圆环旋转黏性液体射流空间不稳定性研究

利用线性稳定性理论, 进行了液体黏性对不同旋转强度下圆环旋转液体射流 空间不稳定性影响的研究. 在推导出的三维扰动下具有固体涡核型旋转速度分布的圆环旋转 黏性液体射流色散方程的基础上, 针对中低速射流, 进行了类反对称模式与类对称模式下圆 环旋转黏性液体射流的空间不稳定性分析. 研究结果表明, 对于旋转强度较大的圆环旋转液 体射流, 液体黏性的增加, 不利于射流的破碎; 随着液体黏性的增加, 射流的特征频率和最 不稳定波数减小. 然而, 对于旋转强度较小的圆环旋转液体射流, 液体黏性的增加, 有利于 射流的破碎; 随着液体黏性的增加, 类反对称模式下射流特征频率先减小后增大, 类对称模 式下射流特征频率增大; 随着液体黏性的增加, 类反对称模式下射流最不稳定波数先减小后 增大, 类对称模式下射流最不稳定波数增大.     

圆环旋转黏性液体射流破碎液滴粒径与速度数量密度分布相关性研究

压力旋流喷嘴被广泛应用于航空发动机、船用发动机、车用汽油缸内直喷发动机、燃气轮机等动力机械的燃油喷射系统中.以压力旋流喷嘴射流为研究对象,开展了圆环旋转黏性液体射流破碎液滴粒径与速度数量密度分布相关性问题研究.对于液体射流,以往的研究往往对破碎液滴粒径数量密度分布或速度数量密度分布进行单独研究,对于这两种数量密度分布之间关系的研究较少;从相关性的角度对圆环旋转黏性液体射流破碎液滴粒径与速度数量密度分布之间的关系进行研究.采用最大熵原理方法建立了圆环旋转黏性液体射流破碎液滴粒径与速度联合概率密度函数.对圆环旋转黏性液体射流破碎液滴粒径与速度联合概率密度函数进行了讨论,对圆环旋转黏性液体射流破碎液滴粒径数量密度分布与速度数量密度分布的相关性问题进行了研究.研究结果表明,为了给出正确的圆环旋转黏性液体射流破碎液滴粒径与速度联合概率密度函数,射流守恒约束条件中必须同时包括质量守恒定律、动量守恒定律以及能量守恒定律;破碎液滴粒径的数量密度分布与速度数量密度分布密切相关;射流旋转强度对破碎液滴粒径数量密度与速度数量密度分布结构影响不大,对破碎液滴粒径数量密度和速度数量密度的分布区域影响较大.      

旋流喷嘴中空旋转射流近区域流动的研究

从理论上分析了旋流喷嘴喷出的中空射流近区域的液膜的运动,在只考虑液膜表面张力的作用下,应用质量守恒和动量定理,建立了描述液膜运动的非线性常微分（积分）方程组,该方程组可以用数值方法方便地求解,结果表明,液体离开旋流喷嘴后在自由空间形成的液膜呈葫芦形状,其速度和液膜厚度等都周期性地变化。本结果是在液厝受拓动失称碎成液滴前的最基本运动状态,可以在射流的近区域内实验观察到,也是进一步从理论液膜破碎雾化过     

横向交流电场下液膜参数不稳定性分析

当将运动的平面液膜置于横向的交流电场之间时会产生参数振荡现象.为了得到交流电场下平面液膜的色散关系并为液膜的破碎行为分析提供理论基础,本文基于漏电介质模型对液体的电学特性进行假设,对平面液膜在直流和交流电场下的参数不稳定性进行了分析.由于主流是基于时间的流动,在稳定性分析中引入了Floquet理论.在文中,将电场定义为...     

Spatial instability of a viscous liquid sheet

In the present study, the spatial instability for a two‐dimensional viscous liquid sheet, which is thinning with time, has been analysed. The study includes the derivation of a spatial dispersion equation, numerical solutions for the growth rate of sinuous disturbances, and parameter sensitivity studies. For a given wave number, the growth rate of the disturbance is essentially a function of Weber number, Reynolds number, and gas/liquid density ratio. The analysis indicates that the cut‐off wave number of the disturbance becomes larger with an increase in Weber number or gas/liquid density ratio. Thus, the liquid sheet should produce finer drops. When the Reynolds number decreases, the higher viscosity has a greater damping effect on shorter waves than longer waves. This could explain that only large drops and ligaments were observed in past measurements for the disintegration of a very viscous sheet. The spatial instability results of the present study were also compared with the temporal theory. The importance of spatial analysis was found and demonstrated for the cases of low Weber numbers. The temporal theory underestimates growth rates when the Weber number is less than 100. The discrepancy between the two theories increases as the Weber number further decreases. Copyright © 2005 John Wiley & Sons, Ltd.     

