An atomistic-continuum hybrid simulation of fluid flows over superhydrophobic surfaces

Recent experiments have found that slip length could be as large as on the order of 1 mu m for fluid flows over superhydrophobic surfaces. Superhydrophobic surfaces can be achieved by patterning roughness on hydrophobic surfaces. In the present paper an atomistic-continuum hybrid approach is developed to simulate the Couette flows over superhydrophobic surfaces in which a molecular dynamics simulation is used in a small region near the superhydrophobic surface where the continuum assumption is not valid and the Navier-Stokes equations are used in a large region for bulk flows where the continuum assumption does hold. These two descriptions are coupled using the dynamic coupling model in the overlap region to ensure momentum continuity. The hybrid simulation predicts a superhydrophobic state with large slip lengths which cannot be obtained by molecular dynamics simulation alone.

Solute transport in nanochannels with roughness-like structures

Newfound attention has been given to solute transport in nanochannels. Because the electric double layer (EDL) thickness is comparable to characteristic channel dimensions, nanochannels have been used to separate ionic species with a constant charge-to-size ratio (i.e., electrophoretic mobility) that otherwise cannot be separated in electroosmotic or pressure- driven flow along microchannels. In nanochannels, the electrical fields within the EDL cause transverse ion distributions and thus yield charge-dependent mean ion speeds in the flow. Surface roughness is usually inevitable during microfabrication of microchannels or nanochannels. Surface roughness is usually inevitable during the fabrication of nanochannels. In the present study, we develop a numerical model to investigate the transport of charged solutes in nanochannels with hundreds of roughness-like structures. The model is based on continuum theory that couples Navier-Stokes equations for flows, Poisson-Boltzmann equation for electrical fields, and Nernst-Planck equation for solute transports. Different operating conditions are considered and the solute transport patterns in rough channels are compared with those in smooth channels. Results indicate that solutes move slower in rough nanochannels than in smooth ones for both pressure- driven and electroosmotic flows. Moreover, solute separation can be significantly improved by surface roughness under certain circumstances.

Numerical Investigation On The Flowfield Of "Swallowtail" Cavity For Supersonic Mixing Enhancement

A "swallowtail" cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the "swallowtail" cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-epsilon turbulence model in a multi-block mesh. Turbulence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the "swallowtail" cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the "swallowtail" cavity structure.

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.

Some problems of edge waves and standing waves on beaches

Some problems of edge waves and standing waves on beaches are examined.

The nonlinear interaction of a wave normally incident on a sloping beach with a subharmonic edge wave is studied. A two-timing expansion is used in the full nonlinear theory to obtain the modulation equations which describe the evolution of the waves. It is shown how large amplitude edge waves are produced; and the results of the theory are compared with some recent laboratory experiments.

Traveling edge waves are considered in two situations. First, the full linear theory is examined to find the finite depth effect on the edge waves produced by a moving pressure disturbance. In the second situation, a Stokes' expansion is used to discuss the nonlinear effects in shallow water edge waves traveling over a bottom of arbitrary shape. The results are compared with the ones of the full theory for a uniformly sloping bottom.

The finite amplitude effects for waves incident on a sloping beach, with perfect reflection, are considered. A Stokes' expansion is used in the full nonlinear theory to find the corrections to the dispersion relation for the cases of normal and oblique incidence.

Finally, an abstract formulation of the linear water waves problem is given in terms of a self adjoint but nonlocal operator. The appropriate spectral representations are developed for two particular cases.

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.