Propagation of weakly nonlinear disturbances of the interface between two layers of fluid

The dynamics of internal waves of small but finite amplitude in a two-layer fluid system bounded by rigid horizontal surfaces at bottom and top is investigated theoretically. For linear disturbances of the fluid interface the authors propose a polynomial approximation of the dispersion relation which has the same asymptotics as the exact formula in the limiting situations of very long and short waves. In the case of three-dimensional, weakly nonlinear disturbances of slowly varying shape (in the coordinate system moving with the wave) an equation like the wave equation is derived. This equation has Stokes solutions coinciding with the well-known results for infinitely deep layers. For fairly long disturbances solitary solutions of the model wave equation which fit the experimental data are determined. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 125–131, January–February, 1994.     

Experimental study on the unusual turbulence intensity distributions in rod-to-wall gap regions

The phenomenon of unusual turbulence intensity distributions in closely spaced rod bundles was experimentally studied. Fully developed turbulence intensities in rod-to-wall gap regions, formed by a single rod regularly mounted in a trapezoidal duct, were measured with a hot-wire anemometer. Starting from a rod setting giving a small bottom rod-to-wall gap, a series of gap spacings were achieved by moving the rod upward, resulting in larger bottom gaps and at the same time smaller top gaps. A region of high turbulence kinetic energy occurred first in the bottom gap region corresponding to the small bottom gap spacing and then shifted to the top gap region for the cases of small top gap spacings. There was no evidence of a high kinetic energy patch when the top gap size was extremely small. To unveil the mechanism behind this phenomenon, measurements on secondary velocities and energy spectra were conducted for one rod setting, and these results are described in detail. It was found that the measured secondary flow patterns could not explain the abnormal turbulence intensity distributions. However, energy density spectra revealed certain peak frequencies that support the argument that cross-gap large-scale eddy motion is of importance as both a transport process and production mechanism for subchannels formed by closely spaced rod bundles.     

Topography and Dispersion Effects in Bottom Layer Dynamics

A hyperbolic model of a shallow water flow is considered with allowance for nonlinear and dispersion effects. The structure of traveling waves above a flat bottom is studied. Stability of small disturbances of a homogeneous flow and development of instability of a nonstationary flow above an inclined bottom are analyzed.     

Modeling of long nonlinear waves on the interface in a horizontal two-layer viscous channel flow

The dynamics of two-dimensional waves of small but finite amplitude are theoretically studied for the case of a two-layer system bounded by a horizontal top and bottom. It is shown that for relatively large steady-state flow velocities and at certain fluid depth ratios the vertical velocity profile is nonlinear. An evolutionary equation governing the fluid interface disturbances and allowing for the long-wave contributions of the layer inertia and surface tension, the weak nonlinearity of the waves, and the unsteady friction on all the boundaries of the system is derived. Steady-state solutions of the cnoidal and solitary wave type for the disturbed flow are determined without regard for dissipation losses. It is found that the magnitude and the direction of the flow can alter not only the lengths of the waves but also their polarity.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 143–158. Original Russian Text Copyright © 2005 by Arkhipov and Khabakhpashev.     

双缆悬索桥空缆状态主缆抗滑安全性研究

为指导双缆悬索桥上下缆垂跨比的取值，明确双缆悬索桥施工阶段主缆抗滑稳定性，提出一种主缆在施工阶段空缆状态下的抗滑安全系数计算方法。基于上缆变下缆的主缆布置方式，通过双缆悬索桥成桥状态反推空缆状态主缆垂度，根据空缆状态下主缆线形为悬链线计算中塔塔顶鞍座处缆力及包角，并据此计算空缆状态抗滑安全系数。建立多塔悬索桥有限元模型对提出的公式进行验证，分析成桥状态上下缆垂跨比和桥梁跨度的取值对空缆到成桥状态主缆垂度变化以及抗滑安全系数的影响。结果表明，采用本文公式计算的双缆悬索桥空缆状态下抗滑安全系数精度较高；上下缆垂跨比对空缆状态主缆抗滑安全性影响较大，抗滑安全系数随着上下缆垂跨比差值的增大迅速减小；空缆状态主缆抗滑安全系数受跨度影响不大，其随跨度增大略有提高。在实际的双缆悬索桥初步设计过程中应考虑施工阶段主缆抗滑稳定性，选择适宜的上下缆垂跨比，采取措施提高施工阶段主缆抗滑安全性。     

