Numerical study on the instability of premixed plane flames in the three-dimensional field

The instability of premixed plane flames in the three-dimensional (3-D) field is investigated by means of the numerical simulation. We show numerically that infinitesimal disturbances superimposed on the flames grow exponentially with time, as predicted in the linear analysis, and obtain the growth rates of disturbances depending on the absolute values of the wave-number vectors. The growth rates of the 3-D flames are consistent with those of the two-dimensional (2-D) flames. The hydrodynamic effect has a destabilizing influence on the instability of flames, and the diffusive-thermal effect has a destabilizing/stabilizing influence for Le < 1/Le > 1. Moreover, we produce the hexagonal cellular structure of the flame front not only for Le < 1 but also for Le > 1, where the spacing between cells in flames for Le < 1 is small compared to that for Le > 1. The spacing of the 3-D flames is 2/√3 times as long as the cell size of the 2-D flames.     

Influence of wall slip on the hydrodynamic behavior of a two-dimensional slider bearing

In the present paper, a multi-linearity method is used to address the nonlinear slip control equation for the hydrodynamic analysis of a two-dimensional (2-D) slip gap flow. Numerical analysis of a finite length slider bearing with wall slip shows that the surface limiting shear stress exerts complicated influences on the hydrodynamic behavior of the gap flow. If the slip occurs at either the stationary surface or the moving surface (especially at the stationary surface), there is a transition point in the initial limiting shear stress for the proportional coefficient to affect the hydrodynamic load support in two opposite ways: it increases the hydrodynamic load support at higher initial limiting shear stresses, but decreases the hydrodynamic load support at lower initial limiting shear stresses. If the slip occurs at the moving surface only, no fluid pressure is generated in the case of null initial limiting shear stress. If the slip occurs at both the surfaces with the same slip property, the hydrodynamic load support goes off after a critical sliding speed is reached. A small initial limiting shear stress and a small proportionality coefficient always give rise to a low friction drag. The project supported by the National Natural Science Foundation of China (10421002, 10332010), the National Basic Research Program of China (2006CB601205), and the Science Research Foundation of Liaoning Province (20052178). The English text was polished by Yunming Chen.     

Wave resistance of a viscous liquid

In this paper we examine the resistance encountered by a system of normal stresses during its rectilinear motion along the surface of a viscous liquid of infinite depth. The problem is solved in the linear formulation, i.e., it is assumed that amplitudes of the waves which arise are small and the waves are shallow. The solution for the two-and three-dimensional problems is obtained in the general case in closed form. In the two-dimensional case a detailed study is made of the case when a constant pressure p₀, moving with the constant velocity U, is given on a segment of length 2l. In the three-dimen-sional problem the case is studied when the normal stress is concentrated on a segment of a straight line of length 2l, which can replace a ship moving along a straight course with the constant velocity U. The integrals obtained in both cases are studied using the stationary phase method, the application of which for the three-dimensional integrals with respect to a volume with boundaries is justified in §1 of the paper. As a result we obtain equations for the wave resistance in the two- (§2) and three-dimensional (§3) cases.     

A Numerical Study Promoting Algebraic Models for the Lewis Number Effect in Atmospheric Turbulent Premixed Bunsen Flames

This numerical investigation carried out on turbulent lean premixed flames accounts for two algebraic – the Lindstedt–Vaos (LV) and the classic Bray–Moss–Libby (BML) – reaction rate models. Computed data from these two models is compared with the experimental data of Kobayashi et al. on 40 different methane, ethylene and propane Bunsen flames at 1 bar, where the mean flame cone angle is used for comparison. Both models gave reasonable qualitative trend for the whole set of data, in overall. In order to characterize quantitatively, firstly, corrections are made by tuning the model parameters fitting to the experimental methane–air (of Le = 1.0) flame data. In case of the LV model, results obtained by adjusting the pre-constant, i.e., reaction rate parameter, C_R, from its original value 2.6 to 4.0, has proven to be in good agreement with the experiments. Similarly, for the BML model, with the tuning of the exponent n, in the wrinkling length scale, L_y = C_l⋅ l_x(s_L/u′)ⁿ from value unity to 1.2, the outcome is in accordance with the measured data. The deviation between the measured and calculated data sharply rises from methane to propane, i.e., with increasing Lewis number. It is deduced from the trends that the effect of Lewis number (for ethylene–air mixtures of Le = 1.2 and propane–air mixtures of Le = 1.62) is missing in both the models. The Lewis number of the fuel–air mixture is related to the laminar flame instabilities. Second, in order to quantify for its influence, the Lewis number effect is induced into both the models. It is found that by setting global reaction rate inversely proportional to the Lewis number in both the cases leads to a much better numerical prediction to this set of experimental flame data. Thus, by imparting an important phenomenon (the Lewis number effect) into the reaction rates, the generality of the two models is enhanced. However, functionality of the two models differs in predicting flame brush thickness, giving scope for further analysis.     

