Compressible turbulent flame speeds of highly turbulent standing flames

In this paper we present the first measurement of turbulent burning velocities of a highly turbulent compressible standing flame induced by shock-driven turbulence in a Turbulent Shock Tube. High-speed schlieren, chemiluminescence, PIV, and dynamic pressure measurements are made to quantify flame–turbulence interaction for high levels of turbulence at elevated temperatures and pressure. Distributions of turbulent velocities, vorticity and turbulent strain are provided for regions ahead and behind the standing flame. The turbulent flame speed is directly measured for the high-Mach standing turbulent flame. From measurements of the flame turbulent speed and turbulent Mach number, transition into a non-linear compressibility regime at turbulent Mach numbers above 0.4 is confirmed, and a possible mechanism for flame generated turbulence and deflagration-to-detonation transition is established.     

Population dynamics in compressible flows

Organisms often grow, migrate and compete in liquid environments, as well as on solid surfaces. However, relatively little is known about what happens when competing species are mixed and compressed by fluid turbulence. In these lectures we review our recent work on population dynamics and population genetics in compressible velocity fields of one and two dimensions. We discuss why compressible turbulence is relevant for population dynamics in the ocean and we consider cases both where the velocity field is turbulent and when it is static. Furthermore, we investigate populations in terms of a continuos density field and when the populations are treated via discrete particles. In the last case we focus on the competition and fixation of one species compared to another.     

Dispersive bottleneck delaying thermalization of turbulent bose-einstein condensates

A new mechanism of thermalization involving a direct energy cascade is obtained in the truncated Gross-Pitaevskii dynamics. A long transient with partial thermalization at small scales is observed before the system reaches equilibrium. Vortices are found to disappear as a prelude to final thermalization. A bottleneck that produces spontaneous effective self-truncation and delays thermalization is characterized when large dispersive effects are present at the truncation wave number. Order of magnitude estimates indicate that self-truncation takes place in turbulent Bose-Einstein condensates. This effect should also be present in classical hydrodynamics and models of turbulence.     

LES based investigation of autoignition in turbulent co-flow configurations

The impact of turbulence on the autoignition of a diluted hydrogen jet in a hot co-flow of air is studied numerically. The LES combustion model used is successfully validated against experimental measurements and 3D DNS. Parametric studies are then carried out by separately varying turbulent intensity and integral length scale in the co-flow, while keeping all other boundary conditions unchanged. It is found that the impact of turbulence on the location of autoignition is non-trivial. For weak to mild turbulence, with a turbulent time scale larger than the minimum ignition delay time, autoignition is facilitated by increased turbulence. This is due to enhanced mixing between fuel and air, creating larger most reactive mixture fraction regions. On the other hand, for turbulent time scales smaller than the ignition delay time, the increased scalar dissipation rate dominates over the effect of increased most reactive mixture fraction regions, which leads to a rise in the autoignition length. Turbulence–chemistry interaction mechanisms are analysed in order to explain these observations.     

Preferential concentration of heavy particles in turbulence

Particle-laden flows are of relevant interest in many industrial and natural systems. When the carrier flow is turbulent, a striking feature is the phenomenon called preferential concentration: particles denser than the fluid have the tendency to inhomogeneously distribute in space, forming clusters and depleted regions. We present an investigation of clustering of small water droplets in homogeneous and isotropic active-grid-generated turbulence. We investigate the effect of Reynolds number (R_λ) and Stokes number (St) on particles clustering in the range R_λ ～ 200?400 and St ～ 2?10. Using Voronoï diagrams, we characterise clustering level and cluster properties (geometry, typical dimension and fractality). The exact same Voronoï analysis is then applied to investigate clustering properties of specific topological points of the velocity field of homogeneous isotropic turbulence obtained from direct numerical simulations at R_λ ～ 220 and 300. The goal is to compare clustering properties of actual particles with those of such points in order to explore the relevance of possible clustering mechanisms, including centrifugal effects (heavy particles sampling preferentially low-vorticity regions) and sweep-stick mechanisms (heavy particles preferentially sticking to low-acceleration points). Our study points towards a leading role of zero-acceleration points and sweep-stick effects, at least for the experimental conditions considered in this study.     

Solvent density mode instability in non-polar solutions

We analyse the origin of the multiple long time scales associated with the long time decay observed in non-polar solvation dynamics by linear stability analysis of solvent density modes where the effects of compressibility and solvent structure are systematically incorporated. The coupling of the solute-solvent interactions at both ground and excited states of the solute with the compressibility and solvent structure is found to have important effects on the time scales. The present theory suggests that the relatively longer time constant is controlled by the solvent compressibility, while the solvent structure at the nearest-neighbour length scale dominates the shorter time constant.      

