Direct numerical simulations of autoignition in turbulent two-phase flows

Three-dimensional direct numerical simulations (DNS) were carried out to investigate the impact of evaporation of droplets on the autoignition process under decaying turbulence. The droplets were taken as point sources and were tracked in a Lagrangian manner. Three cases with the same initial equivalence ratio but different initial droplet size were simulated and the focus was to examine the influence of the droplet evaporation process on the location of autoignition. It was found that an increase in the initial droplet size results in an increase in the autoignition time, that highest reaction rates always occur at a specific mixture fraction ξ_MR, as in purely gaseous flows, and that changes in the initial droplet size did not affect the value of ξ_MR. The conditional correlation coefficient between scalar dissipation rate and reaction rates was only mildly negative, contrary to the strongly negative values for purely gaseous autoigniting flows, possibly due to the continuous generation of mixture fraction by the droplet evaporation process that randomizes both the mixture fraction and the scalar dissipation fields.     

Nonlinear wave-wave interactions in stratified flows: Direct numerical simulations

To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the reduced dynamical equations only wave modes are retained, and vortices and horizontally uniform vertical shears are excluded. Despite the simplifications, our simulations reproduce some key features of oceanic internal-wave spectra: accumulation of energy at near-inertial waves and realistic frequency and horizontal wavenumber dependencies. Furthermore, we provide evidence that formation of the energy spectra in the inertial subrange is dominated by scale-separated interactions with the near-inertial waves. These findings support observationally based intuition that spectral energy density of internal waves is the result of predominantly wave-wave interactions.     

Three-dimensional boundary conditions for numerical simulations of reactive compressible flows with complex thermochemistry

The Navier–Stokes characteristic boundary conditions (NSCBC) is a very efficient numerical strategy to treat boundary conditions in fully compressible solvers. The present work is an extension of the 3D-NSCBC method proposed by Yoo et al. and Lodato et al. in order to account for multi-component reactive flows with detailed chemistry and complex transport. A new approach is proposed for the outflow boundary conditions which enables clean exit of non-normal flows, and the specific treatment of all kinds of edges and corners is carefully addressed. The proposed methodology is successfully validated on various challenging multi-component reactive flow configurations.     

Energy flow in thermostatted non-equilibrium molecular dynamics simulations

Energy transfers between internal kinetic and potential energy reservoirs in a simple liquid are studied by setting the temperature of one energy reservoir to a different value from that of the others and computing the resultant energy flows. In the first set of simulations, the x-directional kinetic temperature was artificially raised above the other five, and in the second, the x-directional configurational temperature was artificially raised above the other five. In both cases, external energy flows balanced, but unexpected energy flows between different directional components of the potential energy were observed. Additional simulations showed that these energy flows occurred regardless of the arrangement of thermostats imposed on the six degrees of freedom and the addition of shear. Heat flow between degrees of freedom that were ostensibly at the same temperature was anomalously observed. It was concluded that a different breakdown of the contributions to the configurational energy that is consistent with the definition of the directional configurational temperatures is required.     

Microscopic-scale simulations of macroscopic flow patterns in non-equilibrium two-dimensional systems

Summary We have used a molecular-dynamics simulation for reproducing the behaviour of a two-dimensional fluid flow submitted to external perturbations and embedded in a non-inertial reference frame. This simple model has been used to verify current hypotheses on the causes generating a cyclonic circulation in the North Tyrrhenian basin, provided one uses suitable perturbation strenghts scaled from the real-world dynamics. Results put in evidence that the onset of a stationary cyclonic circulation which superimposes to the S-N flow requires the simultaneous presence of an orthogonal and an anti-parallel stream. This finding is in agreement with the hypotheses suggested by a preliminary analysis of experimental data. The limits of such models are discussed together with possible extensions to reproduce mesoscopic systems, in order to simulate the coexistence of large- and small-scale dynamics. The model is particularly suited to deal with boundary conditions of general analytical shapes.     