The stability of viscous liquid jets in a swirling gas

Based on the linear analysis of stability, a dispersion equation is deduced which delineates the evolution of a general 3-dimensional disturbance on the free surface of an incompressible viscous liquid jet injected into a gas with swirl. Here, the dimensionless parameterJ _e is again introduced, in the meantime, another dimensionless parameterE called as circulation is also introduced to represent the relative swirling intensity. With respect to the spatial growing disturbance mode, the numerical results obtained from solving the dispersion equation reveal the following facts. First, at the same value ofE, in pace with the changing ofJ _e , the variation of disturbance and the critical disturbance mode still keep the same characters. Second, the present results are the same as that of S.P. Lin whenJ _e >1; but in the range ofJ _e <1, it's no more the case, the swirl decreases the axisymmetric disturbance, yet increases the asymmetric disturbance, furthermore the swirl may make the character of the most unstable disturbance mode changed (axisymmetric or asymmetric); the above action of the swirl becomes much stronger whenJ _e ≪1. The project supported by the National Natural Science Foundation of China     

Response of a viscous annular liquid layer in zero-gravity to different axial excitations of the rigid boundary plates

A cylindrical annular liquid layer between two plates and around a rigid center-core consisting of incompressible and viscous liquid is subjected to different axial excitations, such as one-sided, counter-directional and double-sided unequal excitations. The response of the free liquid surface, the velocity- and pressure-distribution has been determined.

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Zusammenfassung Eine zylindrische Flüssigkeitsschicht bestehend aus inkompressibler und viskoser Flüssigkeit wurde verschiedenen harmonischen Anregungsformen ausgesetzt. Dabei wurden die Fälle einseitiger, doppelseitiger entgegengesetzter und ungleicher doppelseitiger Anregung mit Phase behandelt. Die Vergrößerungsfunktionen für die freie Flüssigkeitsoberfläche, für die Geschwindigkeits- und Druckverteilung wurden bestimmt.

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List of symbols a radius of liquid layer - b radius of inner cylindrical core - (a–b) thickness of layer - e _r , e , k unit vectors in the radial, angular and axial direction resp. - h length of layer - I _m , K _m modified Bessel functions of first and second kind and order m - diameter ratio - p pressure - q 2na/h - q* na/h - r, , z cylindrical coordinates - complex frequency - S sa ²/ - t time - u, w velocity components in the radial- and axial direction - ₀ excitation amplitude - abbreviation - surface tension parameter - surface tension - dynamic viscosity - kinematic viscosity - density of liquid - free liquid surface elevation - dimensionless time - _rz shear stress - reduced forcing frequency - forcing frequency - stream function - _mn natural frequency of non-viscous liquid     

Computation of a drastic flow pattern change in an annular swirling jet caused by a small decrease in inlet swirl

This paper investigates the flow pattern change in an annular jet caused by a sudden change in the level of inlet swirl. The jet geometry consists of an annular channel followed by a specially designed stepped‐conical nozzle, which allows the existence of four different flow patterns as a function of the inlet swirl number. This paper reports on the transition between two of them, called the ‘open jet flow high swirl’ and the ‘Coanda jet flow.’ It is shown that a small sudden decrease of 4% in inlet swirl results in a drastic and irreversible change in flow pattern. The objective of this paper is to reveal the underlying physical mechanisms in this transition by means of numerical simulations. The flow is simulated using the unsteady Reynolds‐averaged Navier–Stokes (URANS) approach for incompressible flow with a Reynolds stress turbulence model. The analysis of the numerical results is based on a study of different forces on a control volume, which consists of the jet boundaries. The analysis of these forces shows that the flow pattern change consists of three different regimes: an immediate response regime, a quasi‐static regime and a Coanda regime. The simulation reveals that the pressure–tangential velocity coupling during the quasi‐static regime and the Coanda effect at the nozzle outlet during the Coanda regime are the driving forces behind the flow pattern change. These physical mechanisms are validated with time‐resolved stereo‐PIV measurements, which confirm the numerical simulations. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear instability of an annular liquid sheet exposed to gas flow