Hydraulic analysis of free-surface flows with solidification

Summary The paper is concerned with a one-dimensional analysis of plane open-channel flow with continuous solidification. The process is of relevance for recent developments in the casting of steel and other metals. The bottom of the channel consists of a rotating casting roll and a horizontal cooling table, where the solidified material is withdrawn with given velocity. The study is restricted to the region downstream of the top of the casting roll. Surface tension is neglected. In the main part of the analysis inviscid fluid flow is considered since the Reynolds number is very large in the applications. It is found that the steady-state solutions are nonunique in a certain parameter range. In addition to a continuous solution, there are two solutions including hydraulic jumps, with one hydraulic jump being located on the casting roll, the other one on the cooling table. Regarding the stability of the non unique solutions, the evolution of disturbances is investigated numerically as an initial-value problem. It is concluded that the hydraulic jump on the cooling table is unstable, while the other discontinuous solution as well as the continuous solution are stable for sufficiently small disturbances. Which stable solution is attained in the steady state, depends on the history of the process. Friction at the liquid/solid interface is taken into account in the last part of the analysis. A constant friction coefficient is assumed. It is found that the history of the process determines the steady-state solution if, and only if, the friction coefficient is sufficiently small. For larger values of the friction coefficient, the steady-state solution is unique and independent of the history of the transient process. Furthermore, for sufficiently large friction coefficients, stable hydraulic jumps are found, in contrast to the inviscid case, also on the cooling table. Received 19 March 1999; accepted for publication 3 May 1999     

Three-dimensional problem of exponentially stratified flow over bottom roughness in the case of finite depth

The three-dimensional problem of the flow of an exponentially stratified fluid of finite depth over bottom roughness is considered in the rigid roof approximation and in the presence of a free surface. In the rigid roof approximation the solution is obtained in the form of a Fourier series in the vertical Lagrangian coordinate, and the series coefficients are expressed in terms of single integrals outside a horizontal strip whose sides are parallel to the flow axis and tangential to the projection of the support of the function describing the bottom roughness. This makes it possible to investigate the near field in regions not considered in [1, 2]. The presence of a small parameter in the boundary condition at the free surface makes it possible to find, in the first approximation, the wave motions and nonwave disturbances at the free surface in the near and far fields. In the near field the width of the wave zone is of the order of the flow depth, expands with distance from the bottom and is broadest at the free surface. As distinct from the annular disturbances within the fluid, the pattern of the nonwave disturbances at the free surface depends on the polar angle. The law of similarity for the diverging waves at the free surface is also obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 101–111, May–June, 1990.The authors are grateful to É. V. Teodorovich for discussing the formulation of the problem.     

Transformation of Long Nonlinear Waves in a Two-Layer Viscous Fluid Between a Gently Sloping Lid and Bottom

Dynamics of three-dimensional disturbances of the interface between two fluid layers of different densities is considered analytically and numerically. An evolutionary integrodifferential equation is derived, which takes into account long-wave contributions of inertia of the layers and surface tension, small but finite amplitude of disturbances of the interface between two incompressible immiscible fluids, gentle slopes of the lid and bottom, and nonstationary shear stresses at all boundaries. Numerical solutions of this model equation for several (most typical) nonlinear problems of transformation of two- and three-dimensional waves are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 45–57, November–December, 2005.     

Evolution of long nonlinear waves on the interface of a stratified viscous fluid flow in a channel

The dynamics of disturbances of the interface between two layers of incompressible immiscible fluids of different densities in the presence of a steady flow between the horizontal bottom and lid is studied analytically and numerically. A model integrodifferential equation is derived, which takes into account long-wave contributions of inertial layers and surface tension of the fluids, small but finite amplitude of disturbances, and unsteady shear stresses on all boundaries. Numerical solutions of this equation are given for the most typical nonlinear problems of transformation of both plane waves of different lengths and solitary waves. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 49–61, July–August, 2007.     

A comparative study of flame-wall interaction and flame-cooling air interaction

This paper presents a three-dimensional (3D) direct numerical simulation (DNS) study of flame-wall interaction (FWI) and flame-cooling air interaction (FCAI). A preheated, methane/air mixture enters a channel with constant temperature walls, where the top wall is effusion cooled. An imposed vertical hot sheet near the inlet creates two flame branches interacting with the top and bottom walls. The flame is observed to be leaner in the region where it interacts with the effusion cooling jets. In this region, the flame is longer and features reduced CO mass fraction. The fluctuations in the heat release rate (HRR) and CO mass fraction are also relatively small near the top wall. Near the bottom wall, finger-like flame structures are formed due to the interaction of turbulent vortices with the flame surface. These flame structures initially move away from the wall as they propagate further downstream before eventually collapsing at the wall. This leads to the creation of regions of high wall heat flux and CO. While analysis of the CO thermochemical state shows a complex picture near the bottom wall, two-dimensional (2D) manifolds can be identified near the top wall. Therefore, a framework to estimate CO mass fraction due to FCAI based on 1D freely-propagating flame solutions is proposed showing a good agreement with the DNS results.     

