Influence of insoluble surfactant on the deformation and breakup of a bubble or thread in a viscous fluid

The influence of surfactant on the breakup of a prestretched bubble in a quiescent viscous surrounding is studied by a combination of direct numerical simulation and the solution of a long-wave asymptotic model. The direct numerical simulations describe the evolution toward breakup of an inviscid bubble, while the effects of small but non-zero interior viscosity are readily included in the long-wave model for a fluid thread in the Stokes flow limit. The direct numerical simulations use a specific but realizable and representative initial bubble shape to compare the evolution toward breakup of a clean or surfactant-free bubble and a bubble that is coated with insoluble surfactant. A distinguishing feature of the evolution in the presence of surfactant is the interruption of bubble breakup by formation of a slender quasi-steady thread of the interior fluid. This forms because the decrease in surface area causes a decrease in the surface tension and capillary pressure, until at a small but non-zero radius, equilibrium occurs between the capillary pressure and interior fluid pressure. The long-wave asymptotic model, for a thread with periodic boundary conditions, explains the principal mechanism of the slender thread's formation and confirms, for example, the relatively minor role played by the Marangoni stress. The large-time evolution of the slender thread and the precise location of its breakup are, however, influenced by effects such as the Marangoni stress and surface diffusion of surfactant. © 2008 Cambridge University Press.

Influence of surfactant solubility on the deformation and breakup of a bubble or capillary jet in a viscous fluid

In a previous study [M. Hameed, J. Fluid Mech. 594, 307 (2008)] the authors investigated the influence of insoluble surfactant on the evolution of a stretched, inviscid bubble surrounded by a viscous fluid via direct numerical simulation of the Navier-Stokes equations, and showed that the presence of surfactant can cause the bubble to contract and form a quasisteady slender thread connecting parent bubbles, instead of proceeding directly toward pinch-off as occurs for a surfactant-free bubble. Insoluble surfactant significantly retards pinch-off and the thread is stabilized by a balance between internal pressure and reduced capillary pressure due to a high concentration of surfactant that develops during the initial stage of contraction. In the present study we investigate the influence of surfactant solubility on thread formation. The adsorption-desorption kinetics for solubility is in the diffusion controlled regime. A long-wave model for the evolution of a capillary jet is also studied in the Stokes flow limit, and shows dynamics that are similar to those of the evolving bubble. With soluble surfactant, depending on parameter values, a slender thread forms but can pinch-off later due to exchange of surfactant between the interface and exterior bulk flow. © 2009 American Institute of Physics.

Influence of liquid bridge volume on the onset of oscillation in floating-zone convection III. Three-dimensional model

An unsteady and three-dimensional model of the floating-half-zone convection on the ground is studied by the direct numerical simulation for the medium of 10 cSt silicon oil, and the influence of the liquid bridge volume on the critical applied temperature difference is especially discussed. The marginal curves for the onset of oscillation are separated into two branches related, respectively, to the slender liquid bridge and the fat liquid bridge. The oscillatory features of the floating-half-zone convection are also discussed.

Receptivity To Free-Stream Disturbance Waves For Hypersonic Flow Over A Blunt Cone

A high-order shock-fitting finite difference scheme is studied and used to do direction numerical simulation (DNS) of hypersonic unsteady flow over a blunt cone with fast acoustic waves in the free stream, and the receptivity problem in the blunt cone hypersonic boundary layers is studied. The results show that the acoustic waves are the strongest disturbance in the blunt cone hypersonic boundary layers. The wave modes of disturbance in the blunt cone boundary layers are first, second, and third modes which are generated and propagated downstream along the wall. The results also show that as the frequency decreases, the amplitudes of wave modes of disturbance increase, but there is a critical value. When frequency is over the critial value, the amplitudes decrease. Because of the discontinuity of curvature along the blunt cone body, the maximum amplitudes as a function of frequencies are not monotone.

