Vortex shedding induced by a solitary wave propagating over a submerged vertical plate

Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet.     

Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure

The shedding and evolution of the vortical structures generated by a solitary wave propagating over a submerged cylindrical structure are investigated experimentally and numerically. The cylindrical structure consists of two concentric cylinders and represents a simplified model for an offshore submerged intake structure typically used in coastal power plants. Flow visualization by dye injection is used to identify the dominant vortical structures near the structure. The flow visualization results show an unexpected flow reversal that causes shedding of secondary vortical structures. The experimental results are used to check a three-dimensional volume of fluid-large eddy simulation (VOF-LES) numerical model. The VOF-LES model is then used to further study the flow structure. A total of six dominant vortical structures generated by the wave motion are identified, followed by two more generated by the flow reversal. In summary, this paper provides the vorticity evolution for a complex fluid–structure interaction problem and a three-dimensional numerical simulation tool has also been validated, which can be extended to study more complex geometries and wave conditions.     

Motion of a solitary wave over a submerged ridge

The two- and three-dimensional motion of a stationary wave in a layer of liquid with a variable depth was studied earlier by Grimshaw [1, 2], who showed that if the unperturbed state of the liquid were a state of rest, then a certain integrated quantity characterizing the energy of the wave (referred to one element on the leading edge of the wave) was conserved during the motion. In the present investigation (which is based on this property) we shall establish the shape of the wave front for the case of steady motion over an infinite submerged cylindrical ridge; we shall present a model describing a wave of limiting amplitude and shall consider the transient perturbation of the steady-state solution. We should note that one particular case (the motion of a straight front, orthogonal to the axis of the ridge, in a direction parallel to this axis) was considered by another method in [3].     

Experimental study on wake flow structures of screen cylinders using PIV

Experiments were conducted in a water flume using Particle Image Velocimetry (PIV) to study the evolution of the vortical structures in the wakes of four types of screen cylinders at a Reynolds number of about 3200. The results were compared with that of a bare cylinder. The screen cylinders were made of stainless steel screen meshes of various porosities (37%, 48%, 61% and 67%) rolled into cylindrical shapes. Smoke wire flow visualisations in a wind tunnel were also conducted in support of the PIV tests. Depending on the porosity of the screen mesh, two vortex formation mechanisms for the screen cylinder wakes were identified. One was associated with wake instability and the other was associated with shear-layer (Kelvin-Helmholtz) convective instability which involved merging through pairing and tripling of small-scale vortices within the shear layers. The former was responsible for the formation of large-scale vortices in the bare cylinder and the screen cylinder wakes with 37% and 48% porosities, while the latter was responsible for the screen cylinder wakes with 61% and 67% porosities. The results also showed that with increasing porosity, the vortex formation region was extended farther downstream and the Reynolds shear stress, the Turbulent Kinetic Energy (TKE) and vortex intensity were decreased constantly.     

PIV measurement of separated flow over a blunt plate with different chord-to-thickness ratios

The influence of the chord-to-thickness ratio (c/t) on the spatial characteristics of the separated shear layer over a blunt plate and the leading-edge vortices embedded in the separated shear layer was studied extensively using planar particle image velocimetry (PIV). Three systems corresponding to different shedding modes were chosen for the comparative study: c/t=3, 6 and 9. The Reynolds number based on the plate's thickness (t) was Re_t=1×10³. A gigapixel CCD camera was used to acquire images with a spatial resolution of 0.06t×0.06t in the measurement range of 9.5t×4.5t. Distributions of statistical quantities, such as the streamline pattern, streamwise velocity fluctuation intensity, shear stress and reverse flow intermittency, showed that the separated shear layer in the system with c/t=3 did not reattach to the plate's surface, while the near‐wake behind the trailing edge was highly unstable because the energetic leading-edge vortices were shed into the wake. The separated shear layer of the system with c/t=6 periodically reattached to the plate's surface, which resulted in intensified fluctuations of the near wake behind the trailing edge. In the longest system (c/t=9), the separated shear layer always reattached to the plate's surface far upstream from the trailing edge, which did not induce large fluctuations of the near wake. Furthermore, the proper orthogonal decomposition (POD) was extensively employed to filter the original velocity fields spatially to identify the large-scale vortices immersed in the separated shear layer easily. The distribution of the v-v correlation coefficients of the spatially filtered flow fields reflected the organized large-scale vortices in the three systems. The number of alternations of the positive and negative correlation coefficients across the flow field were determined to be 1, 2 and 3 for the systems with c/t=3, 6 and 9, respectively; this is in agreement with the shedding mode of each system. The distribution of the swirling strength of the separated shear layer accurately determined the positions and structures of the large-scale vortices formed above the plate surface.     

