Three-dimensional water entry of a solid body: A computational study

Marine vessels are continuously subject to impulsive loading from impact on the water surface. Understanding and quantifying the hydrodynamics generated by the three-dimensional (3D) water impact of a solid body is central to the design of resilient and performing vessels. Computational fluid dynamics (CFD) constitutes a viable tool for the study of water entry problems, which may overcome some of the drawbacks associated with semi-analytical and experimental methods. Here, we present a new computational study of the 3D water entry of a solid body with multiple curvatures. The method of finite volume is utilized to discretize incompressible Navier-Stokes equations in both air and water, and the method of volume of fluid is employed to describe the resulting free-surface multiphase flow. Computational results are validated against available experimental findings obtained using particle image velocimetry in terms of both the flow kinetics and kinematics. Specifically, we demonstrate the accuracy of our CFD solution in predicting the overall force experienced by the hull, the pile-up phenomenon, the velocity field in the water, the distribution of the hydrodynamic loading, and the energy transfer during the impact. Our approach is expected to aid in the validation of new semi-analytical solutions and to offer a viable means for conducting parametric studies and design optimization on marine vessels.     

Assessment of PIV-based analysis of water entry problems through synthetic numerical datasets

The phenomenon of hull-slamming, that is, the sudden impact of a solid body on the water surface, is critical in the design of naval structures. Thus, the development and validation of schemes to predict the slamming load and elucidate energy exchange during water entry are of fundamental importance in a wide range of engineering applications. Recent studies have demonstrated the possibility of using direct flow measurements from particle image velocimetry (PIV) to investigate the kinetics of water entry. Specifically, these efforts have contributed a first characterization of the hydrodynamic loading on impacting wedges and of the energy imparted to the water pile-up and the spray jets. Here, we seek to provide a thorough assessment of such a PIV-based approach through synthetic datasets, in which PIV parameters, such as the camera acquisition rate and the size of the interrogation area, are systematically varied, without experimental confounds. We implement a direct computational framework to study the two-dimensional flow physics generated during the water entry of a rigid wedge. Water and air are treated as immiscible phases and their relative motion is utilized to track the free surface dynamics. Our results show that the PIV-based methodology allows for an accurate reconstruction of the pressure field from the measured velocity field, except for early stages of the impact and for a small region close to the free surface. We also demonstrate that the reconstruction is only marginally affected by the spatial resolution, while a sufficiently high acquisition frequency is required to correctly predict the pressure field in the pile-up region. The proposed computational framework can also find application in the analysis of less studied aspects of water entry problems, such as cycling loading, flow transitions and separation, and formation of spray jets.     

Simultaneous digital image correlation/particle image velocimetry to unfold fluid–structure interaction during air-backed impact

Predicting the response of air-backed panels to impulsive hydrodynamic loading is essential to the design of marine structures operating in extreme conditions. Despite significant effort in this area of research, the lack of full-field measurement techniques of structural dynamics and flow physics hinders our understanding of the fluid–structure interaction. To fill this gap in knowledge, we designed a laboratory-scale experiment to elucidate fluid–structure interaction associated with impulsive hydrodynamic loading on a flexible plate. A combined experimental approach based on digital image correlation (DIC) and particle image velocimetry (PIV) was developed to afford spatially- and temporally-resolved measurements of the plate deflection and fluid velocity. From the velocity field measured through PIV, the hydrodynamic loading on the structure was estimated via a pressure-reconstruction algorithm. Experimental results point at a strong bidirectional coupling between structural dynamics and flow physics, which influence temporal and spatial patterns in counter-intuitive ways. While the plate deflection follows the fundamental in-vacuum mode shape of a clamped plate, the pressure exhibits a complex evolution. Not only does the location of the peak loading on the plate alternates between the clamp and the center as time progresses, but also the time evolution of the peak loading anticipated the peak displacement of the plate. This study contributes a new methodological approach to study fluid–structure interaction in three dimensions, offering insight in the physics of air-backed impact that could inform engineering design and scientific inquiry.     