Influence of a hydrodynamic field on laminar flame stability

The hydrodynamic stability of a plane flame front has been studied by L. D. Landau in [1], where it was shown that it is absolutely unstable.The aim of this note is to clarify the influence of the hydrodynamic field curvature on flame stability. Flame stability is analyzed within the framework of Landau's theory, in which the flame front is represented by a surface on which the velocity, density, and temperature values experience discontinuities. Viscosity, diffusion, and heat conduction are neglected. The front moves at a given constant velocity relative to the gas. The gas is assumed to be incompressible in front of and behind the front.It is shown that fields exist which will both stabilize and destabilize the gas. A cylindrical flame formed by a concentrated source of given intensity is examined (two-dimensional problem). Flame stability is studied for the case of a perturbed flame front. It is shown that in this case, the hydrodynamic field has the effect of stabilizing the flame. For the first perturbation harmonics, the destabilizing effect of gas expansion appears to be relatively weak compared to the stabilizing effect of the velocity field. The first perturbation harmonics attenuate. The destabilizing effect of the velocity field is demonstrated by an example in which the radial flow of the fresh mixture is applied externally, and there exists a concentrated sink flow for the combustion products.The author wishes to express his gratitude to G. I. Barenblatt, A. G. Istratova, and V. B. Librovich for their attention to the paper and valuable advice.     

高径比对GaAs熔体液桥热毛细对流失稳的影响

采用基于谱元法线性稳定性分析方法,研究了高径比对GaAs熔体(Pr=0.068)液桥热毛细对流失稳的影响,同时结合能量分析揭示了热毛细对流的失稳机制.研究结果表明:与典型低普朗特数(例如Pr=0.011)熔体静态失稳模式和典型高普朗特数(例如Pr>1)熔体振荡失稳模式不同,GaAs熔体热毛细对流失稳模式依赖于液桥高径比...     

A BOUNDARY ELEMENT METHOD FOR THE INTERACTION OF FREE-SURFACE WAVES WITH A VERY LARGE FLOATING FLEXIBLE PLATFORM

In this paper a derivation is given of an integro-differential equation for the determination of the deflection of a large floating flexible platform, excited by waves. The formulation is presented for the general three-dimensional case where also a current may be present. For the two-dimensional case (1-D platform) a solution method with orthogonal function expansions turns out to be nonconvergent and therefore we have chosen to use a finite-difference method to tackle the fourth-order derivatives. This method seems to be efficient and may be extended to the general three-dimensional case. In this paper, we present 2-D results only. For the zero current situation the amplitude of the deflection of the platform together with the reflection and transmission coefficients are shown. Furthermore, for several values of the wavelength, the influence of the current is studied. The analysis for the response of a 2-D platform to a moving pressure point is then given.     

Analytic test cases for three-dimensional hydrodynamic models

Exact periodic solutions are generated for the 3-D hydrodynamic equations in linearized form. A linear slip condition is enforced at the bottom, based on the velocity at the bottom. It is shown that the bottom stress can be equivalently expressed in terms of the vertically averaged velocity, and expressions for this bottom stress coefficient are derived in terms of the primary parameters of the problem. As a result, the three-dimensional structure may be assembled from conventional solutions to (a) the 1-D vertical diffusion equation; and (b) the 2-D vertically averaged shallow water equations. In the latter, the bottom stress effects are shown to be complex and frequency-dependent, and an additional rotational term is required for their representation.     

