流量配比对Coil增益分布影响的数值研究

利用三维CFD技术,通过求解层流Navier-stokes方程与组分输运方程,对简化后的化学氧碘激光RADICL模型进行数值模拟与分析,结合10种组分和21个基元反应的化学反应模型,对COIL亚声速段横向射流情况下,不同的主副流流量配比对化学氧碘激光器性能的影响进行分析与比较.结果证明,过高或过低的碘分子浓度状态均不利于合理、可观的小信号增益系数产生.存在一个最佳流量配比范围,与之对应的工作状态下,COIL的小信号增益系数会得到显著提高.

氧碘化学激光器超声速段射流工作方式性能的数值研究

氧碘化学激光器(COIL)的混合喷管内发生的是气体动力学、化学反应动力学以及光学等相互耦合的复杂过程,每个过程都对COIL性能有着至关重要的影响.利用3维计算流体动力学技术,通过求解层流Navier-Stokes方程与组分输运方程对简化的氧碘化学激光RADICL模型进行数值模拟与分析,结合10种组分和21个基元反应的化学反应模型,对COIL超声速段射流情况下喷管内的流动及混合情况,尤其是产率、分解率、泵浦率和小信号增益系数的细致3维空间分布进行研究.结果证明超声速段进行射流有利于提高COIL的性能表现,可以充分利用高增益区,光腔位置增益可以达到0.012 cm~(-1),与亚声速段射流相比总压恢复性能提高,混合有待加强.

计算气动弹性若干研究进展

郭永怀和钱学森先生早在1946年提出了上临界马赫数的概念,即对于亚声速的二维无旋流动,当来流速度达到下临界马赫数时开始出现声速.稍增加来流速度,光滑无旋的亚、超声速混合流动可以继续存在,理论上只有当来流速度达到上临界马赫数出现激波后,光滑无旋流动才被破坏.随后,航空工程界先驱们为提高阻力发散马赫数,降低马赫数1附近的飞机阻力,为突破声障,提出了超临界翼型设计技术,引进了后掠翼设计概念,提出了跨声速面积律理论,导致了20世纪军民用航空飞行器的大规模发展,随着计算机技术和计算方法的进步,不同程度地简化流体控制方程的求解方法得到大发展.基于雷诺平均Navier-Stokes方程的计算流体力学已广泛应用于飞机性能评估、复杂流动机理分析.目前,气动外形优化设计、气动/结构耦合干扰、气动噪声等多学科问题成为空气动力学的研究热点.该文介绍作者的团队近年来在计算气动弹性研究方面的若干进展,作为对郭永怀先生诞辰100周年的怀念.

A CE/SE Scheme for Flows in Porous Media and Its Applications

In this paper, a new computational scheme for solving flows in porous media was proposed. The scheme was based on an improved CE/SE method (the space-time Conservation Element and Solution Element method). We described porous flows by adopting DFB (Brinkman-Forchheimer extended Darcy) equation. The comparison between our computational results and Ghia's confirmed the high accuracy, resolution, and efficiency of our CE/SE scheme. The proposed first-order CE/SE scheme is a new reliable way for numerical simulations of flows in porous media. After investigation of effects of Darcy number on porous flow, it shows that Darcy number has dominant influence on porous flow for the Reynolds number and porosity considered.

高超声速前台阶绕流的计算分析

气动力和气动热的精确计算是高超声速流动分析的关键和难点，一直以来没有得到解决。本 文选择前台阶绕流这一经典问题，分析来流马赫数为10 的氩气流动以及台阶壁面的气动性能。通 过求解Navier-Stokes 方程和直接Monte-Carlo 粒子模拟，得到了高超声速前台阶绕流的精确流 动，并详细分析了计算网格对Navier-Stokes 方程求解结果的影响，同时解释了高超声速流动中热 流和摩阻计算困难的原因。通过壁面边界层的准一维假设，首次提出了壁面热流和剪切力的层流壁 面函数。研究发现，壁面函数很好地描述了高超声速层流边界层内的温度分布和速度分布，为高超 声速流动的气动力和气动热预估提供了有力的工具。