基于双向流固耦合的超空泡射弹入水研究

超空泡射弹通过超空泡减阻技术在水下高速长距离航行, 是对抗水下近距离威胁的有效手段. 为了扩大防御范围、增加杀伤力, 超空泡射弹具有很高的发射速度. 高速超空泡射弹在入水时中受到极大的冲击载荷, 发生显著的结构变形, 结构变形与流场之间存在相互影响和作用, 常规的基于刚体假设的仿真研究方法不再适用. 为了研究高速超空泡射弹入水过程中的结构变形及其对流体动力特性的影响, 通过耦合流体力学求解器和结构动力学求解器, 建立了射弹高速入水双向流固耦合仿真模型, 并通过与文献中的试验结果进行对比验证了该模型空泡形态计算方法和耦合方法的准确性. 使用双向流固耦合的方法对高速射弹在不同初始攻角入水过程中的超空泡流动特性及结构变形特性进行了数值模拟研究, 通过对比流固耦合模型与刚体模型的计算结果, 得到了超空泡射弹的结构弯曲变形对流体动力载荷的影响. 研究结果表明: 高速射弹入水过程中流固耦合效应对超空泡流型及流体动力载荷的计算结果有显著影响; 本文所研究的射弹在考虑流固耦合效应, 带攻角垂直入水两倍弹长的范围内, 超空泡射弹的流体动力载荷与弯曲变形之间形成正反馈; 高速超空泡射弹在入水过程中受到的流体动力载荷及弹体应力应变随入水初始攻角的增加显著增大, 研究对象在初速1400m/s的条件下入水时, 当初始攻角不超过2°时不存在结构安全性问题.      

Incompressible SPH simulation of water entry of a free‐falling object

In this paper an incompressible smoothed particle hydrodynamics (Incom‐SPH) model is used to simulate the interactions between the free surface flow and a moving object. Incom‐SPH method is a two‐step semi‐implicit hydrodynamic formulation of the SPH algorithm and is capable of accurately treating the free surface deformations and impact forces during the solid–fluid interactions. For a free‐falling object, its motion is tracked by an additional Lagrangian algorithm based on Newton's law to couple with the Incom‐SPH program. The developed model is employed to investigate the water entry of a free‐falling wedge. The accuracy of the computations is validated by the good agreement in predicting the relevant hydrokinematic and hydrodynamic parameters. Finally, a numerical test is performed to study the influence of spatial resolution on the water entry features. The Incom‐SPH modeling coupled with the solid–fluid interaction algorithm could provide a promising computational tool to predict the slamming problems in coastal and offshore engineering. Copyright © 2008 John Wiley & Sons, Ltd.     

Vertical immersion of a cylindrical floating solid

This paper is devoted to a study of the vortex-free (irrotational) motion of an ideal incompressible liquid during the vertical immersion of a cylindrical solid. In contrast to problems of impact [1] and the entry of a solid into water [2], the case here treated deals with continuous immersion involving a change in the shape of the free surface but with a constant width of the wetted surface of the solid. The coefficients of the time-dependent power series for the velocity potential, the equation of the free surface, and the pressure on the solid are determined, allowing for all the terms in the Cauchy-Lagrange equation. The results of calculations relating to the immersion of a bottom with an elliptical shape of the submerged part are presented.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 2, pp. 27–31, March–April, 1973.     

Stereoscopic PIV on multiple color-coded light sheets and its application to axial flow in flapping robotic insect wings

Non-scanning volume flow measurement techniques such as 3D-PTV, holographic and tomographic particle image velocimetry (PIV) permit reconstructions of all three components (3C) of velocity and vorticity vectors in a fluid volume (3D). In this study, we present a novel 3D3C technique termed Multiple-Color-Plane Stereo Particle-Image-Velocimetry (color PIV), which allows instantaneous measurements of 3C velocity vectors in six parallel, colored light sheets. We generated the light sheets by passing white light of two strobes through dichroic color filters and imaged the slices by two 3CCD color cameras in Stereo-PIV configuration. The stereo-color images were processed by custom software routines that sorted each colored fluid particle into one of six gray-scale images according to its hue, saturation, and luminance. We used conventional Stereo PIV cross-correlation algorithms to compute a 3D planar vector field for each light sheet and subsequently interpolated a volume flow map from the six vector fields. As a first application, we quantified the wake and axial flow in the vortical structures of a robotic insect (fruit fly) model wing. In contrast to previous findings, the measured data indicate strong axial flow components on the upper wing surface, including axial flow in the leading-edge vortex core. Collectively, color PIV is robust against mechanical misalignments, avoids laser safety issues, and computes instantaneous 3D vector fields in a fraction of the time typical for other 3D systems. Color PIV might thus be of value for volume measurements of highly unsteady flows.     