Experimental investigation of global structures in an incompressible cavity flow using time-resolved PIV

Open-cavity flows are known to exhibit a few well-defined peaks in the power spectral distribution of velocity or pressure signals recorded close to the impinging corner. The measured frequencies are in fact common to the entire flow, indicating some global organisation of the flow. The modal structures, i.e. the spatial distribution of the most characteristic frequencies in the flow, are experimentally investigated using time-resolved particle image velocimetry. Each spatial point, of the resulting two-dimension-two-component (2D–2C) velocity fields, provides time-resolved series of the velocity components V _x and V _y , in a (x, y) streamwise plane orthogonal to cavity bottom. Each local time-series is Fourier-transformed, such as to provide the spectral distribution at any point of the PIV-plane. One finally obtains the spatial structure associated with any frequency of the Fourier spectrum. Some of the modal spatial structures are expected to represent the nonlinear saturation of the global modes, against which the stationary solution of the Navier–Stokes equations may have become linearly unstable. Following Rowley et al. (J Fluid Mech 641:115–127, 2009), our experimental modal structures may even correspond to the Koopman modes of this incompressible cavity flow.     

Hypersonic flow over a narrow delta plate at large angles of attack

The problem of hypersonic flow over a flat delta plate with a high sweepback anglex at angles of attack close to /2 is solved using a numerical algorithm based on transition to the conical solution. The existence of conical flow at /2 with the velocity vector directed towards the apex of the plate is established. Values ofC _p/sin² and the thickness of the shock layer in the plane of symmetry of the plate are given as functions of the hypersonic similarity parameterk=tan tanx. A comparison of the calculated and experimental data shows that they are in good agreement.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.5, pp. 183–185, September–October, 1992.     

PIV analysis of in-cylinder flow structures over a range of realistic engine speeds

In-cylinder PIV measurements have been performed in a four-valve single cylinder optical gasoline direct injection engine, motored at speeds of 750, 2,000 and 3,500 rpm. Mean vector flow fields have been produced during the latter half of the intake stroke in the symmetry plane between the valve pairs. The flow fields show the development of the in-cylinder flow structures at 1.6, 2.4 and 3.2° crank angle steps for a time period of approximately 5 ms at each of the three engine speeds, respectively. Tumble ratios have been calculated for the available field of view showing a change in the flow structure between 2,000 and 3,500 rpm. This is believed to be caused by an increase in the flow of air traveling underneath the recirculation vortex at the higher engine speed. This translates the vortex position upwards and further to the right when compared to the lower engine speeds.     

Numerical simulation of a solitary wave interaction with submerged multi-bodies

The problems of a solitary wave passing over rectangular cylinders have been analysed. The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method. The free surface is dealt with by the Volume of Fluid method (VOF). Results for a solitary wave passing over a single cylinder are compared with the experimental data of Seabra-Santos, Penouard and Temperville^[2] and better agreement is obtained than those obtained from the long wave equation based on the potential flow theory. Results are also given for two cylinders with different gaps. The project supported by the National Natural Science Foundation of China and the Development Foundation of Science and Technology of Shanghai Education Committee and the Royal Society.     

