可压缩涡流场中空泡运动规律及声辐射特性研究

基于可压缩流体力学基本理论, 通过边界积分方程, 采用不同表面压力模型, 求解空泡在计及可压缩性的涡流场中的运动规律; 通过表面离散及坐标变换, 采用Kirchhoff动边界积分方程, 将空泡表面视为运动变形边界, 作为直接噪声源, 获得涡流场中空泡运动产生的时域声压分布; 分析了涡流场参数对空泡运动规律及声辐射特性的影响. 研究结果表明: 计及流场可压缩性, 空泡的脉动幅度会随时间减弱, 辐射声压幅值随之减小; 空泡在涡流场中会发生延展、 颈缩、 撕裂, 并在撕裂后子空泡中形成射流; 当流场中的压力减小时, 空泡运动过程中的最大半径与撕裂前的最大长度逐渐增加, 且当流场中压力较小时, 空泡撕裂时形成的子空泡增多; 空泡辐射声压的指向性较弱, 撕裂会使辐射声压产生突变, 形成极大峰值; 随着涡通量的增大或空泡数的减小, 空泡脉动周期及其诱导的辐射声压波动周期随之延长, 辐射声压峰值逐渐滞后并减小. 本文结果旨在为涡流场中空泡运动规律及声辐射特性的相关研究提供参考. 关键词： 可压缩 涡流场 空泡 声辐射     

Vortex stretching and reconnection in a compressible fluid

Vortex stretching in a compressible fluid is considered. Two-dimensional (2D) and axisymmetric cases are considered separately. The flows associated with the vortices are perpendicular to the plane of the uniform straining flows. Externally-imposed density build-up near the axis leads to enhanced compactness of the vortices — “dressed" vortices (in analogy to “dressed" charged particles in a dielectric system). The compressible vortex flow solutions in the 2D as well as axisymmetric cases identify a length scale relevant for the compressible case which leads to the Kadomtsev-Petviashvili spectrum for compressible turbulence. Vortex reconnection process in a compressible fluid is shown to be possible even in the inviscid case — compressibility leads to defreezing of vortex lines in the fluid.     

Multi-scale Godunov-type method for cell-centered discrete Lagrangian hydrodynamics

This work presents a multi-dimensional cell-centered unstructured finite volume scheme for the solution of multimaterial compressible fluid flows written in the Lagrangian formalism. This formulation is considered in the Arbitrary-Lagrangian–Eulerian (ALE) framework with the constraint that the mesh velocity and the fluid velocity coincide. The link between the vertex velocity and the fluid motion is obtained by a formulation of the momentum conservation on a class of multi-scale encased volumes around mesh vertices. The vertex velocity is derived with a nodal Riemann solver constructed in such a way that the mesh motion and the face fluxes are compatible. Finally, the resulting scheme conserves both momentum and total energy and, it satisfies a semi-discrete entropy inequality. The numerical results obtained for some classical 2D and 3D hydrodynamic test cases show the robustness and the accuracy of the proposed algorithm.     

On slow flows of a weakly stratified relativistic fluid in a static gravitational field

Simplified equations for slow flows of a weakly stratified (in entropy) fluid inside or near a massive astrophysical object have been derived from the variational formulation of ideal general relativistic hydrodynamics under the conditions that the gravitational field in the leading order is centrosymmetric and static and that the effect of a magnetic field is negligibly small. Internal waves and vortices in such systems are soft modes as compared to sound. This circumstance allows the formulation of a “soundproof” Hamiltonian model. This model is an analog of nonrelativistic hydrodynamic anelastic models, which are widely used in studies of internal waves and/or convection in spatially inhomogeneous compressible media in atmospheric physics, geophysics, and astrophysics.     

Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates

We discuss stabilization strategies for finite-difference approximations of the compressible Euler equations in generalized curvilinear coordinates that do not rely on explicit upwinding or filtering of the physical variables. Our approach rather relies on a skew-symmetric-like splitting of the convective derivatives, that guarantees preservation of kinetic energy in the semi-discrete, low-Mach-number limit. A locally conservative formulation allows efficient implementation and easy incorporation into existing compressible flow solvers. The validity of the approach is tested for benchmark flow cases, including the propagation of a cylindrical vortex, and the head-on collision of two vortex dipoles. The tests support high accuracy and superior stability over conventional central discretization of the convective derivatives. The potential use for DNS/LES of turbulent compressible flows in complex geometries is discussed.     

Viscoelastic effects on asymmetric two‐dimensional vortex patterns in a strongly coupled dusty plasma

Strongly coupled dusty plasma medium is often described as a viscoelastic fluid that retains its memory. In a flowing dusty plasma medium, vortices of different sizes appear when the flow does not remain laminar. The vortices also merge to transfer energy between different scales. In the present work, we study the effect of viscoelasticity and compressibility over a localized vortex structure and multiple rotational vortices in a strongly coupled viscoelastic dusty plasma medium. In case of single rotating vortex flow, a transverse wave is generated from the localized vortex source and the evolution time of generated waves is found to be reduced due to finite viscoelasticity and compressibility of the medium. It is found that the viscoelasticity suppresses the dispersion of vorticity. In the presence of multiple vortices, we find, the vortex mergers get highly affected in the presence of memory effect of the fluid, and thus the dynamics of the medium gets completely altered compared to a non‐viscoelastic fluid. For a compressible fluid, viscoelasticity dampens the energy in the sonic waves generated in the medium. Thus a highly viscoelastic and compressible fluid, in some cases, behaves similarly to an incompressible viscoelastic fluid. The wave‐front like rings propagate in elliptical orbits keeping the footprint of the earlier position of the point‐vortex. The rings collide with each other even within the patch vortex region forming regions of high vorticity at the point of intersection and pass through each other.     

A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics

A fourth-order numerical method for the zero-Mach-number limit of the equations for compressible flow is presented. The method is formed by discretizing a new auxiliary variable formulation of the conservation equations, which is a variable density analog to the impulse or gauge formulation of the incompressible Euler equations. An auxiliary variable projection method is applied to this formulation, and accuracy is achieved by combining a fourth-order finite-volume spatial discretization with a fourth-order temporal scheme based on spectral deferred corrections. Numerical results are included which demonstrate fourth-order spatial and temporal accuracy for non-trivial flows in simple geometries.     

Large eddy simulation of a shocked gas cylinder instability induced turbulence

The Navier-Stokes equations for compressible fluid are solved with the operator splitting technique and LES (large eddy simulation) with the Smagorinsky model. A computational code MVFT (multi-viscosity-fluid and turbulence) is developed to study hydrodynamic instability and the induced turbulent mixing for multi compressible fluid. In order to validate the code MVFT,the LANL's shock tube experiment of shocked SF6 gas cylinder is simulated with the initial state of SF6 gas cylinder described by dissipative ...     

Matrix formulation of hydrodynamics and extension of ptolemaic flows to three-dimensional motions

A new matrix formulation of Lagrange hydrodynamic equations is proposed. Exact solutions of those equations are obtained in matrix form. It is found that precession of vortex lines around some fixed axis in space is a general property of the flows described by those solutions. Two types of fluid motion are studied. Flows of the first type have straight vortex lines, and their particle trajectories are windings on toroidal surfaces. The other flows have plane particle trajectories, and their vortex lines are arbitrarily shaped plane curves. All these motions are shown to be three-dimensional generalizations of plane Ptolemaic flows [1,2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 6, pp. 783–796, June, 1996.The authors express their gratitude to the Russian Foundation for Fundamental Research for support of these investigations under Grant No. 96-01-00585 and to INTAS Foundation for support under Grant No. 93-1373.     