A Geometric Interpretation of the Second-Order Structure Function Arising in Turbulence

We primarily deal with homogeneous isotropic turbulence and use a closure model for the von Kármán-Howarth equation to study several geometric properties of turbulent fluid dynamics. We focus our attention on the application of Riemannian geometry methods in turbulence. Some advantage of this approach consists in exploring the specific form of a closure model for the von Kármán-Howarth equation that enables to equip a model manifold (a cylindrical domain in the correlation space) by a family of inner metrics (length scales of turbulent motion) which depends on time. We show that for large Reynolds numbers (in the limit of large Reynolds numbers) the radius of this manifold can be evaluated in terms of the second-order structure function and the correlation distance. This model manifold presents a shrinking cylindrical domain as time evolves. This result is derived by using a selfsimilar solution of the closure model for the von Kármán-Howarth equation under consideration. We demonstrate that in the new variables the selfsimilar solution obtained coincides with the element of Beltrami surface (or pseudo-sphere): a canonical surface of the constant sectional curvature equals − 1.      

Cross-scale effects in solar-wind turbulence

The understanding of the small-scale termination of the turbulent energy cascade in collisionless plasmas is nowadays one of the outstanding problems in space physics. In the absence of collisional viscosity, the dynamics at small scales is presumably kinetic in nature; the identification of the physical mechanism which replaces energy dissipation and establishes the link between macroscopic and microscopic scales would open a new scenario in the study of turbulent heating in space plasmas. We present a numerical analysis of kinetic effects along the turbulent energy cascade in solar-wind plasmas which provides an effective unified interpretation of a wide set of spacecraft observations and shows that, simultaneously with an increase in the ion perpendicular temperature, strong bursts of electrostatic activity in the form of ion-acoustic turbulence are produced together with accelerated beams in the ion distribution function.     

Jet noise prediction using different turbulent scales

The turbulent energy dissipation rate time-scale and length-scale has been routinely used for the prediction of noise from turbulent flows, particularly jet streams. However, this is not the only possible choice. In general, scales evolving in a turbulent medium are threefold. First, those associated with the mean flow; second, those attributed to the turbulence and the mean flow interactions; and third, scales related to the turbulence-turbulence interactions. In this paper, special attention will be paid to further study of the underlying physics of aerodynamic noise by examining various time-scales. To do so, three time scales, namely, dissipation, production, and strain rate time scales, are defined and used in the source modelling to emphasis the effect of the turbulence structures at different jet regions on the jet noise production mechanism. The required mean value and turbulence parameters are obtained using a modified k − ∈ turbulence model, and Lighthill’s Acoustic Analogy is used for the prediction of the emanated noise. The text was submitted by the authors in English.     

A multi-scale simulation method for high Reynolds number wall-bounded turbulent flows

We present an assessment and enhancement of the hybrid two-level large-eddy simulation method (A.G. Gungor and S. Menon, A new two-scale model for large eddy simulation of wall-bounded flows, Prog. Aerosp. Sci. 46 (2010), pp. 28–45), a multi-scale formulation for simulation of high Reynolds number wall-bounded turbulent flows. The assessment of the method is performed by examining role of static and dynamic blending functions used to perform hybridisation of two-level simulation (K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows, J. Comput. Phys. 220 (2006), pp. 290–311; K. Kemenov and S. Menon, Explicit small-scale velocity simulation for high-Re turbulent flows. Part 2: Non-homogeneous flows, J. Comput. Phys. 222 (2007), pp. 673–701) and large-eddy simulation methods. The sensitivity of first- and second-order turbulence statistics to the type of blending functions is investigated by simulating a fully developed turbulent flow in a channel at a friction Reynolds number Re_τ = 395 and comparing the results with those obtained using a direct numerical simulation. The first-order statistics do not show any significant differences for different blending functions, but the second-order statistics show some minor differences. The dynamic evaluation of the hybrid region and the blending function is necessary for non-equilibrium and complex flows where use of a static blending function can lead to inaccurate results. We propose two criteria for the dynamic evaluation; first evaluates extent of the hybrid region based on the subgrid turbulent kinetic energy and the second estimates the blending function based on a characteristic length scale. The computational efficiency of the method is enhanced by incorporating a hybrid programming paradigm where a standard domain decomposition by the message-passing-interface library is combined with the open multi-processing based parallelisation. A further enhancement of the method is achieved by incorporating a closure model for the unclosed hybrid terms in the governing equations, which appear due to hybridisation of two-level- and large-eddy-simulation methods. The model is based on an order of magnitude approximation and a preliminary assessment of the model shows improvement of turbulence statistics when used to simulate turbulent flow in a periodic channel. The assessment and improvements to the multi-scale method make it more suitable for simulation of practical wall-bounded turbulent flows at higher Reynolds number than a conventional large-eddy simulation. This is demonstrated by simulating two representative cases; turbulent flow at high Reynolds number in a periodic channel and flow over a bump placed on the lower surface of a channel, where a relatively coarser computational grid is found to be sufficient for reasonably accurate results.     