Stability for Rayleigh–Benard Convective Solutions of the Boltzmann Equation

We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard setup). We consider a 2-dimensional convective stationary solution, which for small Knudsen numbers is close to the convective stationary solution of the Oberbeck–Boussinesq equations, near and above the bifurcation point, and prove its stability under 2-d small perturbations, for Rayleigh numbers above and close to the bifurcation point and for small Knudsen numbers.     

Deep swirling flow down a plughole with air entrainment

Experiments have been carried out to determine the water depth required to entrain a given amount of air with a given circulating water flow discharging through a vertical pipe set in the flat bottom of a vessel. The circulation angle, , between the radial direction and the velocity vector far from discharge pipe was set at 0°, 10°, 30° or 60°.

It is shown that results are not dependent upon the diameter of the offtake pipe, if that is sufficiently small, and results are then expressed either as a dimensionless water depth vs a dimensionless ratio of the flow rates of the two phases or as a dimensionless flow rate of one phase vs the dimensionless flow rate of the other phase. An approximate theory describes trends in the data and is mostly in good quantitative agreement.

The results are used to examine the work of others on the entrainment of air or steam by water flowing along the bottom of a horizontal pipe into a small bottom offtake and the similar entrainment of water by air or steam flowing into a small top offtake. These systems occur in certain PWR loss of coolant accidents.     

Viscous effects in liquid encapsulated liquid bridges

An analytical derivation of the surface deflections and the streamfunctions for the flow inside a liquid encapsulated liquid bridge has been derived using an asymptotic expansion about a small capillary number. The model assumes an initially flat and cylindrical interface under the assumption that the densities of both fluids are equal. To simplify the analysis, the top and bottom walls are assumed to be stress-free and the Reynolds number is assumed to be negligible. Flow is generated either by a moving outer wall (shear-driven flow) or by applying a temperature difference across the top and bottom walls (Marangoni-driven flow). The resulting equations show that for the shear-driven flow, as the viscosity ratio increases, the surface deflections increase monotonically. For the Marangoni-driven flow there exist values of the viscosity ratio where the surface deflections reach a minimum and then switch signs. This investigation shows that it may be possible in more realistic systems to use an outer encapsulating liquid of the proper viscosity ratio to stabilize the liquid–liquid interface during float zone crystal growth.     

代理模型在机翼油箱晃动适航审定中的应用

飞机飞行过程中,机翼油箱易受扰动或激励作用而产生低频晃动,引起机翼油箱壁面变形失效.本文将响应面代理模型引入飞机复合材料燃油箱晃动适航审定工作,以晃动频率、晃动幅值和油箱载液比为自变量,以油箱外壁面最大主应变峰值为响应,建立了油箱上下蒙皮响应面统计模型,给出油箱上下蒙皮最大主应变峰值与激励频率、幅值和油箱载液比等因素的显式响应函数.开展物理全尺寸试验和流固耦合数值模拟验证代理模型的有效性.结果 表明,上下蒙皮最大主应变峰值呈非线性趋势,存在最危险载液比使得主应变峰值最大化,且油箱破坏多发生在下蒙皮.     

Direct numerical simulation of a turbulent Couette-Poiseuille flow,part 2: Large- and very-large-scale motions

A direct numerical simulation dataset of a fully developed turbulent Couette-Poiseuille flow is analyzed to investigate the spatial organization of streamwise velocity-fluctuating u-structures on large and very large scales. Instantaneous and statistical flow fields show that negative-u structures with a small scale on a stationary bottom wall grow throughout the centerline due to the continuous positive mean shear, and they penetrate to the opposite moving wall. The development of an initial vortical structure related to negative-u structures on the bottom wall into a large-scale hairpin vortex packet with new hairpin vortices, which are created upstream and close to the wall, is consistent with the auto-generation process in a Poiseuille flow (Zhou et al., J. Fluid Mech., vol. 387, 1999, pp. 353–396). Although the initial vortical structure associated with positive-u structures on the top wall also grows toward the bottom wall, the spatial development of the structure is less coherent with weak strength due to the reduced mean shear near the top wall, resulting in less turbulent energy on the top wall. The continuous growth of the structures from a wall to the opposite wall explains the enhanced wall-normal transport of the streamwise turbulent kinetic energy near the centerline. Finally, an inspection of the time-evolving instantaneous fields and conditional averaged flow fields for the streamwise growth of a very long structure near the centerline exhibits that a streamwise concatenation of adjacent large-scale u-structures creates a very-large-scale structure near the channel centerline.     

