A novel pressure–velocity formulation and solution method for fluid–structure interaction problems

In the standard approach for simulating fluid–structure interaction problems the solution of the set of equations for solids provides the three displacement components while the solution of equations for fluids provides the three velocity components and pressure. In the present paper a novel reformulation of the elastodynamic equations for Hookean solids is proposed so that they contain the same unknowns as the Navier–Stokes equations, namely velocities and pressure. A separate equation for pressure correction is derived from the constitutive equation of the solid material. The system of equations for both media is discretised using the same method (finite volume on collocated grids) and the same iterative technique (SIMPLE algorithm) is employed for the pressure–velocity coupling. With this approach, the continuity of the velocity field at the interface is automatically satisfied. A special pressure correction procedure that enforces the compatibility of stresses at the interface is also developed. The new method is employed for the prediction of pressure wave propagation in an elastic tube. Computations were carried out with different meshes and time steps and compared with available analytic solutions as well as with numerical results obtained using the Flügge equations that describe the deformation of thin shells. For all cases examined the method showed very good performance.     

Particle pairing using genetic algorithms for PIV

This paper presents a new particle pairing algorithm using “Genetic Algorithms” for DPIV (Digital Particle Image Velocimetry), which are searching algorithms for obtaining an optimal solution based on the mechanism of evolution. The particle pairing between two tracer images with a constant time interval is needed to obtain a velocity vector field. Since the algorithm adopts a fitness function which totally evaluates the similarity between respective small particle patterns in the two tracer images over the field, it promises to give a more correct velocity vector distribution than the conventional PTV (Particle Tracking Velocimetry) which identifies each particle based on its local information. In addition, a particle pattern matching for the similarity is performed after correcting fluid rotation. It therefore is robust against a high particle density and an increase in the time interval. The algorithm is applied to the PIV standard images distributed through the Internet (http://www.vsj.or.jp/piv). It gives a correct velocity vector distribution as a result even if a pair of the successive images has a large time interval.     

Gradient-based PIV using neural networks

This paper proposes a new gradient-based PIV using an artificial neural network for acquiring the characteristics of a two-dimensional flow field. The neural network can effectively realize an accurate approximation of the vector field by introducing some knowledge on the characteristic property. The neural network is trained by using spatial and temporal image gradients so that the basic equation of the gradient-based method is satisfied. Since the neural network itself learns the stream function, the continuity equation of flow is consequently satisfied in the measured velocity vector field. The new gradient-based PIV can be applied to even partly lacking visualized images.     

Stereoscopic PIV measurements of flow in and around axial flow fan

To analyze the complex three-dimensional flow structure of an axial flow fan and determine the validity of its application, PIV is used to provide detailed space and time resolved experimental data for understanding and control of flow field. The high resolution stereoscopic PIV system was successfully employed in this study for the investigation of flow structure around the axial flow fan. Using the once-per-revolution signal from the rotor, image fields were captured at a fixed position of the blades and hence provides the ability to do phase-averaging. The three-dimensional instantaneous velocity fields, phase-averaged velocity fields, instantaneous and mean vorticity distributions of the stereoscopic PIV measurement results were represented at typical planes of the flow field. Phaseaveraged velocity fields were calculated based on 200 frames of the instantaneous stereoscopic PIV measurement results. From the velocity distribution, the vorticity and turbulent intensity distribution, which are known to be major factors of fan noise, were calculated and its diffusion was discussed as they travel downstream. From the reconstructed three-dimensional velocity iso-surface at 8 cross planes of the outlet flow fields, the three-dimensional features can be seen clearly.     

A new super-resolution PIV accelerated by characteristic pixel selection

A new high-speed super-resolution PIV was proposed using characteristic pixel selection to accelerate the successive abandonment (SA) with recursive window subdivision. The performance and applicability of the proposed PIV were evaluated. In the SA calculation with the characteristic pixel selection, 1000 candidates are narrowed down to only one at over 50 % of the measurement points, and the number of error vectors is reduced because the difference between the cumulative intensities of a correct candidate and of other ones becomes clear due to the characteristics of selected pixels. In all recursive processes, error checks are carefully performed using the summation of the distribution of the cumulative intensity difference distribution, which is suitable for the SA method. In a comparison of the time per velocity vector, the present super-resolution PIV was shown to be 10 times faster than the former ordinary resolution PIV. Another feature of the present super-resolution PIV is that the velocity vectors are obtained in the region very close to the image boundaries and masked regions by using the recursive algorithm.     

