旋流两相流动的DSM—PDF两相湍流模型

本文提出了气相雷诺应力方程模型和颗粒概率密度输运方程模型相结合而构成的ＤＳＭ—ＰＤＦ两相湍流模型,并用该模型和ｋ－ε－Ｋｐ模型模拟了文献中测量的旋流数为０．４７的旋流突扩气粒两相流动．和测量结果的对照表明,两模型都能较好地模拟族流数不高的两相流动平均速度场,但ＤＳＭ—ＰＤＦ模型可以揭示出两相湍流的各向异性,因此有预报强旋两相流动的潜力．     

用统一二阶矩模型模拟强旋湍流气粒两相流动的初探

本文初步探索用统一二阶矩（USM）两相湍流模型及K-ε-kp模型预报旋流数为1.5的轴向-切向进风、轴向供粉的强旋气粒两相流动，预报结果与实验的对比表明，USM模型在预报强族流动两相时平均切向速度场上优于K-ε-Kp模型，并且能够合理地给出与实验定性一致的两相湍流脉动的各向异性．     

用视密度加权平均二阶矩模型模拟旋流两相流动

本文用视密度加权平均代替时平均,建立了视密度加权平均的统一二阶矩两相湍流模型方程组（ＭＵＳＭ）,其中用体积分数代替了数密度,用颗粒驰豫时间作为封闭两相脉动速度关联方程耗散项的时间尺度,并引入了颗粒视在的气体速度脉动的输运方程。用ＭＵＳＭ模型模拟了旋流数为０．４７的气粒两相流动。并和实验结果及时间平均的ＵＳＭ模型的模拟结果进行了对照,两种模型均能较好地预报的两相的轴向和切向速度,轴向和切向脉动速度。此外,ＭＵＳＭ模型可以减少所用方程数,节省计算量。因此视密度加权平均的统一二阶矩两相湍流模型是一种对时间平均的统一二阶矩模型的改进,今后可以进一步扩大应用。     

DSM-LPDF两相湍流模型及旋流两相流动的模拟

本文由流体－颗粒速度的拉氏联合概率密度函数（ＰＤＦ）输运方程出发,用Ｓｉｍｏｎｉｎ建议的Ｌａｎｇｅｖｉｎ模型封闭颗粒所遇到流体瞬时速度的条件期望项,并用Ｍｏｎｔｅ Ｃａｒｌｏ方法直接求解 ＰＤＦ输运方程,将其和求解流体雷诺应力方程模型的有限差分方法结合,建立了雷诺应力－拉氏ＰＤＦ（ＤＳＭ－ＬＰＤＦ,简称ＤＬ）两相湍流模型．用此模型模拟了旋流数为０．４７的突扩旋流气粒两相流动,并与文献中ＰＤＰＡ实验和用类似于单相流动湍流模型封闭方法的时平均统一二阶矩（ＵＳＭ）模型的预报进行了对比．     

下降管中稠密两相湍流的数值模拟

本文将统一二阶矩两相湍流模型和颗粒动力学理论结合,推导并封闭了稠密两相流考虑颗粒间碰撞的统一二阶矩两相湍流模型。该模型用颗粒动力学理论模拟颗粒之间的碰撞,用各向异性的统一二阶矩模型考虑气相和颗粒相的湍流脉动,并用输运方程描述气固两相湍流之间的相互作用。最后用该模型对下降管中的气粒两相流动进行了模拟,模拟所得的沿径向颗粒浓度分布和速度分布与实验吻合较好,预报结果也反应出了颗粒雷诺应力的各向异性。     

旋涡流化床悬浮空间强旋湍流回流流动的数值模拟

旋涡流化床悬浮空间强旋湍流回流流动是十分复杂的湍流流动过程。本文基于对旋涡流化床悬浮空间气固两相悬浮流动规律的认识和强旋湍流各向异性的特点,建立和发展了适用于旋风流动的雷诺代数应力模型(ASM),使其既能体现雷诺应力输运方程的基本特征,又具有模型简单和计算经济的优点。结合压力速度校正的SIMPLE算法程     

气泡-液体多股射流二阶矩两相湍流模型的模拟

本文采用二阶矩两相湍流模型模拟了气泡－液体闭式多股射流。研究结果显示出预报的两相速度、雷诺应力和气泡体积分数分布的合理性，以及在速度较高和剪切较强的情况下，气泡湍流脉动仍然大于液体湍流脉动，气泡增强液体湍流，气液两相湍流脉动均存在各向异性，而且气泡脉动的各向异性比液体脉动的大等规律。     

k－ε－PDF两相湍流模型和台阶后方气粒两相流动的模拟

本文提出了两相湍流的ｋ－ε－ＰＤＦ模型。ＰＤＦ模型所得的湍流两相流动的统计平均方程，与雷诺时均方程有相似的形式，但ＰＤＦ模型可精确计算出颗粒相各方程的脉动关联项。本文将该模型用于预报台阶后方湍流两相流动，与ｋ－ε－ｋｐ模型相比，它可以更合理地预报出颗粒湍流的各向异性。     