Creating and manipulating vortices in atomic wave functions with short electric field pulses

We demonstrate the creation of vortices in the electronic probability density of an atom subject to short electric field pulses, how these vortices evolve and can be manipulated by varying the applied pulses, and that they persist to macroscopic distances in the spectrum of ejected electrons. This opens the possibility to use practical femtosecond or shorter laser pulses to create and manipulate these vortex quasiparticles at the atomic scale and observe them in the laboratory. Within a hydrodynamic interpretation we also show, since the Schr?dinger equation is a particular instance of the Navier-Stokes equations, that for compressible fluids vortices can appear spontaneously and with a certain time delay, which is not expected to occur from the conventional point of view, illustrating applicability of the present study to vortex formation more broadly.     

Lagrangian analysis of the formation and mass transport of compressible vortex rings generated by a shock tube

In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation,a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangiancoherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver sectionat the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transportduring the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation numberfor the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by ellipticLCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSsencompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The otherparts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the ellipticLCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. Inaddition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.     

Simulating coupled dynamics of a rigid-flexible multibody system and compressible fluid

As a subsequent work of previous studies of authors, a new parallel computation approach is proposed to simulate the coupled dynamics of a rigid-flexible multibody system and compressible fluid. In this approach, the smoothed particle hydrodynamics (SPH) method is used to model the compressible fluid, the natural coordinate formulation (NCF) and absolute nodal coordinate formulation (ANCF) are used to model the rigid and flexible bodies, respectively. In order to model the compressible fluid properly and efficiently via SPH method, three measures are taken as follows. The first is to use the Riemann solver to cope with the fluid compressibility, the second is to define virtual particles of SPH to model the dynamic interaction between the fluid and the multibody system, and the third is to impose the boundary conditions of periodical inflow and outflow to reduce the number of SPH particles involved in the computation process. Afterwards, a parallel computation strategy is proposed based on the graphics processing unit (GPU) to detect the neighboring SPH particles and to solve the dynamic equations of SPH particles in order to improve the computation efficiency. Meanwhile, the generalized-alpha algorithm is used to solve the dynamic equations of the multibody system. Finally, four case studies are given to validate the proposed parallel computation approach.     

Use of recompressed impulse response to identify sources and paths of structure-borne noise in wide flange I-beams and pipes conveying fluid

A procedure is described for identifying sources and paths of structure-born noise in structures built up from wide flange I-beams, as well as piping systems conveying compressible and incompressible fluid. The use of impulse response or modified impulse response to estimate time-delays frequently is of little value because the wave propagation is dispersive. With reflections present, it is impossible to distinguish and identify the wide peaks. If one can establish the dispersion law, namely, the relation between frequency and wave number, one can “recompress” the impulse response in a certain sense, with respect to length of paths. The peaks are fairly narrow and one can identify noise paths. A discussion is given for various dispersion relations, together with theoretical justification and practical implementation. Some experimental results are given.     

Nonlinear finite amplitude vibrations of sharp-edged beams in viscous fluids

In this paper, we study flexural vibrations of a cantilever beam with thin rectangular cross section submerged in a quiescent viscous fluid and undergoing oscillations whose amplitude is comparable with its width. The structure is modeled using Euler–Bernoulli beam theory and the distributed hydrodynamic loading is described by a single complex-valued hydrodynamic function which accounts for added mass and fluid damping experienced by the structure. We perform a parametric 2D computational fluid dynamics analysis of an oscillating rigid lamina, representative of a generic beam cross section, to understand the dependence of the hydrodynamic function on the governing flow parameters. We find that increasing the frequency and amplitude of the vibration elicits vortex shedding and convection phenomena which are, in turn, responsible for nonlinear hydrodynamic damping. We establish a manageable nonlinear correction to the classical hydrodynamic function developed for small amplitude vibration and we derive a computationally efficient reduced order modal model for the beam nonlinear oscillations. Numerical and theoretical results are validated by comparison with ad hoc designed experiments on tapered beams and multimodal vibrations and with data available in the literature. Findings from this work are expected to find applications in the design of slender structures of interest in marine applications, such as biomimetic propulsion systems and energy harvesting devices.     