A second-order dynamic subgrid-scale stress model

A second-order dynamic model based on the general relation between the subgrid-scale stress and the velocity gradient tensors was proposed. A priori test of the second-order model was made using moderate resolution direct numerical simulation date at high Reynolds number ( Taylor microscale Reynolds number R-lambda = 102 similar to 216) for homogeneous, isotropic forced flow, decaying flow, and homogeneous rotating flow. Numerical testing shows that the second-order dynamic model significantly improves the correlation coefficient when compared to the first-order dynamic models.

A high order accurate difference scheme for complex flow fields

A high order accurate finite difference method for direct numerical simulation of coherent structure in the mixing layers is presented. The reason for oscillation production in numerical solutions is analyzed, It is caused by a nonuniform group velocity of wavepackets. A method of group velocity control for the improvement of the shock resolution is presented. In numerical simulation the fifth-order accurate upwind compact difference relation is used to approximate the derivatives in the convection terms of the compressible N-S equations, a sixth-order accurate symmetric compact difference relation is used to approximate the viscous terms, and a three-stage R-K method is used to advance in time. In order to improve the shock resolution the scheme is reconstructed with the method of diffusion analogy which is used to control the group velocity of wavepackets. (C) 1997 Academic Press.

可压缩双组分混合层的直接数值模拟研究

通过数值求解可压缩Navier-Stokes方程模拟了三维可压缩双组分混合层问题,着重研究了双组分密度比和可压缩效应对混合层发展演化的影响.研究表明,随着密度比的增大,混合层扰动增长率降低.在混合层发展初期,可压缩性作用尤其是斜压效应对旋涡的发展起主导作用;在混合层发展后期,可压缩性影响减弱,旋涡的拉伸扭转效应占主导作用.同时,还分析讨论了可压缩混合层中湍流的转捩及拟序结构的演化过程.

可压缩流气动声场的数值模拟

气动声学是一门流动力学和声学之间的交叉学科，主要研究流动及其与物体相互作用产生噪声的机理。动用计算技术研究气动声学问题的手段称为计算气动声学。本文的目的是，基于高精度数值算法的研究，分别运用Lighthill比拟理论、Kirchhoff积分和直接数值模拟等方法，针对翼型绕流、激波-涡干扰和轴对称射流，研究了物面非定常脉动压力、涡脱落、激波-涡干扰以及涡对并等产生噪声的机理。首先针对声场与主流场在能级和特征尺度等方面的差异，从空间离散角度分析了几种差分格式，表明迎风紧致格式/对称紧致格式有较小的数值色散、耗散和各向异性误差，因而适用于气动噪声的计算。以Runge-Kutta格式为例，对时间离散带来的误差进行了分析。指出对声波计算来说，仅考虑格式稳定性是不够的，时间步长还受到允许色散误差和耗散误差的限制。基于保色戎关系的思想，构造了优化Runge-Kutta格式。处例显示优化Runge-Kutta格式相对于经典格式有更高的计算效率。采用3阶迎风紧致格式和3阶Runge-Kutta格式数值模拟了NACA0012翼型的可压缩非定常绕流流场，并将此流场作为近场声源，运用声学比拟理论对偶极子声和四极子声进行研究。结果指出，主流速度对远场声压有决定性影响，在来流马赫数较大时，四极子噪声和偶极子噪声具有相同量级，不能被忽略，表明了可压缩效应对声场的影响。采用5阶迎风紧致格式和4阶Runge-Kutta格式求解非定常可压缩Navier-Stokes方程，对激波-单涡/双涡干扰导致的声场进行了直接数值模拟。详细研究了激波-涡干扰产生噪声的机理，指出噪声的产生及其性质和激波变形密切相关。研究了近场噪声衰减和传播距离r的关系，发现噪声衰减大致和r~(4/5)而不是r~(1/2)成反比关系，提出这种差异是由流场的非线性效应引起的。构造了Kirchhoff积分和非定常流动计算相结合的算法。采用5阶迎风紧致格式和3阶Runge-Kutta格式对亚声速轴对称射流进行直接数值模拟。将射流流场作为近场声源，结合Kirchhoff方法求解远场 气动噪声。数值结果表明远场噪声具有方向性，噪声声压在离开对称轴20°处达到最大值。随着传播距离增大，噪声方向性逐渐减弱。