两相流气相湍流双时间尺度耗散模型

本文提出了两相流气相湍流变动的双时间尺度耗散模型,包括气相耗散率的双时间尺度耗散模型和两相速度关联的双时间尺度各向异性耗散模型。用所提出封闭模型模拟了旋流数为0.47的气粒两相流动,发现所提出的湍流变动模型对气相脉动速度的预报结果比原有的单时间尺度模型的预报结果有明显的改进,但是颗粒尾涡的作用仍然需要进一步研究。     

炉内两相流动和煤粉燃烧的双流体-轨道模型

本文首次用双流体一轨道（连续介质－轨道ＣＴ）模型对大尺寸四角喷燃炉内气粒两相流动及煤粉燃烧进行了模拟。该模型基于欧拉气相方程组、欧拉颗粒连续方程和动量方程以及拉氏颗粒能量和质量变化的方程,对各子模型用ｋ－ε－ｋｐ两相湍流模型,ＥＢＵ－Ａｒｒｈｅｎｉｕｓ湍流燃烧模型,煤粉颗粒的水分蒸发,热解挥发和焦炭燃烧的扩散－动力模型,ＤＯ（离散坐标）辐射模型。采用了将坐标扭转一定角度的方法减小入口射流和网格斜交造成的伪扩散。编制了ＬＥＡＧＡＰ－ＦＵＲＮＡＣＥ－３程序,分别对冷态模型炉内两相流动和大尺寸炉内三维两相流动和煤粉燃烧进行了模拟,并与颗粒轨道（ＳＴ）模型的模拟结果进行了对照。采用ＰＤＰＡ对冷态模型炉内气粒两相流场进行了测量。冷态两相流动的模拟与实验结果的对比表明ＣＴ模型的模拟结果和实验符合较好,ＳＴ模型所得颗粒浓度分布和实验山入较大。热态模拟的结果给出了两相速度,气相温度,组分浓度和壁面热流分布。模拟结果定性合理。模拟结果显示在出口处由于气流旋转,有一局部高温区存在。     

Asymptotics of unit Burger number rotating and stratified flows for small aspect ratio

Rotating and stably stratified Boussinesq flow is investigated for Burger number unity in domain aspect ratio (height/horizontal length) δ<1 and δ=1. To achieve Burger number unity, the non-dimensional rotation and stratification frequencies (Rossby and Froude numbers, respectively) are both set equal to a second small parameter ?<1. Non-dimensionalization of potential vorticity distinguishes contributions proportional to (?δ)⁻¹, δ⁻¹ and O(1). The (?δ)⁻¹ terms are the linear terms associated with the pseudo-potential vorticity of the quasi-geostrophic limit. For fixed δ=1/4 and a series of decreasing ?, numerical simulations are used to assess the importance of the δ⁻¹ contribution of potential vorticity to the potential enstrophy. The change in the energy spectral scalings is studied as ? is decreased. For intermediate values of ?, as the flow transitions to the (δ?)⁻¹ regime in potential vorticity, both the wave and vortical components of the energy spectrum undergo changes in their scaling behavior. For sufficiently small ?, the (δ?)⁻¹ contributions dominate the potential vorticity, and the vortical mode spectrum recovers k⁻³ quasi-geostrophic scaling. However, the wave mode spectrum shows scaling that is very different from the well-known k⁻¹ scaling observed for the same asymptotics at δ=1. Visualization of the wave component of the horizontal velocity at δ=1/4 reveals a tendency toward a layered structure while there is no evidence of layering in the δ=1 case. The investigation makes progress toward quantifying the effects of aspect ratio δ on the ?→0 asymptotics for the wave component of unit Burger number flows. At the lowest value of ?=0.002, it is shown that the horizontal kinetic energy spectral scalings are consistent with phenomenology that explains how linear potential vorticity constrains energy in the limit ?→0 for fixed δ.     

On Symmetry Flows of Noncommutative Kadomtsev-Petviashvili Hierarchy

We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili (NCKP) hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.     

A scaling law in the hydrodynamics of anisotropic viscous liquids

Summary We show that 1) the stationary flow of an isotropic liquid in a given viscosimeter is described by the same equations valid for a wellaligned nematic liquid crystal, having suitable values of the five viscosity coefficients, flowing in a viscosimeter like the previous one, but whose dimensions along the average molecular directionň are contracted; 2) a similar equivalence exists for a nematic flowing in a suitably chosen viscosimeter in two experiments which differ only for the direction ofň. This equivalence allows us to exactly compensate boundary effects in the measurement of the ratio between two of the Miesowicz viscosity coefficients. Furtherly a new particularly simple derivation of the Rayleigh dissipation function for nematics is given. To speed up publication, the author of this paper has agreed to not receive the proofs for correction.     