Diffraction of a solitary wave by a thin wedge

The diffraction of a solitary wave by a thin wedge with vertical walls is studied when the incident solitary wave is directed along the wedge axis. The method of multiple scales is extended to this problem and reduces the task to that of solving the two-dimensional KdV equation with proper boundary and initial conditions. The finite-difference numerical procedure is carried out with the fractional step algorithm in which difference schemes are all implicit. Except the maximum run-up at the wall, the results in this paper are found to corroborate the Melville's experiments not only qualitatively but also quantitatively. The maximum run-up of our results agrees well with Funakoshi's numerical one but it is considerably larger than that in Melville's experiment. An important reason for this discrepancy is believed to be the effect of viscous boundary layer on the vertical side wall.     

Application of local grid refinement to vortex motion due to a solitary wave passing over a submerged body

A numerical method based on the streamfunction–vorticity formulation is applied to simulate the two‐dimensional, transient, viscous flow with a free surface. This method successfully uses the locally refined grid in an inviscid–viscous model to explore the processes of vortex formation due to a solitary wave passing over a submerged bluff body. The two particular bodies considered here are a blunt rectangular block and a semicircular cylinder. Flow visualization to track dyelines is carried out in the laboratory in order to confirm the validity of the numerical results. Numerical results examined by different grid configurations ensure the locally refined grid to be useful in practical application. Flow phenomena, including the vortex motion and wave patterns during non‐linear wave–structure interaction, are also discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Bragg scattering of waves propagating over a series of poro-elastic submerged breakwaters

This paper presents a mathematical study for the Bragg scattering of water waves propagating over a series of rectangular poro-elastic submerged breakwaters. Based on the linear wave theory and the improved Biot's theory of poro-elastic media with suitable matching conditions, an analytical solution was obtained as a function of elasticity, permeability and geometry of the submerged breakwaters. Experiments were also conducted in a wave flume to verify the present analytical study. In addition, the Bragg resonances for different influence parameters were studied. Satisfactory agreement between the theoretical predictions and the laboratory observations demonstrates the applicability of the present analytical result.     

An orthogonal-plane PIV technique for the investigations of three-dimensional vortical structures in a turbulent boundary layer flow

An experimental investigation was carried out regarding a three-dimensional topology of a zero-pressure gradient turbulent boundary layer. In this study, the polarization separation technique has been applied to the PIV measurements. Two mutually perpendicular measurement planes have been employed in x–y and x–z planes, respectively. Synchronization between a stereoscopic PIV with another plane PIV system was made toward the detection of such salient features of the coherent structure as the legs and the head of the hairpin vortices. Polarization rotation via a half-waveplate and subsequent particle image separation using polarizer minimized the spurious particle images. The PIV results clearly demonstrate the presence of hairpin-like coherent vortical structures and coincidence between the near-wall quasi-streamwise vortex pair and the legs of the hairpin vortex.     

Scattering of water waves by a submerged thin vertical elastic plate

The problem of water wave scattering by a thin vertical elastic plate submerged in infinitely deep water is investigated here assuming linear theory. The boundary condition on the elastic plate is derived from the Bernoulli–Euler equation of motion satisfied by the plate. This is converted into the condition that the normal velocity of the plate is prescribed in terms of an integral involving the difference in velocity potentials (unknown) across the plate multiplied by an appropriate Green’s function. The reflection and transmission coefficients are obtained in terms of integrals involving combinations of the unknown velocity potential on the two sides of the plate and its normal derivative on the plate, which satisfy three simultaneous integral equations, solved numerically. These coefficients are computed numerically for various values of different parameters and are depicted graphically against the wave number for different situations. The energy identity relating these coefficients is also derived analytically by employing Green’s integral theorem. Results for a rigid plate are recovered when the parameters characterizing the elastic plate are chosen negligibly small.     