Calculating pressure fields on the basis of PIV-measurements for supersonic flows

The velocity fields obtained by PIV (Particle Image Velocimetry) in supersonic flows are not sufficient to determine the integral characteristics of the flow. Additional data, for example, on pressure can be obtained from the solution of the Navier?Stokes equations. For incompressible flows, the solution of these equations is not too complicated. However, for supersonic flows, the need to take into account the flow density and the increasing number of experimental errors make it more difficult. This paper proposes a new method for calculating density and pressure from PIV data on the basis of the continuity equation. This method is robust and easy to implement for compressible flows.     

A coupled pressure-based computational method for incompressible/compressible flows

Pressure-based flow solvers couple continuity and linearized truncated momentum equations to derive a Poisson type pressure correction equation and use the well known SIMPLE algorithm. Momentum equations and the pressure correction equation are typically solved sequentially. In many cases this method results in slow and often difficult convergence. The current paper proposes a novel computational algorithm, solving for pressure and velocity simultaneously within a pressure-correction coupled solution approach using finite volume method on structured and unstructured meshes. The method can be applied to both incompressible and subsonic compressible flows. For subsonic compressible flows, the energy equation is also coupled with flow field and the density of fluid is obtained by equation of state. The procedure eliminates the pressure correction step, the most expensive component of the SIMPLE-like algorithms. The proposed coupled continuity-momentum-energy equation method can be used to simulate steady state or transient flow problems. The method has been tested on several CFD benchmark cases with excellent results showing dramatically improved numerical convergence and significant reduction in computational time.     

Interaction of two parallel plane jets of different velocities

The interaction of two parallel plane jets of different velocities is studied by flow visualization and PIV measurement to examine the influence of velocity ratio on the development ofjets in the initial region. It is found that the parallel plane jets develop toward the high velocity side and the jet width is reduced with a decrease in the jet velocity ratio. Corresponding to the variation of mean velocity field to the velocity ratio, the magnitudes of turbulence intensities, Reynolds stress and static pressure are weakened in the merging region of the jets and their peak locations of the properties are shifted to the high velocity side. These results indicate that the interaction of two parallel jets is weakened with a decrease in the velocity ratio of the jets.     

旗面周期摆动的实验研究

用实验方法研究了旗面周期摆动的运动过程,采用改进的算法优化了粒子图像测速仪测量结果,定量得了水洞中摆动旗面的近壁流场信息.通过选定旗面包络上的一个拐点,将其振幅作为特征长度重新计算旗面运动的Strouhal数.多组实验结果中,新的Strouhal数均为0.21左右,这与相同Reynolds数下圆柱绕的Strouhal数结果相近.     

A class of Cartesian grid embedded boundary algorithms for incompressible flow with time-varying complex geometries

We present a class of numerical algorithms for simulating viscous fluid problems of incompressible flow interacting with moving rigid structures. The proposed Cartesian grid embedded boundary algorithms employ a slightly different idea from the traditional direct-forcing immersed boundary methods: the proposed algorithms calculate and apply the force density in the extended solid domain to uphold the solid velocity and hence the boundary condition at the rigid-body surface. The principle of the embedded boundary algorithm allows us to solve the fluid equations on a Cartesian grid with a set of external forces spread onto the grid points occupied by the rigid structure. The proposed algorithms use the MAC (marker and cell) algorithm to solve the incompressible Navier-Stokes equations. Unlike projection methods, the MAC scheme incorporates the gradient of the force density in solving the pressure Poisson equation, so that the dipole force, due to the jump of pressure across the solid-fluid interface, is directly balanced by the gradient of the force density. We validate the proposed algorithms via the classical benchmark problem of flow past a cylinder. Our numerical experiments show that numerical solutions of the velocity field obtained by using the proposed algorithms are smooth across the solid-fluid interface. Finally, we consider the problem of a cylinder moving between two parallel plane walls. Numerical solutions of this problem obtained by using the proposed algorithms are compared with the classical asymptotic solutions. We show that the two solutions are in good agreement.     