Simulation of gas flow over a micro cylinder

Gas flow over a micro cylinder is simulated using both a compressible Navier-Stokes solver and a hybrid continuum /particle approach. The micro cylinder flow has low Reynolds number because of the small length scale and the low speed, which also indicates that the rarefied gas effect exists in the flow. A cylinder having a diameter of 20 microns is simulated under several flow conditions where the Reynolds number ranges from 2 to 50 and the Mach number varies from 0.1 to 0.8. It is found that the low Reynolds number flow can be compressible even when the Mach number is less than 0.3, and the drag coefficient of the cylinder increases when the Reynolds number decreases. The compressible effect will increase the pressure drag coefficient although the friction coefficient remains nearly unchanged. The rarefied gas effect will reduce both the friction and pressure drag coefficients, and the vortex in the flow may be shrunk or even disappear.

Numerical simulation of condensation of bubbles under microgravity conditions by moving mesh method in the double-staggered grid

A numerical 2D method for simulation of two-phase flows including phase change under microgravity conditions is presented in this paper, with a level set method being coupled with the moving mesh method in the double-staggered grid systems. When the grid lines bend very much in a curvilinear grid, great errors may be generated by using the collocated grid or the staggered grid. So the double-staggered grid was adopted in this paper. The level set method is used to track the liquid-vapor interface. The numerical analysis is fulfilled by solving the Navier-Stokes equations using the SIMPLER method, and the surface tension force is modeled by a continuum surface force approximation. A comparison of the numerical results obtained with different numerical strategies shows that the double-staggered grid moving-mesh method presented in this paper is more accurate than that used previously in the collocated grid system. Based on the method presented in this paper, the condensation of a single bubble in the cold water under different level of gravity is simulated. The results show that the condensation process under the normal gravity condition is different from the condensation process under microgravity conditions. The whole condensation time is much longer under the normal gravity than under the microgravity conditions.

Smoothed Particle Hydrodynamics (SPH): an Overview and Recent Developments

Smoothed particle hydrodynamics (SPH) is a meshfree particle method based on Lagrangian formulation, and has been widely applied to different areas in engineering and science. This paper presents an overview on the SPH method and its recent developments, including (1) the need for meshfree particle methods, and advantages of SPH, (2) approximation schemes of the conventional SPH method and numerical techniques for deriving SPH formulations for partial differential equations such as the Navier-Stokes (N-S) equations, (3) the role of the smoothing kernel functions and a general approach to construct smoothing kernel functions, (4) kernel and particle consistency for the SPH method, and approaches for restoring particle consistency, (5) several important numerical aspects, and (6) some recent applications of SPH. The paper ends with some concluding remarks.

The flow between rotating coaxial disks

Numerical approximations of nonunique solutions of the Navier-Stokes equations are obtained for steady viscous incompressible axisymmetric flow between two infinite rotating coaxial disks. For example, nineteen solutions have been found for the case when the disks are rotating with the same speed but in opposite direction. Bifurcation and perturbed bifurcation phenomena are observed. An efficient method is used to compute solution branches. The stability of solutions is analyzed. The rate of convergence of Newton's method at singular points is discussed. In particular, recovery of quadratic convergence at "normal limit points" and bifurcation points is indicated. Analytical construction of some of the computed solutions using singular perturbation techniques is discussed.

Compressible flows at small Reynolds numbers

The problem of the slow viscous flow of a gas past a sphere is considered. The fluid cannot be treated incompressible in the limit when the Reynolds number Re, and the Mach number M, tend to zero in such a way that Re ~ o(M^2 ). In this case, the lowest order approximation to the steady Navier-Stokes equations of motion leads to a paradox discovered by Lagerstrom and Chester. This paradox is resolved within the framework of continuum mechanics using the classical slip condition and an iteration scheme that takes into account certain terms in the full Navier-Stokes equations that drop out in the approximation used by the above authors. It is found however that the drag predicted by the theory does not agree with R. A. Millikan's classic experiments on sphere drag.

The whole question of the applicability of the Navier-Stokes theory when the Knudsen number M/Re is not small is examined. A new slip condition is proposed. The idea that the Navier-Stokes equations coupled with this condition may adequately describe small Reynolds number flows when the Knudsen number is not too large is looked at in some detail. First, a general discussion of asymptotic solutions of the equations for all such flows is given. The theory is then applied to several concrete problems of fluid motion. The deductions from this theory appear to interpret and summarize the results of Millikan over a much wider range of Knudsen numbers (almost up to the free molecular or kinetic limit) than hitherto Believed possible by a purely continuum theory. Further experimental tests are suggested and certain interesting applications to the theory of dilute suspensions in gases are noted. Some of the questions raised in the main body of the work are explored further in the appendices.