Investigation over the recirculation influence on the combustion of micro organic dust particles

This paper investigates the role of recircnlation and non-unity Lewis number on the combustion of organic dust particles. Since recirculation effect is more noticeable in micro-combustors, it is necessary to propose a modeling approach of this phenomenon to better simulate the performance of micro-combustors. In this research, in order to model the combustion of organic dust particles, it is assumed that the dust particles va- porize first to yield a known chemical structure which is oxidized in the gas phase, and the chemical structure of this gaseous fuel is assumed methane. To study the flame structure and solve the governing equations, it is considered that the flame structure consists of three zones titled the preheat-vaporization zone, the narrow reaction zone and finally the post flame zone. The recirculation phenomenon is evaluated by entering the exhausted heat from the post flame zone into the preheat zone. The solution is based on the follow- ing approach. First, the governing equations in each zone are nondimensionalized. Then the needed boundary and matching conditions are applied in each zone. After that, these equations and the required boundary and matching conditions are simultaneously solved with the analytical model. Consequently, the remarkable effects of recirculation and non- unity Lewis number on the combustion characteristics of the organic dust particles such as burning velocity and temperature profiles for different particle radii are obtained. The results show reasonable agreement with published experimental data.     

Stability analysis of the whirl motion of a breathing cracked rotor with asymmetric rotational damping

The stability of the whirl motion of a breathing cracked rotor with the distinction of stationary damping and the asymmetric rotational damping is studied. By Lagrange’s principal, the motion equations are formed in rotational frame such that the multi-asymmetric system, i.e., asymmetric rotational damping and asymmetric time-periodic varying stiffness, is simplified to be a system with anisotropic damping and anisotropic time-periodical varying stiffness in rotational operation. Based on the multiple scales solution of the simplified whirling equation in moving frame, root locus method for stability analysis is proposed. Different from the former stability estimation method, the corresponding Campbell diagram, decay rate plot, and root locus plot of the fifth-order approach are derived to prove the effects of both crack depth and damping effects. The numerical results of the instabilizing effects of the crack depth are well agreeing with the previous studies. In addition, the destabilizing influence of the rotational damping on the breathing cracked rotor is presented for the first time.     

Turbulent air flow over a moving curved surface

A numerical model of turbulent air flow over a curved surface is described. The model is based on two-dimensional nonlinear Reynolds equations and continuity equations written in a coordinate system moving with the profile of the curved surface. The Reynolds stresses are represented in the form of the product of the isotropic turbulent viscosity coefficient, which increases linearly with height, and the deformation tensor of the mean velocity field. Flow over a stationary sinusoidal surface and a sinusoidal gravity wave on water is simulated. The structure of the velocity and pressure wave fields is obtained. The differences in flow over stationary and moving surfaces are analyzed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–24, September–October, 1986.     

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger , two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.     

耦合火焰不稳定的爆炸超压预测

基于火焰不稳定和爆炸超压的耦合机制,通过向光滑火焰模型中引入褶皱因子,建立了褶皱火焰模型和湍流火焰模型,对密闭燃烧室内爆炸超压进行理论预测,且对比了绝热压缩和等温压缩对爆炸超压预测的影响规律。结果表明:在增强的流体动力学不稳定作用下,膨胀火焰失稳加剧,且在定容燃烧阶段形成胞状火焰;光滑火焰模型忽略了火焰不稳定,爆炸超压理论预测值比实验值偏低,且等温压缩下超压预测值低于绝热压缩下的预测值;湍流火焰模型高估了火焰褶皱程度,超压预测值远高于实验值;褶皱火焰模型可成功预测丙烷/空气爆炸压力和燃烧室体积V=25.6 m3的甲烷/空气爆炸压力;对于甲烷/空气爆炸,燃烧室体积V≤1.25 m3时,实验压力值介于褶皱火焰模型和绝热光滑火焰模型预测值之间。     

一维六方准晶中星形静态裂纹和运动裂纹的解析解

利用复变函数方法研究了一维六方准晶中星形静态裂纹和运动裂纹的反平面剪切问题,得到了星形裂纹尖端处应力强度因子和动应力强度因子的解析解.当裂纹条数给定时,由此可得到直线裂纹,Griffith裂纹,共点均匀分布三裂纹,对称十字形裂纹,米字型裂纹(对称八裂纹)静力学和动力学问题的解析解.当k=4时,用数值算例讨论了声子场-相位子场耦合系数和裂纹运动速度对动应力强度因子的影响.当速度趋于0时,运动裂纹的解可以退化为静态裂纹的解.     