扩张尾裙对跨介质航行器高速入水转平弹道特性影响

扩张尾裙是影响跨介质航行器高速入水转平弹道及其稳定性的关键因素.采用流体体积多相流模型和动网格技术,建立了跨介质超空泡航行器高速入水多相流场弹道耦合计算方法,并通过试验验证了计算方法的准确性和适用性.通过对跨介质航行器高速入水转平过程进行数值模拟研究,获得尾裙外形对航行器入水转平过程中空泡发展形态、流体动力特性与弹道特性的影响,并分析尾裙扩张角度对高速入水转平弹道的影响规律.结果表明:不同预置舵角下的无尾裙外形航行器在入水转平过程中,攻角持续增大,最终导致弹道发散,带尾裙外形航行器在入水后尾裙沾湿形成了恢复力矩,获得了稳定的入水转平弹道;设计的1.5°, 6°, 8°尾裙角度的航行器形成了稳定滑水、单侧尾拍以及双侧尾拍3种弹道特征,且均能实现稳定高速入水转平弹道;稳定滑水弹道原理为预置舵角与尾裙滑水耦合作用下达到的动态平衡,该弹道综合阻力系数最小,转弯效率最高,动载荷最小,是跨介质航行器高速入水的理想弹道转平形式.     

Live monitoring of the distributed strain field in impulsive events through fiber Bragg gratings

In this paper, we propose a measurement technique based on local strain measurements to perform real-time reconstruction of the overall structural deformation and the distributed stress field produced by the impact of a body on a water free surface. In particular, we seek establishing a measurement chain capable of acquiring and elaborating the signals at high frequency, so that it can be utilized to study rapidly varying strain fields, such as those occurring in impulsive events. Fiber Bragg gratings are utilized to sense the local structural deformation. Experiments are conducted on flexible plastic wedges with variable deadrise angles impacting on a quiescent fluid surface. The experimental tests are performed in free fall and we explore variations of the entry velocity by varying the drop height. The structural deformation is reconstructed from point-wise strain measurements utilizing a modal reconstruction methodology. The impact dynamics are analysed through accelerometers and linear position sensors. Results show that the impact behaviour of the flexible body is characterized by a main overall deformation where the structure is distorted in the direction of the loading, whereby marked vibrations, whose amplitude increase with the entry velocity, dominate the dynamic response. The influence of the mode shapes considered in the present analysis on the accuracy of the results is also observed. The proposed methodology allows for a fairly high acquisition frequency, which translates into a real-time structural reconstruction technique. Results show that the proposed methodology can be a valuable tool for the live monitoring of structures undergoing impact events.     

旋转射弹高速倾斜入水多相流场与弹道数值模拟

基于VOF多相流模型和有限体积法求解水、汽、气多相流动的RANS方程,结合重叠网格技术和six DOF算法对某一型号舰载射弹倾斜入水过程进行数值模拟研究。首先基于该方法研究了射弹旋转效应对射弹运动特性及流体动力特性的影响,然后对不同入水角下倾斜入水过程进行分析,得到不同倾角下旋转射弹入水空泡形态发展规律、弹体运动特征及流体动力特性变化规律。研究结果表明:射弹的旋转有利于弹体在初始对称面内的弹道稳定性,但会降低弹体侧向稳定性,使射弹受到的阻力系数、俯仰力矩系数变小;入水角越小,形成的空泡越不对称,由射弹运动状态的改变引起的空泡形态变化越明显,在超空泡航行阶段,弹体运动较稳定,不同角度下流体动力系数差别很小,当弹体下表面刺破空泡壁沾湿时,弹体运动状态发生较大变化,流体动力系数迅速增大,此时入水角度过小,弹体容易失稳;弹体的沾湿对空泡形态、弹体运动稳定性和流体动力特性有着重要的影响。     

Local water slamming impact on sandwich composite hulls

The local water slamming refers to the impact of a part of a ship hull on stationary water for a short duration during which high local pressures occur on the hull. We simulate slamming impact of rigid and deformable hull bottom panels by using the coupled Lagrangian and Eulerian formulation included in the commercial software LS-DYNA. We use the Lagrangian formulation to describe plane-strain deformations of the hull panel and consider geometric nonlinearities. The Eulerian formulation is used to analyze deformations of the water. Deformations of the hull panel and of the water are coupled through the hydrodynamic pressure exerted by water on the hull, and the velocity of particles on the hull wetted surface affecting deformations of the water. The continuity of surface tractions and the inter-penetrability of water into the hull are satisfied by using a penalty method. The computer code is verified by showing that the computed pressure distributions for water slamming on rigid panels agree well with those reported in the literature. The pressure distributions computed for deformable panels are found to differ from those obtained by using a plate theory and Wagner's slamming impact theory. We have also delineated jet flows near the edges of the wetted hull, and studied delamination induced in a sandwich composite panel due to the hydroelastic pressure.     