A unified gas-kinetic scheme for continuum and rarefied flows

With discretized particle velocity space, a multiscale unified gas-kinetic scheme for entire Knudsen number flows is constructed based on the BGK model. The current scheme couples closely the update of macroscopic conservative variables with the update of microscopic gas distribution function within a time step. In comparison with many existing kinetic schemes for the Boltzmann equation, the current method has no difficulty to get accurate Navier–Stokes (NS) solutions in the continuum flow regime with a time step being much larger than the particle collision time. At the same time, the rarefied flow solution, even in the free molecule limit, can be captured accurately. The unified scheme is an extension of the gas-kinetic BGK-NS scheme from the continuum flow to the rarefied regime with the discretization of particle velocity space. The success of the method is due to the un-splitting treatment of the particle transport and collision in the evaluation of local solution of the gas distribution function. For these methods which use operator splitting technique to solve the transport and collision separately, it is usually required that the time step is less than the particle collision time. This constraint basically makes these methods useless in the continuum flow regime, especially in the high Reynolds number flow simulations. Theoretically, once the physical process of particle transport and collision is modeled statistically by the kinetic Boltzmann equation, the transport and collision become continuous operators in space and time, and their numerical discretization should be done consistently. Due to its multiscale nature of the unified scheme, in the update of macroscopic flow variables, the corresponding heat flux can be modified according to any realistic Prandtl number. Subsequently, this modification effects the equilibrium state in the next time level and the update of microscopic distribution function. Therefore, instead of modifying the collision term of the BGK model, such as ES-BGK and BGK–Shakhov, the unified scheme can achieve the same goal on the numerical level directly. Many numerical tests will be used to validate the unified method.     

蒙特卡罗模拟在非平衡动态系统中的应用

非平衡系统几乎存在于自然和人造系统的各个层面上,它以非零连续的流量为特征。完全非对称简单排他过程被认为是对这类系统建模和模拟的一个范例。对蒙特卡罗方法如何模拟该类系统进行了介绍。分析了通过蒙特卡罗模拟观察到的一些有趣的物理现象如自发性对称破缺、有限尺寸效应和跳跃过程。非对称的低-低密度相破缺与系统的有限尺寸效应密切相关,建议开展更细致的蒙特卡罗模拟以进一步加深对仍处于争论中的非平衡系统有限尺寸效应的认识。     

蒙特卡罗模拟在非平衡动态系统中的应用

非平衡系统几乎存在于自然和人造系统的各个层面上,它以非零连续的流量为特征。完全非对称简单排他过程被认为是对这类系统建模和模拟的一个范例。对蒙特卡罗方法如何模拟该类系统进行了介绍。分析了通过蒙特卡罗模拟观察到的一些有趣的物理现象如自发性对称破缺、有限尺寸效应和跳跃过程。非对称的低-低密度相破缺与系统的有限尺寸效应密切相关,建议开展更细致的蒙特卡罗模拟以进一步加深对仍处于争论中的非平衡系统有限尺寸效应的认识。     

Accuracy analysis of high-order lattice Boltzmann models for rarefied gas flows

In this work, we have theoretically analyzed and numerically evaluated the accuracy of high-order lattice Boltzmann (LB) models for capturing non-equilibrium effects in rarefied gas flows. In the incompressible limit, the LB equation is shown to be able to reduce to the linearized Bhatnagar–Gross–Krook (BGK) equation. Therefore, when the same Gauss–Hermite quadrature is used, LB method closely resembles the discrete velocity method (DVM). In addition, the order of Hermite expansion for the equilibrium distribution function is found not to be directly correlated with the approximation order in terms of the Knudsen number to the BGK equation for incompressible flows. Meanwhile, we have numerically evaluated the LB models for a standing-shear-wave problem, which is designed specifically for assessing model accuracy by excluding the influence of gas molecule/surface interactions at wall boundaries. The numerical simulation results confirm that the high-order terms in the discrete equilibrium distribution function play a negligible role in capturing non-equilibrium effect for low-speed flows. By contrast, appropriate Gauss–Hermite quadrature has the most significant effect on whether LB models can describe the essential flow physics of rarefied gas accurately. Our simulation results, where the effect of wall/gas interactions is excluded, can lead to conclusion on the LB modeling capability that the models with higher-order quadratures provide more accurate results. For the same order Gauss–Hermite quadrature, the exact abscissae will also modestly influence numerical accuracy. Using the same Gauss–Hermite quadrature, the numerical results of both LB and DVM methods are in excellent agreement for flows across a broad range of the Knudsen numbers, which confirms that the LB simulation is similar to the DVM process. Therefore, LB method can offer flexible models suitable for simulating continuum flows at the Navier–Stokes level and rarefied gas flows at the linearized Boltzmann model equation level.     

Visualization techniques in plasma numerical simulations

Numerical simulations of plasma processes usually yield a huge amount of raw numerical data. Information about electric and magnetic fields and particle positions and velocities can be typically obtained. There are two major ways of elaborating these data. First of them is calledplasma diagnostics. We can calculate average values, variances, correlations of variables, etc. These results may be directly comparable with experiments and serve as the typical quantitative output of plasma simulations. The second possibility is theplasma visualization. The results are qualitative only, but serve as vivid display of phenomena in the plasma followed-up. An experience with visualizing electric and magnetic fields via Line Integral Convolution method is described in the first part of the paper. The LIC method serves for visualization of vector fields in two dimensional section of the three dimensional plasma. The field values can be known only in grid points of three-dimensional grid. The second part of the paper is devoted to the visualization techniques of the charged particle motion. The colour tint can be used for particle’s temperature representation. The motion can be visualized by a trace fading away with the distance from the particle. In this manner the impressive animations of the particle motion can be achieved.     