A Monte Carlo model for seeded atomic flows in the transition regime

A simple model for the numerical determination of separation effects in seeded atomic gas flows is presented. The model is based on the known possibility to provide a statistically convergent estimate of the exact solution for a linear transport equation using the test particle Monte Carlo method. Accordingly, the flow field of the main gas is preliminary calculated and as a second step the linear transport equations obtained by fixing the target distribution in the collision term of the Boltzmann equation for both main and minority components are solved. Both solutions are based on appropriately devised test particle Monte Carlo methods. The second step, the critical one in evaluating the separation effects, is exact and thereby completely free of numerical diffusion. The model is described in details and illustrated by 2D test cases of atomic separation in shock fronts.     

On Symmetry Flows of Noncommutative Kadomtsev-Petviashvili Hierarchy

We discuss symmetry flows of noncommutative Kadomtsev-Petviashvili （NCKP） hierarchy. An operatorbased formulation, alternative to the star-product approach of extended symmetry flows is presented. Noncommutative additional symmetry flows of the NCKP hierarchy are formulated. A rescaling symmetry flow which is associated with the rescaling of whole coordinates is introduced.     

A improved incompressible lattice Boltzmann model for time-independent flows

It is well known that the lattice Boltzmann equation method (LBE) can model the incompressible Navier-Stokes (NS) equations in the limit where density goes to a constant. In a LBE simulation, however, the density cannot be constant because pressure is equal to density times the square of sound speed, hence a compressibility error seems inevitable for the LBE to model incompressible flows. This work uses a modified equilibrium distribution and a modified velocity to construct an LBE which models time-independent (steady) incompressible flows with significantly reduced compressibility error. Computational results in 2D cavity flow and in a 2D flow with an exact solution are reported.     

Cumulative compressibility effects on slow reactive dynamics in turbulent flows

Reactions in turbulent flows, chemical reactions or combustion, are common. Typically reaction time scales are much shorter than turbulence timescales. In biological applications, as it is the case for bacterial and plankton populations living under the influence of currents in oceans and lakes, the typical lifetime can be long and thus can fall well within the inertial range of turbulence time scales. Under these conditions, turbulent transport interacts in a very complex way with the dynamics of growth and death of the individuals in the population. In the present paper, we quantitatively investigate the effect of the flow compressibility on the dynamics of populations. Small effective compressibility can be induced by several physical mechanisms, such as, e.g., by the density mismatch, by a small but finite size of microorganisms, and by gyrotaxis (an interaction between swimming and shear). We report, for the first time, how even a tiny effective compressibility can produce a dramatically large effect on global quantities like the carrying capacity of the ecosystem. We interpret our findings by means of a cumulative effect made possible by the long replication times of the organisms with respect to turbulence time scales. A statistical quantification of the fluctuations of population concentration is presented.     

Computation of fluid flows in non-inertial contracting, expanding, and rotating reference frames

We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or rotation of the flow. We consider the formulation of Euler equations of fluid dynamics in a homologously expanding/contracting and/or rotating reference frame. The frame motion is adjusted to minimize local fluid velocities. Such approach allows to accommodate very efficiently large degrees of change in the flow extent. Moreover, by excluding the contribution of the bulk flow to the total energy the method eliminates the high Mach number problem in the flows of interest. An important practical advantage of the method is that it can be easily implemented with virtually any Eulerian hydrodynamic scheme and adaptive mesh refinement (AMR) strategy.We also consider in detail equation invariance and existence of conservative formulation of equations for special classes of expanding/contracting reference frames. Special emphasis is placed on extensive numerical testing of the method for a variety of reference frame motions, which are representative of the realistic applications of the method. We study accuracy, conservativity, and convergence properties of the method both in problems which are not its optimal applications as well as in systems in which the use of this method is maximally beneficial. Such detailed investigation of the numerical solution behavior is used to define the requirements that need to be considered in devising problem-specific fluid motion feedback mechanisms.     

Thermal boundary layer for non-Newtonian fluid

Summary Analytical and numerical solutions for the momentum and thermal boundary layer equations of a non-Newtonian power law fluid are presented. The flow is assumed to be under the influence of an external magnetic fieldB (x) applied perpendicular to the surface and an electric fieldE(x) perpendicular toB(x) and the direction of the longitudinal velocity in the boundary layer. For the power law fluid it is assumed that the shear stress is proportional to then-th power of the velocity gradient andn is called the flow index. The variations of the velocity fieldf′, the temperature field θ, the shear stress on the surfaceτ _W , the displacement thicknessδ ₁ and the momentum thicknessδ ₂ with the magnetic-field parameter γ, the flow indexn, the heat transfer indexS and the Prandtl number Pr are studied. It is found that, if the outer flow velocityU(x) (potential flow) is proportional to the arc lengthx raised to a powerm, then the similarity solution for the thermal boundary layer equation is possible only whenm=1/3, which represents flow past a wedge of included angle π/2. It is established that the temperature of the wedge increases with the increase of γ, Pr,S and the decrease ofn. In general the magnetic field can be used as a heater for the surface of the wedge.