheets up to the droplets. Issued from RANS formalisms, this transport equation extends the usual spherical geometry given to the liquid structures that compose the subgrid spray. This equation contains several source terms that act on the creation and destruction of the liquid/gas interface. Considering that major breakup processes are due to turbulence in the field near the injector, an appropriate source term is proposed. This source term, also derived from RANS models, introduces a local critical value of surface density related to a critical Weber number that provides information concerning the local equilibrium between turbulent kinetic energy and surface energy. Concerning the velocity field, a standard Smagorinsky approach is considered. The initial results, obtained through the simulation of the atomization of a liquid jet, confirm that the subgrid term of the liquid volume fraction transport equation determines the transition between the resolved interface and the subgrid spray. A LES model for continuous two-phase flows, termed CLES in this paper, is proposed. The CLES model allows for a better description of the liquid dispersion within the calculation domain from both qualitative and quantitative points of view when compared with the usual LES formalism that does not consider subgrid terms for the interfacial contribution. Mean liquid volume fraction profiles are well captured with CLES when compared to '{\it a posteriori}' DNS simulations, and only a weak grid dependency is observed. Grid dependency is generally a major drawback when carrying out LES of interfacial flows. The surface density and behavior are well estimated and described by using a dedicated transport equation. Based on this parameter and thanks to a good estimation of the critical Weber number value, relevant characteristic scales of the subgrid spray in the atomization regime can be obtained.

Relevance of the subgrid-scales for large eddy simulations of turbulence–radiation interactions in a turbulent plane jet

An a priori study based on direct numerical simulation (DNS) of a non-isothermal turbulent plane jet has been carried out in order to analyse the role of the small-scales of turbulence on thermal radiation. Filtered DNS and large eddy simulation (LES) without subgrid-scale (SGS) model have been estimated for the radiative heat transfer. The comparison of the results highlights the subgrid-scale influence over the filtered radiation quantities, such as the radiative intensity and the radiative emission. The influence of the optical thickness is also studied. It is shown that the subgrid-scales are not significant near the centerline of the jet, where the radiative heat transfer is more important, and therefore that the SGS can be neglected in this configuration. However, when the optical thickness increases, the SGS become relevant and SGS modeling may be needed.

MODELING COLLISION OUTCOME IN MODERATELY DENSE SPRAYS

To simulate primary atomization, the dense zone of sprays has to be addressed and new atomization models have been developed as the Eulerian-Lagrangian spray atomization (ELSA) model [Blaisot, J. B., and Yon, J., (2005) Exp. Fluids, 39(6), pp. 977−994]. A transport equation for the liquid/gas interface density is stated and extends the concept of droplet diameter. Several related source terms require modeling attention. This work describes the contribution of collision and coalescence processes. Several questions arise: Is it possible to represent collision/coalescence from an Eulerian description of the flow? What are the key parameters? What are the particular features of collision in dense spray? To answer these questions, a Lagrangian test case, carefully resolved statistically, is used as a basis to evaluate Eulerian models. It is shown that a significant parameter is the equilibrium Weber number. If it is known, Eulerian models are able to reproduce the main features of Lagrangian simulations. To overcome the Lagrangian collision model simplification that mostly considers collisions between spherical droplets, a new test case was designed to focus on the collision process in dense spray. The numerical code, Archer, which is developed to handle interface behaviors in two-phase flow by way of direct numerical simulation (DNS) [Iyer, V., and Abraham, J., (2005), Atomization Sprays, 15(3), pp. 249−269], was used. Thanks to DNS simulations and experimental observations, the importance of nonspherical collisions is demonstrated. Despite some classical drawbacks of DNS, we observed that an equilibrium Weber number can be determined in the considered test case. This work emphasizes the ability of interface DNS simulations to describe complex turbulent two-phase flows with interfaces and to stand as a complement to new experiments.