Molecular simulations of electroosmotic flows in rough nanochannels

A highly efficient molecular dynamics algorithm for micro and nanoscale electrokinetic flows is developed. The long-range Coulomb interactions are calculated using the Particle–Particle Particle–Mesh (P³M) approach. The Poisson equation for the electrostatic potential is solved in physical space using an iterative multi-grid technique. After validation, the method is used to study electroosmotic flow in nanochannels with regular or random roughness on the walls. The results show that roughness reduces the electroosmotic flow rate dramatically even though the roughness is very small compared to the channel width. The effect is much larger than for pressure driven flows because the driving force is localized near the walls where the charge distribution is high. Non-Newtonian behavior is also observed at much lower flow rates. Systematic investigation of the effect of surface charge density and random roughness will help to better understand the mechanism of electrokinetic transport in rough nanochannels and to design and optimize nanofluidic devices.     

Construction of low dissipative high-order well-balanced filter schemes for non-equilibrium flows

The goal of this paper is to generalize the well-balanced approach for non-equilibrium flow studied by Wang et al. (2009) [29] to a class of low dissipative high-order shock-capturing filter schemes and to explore more advantages of well-balanced schemes in reacting flows. More general 1D and 2D reacting flow models and new examples of shock turbulence interactions are provided to demonstrate the advantage of well-balanced schemes. The class of filter schemes developed by Yee et al. (1999) [33], Sjögreen and Yee (2004) [27] and Yee and Sjögreen (2007) [38] consist of two steps, a full time step of spatially high-order non-dissipative base scheme and an adaptive non-linear filter containing shock-capturing dissipation. A good property of the filter scheme is that the base scheme and the filter are stand-alone modules in designing. Therefore, the idea of designing a well-balanced filter scheme is straightforward, i.e. choosing a well-balanced base scheme with a well-balanced filter (both with high-order accuracy). A typical class of these schemes shown in this paper is the high-order central difference schemes/predictor–corrector (PC) schemes with a high-order well-balanced WENO filter. The new filter scheme with the well-balanced property will gather the features of both filter methods and well-balanced properties: it can preserve certain steady-state solutions exactly; it is able to capture small perturbations, e.g. turbulence fluctuations; and it adaptively controls numerical dissipation. Thus it shows high accuracy, efficiency and stability in shock/turbulence interactions. Numerical examples containing 1D and 2D smooth problems, 1D stationary contact discontinuity problem and 1D turbulence/shock interactions are included to verify the improved accuracy, in addition to the well-balanced behavior.     

气动激光器喷管非平衡流2维数值仿真

将Anderson的两振型三温度弛豫模型和严海星整理的弛豫数据相结合,采用2维守恒型方程组对按照最小长度喷管型面设计方法设计的、面积比分别为50和20的气动激光器喷管非平衡流场进行了数值仿真。小信号增益计算结果在每个计算点都和J.S.Vamos等人针对这两种喷管的小信号增益测量试验结果符合很好.解决了传统的准1维非平衡流分析方法不能很好地和试验结果相符的问题.对气动激光器喷管性能设计提供了更精确的评估方法。     

气动激光器喷管非平衡流2维数值仿真

将Anderson的两振型三温度弛豫模型和严海星整理的弛豫数据相结合,采用2维守恒型方程组对按照最小长度喷管型面设计方法设计的、面积比分别为50和20的气动激光器喷管非平衡流场进行了数值仿真。小信号增益计算结果在每个计算点都和J. S. Vamos等人针对这两种喷管的小信号增益测量试验结果符合很好,解决了传统的准1维非平衡流分析方法不能很好地和试验结果相符的问题,对气动激光器喷管性能设计提供了更精确的评估方法。     

The effect of surface roughness on rarefied gas flows by lattice Boltzmann method

This paper studies the roughness effect combining with effects of rarefaction and compressibility by a lattice Boltzmann model for rarefied gas flows at high Knudsen numbers. By discussing the effect of the tangential momentum accommodation coefficient on the rough boundary condition, the lattice Boltzmann simulations of nitrogen and helium flows are performed in a two-dimensional microchannel with rough boundaries. The surface roughness effects in the microchannel on the velocity field, the mass flow rate and the friction coefficient are studied and analysed. Numerical results for the two gases in micro scale show different characteristics from macroscopic flows and demonstrate the feasibility of the lattice Boltzmann model in rarefied gas dynamics.