On streamwise vortical structures in the near-field of axisymmetric shear layers

Pairs of counter-rotating streamwise vortical structures have been observed using the LIF (Laser Induced Fluorescence) flow visualization technique by means of regular, video and high-speed photography in the near-field of an axisymmetric water jet. The temporal evolution of these structures at fixedx/d=1.0, 2.0, 4.0, and 6.0 in planes perpendicular to the flow direction for Reynolds numbersRe=cd/v=6000 has been the focus of attention in this investigation (d = nozzle diameter,c = mean exit velocity). These streamwise vortical structures also appear when the formation of Taylor-Görtler vortices in the nozzle is suppressed. So far basic questions pertaining to the generation and development of these secondary structures remain unanswered. Understanding of instability and interaction mechanisms can be gained by the analysis of these structures. These also contribute to entrainment and mixing due to their dynamics and large interfacial area.

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Sommario Coppie di strutture tubolari controrotanti sono state osservate usando la tecnica di visualizzazione del flusso LIF (Laser Induced Fluorescence), per mezzo di una telecamera ad alta e bassa velocità, nel campo vicino ad un getto d'acqua assialsimmetrico. Lo studio dell'evoluzione temporale di queste strutture, fissatox/d=1.0, 2.0, 4.0 e 6.0 in piani perpendicolari alla direzione del flusso ed in sezioni longitudinali perx/d=0÷6.0, per numeri di Reynolds Re=cd/v=6000, è stato il punto principale della presente indagine. Queste strutture vorticose appaiono persino quando la formazione dei vortici di Taylor-Görtler è soppressa attivamente e passivamente. Si osserva che rimangono senza risposta questioni basilari concernenti la generazione e lo sviluppo di queste strutture secondarie. Attraverso l'analisi di queste strutture è possibile far progressi nella conoscenza dell'instabilità e dei meccanismi d'interazione. Inoltre, tali strutture contribuiscono all'intrappolamento ed al mescolamento dovuti alla loro dinamica ed alla larga area interfacciale.

     

Boundary element calculation of shallow water waves

A boundary element method is proposed for studying periodic shallow water problems. The numerical model is based on the shallow water equation. The key feature of this method is that the boundary integral equations are derived using the weighted residual method and the fundamental solutions for shallow water wave problems are obtained by solving the simultaneous singular equations. The accuracy of this method is studied for the wave reflection problem in a rectangular tank. As a result of this test, it has been shown that the number of element divisions and the distribution of nodes are significant to the accuracy. For numerical examples of external problems, the wave diffraction problems due to single cylindrical, double cylindrical and plate obstructions are analysed and compared with the exact and other numerical solutions. Relatively accurate solutions are obtained.     

Study of axial acoustic radiation force on a sphere in a Gaussian quasi-standing field

Based on the finite series method, the Gaussian standing or quasi-standing beam is expressed in terms of spherical wave functions and a weighting parameter, which describe the beam shape and location relative to the particle. An expression is derived for the radiation force on a sphere centered on the axis of a Gaussian standing or quasi-standing wave propagating in an ideal fluid. Rigid, fluid, elastic, and viscoelastic spheres immersed in water are treated as examples. In addition, a method is proposed to compute the axial acoustic radiation force when the sphere is translated axially. Results indicate the capability of the proposed method to manipulate and separate spheres based on their mechanical and acoustical properties. The interaction of a Gaussian quasi-standing beam with a sphere can result in periodic axial force under specific operating conditions. The results presented here may provide a theoretical basis for the development of acoustical tweezers in a Gaussian standing beam, which would be useful in micro-fluidic lab-on-chip applications.     

Variety of acoustic streaming in 2D resonant channels

Acoustic streaming in 2D resonant channels with uniform or non-uniform cross-sections is studied within this work. An inertial force as well as a vibrating boundary are assumed for driving the acoustic field. The method of successive approximations is employed to derive linear equations for calculation of primary acoustic and time-averaged secondary fields including the radiation pressure and the mass transport velocity. The model equations have a standard form which allows their numerical integration using a universal solver; in this case, COMSOL Multiphysics was employed. As this software is based on the finite element method, it is simple and straightforward to perform the calculations with moderate computational costs even for complex geometries, which makes the proposed approach an operative tool for study of acoustic streaming. The numerical results are validated for the case of a rectangular channel by comparison with previously published analytical results; an excellent agreement is found. The numerical results show that the acoustic streaming can be quite complex even in rectangular channels and its structure depends on the manner of driving. Examples of acoustic streaming in wedged and elliptical channels are given to demonstrate a strong dependence of the acoustic streaming structure on the resonator shape.     

Homogenization of acoustic waves in strongly heterogeneous porous structures

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.     