Density fluctuation spectrum in whistler turbulence

We develop a nonlinear two-dimensional fluid model of whistler turbulence that includes effect of electron fluid density perturbations. The latter is coupled nonlinearly with wave magnetic field. This coupling leads essentially to finite compressibility effects in whistler turbulence model. We find from our simulations that despite strong compressibility effects, the density fluctuations follow the evolution of the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the coupled density fluctuations are found to follow a Kolmogorov-like phenomenology in the inertial range turbulence. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like k−7/3 spectrum, where k is a characteristic wavenumber.     

Understanding the sub-critical transition to turbulence in wall flows

In contrast with free shear flows presenting velocity profiles with inflection points which cascade to turbulence in a relatively mild way, wall bounded flows are deprived of (inertial) instability modes at low Reynolds numbers and become turbulent in a much wilder way, most often marked by the coexistence of laminar and turbulent domains at intermediate Reynolds numbers, well below the range where (viscous) instabilities can show up. There can even be no unstable mode at all, as for plane Couette flow (pCf) or for Poiseuille pipe flow (Ppf) that are currently the subject of intense research. Though the mechanisms involved in the transition to turbulence in wall flows are now better understood, statistical properties of the transition itself are yet unsatisfactorily assessed. A widely accepted interpretation rests on non-trivial solutions of the Navier-Stokes equations in the form of unstable travelling waves and on transient chaotic states associated to chaotic repellors. Whether these concepts typical of the theory of temporal chaos are really appropriate is yet unclear owing to the fact that, strictly speaking, they apply when confinement in physical space is effective while the physical systems considered are rather extended in at least one space direction, so that spatiotemporal behaviour cannot be ruled out in the transitional regime. The case of pCf will be examined in this perspective through numerical simulations of a model with reduced cross-stream (y) dependence, focusing on the in-plane (x, z) space dependence of a few velocity amplitudes. In the large aspect-ratio limit, the transition to turbulence takes place via spatiotemporal intermittency and we shall attempt to make a connection with the theory of first-order (thermodynamic) phase transitions, as suggested long ago by Pomeau.      

Effects of variable specific heat on energy transfer in a high-temperature supersonic channel flow

An energy transfer mechanism in high-temperature supersonic turbulent flow for variable specific heat (VSH) condition through turbulent kinetic energy (TKE), mean kinetic energy (MKE), turbulent internal energy (TIE) and mean internal energy (MIE) is proposed. The similarities of energy budgets between VSH and constant specific heat (CSH) conditions are investigated by introducing a vibrational energy excited degree and considering the effects of fluctuating specific heat. Direct numerical simulation (DNS) of temporally evolving high-temperature supersonic turbulent channel flow is conducted at Mach number 3.0 and Reynolds number 4800 combined with a constant dimensional wall temperature 1192.60 K for VSH and CSH conditions to validate the proposed energy transfer mechanism. The differences between the terms in the two kinetic energy budgets for VSH and CSH conditions are small; however, the magnitude of molecular diffusion term for VSH condition is significantly smaller than that for CSH condition. The non-negligible energy transfer is obtained after neglecting several small terms of diffusion, dissipation and compressibility related. The non-negligible energy transfer involving TIE includes three processes, in which energy can be gained from TKE and MIE and lost to MIE. The same non-negligible energy transfer through TKE, MKE and MIE is observed for both the conditions.     

On the effects of buoyancy on higher order moments in lazy plumes

Jets and plumes are shear flows created by momentum and buoyant sources. They can be classified as either pure jets, forced plumes, pure plumes, or lazy plumes. Lazy plumes are characterised as having a high source buoyancy flux relative to the momentum flux. We use direct numerical simulations to simulate lazy plumes to ascertain the effects of increasing plume ‘laziness’ on the higher order moments, such as Reynolds stresses, third order moments and turbulent kinetic energy budgets. The mildly lazy plumes behaved like most plumes in terms of higher order statistics: a self-similar collapse some distance downstream and peak values comparable to previous experiments and simulations. The highly lazy plumes did not show a self-similar collapse and, in most cases, had higher peak values in all moments. The highly lazy plumes had higher levels of turbulence intensities due to the high buoyancy flux, leading to significant buoyancy-induced turbulence production downstream.     