Flow field analysis by large-area interrogation in particle image velocimetry

The evaluation of flow records obtained by particle image velocimetry (PIV) employs the interrogation of certain regions in the flow image. Basic relations are derived for the case that the velocity is not constant within the region of interrogation. The influence of a distribution of velocities on the Young's fringe system and its Fourier transform, the autocorrelation of the flow record, are discussed. The considerations show that there is an easy access to statistical parameters of the flow by carrying out large-field interrogation. The autocorrelation function will reproduce the probability density function of the velocity, and there is no need for a large number of time-consuming small-area interrogations. Furthermore, the effects of velocity variations in ordinary fringe analysis are discussed. Examples are given from synthetic PIV records and measurements in a wind tunnel.     

Application of PIV to over-expanded supersonic flows: Possibilities and limits

Two-dimensional velocity distributions outside a Mach 2.0 supersonic nozzle have been investigated using a digital particle im age velocimetry (PIV). Mean velocities , vor ticity field and volume dilatation field were obtained from PIV images using 0 .33 μm titanium dioxide (TiO₂) particle. The seeding particle of larger size , 1.4 μrn Ti0₂, was also used for the experimental comparison of velocity lag downstream of shock waves. The results have been compared and analyzed with schlieren photographs for the locations of shock waves and over-expanded shock structure to inspect possibilities and limits of a PIV technique to over-expanded supersonic flows. It is found that although the quantitative velocity measurement using PIV on over-expanded supersonic flows with large velocity and pressure gradients is limited, the locations of normal shock and oblique shock waves can be resolved by the axial/radial velocity fields, and over-expanded shock structure can be predicted by vorticity field and volume dilatation field which are acquired from the spatial differential of the velocity field.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.     

Three-dimensional bubbly flow measurement using PIV

The experimental flow visualization tool, Particle Image Velocimetry (PIV), is being extended to determine the velocity fields in three-dimensional, two-phase fluid flows. In the past few years, the technique has attracted quite a lot of interest. PIV enables fluid velocities across a region of a flow to be measured at a single instant in time in the whole volume (global) of interest. This instantaneous velocity profile of a given flow field is determined by digitally recording particle (microspheres or bubbles) images within the flow over multiple successive video frames and then conducting flow pattern identification and analysis of the data. This paper presents instantaneous velocity measurements in various three-dimensional, bubbly two-phase flow situations. This information is useful for developing or improving existing computer constitutive models that simulate this type of flow field. It is also useful for understanding the detailed structure of two-phase flows.     

Applications of controlled-flow laser-polarized xenon gas to porous and granular media study

We report initial NMR studies of continuous flow laser-polarized xenon gas, both in unrestricted tubing, and in a model porous media. The study uses Pulsed Gradient Spin Echo-based techniques in the gas-phase, with the aim of obtaining more sophisticated information than just translational self-diffusion coefficients. Pulsed Gradient Echo studies of continuous flow laser-polarized xenon gas in unrestricted tubing indicate clear diffraction minima resulting from a wide distribution of velocities in the flow field. The maximum velocity experienced in the flow can be calculated from this minimum, and is seen to agree with the information from the complete velocity spectrum, or motion propagator, as well as previously published images. The susceptibility of gas flows to parameters such as gas mixture content, and hence viscosity, are observed in experiments aimed at identifying clear structural features from echo attenuation plots of gas flow in porous media. Gas-phase NMR scattering, or position correlation flow-diffraction, previously clearly seen in the echo attenuation data from laser-polarized xenon flowing through a 2 mm glass bead pack is not so clear in experiments using a different gas mixture. A propagator analysis shows most gas in the sample remains close to static, while a small portion moves through a presumably near-unimpeded path at high velocities.     