A Model of Buoyancy-Driven Two-Phase Countercurrent Fluid Flow

We seek simple analytical solutions in a model of gas flow driven by a combination of buoyancy, viscous, and capillary forces. Traveling-wave solutions describe propagation of the top and bottom of the gas plume. The top of the plume has low gas saturation, but propagates much faster than the bottom. The theoretical maximum of the velocity of propagation of the top of the plume provides a simple conservative estimate of the time until plume evolution will dramatically slow down. A sequence of rarefaction and traveling-wave solutions characterizes the transition zones between the top and bottom stable regions. The analytical results are applied to studying carbon dioxide flow caused by leaks from deep geological formations used for CO₂ storage. The results are also applicable for modeling flow of natural gas leaking from seasonal gas storage, or for modeling of secondary hydrocarbon migration.     

三维气泡与自由表面相互作用的直接数值模拟

采用VOF中的PLIC界面重构方法数值模拟了三维气泡在液流中上升并与自由表面相互作用的运动.分别考察了不同初始高度,有无来流及有无再生气泡对气泡上升高度、上升速度、压力及与自由表面相互作用等的影响.结果表明:气泡初始位置越低,顶端上升的高度越大,自由面隆起的范围更广.越靠近自由表面,底部射流横向发展越窄,而向上的压力梯度,气泡上升速度,底部射流上升高度越大,反之则反;但如果底部射流均在接近自由表面以前已横向发展充分,则差别不大.气泡外形、上升高度、破裂时间以及上升速度与来流无关.产生再生气泡后,原生气泡与再生气泡相吸,相互加速对方的上升;自由表面抬升的高度增幅较大,范围拓宽,上升速度也大大增加,且再生气泡越多,自由表面隆起的范围越大.     

Stationäre Temperatur oder Konzentrationsfelder in endlichen Zylindern für verschiedene Randbedingungen erster Art

Steady state temperature fields within a finite circular cylinder are calculated for the boundary conditions of constant temperature at the bottom and the wall of the cylinder whereas its top temperature is described by some temperature distributions which can be expressed by polynomial functions. These temperature distributions are evaluated for the cases, that the temperature drops from the center point value T₁ linearly or parabolically to a specified value T₂ at a certain distance r₁. The results are given in terms of dimensionless numbers. The “disturbing” temperatures at the cylinder top influence the temperatures within the cylinders less if the distance r₁ is small, over which the temperature changes from T₁ to T₂, if this change occurs linearly, if T₂ approaches the value of the wall and bottom temperature and if the cylinders are slender, e. g. if their length are greater than their radius. The slenderness of the cylinders has an important influence. By analogy the results are valid also for concentration fields.     

High Frequency Measurements of Viscoelastic Properties of Hydrogels for Vocal Fold Regeneration

This report describes a torsional wave experiment used to measure the viscoelastic properties of vocal fold tissues and soft materials over the range of phonation frequencies. A thin cylindrical sample is mounted between two hexagonal plates. The assembly is enclosed in an environmental chamber to maintain the temperature and relative humidity at in vivo conditions. The bottom plate is subjected to small oscillations by means of a galvanometer driven by a frequency generator that steps through a sequence of frequencies. At each frequency, measured rotations of the top and bottom plates are used to determine the ratio of the amplitudes of the rotations of the two plates. Comparisons of the frequency dependence of this ratio with that predicted for torsional waves in a linear viscoelastic material allows the storage modulus and the loss angle, in shear, to be calculated by a best-fit procedure. Experimental results are presented for hydrogels that are being examined as potential materials for vocal fold regeneration.     

宽幅钢箱梁环焊缝焊接顺序优化研究

基于热弹塑性有限元法,采用ANSYS软件建立了网格疏密过渡的单箱五室钢箱梁壳单元模型;结合高效的分段移动热源,实现了对大型复杂长焊缝结构焊接全过程的数值模拟,并定性对比了宽幅钢箱梁在不同的环焊缝焊接顺序下顶板和底板的变形情况.分析结果表明:腹板焊缝的焊接顺序对竖向最大变形值(绝对值)的影响不大,其值主要取决于顶板和底板...