The Equation of State and Petrogenesis of Komatiite

(1) Equation of State of Komatiite

The equation of state (EOS) of a molten komatiite (27 wt% MgO) was detennined in the 5 to 36 GPa pressure range via shock wave compression from 1550°C and 0 bar. Shock wave velocity, U_S, and particle velocity, U_P, in km/s follow the linear relationship U_S = 3.13(±0.03) + 1.47(±0.03) U_P. Based on a calculated density at 1550°C, 0 bar of 2.745±0.005 glee, this U_S-U_P relationship gives the isentropic bulk modulus K_S = 27.0 ± 0.6 GPa, and its first and second isentropic pressure derivatives, K'_S = 4.9 ± 0.1 and K"_S = -0.109 ± 0.003 GPa^-1.

The calculated liquidus compression curve agrees within error with the static compression results of Agee and Walker [1988a] to 6 GPa. We detennine that olivine (FO₉₄) will be neutrally buoyant in komatiitic melt of the composition we studied near 8.2 GPa. Clinopyroxene would also be neutrally buoyant near this pressure. Liquidus garnet-majorite may be less dense than this komatiitic liquid in the 20-24 GPa interval, however pyropic-garnet and perovskite phases are denser than this komatiitic liquid in their respective liquidus pressure intervals to 36 GPa. Liquidus perovskite may be neutrally buoyant near 70 GPa.

At 40 GPa, the density of shock-compressed molten komatiite would be approximately equal to the calculated density of an equivalent mixture of dense solid oxide components. This observation supports the model of Rigden et al. [1989] for compressibilities of liquid oxide components. Using their theoretical EOS for liquid forsterite and fayalite, we calculate the densities of a spectrum of melts from basaltic through peridotitic that are related to the experimentally studied komatiitic liquid by addition or subtraction of olivine. At low pressure, olivine fractionation lowers the density of basic magmas, but above 14 GPa this trend is reversed. All of these basic to ultrabasic liquids are predicted to have similar densities at 14 GPa, and this density is approximately equal to the bulk (PREM) mantle. This suggests that melts derived from a peridotitic mantle may be inhibited from ascending from depths greater than 400 km.

The EOS of ultrabasic magmas was used to model adiabatic melting in a peridotitic mantle. If komatiites are formed by >15% partial melting of a peridotitic mantle, then komatiites generated by adiabatic melting come from source regions in the lower transition zone (≈500-670 km) or the lower mantle (>670 km). The great depth of incipient melting implied by this model, and the melt density constraint mentioned above, suggest that komatiitic volcanism may be gravitationally hindered. Although komatiitic magmas are thought to separate from their coexisting crystals at a temperature =200°C greater than that for modern MORBs, their ultimate sources are predicted to be diapirs that, if adiabatically decompressed from initially solid mantle, were more than 700°C hotter than the sources of MORBs and derived from great depth.

We considered the evolution of an initially molten mantle, i.e., a magma ocean. Our model considers the thermal structure of the magma ocean, density constraints on crystal segregation, and approximate phase relationships for a nominally chondritic mantle. Crystallization will begin at the core-mantle boundary. Perovskite buoyancy at > 70 GPa may lead to a compositionally stratified lower mantle with iron-enriched mangesiowiistite content increasing with depth. The upper mantle may be depleted in perovskite components. Olivine neutral buoyancy may lead to the formation of a dunite septum in the upper mantle, partitioning the ocean into upper and lower reservoirs, but this septum must be permeable.