可压平面混合层稳定性分析及数值模拟

可压平面混合层是包含复杂多时空尺度运动的非定常流体力学部问题，具有深刻的理论意义和广泛的应用背景。针对该问题所涉及内容的多面性，本文的目的是，基于高精度、高分辨率数值算法的构造、发展和数值行为分析，采用线性稳定性分析和直接数值模拟方法。从理论和计算两方面集中研究压缩性效应、粘性效应、初值效应以及燃烧反应放热效应等对可压平面混合层早期稳定性行为和大尺度拟序涡结构非线性演化的影响。以混合层已有研究成果的分析和综述为开端，论文主体共包括四部分：第一部分是可压平面混合层时间/空间模式数值线性稳定性分析。实现了高精度对称紧致差分格式（SCD）对可压粘性扰动线性稳定性边值问题的求解，对导出的线性和非线性离散特征值问题，提出了两个高效局部解法。研究涉及二维/三维扰动波、无粘/粘性扰动波、特征函数和特征值谱、第一/第二模态、超声速快/慢模态、速度比和密度比等。验证了对流Mach数Mc为一个合理的压缩性参数。指出压缩性效应和粘性效应对最不稳定扰动波的波数（频率）和增长率呈相拟的抑制作用，且时间模式稳定性分析结果在许多方面是可信的。从随机和线性扰动场出发，采用高精度五阶迎风紧致和六阶对称紧致混合差分算法（UCD5/SCD6）对可压平面混合层的稳定性特征进行了直接数值模拟，揭示了初始主导线性扰动与一些实际涡结构非线性作用形态间的内在关联，印证了线性稳定性分析方法的合理性和有效性。第二部分是高精度迎风紧致差分格式（UCD）时空全离散数值行为分析。导出了其一维/二维一般色散表达式。研究表明，UCD格式在高波数区具有内在的全离散耗散和色散特性；其数值群速度的快/慢特征可因CFL数不同而改变；在稳定CFL数下简单附加人工粘性可强化UCD格式在高波数区的耗散量；提高时间精度可放宽稳定CFL数限制；UCD格式的二维全离散色散介质中存在三个不同性质的数值波，其全离散稳定性由数值声波主控。第三部分实现了高精度UCD5/SCD6差分算法对空间发展可压平面混合层的直接数值模拟。通过亚谐扰动波的个数和扰动频率的控制，捕捉到了基频涡的饱和、一次和二次对并等现象，显示了大尺度涡结构与入中初始扰动方式之间的内在联系。利用参数Mc观察了压缩性效应对大尺度涡空间演化及其相互作用的影响。第四部分实现了高精度UCD5/SCD6差分算法对非预混扩散火焰化学反应平面混合层的直接数值模拟。研究指出，放热效应可抑制和延迟涡的形成，使基频涡卷拉伸甚至丧失，混合层Reynolds 应力ρu'v'和流向速度波动关联项u'v'下降，以致涡结构与外流动量交换和标量输运减少，脉动输运能力被削弱，从而混合效率、产物生成率和混合层增长率下降，放热主要通过膨胀效应和斜压效应来抑制大尺度涡的演化。

Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence

A scale-similarity model for Lagrangian two-point, two-time velocity correlations LVCs in isotropic turbulence is developed from the Kolmogorov similarity hypothesis. It is a second approximation to the isocontours of LVCs, while the Smith-Hay model is only a first approximation. This model expresses the LVC by its space correlation and a dispersion velocity. We derive the analytical expression for the dispersion velocity from the Navier-Stokes equations using the quasinormality assumption. The dispersion velocity is dependent on enstrophy spectra and shown to be smaller than the sweeping velocity for the Eulerian velocity correlation. Therefore, the Lagrangian decorrelation process is slower than the Eulerian decorrelation process. The data from direct numerical simulation of isotropic turbulence support the scale-similarity model: the LVCs for different space separations collapse into a universal form when plotted against the separation axis defined by the model.