DNS for flow separation control around an airfoil by pulsed jets

Direct numerical simulation (DNS) for flow separation and transition around a NACA-0012 airfoil with an attack angle of 4° and Reynolds number of 100,000 has been reported in our previous paper. The details of flow separation, formation of the detached shear layer, Kelvin–Helmholtz instability (inviscid shear layer instability) and vortex shedding, interaction of nonlinear waves, breakdown, and re-attachment are obtained and analyzed. The power spectral density of pressure shows the low frequency of vortex shedding caused by the Kelvin–Helmholtz instability still dominates from the leading edge to trailing edge. Based on our understanding on the flow separation mechanism, we try to reveal the mechanism of the flow separation control using blowing jets and then optimize the jets. DNS simulations for flow separation control by blowing jets (pulsed and pitched and skewed jets) are reported and analyzed. The effects of different unsteady blowing jets on the surface at the location just before the separation points are studied. The length of separation bubble is significantly reduced (almost removed) after unsteady blowing technology is applied. The mechanism of early transition caused by the blowing jets was found. A blowing jet with K–H frequency, sharp shape function (very small mass blowing), pitching and skewing obtained the best efficiency based on the increase of the ratio of lift over drag and decrease of blowing mass flow. In this work, a DNS code with high-order accuracy and high-resolution developed by the computational fluid dynamics group at University of Texas at Arlington is applied.

Evaluation of assumed-PDF methods in two-phase flows using direct numerical simulation

The hypothesis of uncorrelated temperature ( T) and vapor-fuel mass fraction ( Y v), frequently made when modeling reaction rates using assumed-PDF models, is examined utilizing transitional databases from direct numerical simulation (DNS) of three-dimensional mixing-layers two-phase (TP) flows with evaporation. Because the databases do not contain chemical reaction, which would further correlate variables, finding here a correlation between T and Y v is sufficient for invalidating reaction rate modeling of the joint ( T, Y v) probability distribution function (PDF) as a product of the marginal PDFs. The databases comprise four multicomponent fuels, two mass loadings and two free-stream gas temperatures. For comparison, databases for single-phase (SP) flows are also analyzed at two initial Reynolds numbers. The examination is conducted in the mixing layer excluding the free streams and in a more restricted part of the mixing layer constituting its core. The analysis is performed at the DNS and large eddy simulation (LES) scales, and subgrid scale (SGS). To obtain the LES database, the DNS database is filtered, and an evaluation of the examined correlation at the LES and SGS scales is made at two filter sizes. At the DNS scale, T and Y v are practically uncorrelated for SP flows, showing the weak influence of the perfect-gas equation of state, whereas for TP flows the correlation is strong and increases with mass loading indicating the powerful effect of the phase change. At the LES scale, the findings emulate those at the DNS scale. The fluctuations of the SGS scale are uncorrelated for SP flows, but the product of the marginal PDFs is different from the joint PDF. For TP flows, the fluctuations are correlated and the correlation increases with temperature, casting doubt on current assumed PDFs used to model chemistry in reacting sprays. These results are independent of filter size. The joint PDFs for TP and SP fluctuations are successfully modeled.

Langevin models of turbulence: Renormalization group, distant interaction algorithms or rapid distortion theory?

A new dynamical turbulence model is validated by comparisons of its numerical simulations with fully resolved, direct numerical simulations (DNS) of the Navier–Stokes equations in three-dimensional, isotropic, homogeneous conditions. In this model the small-scale velocities are computed using a Langevin, linear, inhomogeneous, stochastic equation that is derived from a quasi-linear approximation of the Navier–Stokes equations, in the spirit of rapid distortion theory (RDT). The values of the turbulent viscosity involved in our Langevin model are compared with a theoretical prescription based on the renormalization group and the distant interaction algorithms (DSTA) model. We show that the empirical turbulent viscosities derived from simulations of the Langevin model are in good quantitative agreement with the DSTA predictions. Finally, Langevin simulations are compared with DNS and large eddy simulations based on the eddy-damped quasi-normal Markovian closure. The Langevin RDT model is able to reproduce the correct spectrum shape, intermittency statistics, and coherent flow structures for both the resolved and the largest sub-grid scales. It also predicts the evolution of the resolved scales better than the alternative models.