(2) Viscosity Measurement with Shock Waves

We have examined in detail the analytical method for measuring shear viscosity from the decay of perturbations on a corrugated shock front The relevance of initial conditions, finite shock amplitude, bulk viscosity, and the sensitivity of the measurements to the shock boundary conditions are discussed. The validity of the viscous perturbation approach is examined by numerically solving the second-order Navier-Stokes equations. These numerical experiments indicate that shock instabilities may occur even when the Kontorovich-D'yakov stability criteria are satisfied. The experimental results for water at 15 GPa are discussed, and it is suggested that the large effective viscosity determined by this method may reflect the existence of ice VII on the Rayleigh path of the Hugoniot This interpretation reconciles the experimental results with estimates and measurements obtained by other means, and is consistent with the relationship of the Hugoniot with the phase diagram for water. Sound waves are generated at 4.8 MHz at in the water experiments at 15 GPa. The existence of anelastic absorption modes near this frequency would also lead to large effective viscosity estimates.

(3) Equation of State of Molybdenum at 1400°C

Shock compression data to 96 GPa for pure molybdenum, initially heated to 1400°C, are presented. Finite strain analysis of the data gives a bulk modulus at 1400°C, K'_S. of 244±2 GPa and its pressure derivative, K'_OS of 4. A fit of shock velocity to particle velocity gives the coefficients of U_S = C_O+S U_P to be C_O = 4.77±0.06 km/s and S = 1.43±0.05. From the zero pressure sound speed, C_O, a bulk modulus of 232±6 GPa is calculated that is consistent with extrapolation of ultrasonic elasticity measurements. The temperature derivative of the bulk modulus at zero pressure, θK_OSθT|_P, is approximately -0.012 GPa/K. A thermodynamic model is used to show that the thermodynamic Grüneisen parameter is proportional to the density and independent of temperature. The Mie-Grüneisen equation of state adequately describes the high temperature behavior of molybdenum under the present range of shock loading conditions.

Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.

Non-Linear Scale Interactions in a Forced Turbulent Boundary Layer

This thesis explores the dynamics of scale interactions in a turbulent boundary layer through a forcing-response type experimental study. An emphasis is placed on the analysis of triadic wavenumber interactions since the governing Navier-Stokes equations for the flow necessitate a direct coupling between triadically consist scales. Two sets of experiments were performed in which deterministic disturbances were introduced into the flow using a spatially-impulsive dynamic wall perturbation. Hotwire anemometry was employed to measure the downstream turbulent velocity and study the flow response to the external forcing. In the first set of experiments, which were based on a recent investigation of dynamic forcing effects in a turbulent boundary layer, a 2D (spanwise constant) spatio-temporal normal mode was excited in the flow; the streamwise length and time scales of the synthetic mode roughly correspond to the very-large-scale-motions (VLSM) found naturally in canonical flows. Correlation studies between the large- and small-scale velocity signals reveal an alteration of the natural phase relations between scales by the synthetic mode. In particular, a strong phase-locking or organizing effect is seen on directly coupled small-scales through triadic interactions. Having characterized the bulk influence of a single energetic mode on the flow dynamics, a second set of experiments aimed at isolating specific triadic interactions was performed. Two distinct 2D large-scale normal modes were excited in the flow, and the response at the corresponding sum and difference wavenumbers was isolated from the turbulent signals. Results from this experiment serve as an unique demonstration of direct non-linear interactions in a fully turbulent wall-bounded flow, and allow for examination of phase relationships involving specific interacting scales. A direct connection is also made to the Navier-Stokes resolvent operator framework developed in recent literature. Results and analysis from the present work offer insights into the dynamical structure of wall turbulence, and have interesting implications for design of practical turbulence manipulation or control strategies.

Fast Lattice Green's Function Methods for Viscous Incompressible Flows on Unbounded Domains

In this thesis, a collection of novel numerical techniques culminating in a fast, parallel method for the direct numerical simulation of incompressible viscous flows around surfaces immersed in unbounded fluid domains is presented. At the core of all these techniques is the use of the fundamental solutions, or lattice Green’s functions, of discrete operators to solve inhomogeneous elliptic difference equations arising in the discretization of the three-dimensional incompressible Navier-Stokes equations on unbounded regular grids. In addition to automatically enforcing the natural free-space boundary conditions, these new lattice Green’s function techniques facilitate the implementation of robust staggered-Cartesian-grid flow solvers with efficient nodal distributions and fast multipole methods. The provable conservation and stability properties of the appropriately combined discretization and solution techniques ensure robust numerical solutions. Numerical experiments on thin vortex rings, low-aspect-ratio flat plates, and spheres are used verify the accuracy, physical fidelity, and computational efficiency of the present formulations.