Turbulent collision of inertial particles: point-particle based, hybrid simulations and beyond

Point-particle based direct numerical simulation (PPDNS) has been a productive research tool for studying both single-particle and particle-pair statistics of inertial particles suspended in a turbulent carrier flow. Here we focus on its use in addressing particle-pair statistics relevant to the quantification of turbulent collision rate of inertial particles. PPDNS is particularly useful as the interaction of particles with small-scale (dissipative) turbulent motion of the carrier flow is mostly relevant. Furthermore, since the particle size may be much smaller than the Kolmogorov length of the background fluid turbulence, a large number of particles are needed to accumulate meaningful pair statistics. Starting from the relative simple Lagrangian tracking of so-called ghost particles, PPDNS has significantly advanced our theoretical understanding of the kinematic formulation of the turbulent geometric collision kernel by providing essential data on dynamic collision kernel, radial relative velocity, and radial distribution function. A recent extension of PPDNS is a hybrid direct numerical simulation (HDNS) approach in which the effect of local hydrodynamic interactions of particles is considered, allowing quantitative assessment of the enhancement of collision efficiency by fluid turbulence. Limitations and open issues in PPDNS and HDNS are discussed. Finally, on-going studies of turbulent collision of inertial particles using large-eddy simulations and particle- resolved simulations are briefly discussed.

Influence of Rayleigh-Taylor Instability on Liquid Propellant Reorientation in a Low-Gravity Environment

A computational simulation is conducted to investigate the influence of Rayleigh-Taylor instability on liquid propellant reorientation flow dynamics for the tank of CZ-3A launch vehicle series fuel tanks in a low-gravity environment. The volume-of-fluid (VOF) method is used to simulate the free surface flow of gas-liquid. The process of the liquid propellant reorientation started from initially flat and curved interfaces are numerically studied. These two different initial conditions of the gas-liquid interface result in two modes of liquid flow. It is found that the Rayleigh-Taylor instability can be reduced evidently at the initial gas-liquid interface with a high curve during the process of liquid reorientation in a low-gravity environment.

Stability of Hypervelocity Boundary Layers

The early stage of laminar-turbulent transition in a hypervelocity boundary layer is studied using a combination of modal linear stability analysis, transient growth analysis, and direct numerical simulation. Modal stability analysis is used to clarify the behavior of first and second mode instabilities on flat plates and sharp cones for a wide range of high enthalpy flow conditions relevant to experiments in impulse facilities. Vibrational nonequilibrium is included in this analysis, its influence on the stability properties is investigated, and simple models for predicting when it is important are described.

Transient growth analysis is used to determine the optimal initial conditions that lead to the largest possible energy amplification within the flow. Such analysis is performed for both spatially and temporally evolving disturbances. The analysis again targets flows that have large stagnation enthalpy, such as those found in shock tunnels, expansion tubes, and atmospheric flight at high Mach numbers, and clarifies the effects of Mach number and wall temperature on the amplification achieved. Direct comparisons between modal and non-modal growth are made to determine the relative importance of these mechanisms under different flow regimes.

Conventional stability analysis employs the assumption that disturbances evolve with either a fixed frequency (spatial analysis) or a fixed wavenumber (temporal analysis). Direct numerical simulations are employed to relax these assumptions and investigate the downstream propagation of wave packets that are localized in space and time, and hence contain a distribution of frequencies and wavenumbers. Such wave packets are commonly observed in experiments and hence their amplification is highly relevant to boundary layer transition prediction. It is demonstrated that such localized wave packets experience much less growth than is predicted by spatial stability analysis, and therefore it is essential that the bandwidth of localized noise sources that excite the instability be taken into account in making transition estimates. A simple model based on linear stability theory is also developed which yields comparable results with an enormous reduction in computational expense. This enables the amplification of finite-width wave packets to be taken into account in transition prediction.

Small scale turbulence in high Karlovitz number premixed flames

The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω² = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τ_η, just as in homogeneous isotropic turbulence. As τ_η is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO₂ and soot production to increasing engine efficiency.

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.