面元法求解有限水深船舶兴波及水底压力变化

应用势流理论中的格林函数方法计算了船舶定常运动的水动力参数,将有限水深Kelvin移动兴波源格林函数分解成三部分:简单Rankine源集合、局部扰动项和波函数项。在亚临界和超临界航速时,采用不同的积分顺序来消除被积函数的奇异性。利用面元法在船体表面上分布Kelvin源,计算了有限水深下船体表面的源强、压力分布及表面兴波,比较了有限与无限水深结果的区别和联系,进一步求解了船舶航行时引起的水底压力变化,计算结果与实验测量结果吻合良好。     

Investigation of the accuracy of different methods of interferogram analysis for calculation of local free convection heat transfer coefficient on axisymmetric objects

An experimental study using a Mach–Zehnder interferometer has been carried out in order to investigate the accuracy of four different methods of interferogram analysis for obtaining free convection heat transfer coefficient on heated axisymmetric objects. Different methods of reference fringe interferogram analysis can be categorized as classical and transform methods. In transform methods, a mathematical transform method is applied to solve the governing integral equation while in the classical methods the integral equation is approximated by a finite summation. Classical methods are also divided into two groups according to the equations which are based upon. Experiments have been carried out on a vertical isothermal cylinder in air with three different surface temperatures. Four methods of interferogram analysis which are three classical and a transform method have been used to calculate the temperature distributions and the local free convection heat transfer coefficients at different cross sections. In order to investigate the accuracy of the methods, experimental values of the local heat transfer coefficient have been compared with the numerical solution and the mean relative error of each method has been obtained. Results show that the transform method is the most accurate one with the shortest solution time. It is also shown that assuming more complex functions for variation of index of refraction in the classical methods could lead to more accurate results.     

A new method for the calculation of steady periodic capillary-gravity waves on water of arbitrary uniform depth

This paper presents a method for the calculation of steady periodic capillary-gravity waves on water of arbitrary uniform depth. The method developed by Debiane and Kharif in 1997 for infinite depth is extended to finite depth. The water-wave problem is reduced to a system of nonlinear algebraic equations which is solved using Newton's method. For the resonant configurations, the method does not suffer from the Wilton's failures and is valid for all depths. In addition, it is shown that the method allows the computation of solitary waves and generalized solitary waves.     

Real-time numerical calculation for penetration depth of projectiles into concrete targets

Based on the acceleration data measured by penetration experiments with ogive-nose projectiles into semi-infinite concrete targets, a fuzzy method which can calculate the real-time penetration depth was developed. In the proposed method, the whole process of penetration was divided into three stages according to the instantaneous velocity, and each stage was described by different models. By judging the calculation error, threshold velocities between stages were automatically determined. Meanwhile, the striking velocity of the penetration process was calculated using the acceleration in whole trajectory. The calculated values by model are in reasonably good agreement with the measured data from experiments.     

Axial acoustic radiation force on a rigid cylinder near an impedance boundary for on-axis Gaussian beam

This work presents a theoretical model to calculate the acoustic radiation force on a rigid cylindrical particle immersed in an ideal fluid near a boundary for an on-axis Gaussian beam. An exact solution of the axial acoustic radiation force function is derived for a cylindrical particle by applying the translation addition theorem of cylindrical Bessel function. We analyzed the effects of the impedance boundary on acoustic radiation force of a rigid cylinder immersed in water near an impedance boundary with particular emphasis on the radius of the rigid cylinder and the distance from the cylinder center to impedance boundary. Simulation results reveal that the existence of particle trapping behavior depends on the choice of nondimensional frequency as well as the offset distance from the impedance boundary. The value of the radiation force function varies when the cylinder lies at the different position of the on-axis Gaussian beam. For the particle with different radius, the acoustic radiation force functions vary significantly with frequency. This study provides a theoretical basis for acoustic manipulation, which may benefit to the improvement and development of the acoustic control technology.     

Surface waves propagation in shallow water: A finite element model

A two-dimensional (in-plane) numerical model for surface waves propagation based on the non-linear dispersive wave approach described by Boussinesq-type equations, which provide an attractive theory for predicting the depth-averaged velocity field resulting from that wave-type propagation in shallow water, is presented. The numerical solution of the corresponding partial differential equations by finite-difference methods has been the subject of several scientific works. In the present work we propose a new approach to the problem: the spatial discretization of the system composed by the Boussinesq equations is made by a finite element method, making use of the weighted residual technique for the solution approach within each element. The model is validated by comparing numerical results with theoretical solutions and with results obtained experimentally.     

求解轴对称结构侧向冲击响应的一种快速算法

轴对称结构在侧向冲击载荷下的动力响应分析,一般采用解析、半解析法或者直接进行有限元数值模拟,这些方法均有一定的局限性.本文依据线性动力学问题的叠加原理,提出了一种基于有限元分析和线性叠加的快速算法.该方法首先采用多条母线对载荷进行离散,然后采用有限元计算结构在单个"载荷单元"作用下的动力响应,最后采用坐标旋转和线性叠加的方法计算得到结构在复杂分布载荷作用下的响应.算例表明,本文提出的算法是正确、有效的,并且具有快速、简便、灵活的特点.     