粒子图象测速技术在内燃机缸内流场研究中的应用

本文应用粒子图象测速技术（PIV）对内燃机压缩过程中的缸内流场进行了实验研究。开发的实验装置可真实模拟内燃机的进气、压缩和膨胀行程，并且适于开设大窗口以测取大区域的全场速度分布。开发建立的PIV拍摄及数据处理系统实现了对瞬态全场流动参数的较精确的测量处理，可直观地给出流场中的涡流特征。文中有部分结果实例。     

Ultrasonic tomographic reconstruction of liquid flows using phase-conjugate waves

The possibility of using phase conjugation in ultrasonic tomography to reconstruct the distribution of liquid flow velocities is discussed. The results of experiments aimed at reconstructing the distribution of flow velocities in the vortex cross section by the back projection method are shown. A mathematical model of acoustic wave propagation in a medium with a stationary liquid flow and an algorithm for reconstructing the velocity distribution using a 64-element acoustic antenna have been developed. The results of numerical experiment are discussed.     

Enhancement of measurement accuracy of X‐ray PIV in comparison with the micro‐PIV technique

The X‐ray PIV (particle image velocimetry) technique has been used as a non‐invasive measurement modality to investigate the haemodynamic features of blood flow. However, the extraction of two‐dimensional velocity field data from the three‐dimensional volumetric information contained in X‐ray images is technically unclear. In this study, a new two‐dimensional velocity field extraction technique is proposed to overcome technological limitations. To resolve the problem of finding a correction coefficient, the velocity field information obtained by X‐ray PIV and micro‐PIV techniques for disturbed flow in a concentric stenosis with 50% severity was quantitatively compared. Micro‐PIV experiments were conducted for single‐plane and summation images, which provide similar positional information of particles as X‐ray images. The correction coefficient was obtained by establishing the relationship between velocity data obtained from summation images (V_S) and centre‐plane images (V_C). The velocity differences between V_S and V_C along the vertical and horizontal directions were quantitatively analysed as a function of the geometric angle of the test model for applying the present two‐dimensional velocity field extraction technique to a conduit of arbitrary geometry. Finally, the two‐dimensional velocity field information at arbitrary positions could be successfully extracted from X‐ray images by using the correction coefficient and several velocity parameters derived from V_S.     

A PIV study of a supersonic impinging jet

The characteristics of supersonic impinging jets are investigated using Particle Image Velocimetry (PIV). The purpose of the experiments is to understand the jet induced forces on STOVL aircraft while hovering close to the ground. For this purpose, a large diameter circular plate was attached at the nozzle exit. The oscillations of the impinging jet generated due to a feedback loop are captured in the PIV images. The instantaneous velocity field measurements are used to describe flow characteristics of the impinging jet. The important flow features such as oscillating shock waves, slipstream shear layers and large scale structures are captured clearly by the PIV. The presence of large scale structures in the impinging jet induced high entrainment velocity in the near hydrodynamic field, which resulted in lift plate suction pressures. A passive control device is used to interfere with the acoustic waves travelling in the ambient medium to suppress the feedback loop. As a consequence, the large scale vortical structures disappeared completely leading to a corresponding reduction in the entrainment.     

Adaptive multiscale finite-volume method for nonlinear multiphase transport in heterogeneous formations

In the previous multiscale finite-volume (MSFV) method, an efficient and accurate multiscale approach was proposed to solve the elliptic flow equation. The reconstructed fine-scale velocity field was then used to solve the nonlinear hyperbolic transport equation for the fine-scale saturations using an overlapping Schwarz scheme. A coarse-scale system for the transport equations was not derived because of the hyperbolic character of the governing equations and intricate nonlinear interactions between the saturation field and the underlying heterogeneous permeability distribution. In this paper, we describe a sequential implicit multiscale finite-volume framework for coupled flow and transport with general prolongation and restriction operations for both pressure and saturation, in which three adaptive prolongation operators for the saturation are used. In regions with rapid pressure and saturation changes, the original approach, with full reconstruction of the velocity field and overlapping Schwarz, is used to compute the saturations. In regions where the temporal changes in velocity or saturation can be represented by asymptotic linear approximations, two additional approximate prolongation operators are proposed. The efficiency and accuracy are evaluated for two-phase incompressible flow in two- and three-dimensional domains. The new adaptive algorithm is tested using various models with homogeneous and heterogeneous permeabilities. It is demonstrated that the multiscale results with the adaptive transport calculation are in excellent agreement with the fine-scale solutions. Furthermore, the adaptive multiscale scheme of flow and transport is much more computationally efficient compared with the previous MSFV method and conventional fine-scale reservoir simulation methods.