Large eddy simulation of a light gas stratification break-up by an entraining turbulent fountain

The erosion process of a stably stratified light gas layer by a vertical turbulent fountain of denser fluid inside a generic containment – for which experimental reference data are available – is studied computationally using large eddy simulation (LES). In addition, various Reynolds averaged Navier–Stokes (RANS) models are applied aiming at a comparative assessment of different computational approaches for the considered case. With the LES methodology included into the present modelling study, a novelty to date is established for fountain-stratification interaction inside generic containments. The high Reynolds number RANS models applied in the framework of this study include both the realisable k–? eddy viscosity model (EVM) as well as the basic Reynolds stress model (RSM). Furthermore, we show that certain regimes of the present configuration can be predicted using an analytically derived scaling approach. Various data beyond the experimentally obtained ones are computationally provided in order to facilitate the calibration of less costly statistical turbulence models and lumped parameter codes, since the presently considered configuration is regarded to be a valuable small-scale equivalent for containment flow applications.     

Studies of the flow and turbulence fields in a turbulent pulsed jet flame using LES/PDF

A turbulent piloted jet flame subject to a rapid velocity pulse in its fuel jet inflow is proposed as a new benchmark case for the study of turbulent combustion models. In this work, we perform modelling studies of this turbulent pulsed jet flame and focus on the predictions of its flow and turbulence fields. An advanced modelling strategy combining the large eddy simulation (LES) and the probability density function (PDF) methods is employed to model the turbulent pulsed jet flame. Characteristics of the velocity measurements are analysed to produce a time-dependent inflow condition that can be fed into the simulations. The effect of the uncertainty in the inflow turbulence intensity is investigated and is found to be very small. A method of specifying the inflow turbulence boundary condition for the simulations of the pulsed jet flame is assessed. The strategies for validating LES of statistically transient flames are discussed, and a new framework is developed consisting of different averaging strategies and a bootstrap method for constructing confidence intervals. Parametric studies are performed to examine the sensitivity of the predictions of the flow and turbulence fields to model and numerical parameters. A direct comparison of the predicted and measured time series of the axial velocity demonstrates a satisfactory prediction of the flow and turbulence fields of the pulsed jet flame by the employed modelling methods.     

On primitive variable behaviour near shocks in ensemble-averaged methods

Models for averaged shock corrugation effects and the impact of turbulent entropy or acoustic modes on the energy equation are presented, for application in Reynolds-Averaged Navier Stokes(RANS) simulations of shock-turbulence interactions. Unlike previous work that has focused the modification of turbulent statistics by the shock, the proposed models are introduced to capture the effects of the turbulence on the profiles of primitive variables - mean density, velocity, and pressure. By producing accurate profiles for the primitive variables, it is shown that the proposed models improve numerical convergence behaviour with mesh refinement about a shock, and introduce the physical effects of shock asphericity in a converging shock geometry. These effects are achieved by local closures to turbulent statistics in the averaged Navier-Stokes equations, and can be applied in conjunction with existing Reynolds stress closures that have been constructed for broader applications beyond shock-turbulence interactions.     

Statistics of particle pair relative velocity in the homogeneous shear flow

Small scale clustering of inertial particles and relative velocity of particle pairs have been fully characterized for statistically steady homogeneous isotropic flows. Depending on the particle Stokes relaxation time, the spatial distribution of the disperse phase results in a multi-scale manifold characterized by local particle concentration and voids and, because of finite inertia, the two nearby particles have high probability to exhibit large relative velocities. Both effects might explain the speed-up of particle collision rate in turbulent flows. Recently it has been shown that the large scale geometry of the flow plays a crucial role in organizing small scale particle clusters. For instance, a mean shear preferentially orients particle patterns. In this case, depending on the Stokes time, anisotropic clustering may occur even in the inertial range of scales where the turbulent fluctuations which drive the particles have already recovered isotropy. Here we consider the statistics of particle pair relative velocity in the homogeneous shear flow, the prototypical flow which manifests anisotropic clustering at small scales. We show that the mean shear, by imprinting anisotropy on the large scale velocity fluctuations, dramatically affects the particle relative velocity distribution even in the range of small scales where the anisotropic mechanisms of turbulent kinetic energy production are sub-dominant with respect to the inertial energy transfer which drives the carrier fluid velocity towards isotropy. We find that the particles’ populations which manifest strong anisotropy in their relative velocities are the same which exhibit small scale clustering. In contrast to any Kolmogorov-like picture of turbulent transport these phenomena may persist even below the smallest dissipative scales where the residual level of anisotropy may eventually blow-up. The observed anisotropy of particle relative velocity and spatial configuration is suggested to influence the directionality of the collision probability, as inferred on the basis of the so-called “ghost collision” model.     

各向异性浮力紊流的显式代数应力模型及其验证

在Wallin & Johansson的显式代数雷诺应力模型(EARSM)基础上,引入浮力的紊动效应,使该模型能够反映浮力对紊流运动的影响.利用同位网格上的SIMPLEC算法,模拟了T-型连接管内的温度混合流动.与实验资料和DNS计算结果比较表明,提出的模型能够反映各向异性的浮力紊流特征,而且模型在计算进程中显示出良好的数值收敛性能,与涡粘性两方程模型的计算花费相当.