Nonlinear instability and breakup of an annular liquid sheet has been modeled in this paper. The liquid sheet is considered to move axially and is exposed to co-flowing inner and outer gas streams. Also, the effect of outer gas swirl on sheet breakup has been studied. In the developed model a perturbation expansion method has been used with the initial magnitude of the disturbance as the perturbation parameter. This is a comprehensive model in that other geometries of planar sheet and a coaxial jet can be obtained as limiting cases of very large inner radius and inner radius equal to zero, respectively. In this temporal analysis, the effect of liquid Weber number, initial disturbance amplitude, inner gas-to-liquid velocity ratio, outer gas-to-liquid velocity ratio and outer gas swirl strength on the breakup time is investigated. The model is validated by comparison with earlier analytical studies for the limiting case of a planar sheet as well as with experimental data of sheet breakup length available in literature. It is shown that the linear theory cannot predict breakup of an annular sheet and the developed nonlinear model is necessary to accurately determine the breakup length. In the limiting case of a coaxial jet, results show that gas swirl destabilizes the jet, makes helical modes dominant compared to the axisymmetric mode and decreases jet breakup length. These results contradict earlier linear analyses and agree with experimental observations. For an annular sheet, it is found that gas flow hastens the sheet breakup process and shorter breakup lengths are obtained by increasing the inner and the outer gas velocity. Axially moving inner gas stream is more effective in disintegrating the annular sheet compared to axially moving outer gas stream. When both gas streams are moving axially, the liquid sheet breakup is quicker compared to that with any one gas stream. In the absence of outer gas swirl, the axisymmetric mode is the dominant instability mode. However, when outer gas flow has a swirl component higher helical modes become dominant. With increasing outer gas swirl strength, the maximum disturbance growth rate increases and the most unstable circumferential wave number increases resulting in a highly asymmetric sheet breakup with shorter breakup lengths and thinner ligaments.     

Absolute and convective instability of a liquid sheet with transverse temperature gradient

The spatial–temporal instability behavior of a viscous liquid sheet with temperature difference between the two surfaces was investigated theoretically. The practical situation motivating this investigation is liquid sheet heated by ambient gas, usually encountered in industrial heat transfer and liquid propellant rocket engines. The existing dispersion relation was used, to explore the spatial–temporal instability of viscous liquid sheets with a nonuniform temperature profile, by setting both the wave number and frequency complex. A parametric study was performed in both sinuous and varicose modes to test the influence of dimensionless numbers on the transition between absolute and convective instability of the flow. For a small value of liquid Weber number, or a great value of gas-to-liquid density ratio, the flow was found to be absolutely unstable. The absolute instability was enhanced by increasing the liquid viscosity. It was found that variation of the Marangoni number hardly influenced the absolute instability of the sinuous mode of oscillations; however it slightly affected the absolute instability in the varicose mode.     

Investigation of instability in vertical liquid films as an initial value problem

The instability of plane-parallel vertical viscous layer downflow is investigated. We solve not the classical eigenvalue problem for the Orr-Sommerfeld equation but a Cauchy problem with respect to time and a boundary-value problem with respect to the spatial variable for a linearized system of equations. The problem is solved by means of a Laplace transformation in time and a Fourier transformation in the spatial variable. Subsequently, using the residue theorem and the method of steepest descent makes it possible to predict asymptotically the perturbation behavior as time t → ∞. The system is convectively unstable and a localized perturbation spreads out at the velocities of the trailing and leading fronts. The packet behavior is investigated over a wide range of the flow parameters.     

Approximate solutions for the problem of liquid film flow over an unsteady stretching sheet with thermal radiation and magnetic field

The proposed method is based on replacement of the unknown function by a truncated series of the shifted Legendre polynomial expansion. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error for the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shifted Legendre coefficients. Thus, after solving this system of equations, the shifted Legendre coefficients are obtained. This efficient numerical method is used to solve the system of ordinary differential equations which describe the thin film flow and heat transfer with the effects of the thermal radiation, magnetic field, and slip velocity.