生物芯片中周期性电渗驱动液体薄膜的流动特性

研究了二维周期性电渗驱动液体薄膜的流动特性. 以Debye-Hückel 假设近似下线性化的Poisson-Boltzmann方程描述双电层电动势分布和电荷密度的分布关系, 与黏性不可压缩流体Navier-Stokes方程相耦合, 得到流体在自由面与固壁之间的周期电渗流流场的精确解. 结果显示, 薄膜内速度振幅与流体黏性密切相关, 雷诺数越大, 速度振幅就越小. 该文还细致分析了雷诺数和自由面ζ电势对自由面的流速振幅和薄膜内速度相位差的影响.     

Three-dimensional oscillations of a cantilever pipe conveying fluid

The aim of the study described in this paper is to investigate the two-dimensional (2-D) and three-dimensional (3-D) flutter of cantilevered pipes conveying fluid. Specifically, by means of a complete set of non-linear equations of motion, two questions are addressed: (i) whether for a system losing stability by either 2-D or 3-D flutter the motion remains of the same type as the flow velocity is increased substantially beyond the Hopf bifurcation precipitating the flutter; (ii) whether the bifurcational behaviour of a horizontal system and a vertical one (sufficiently long for gravity to have an important effect on the dynamics) are substantially similar. Stability maps and tables are used to delineate areas in a flow velocity versus mass parameter plane where 2-D or 3-D motions occur, and limit-cycle motions are illustrated by phase-plane plots, PSDs and cross-sectional diagrams showing whether the motion is circular (3-D) or planar (2-D).     

Development of three-dimensional disturbances in a boundary layer

In the region of transition from a two-dimensional laminar boundary layer to a turbulent one, three-dimensional flow occurs [1–3]. It has been proposed that this flow is formed as the result of nonlinear interaction of two-dimensional and three-dimensional disturbances predicted by linear hydrodynamic stability theory. Using many simplifications, [4, 5] performed a calculation of this interaction for a free boundary layer and a boundary layer on a wall with a very coarse approximation of the velocity profile. The results showed some argreement with experiment. On the other hand, it is known that disturbances of the Tollmin—Schlichting wave type can be observed at sufficiently high amplitude. This present study will use the method of successive linearization to calculate the primary two- and three-dimensional disturbances, and also the average secondary flow occurring because of nonlinear interaction of the primary disturbances. The method of calculation used is close to that of [4, 5], the disturbance parameters being calculated on the basis of a Blazius velocity profile. A detailed comparison of results with experimental data [1] is made. It developed that at large disturbance amplitude the amplitude growth rate differs from that of linear theory, while the spatial distribution of disturbances agree s well with the distribution given by the natural functions and their nonlinear interaction. In calculating the secondary flow an experimental correction was made to the amplitude growth rate.     

Hydrodynamics and heat transfer characteristics of G–S magnetically stabilized beds consisting of admixtures of shale oil and magnetic particles

The hydrodynamic and heat transfer behavior of a bed consisting of magnetic and shale oil particle admixtures under the effect of a transverse magnetic field is investigated. The phase diagram, bed void fraction are studied under wide range of the operating conditions i.e., gas velocity, magnetic field intensity and fraction of the magnetic particles. It is found that the range of the stabilized regime is reduced as the magnetic fraction decreases. In addition, the bed voidage at the onset of fluidization decreases as the magnetic fraction decreases. On the other hand, Nusselt number and consequently the heat transfer coefficient is found to increase as the magnetic fraction decreases. An empirical equation is investigated to relate the effect of the gas velocity, magnetic field intensity and fraction of the magnetic particles on the heat transfer behavior in the bed.     

Three-dimensional free-surface suspended particles transport in the South Biscayne Bay,Florida

A three-dimensional, time-dependent free surface model has been developed which takes account of topographical and meterological parameters for application to suspended particles transport. This investigation of suspended particles transport is the most realistic in regard to treating the moving free-surface in computing the hydrodynamic field. A unique mass-conserving numerical model is used for solving the concentration equation by an explicit finite difference scheme. The paper presents a mathematical model which can be applied to surface water dispersion of particulates associated with dredging operations and land-fill. The effects of settling velocity and bottom bed deposition rate are compared and discussed.     

Regular reflection of a shock wave from a solid wall in a stream of fuel mixture

The two-dimensional stationary problem of regular reflection of a shock wave from a plane solid wall in a fuel gas mixture is examined in the case when the mixture is ignited at the intersection of the incident wave with the wall and a flame front is formed behind the reflected shock wave. The shock waves and the flame front are considered plane surfaces of discontinuity. The fuel mixture and the reaction products are considered perfect, inviscid, and non-heat-conducting gases.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 161–163, July–August, 1978.