Numerical study of an oscillatory turbulent flow over a flat plate

Oscillatory turbulent flow over a flat plate is studied using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model is employed in LES and Saffman's turbulence model is used in RANS. The flow behaviors are discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime are also investigated for different Reynolds numbers. The project supported by the Youngster Funding of Academia Sinica and by the National Natural Science Foundation of China     

Visualization of flow structures in a turbulent boundary layer using a new technique

In this paper, an experimental investigation on the flow structures in a turbulent boundary layer employing a special laser light sheet-Hydrogen bubble flow visualization technique is described. It is observed that the high/low speed streaks are directly related to the hairpin or horseshoe-like vortices. This observation can give a better understanding of the physical mechanism in the turbulent boundary layer. Fluid Mechanic Institute, BUAA     

Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in the logarithmic region of the turbulent boundary layer in a water tunnel.The Reynolds number based on momentum thickness is Reθ = 2 460.The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low speed fluid,which is flanked on either side by highspeed ones.Statistical support for the existence of hairpins is given by conditional averaged eddy within an increasing spanwise width as the distance from the wall increases,and the main vortex characteristic in different wall-normal regions can be reflected by comparing the proportion of ejection and its contribution to Reynolds stress with that of sweep event.The pre-multiplied power spectra and two-point correlations indicate the presence of large-scale motions in the boundary layer,which are consistent with what have been termed very large scale motions(VLSMs).The three dimen-sional spatial correlations of three components of velocity further indicate that the elongated low-speed and highspeed regions will be accompanied by a counter-rotating roll modes,as the statistical imprint of hairpin packet structures,all of which together make up the characteristic of coherent structures in the logarithmic region of the turbulent boundary layer(TBL).     

Experimental study of vortex structures in a hypersonic shock layer on a flat plate

The characteristics of travelling perturbations of density in a hypersonic shock layer on a flat plate for the Mach number M_∞=21 and unit Reynolds numberRe ₁=6·10⁵ m⁻¹ were experimentally studied by the method of electron-beam fluorescence. The perturbations were generated by interaction of the shock layer behind an oblique gas-dynamic whistle and the leading edge of the plate. The cases of unsteady and quasi-steady interaction were considered. In both cases, vortex disturbances of finite amplitude were generated. The measurements were performed at the fundamental frequency F=0.6·10⁻⁴ and at the harmonic; the streamwise phase velocities, the growth rates of the disturbances, and the angles of wave propagation were obtained. The measurement results are compared with some experimental data for subsonic flows, some particular results of the linear stability theory for compressible flows, and the results obtained on the basis of a simple model of the nonlinear stage of disturbance evolution in a hypersonic boundary layer. Institute of Theoretical and Applied Mechanics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 6, pp. 41–47, November–December, 1999.     

PIV study on a shock-induced separation in a transonic flow

A transonic interaction between a steady shock wave and a turbulent boundary layer in a Mach 1.4 channel flow is experimentally investigated by means of particle image velocimetry (PIV). In the test section, the lower wall is equipped with a contour profile shaped as a bump allowing flow separation. The transonic interaction, characterized by the existence in the outer flow of a lambda shock pattern, causes the separation of the boundary layer, and a low-speed recirculating bubble is observed downstream of the shock foot. Two-component PIV velocity measurements have been performed using an iterative gradient-based cross-correlation algorithm, providing high-speed and flexible calculations, instead of the classic multi-pass processing with FFT-based cross-correlation. The experiments are performed discussing all the hypotheses linked to the experimental set-up and the technique of investigation such as the two-dimensionality assumption of the flow, the particle response assessment, the seeding system, and the PIV correlation uncertainty. Mean velocity fields are presented for the whole interaction with particular attention for the recirculating bubble downstream of the detachment, especially in the mixing layer zone where the effects of the shear stress are most relevant. Turbulence is discussed in details, the results are compared to previous study, and new results are given for the turbulent production term and the return to isotropy mechanism. Finally, using different camera lens, a zoom in the vicinity of the wall presents mean and turbulent velocity fields for the incoming boundary layer.