基于自然单元法的轴对称结构极限上限分析

自然单元法是一种以自然邻近插值为试函数的新兴无网格数值方法,其形函数的计算不涉及矩阵求逆,也不需要任何人为参数。为了充分发挥自然单元法的优势,本文基于极限分析上限定理建立了轴对称结构极限上限分析的整套求解算法。轴对称结构的位移场由自然邻近插值构造,并且采用罚函数法处理材料的不可压条件。为了消除目标函数非光滑所引起的数值困难,采用逐步识别刚性区和塑性区,并对两者用不同方法进行处理。数值算例结果表明,本文提出的轴对称结构极限上限分析方法是行之有效的。     

Frequency-domain analysis of non-linear wave effects on offshore platform responses

In this study, the effects of second-order non-linear random waves on the structural response of slender fixed offshore platforms are investigated based on frequency-domain Volterra-series approach and previously proposed correlation function/FFT-based cumulant spectral method. The cumulants of non-Gaussian water particle kinematics are derived and, Morison force is approximated in cubic functional transformations of Gaussian processes. Volterra series is applied to evaluate the power spectra of wave force and induced structural displacement. The more convenient and more efficient power spectral and tri-spectral analyses by cumulant spectral method are presented as well. The thereby estimated variance, skewness and kurtosis excess agree well with time-domain simulation results. It is found that non-linear wave effects result in stronger non-Gaussian behavior of wave force and structural response, especially in seas of finite water depth.     

The influence of normal flow boundary conditions on spurious modes in finite element solutions to the shallow water equations

Finite element solutions of the primitive equation (PE) form of the shallow water equations are notorious for the severe spurious 2Δx modes which appear. Wave equation (WE) solutions do not exhibit these numerical modes. In this paper we show that the severe spurious modes in PE solutions are strongly influenced by essential normal flow boundary conditions in the coupled continuity-momentum system of equations. This is demonstrated through numerical examples that avoid the use of essential normal flow boundary conditions either by specifying elevation values over the entire boundary or by implementing natural flow boundary conditions in the weak weighted residual form of the continuity equation. Results from a series of convergence tests show that PE solutions are of nearly the same quality as WE solutions when spurious modes are suppressed by alternative specification of the boundary conditions. Network intercomparisons indicate that varying nodal support does not excite spurious modes in a solution, although it does enhance the spurious modes introduced when an essential normal flow boundary condition is used. Dispersion analysis of discrete equations for interior and boundary nodes offers an explanation of the observed solution behaviour. For certain PE algorithms a mixed situation can arise where the boundary nodes exhibit a monotonic (noise-free) dispersion relationship and the interior nodes exhibit a folded (noisy) dispersion relationship. We have found that the mixed situation occurs when all boundary nodes are specified elevation nodes (which are enforced as essential conditions in the continuity equation) or when specified flow boundary nodes are treated as natural boundary conditions in the continuity equation. In either case the effect is to generate a solution that is essentially free of noise. Apparently, the monotonic dispersion behaviour at the boundaries suppresses the otherwise noisy behaviour caused by the folded dispersion relation on the interior.     

A comparison of boundary element and finite element methods for modeling axisymmetric polymeric drop deformation

A modified boundary element method (BEM) and the DEVSS‐G finite element method (FEM) are applied to model the deformation of a polymeric drop suspended in another fluid subjected to start‐up uniaxial extensional flow. The effects of viscoelasticity, via the Oldroyd‐B differential model, are considered for the drop phase using both FEM and BEM and for both the drop and matrix phases using FEM. Where possible, results are compared with the linear deformation theory. Consistent predictions are obtained among the BEM, FEM, and linear theory for purely Newtonian systems and between FEM and linear theory for fully viscoelastic systems. FEM and BEM predictions for viscoelastic drops in a Newtonian matrix agree very well at short times but differ at longer times, with worst agreement occurring as critical flow strength is approached. This suggests that the dominant computational advantages held by the BEM over the FEM for this and similar problems may diminish or even disappear when the issue of accuracy is appropriately considered. Fully viscoelastic problems, which are only feasible using the FEM formulation, shed new insight on the role of viscoelasticity of the matrix fluid in drop deformation. Copyright © 2001 John Wiley & Sons, Ltd.     

时域Rankine源法求解有限水深船舶在规则波中的水底压力变化

应用势流理论中的Rankine源面元法和时域步进法,求解了有限水深船舶在规则波中运动的水底压力变化。将速度势分解成基本势、局部势和记忆势,以叠模解作为基本势对自由表面条件和物面条件进行了线性化,通过在水底布置面元来满足水底条件。利用研制的水底压力-水面波浪测量系统,测量了不同入射波船模表面波形与水底压力的时历曲线,理论计算与实验结果符合较好,验证了自编程序的正确性。通过对比二者的等高线图发现,水底压力与表面波形的峰谷有较好的一致性,并且压力较波形更为平滑。