Generalized Basset-Boussinesq-Oseen equation for unsteady forces on a sphere in a compressible flow

Viscous compressible flow around a sphere is considered in the limit of zero Reynolds and Mach numbers. An exact expression for the force on the sphere undergoing arbitrary motion with compressibility effects is presented. Quasisteady, inviscid-unsteady, and viscous-unsteady force components are identified. Numerical results are in excellent agreement with the theory. The present formulation offers an explicit expression for the unsteady force in the time domain and can be considered as a generalization of the Basset-Boussinesq-Oseen equation to compressible flow.     

Stochastic hard-sphere dynamics for hydrodynamics of nonideal fluids

A novel stochastic fluid model is proposed with a nonideal structure factor consistent with compressibility, and adjustable transport coefficients. This stochastic hard-sphere dynamics (SHSD) algorithm is a modification of the direct simulation Monte Carlo algorithm and has several computational advantages over event-driven hard-sphere molecular dynamics. Surprisingly, SHSD results in an equation of state and a pair correlation function identical to that of a deterministic Hamiltonian system of penetrable spheres interacting with linear core pair potentials. The fluctuating hydrodynamic behavior of the SHSD fluid is verified for the Brownian motion of a nanoparticle suspended in a compressible solvent.     

Vortical dynamics in the wake of water strider locomotion

Abstract  

Previous studies reported that the hydrodynamic propulsion of the water strider also results from transferring momentum to the underlying fluid through hemispherical dipolar vortices shed by its driving legs. However, there are no accuracy experimental measurements of these vortical structures to prove the mechanics of vortical propulsion. Here, we reveal the vortical structures by reporting the simultaneous measurements of the water strider’s motion and the fluid velocity field with the high-speed PIV, and proposing a new method of calculating the vortex kinetic energy and vortex momentum. We found that the asymmetrical vortical structure in each dipolar vortex, generated by one driving stroke, propels the water strider forward, and the outer elliptic vortex is weaker than the inner circular vortex. The movement of the dipolar vortex is divided into two stages: (1) translating backward and (2) return curving. In this way, the water strider obtains the maximum velocity with minimal consumption of energy. The fluid vortical momentum, generated by the driving stroke, accounts for about 64–90% of the water strider’s momentum.     

A nonlinear PSE method for two-fluid shear flows with complex interfacial topology

A nonlinear stability method is developed for laminar two-fluid shear flows which undergo changes in the interface topology. The method is based on the nonlinear parabolized stability equations (PSE) and incorporates a scalar-based interface capturing (IC) scheme in order to track complex deformations of the fluid interface. In doing so, the formulation retains the flexibility and physical insight of instability-wave based methods, while providing hydrodynamic modeling capabilities similar to direct numerical calculations: the new formulation, referred to as the IC-PSE, can capture the nonlinear physical mechanisms responsible for generating large-scale, two-fluid structures, without incurring heavy computational costs. This approach is valid for spatially developing, laminar two-fluid shear flows which are convectively unstable, and can naturally account for the growth of finite amplitude interfacial waves, along with changes to the interfacial topology. We demonstrate the accuracy of the IC-PSE against direct Navier–Stokes calculations for two-fluid mixing layers with density and viscosity stratification. The comparisons show that the IC-PSE can predict the dynamics of the instability waves and capture the formation of Kelvin–Helmholtz vortex rolls and large scale liquid structures, at an order of magnitude less computational cost than direct calculations. The role of surface tension in the IC-PSE formulation is shown to be valid for flows in which Re/We ? 1, and the method accurately predicts the formation and non-linear evolution of flow structures in this limit. This is demonstrated for spatially developing mixing layers which lead to vortex roll-up and ligaments, prior to droplet formation. The pinch-off process itself is a high surface tension phenomenon and in not considered herein. The method also accurately captures the effect of interfacial waves on the mean flow, and the topology changes during the non-linear evolution of the two-fluid structures.