3D particle image velocimetry of the flow field around a sphere sedimenting near a wall: Part 1. Effects of Weissenberg number

The flow fields surrounding a sphere sedimenting through a liquid near a vertical wall are characterized using 3D stereoscopic particle-image velocimetry (PIV) experiments. Three different fluids, a Newtonian reference fluid, a constant (shear) viscosity Boger fluid, and a shear-thinning elastic fluid, are used to determine the effects of both elasticity and shear-thinning on the flow field. All three fluids have similar zero shear viscosities. The Weissenberg number is manipulated by varying the diameter and the composition of the ball. Significant differences are found for the different types of fluid, demonstrating both the influence of elasticity and shear-thinning on the velocity fields. In addition, the impact of the wall on the flow field is qualitatively different for each fluid. We find that the flow behind the sphere is strongly dependent on the fluid properties as well as the elasticity. Also, the presence of a negative wake is found for the shear-thinning fluid at high Weissenberg number (Wi > 1).     

粒子图像测速技术研究进展

粒子图像测速技术(PIV)作为一种全新的无扰、瞬态、全场速度测量方法,在流体力学及空气动力学研究领域具有极高的学术意义和实用价值.本文对PIV技术的原理、分类作了简要地介绍,详细归纳和评述了现有的各种速度信息的提取方法,并对拓扑图论、神经网络、遗传算法、模糊聚类等新技术在PIV中的应用以及三维PIV技术、两相流PIV测试技术进行了介绍.指出当前PIV技术除了向三维和多相流方向发展外,如何提高PIV的测量精度以及缩短计算时间仍然是目前研究的主要目标.PIV技术随着计算机技术、激光技术和CCD性能的发展,必将取得更大的发展与突破      

Lagrangian and Eulerian pressure field evaluation of rod-airfoil flow from time-resolved tomographic PIV

This work investigates the rod-airfoil air flow by time-resolved Tomographic Particle Image Velocimetry (TR-TOMO PIV) in thin-light volume configuration. Experiments are performed at the region close to the leading edge of a NACA0012 airfoil embedded in the von Kármán wake of a cylindrical rod. The 3D velocity field measured at 5 kHz is used to evaluate the instantaneous planar pressure field by integration of the pressure gradient field. The experimental data are treated with a discretized model based on multiple velocity measurements. The time separation used to evaluate the Lagrangian derivative along a fluid parcel trajectory has to be taken into account to reduce precision error. By comparing Lagrangian and Eulerian approaches, the latter is restricted to shorter time separations and is found not applicable to evaluate pressure gradient field if a relative precision error lower than 10% is required. Finally, the pressure evaluated from tomographic velocity measurements is compared to that obtained from simulated planar ones to discuss the effect of 3D flow phenomena on the accuracy of the proposed technique.     

固体颗粒对沟槽湍流边界层影响的实验研究

本文采用粒子图像测速技术(particles image velocimetry, PIV)研究固体颗粒对放置在平板湍流边界层中的平壁和沟槽壁面减阻效果的影响. 实验对清水和加入粒径为155 μm聚苯乙烯颗粒的流法向二维速度场信息进行采集, 对不同工况下的平均速度剖面、雷诺应力和湍流度等统计量进行对比, 分析流体在边界层中的行为. 运用空间局部平均结构函数提取了不同工况湍流边界层喷射?扫掠行为的空间拓扑结构并进行比较. 结果发现, 在不同的壁面条件下, 粒子加入后的对数律区中无量纲速度均略大于清水组, 雷诺切应力有所降低, 湍流度有所减弱. 对于不同流场速度下的沟槽而言, 颗粒的加入均降低了壁面附近的阻力, 而颗粒单独作用于光滑壁面的减阻效果并不明显. 加入粒子后的相干结构数目有所增加, 法向脉动速度下降. 沟槽壁面附近的相干结构数目有所增加, 法向脉动速度在自由来流速度较大时有所上升, 在速度较小时有所下降. 这表明不同减阻状况下的沟槽均能将大涡破碎成更多的涡, 并且粒子的加入强化了这种破碎作用.      

Flow patterns and interfacial velocities near a moving contact line

Experimental data on velocity fields and flow patterns near a moving contact line is shown to be at variance with existing hydrodynamic theories. The discrepancy points to a new hydrodynamic paradox and suggests that the hydrodynamic approach may be incomplete and further parameters or forces affecting the surfaces may have to be included. A contact line is the line of intersection of three phases: (1) a solid, (2) a liquid, and (3) a fluid (liquid or gas) phase. A moving contact line develops when the contact line moves along the solid surface. A flat plate moved up and down, inside and out of a liquid pool defines a simple, reliable experimental model to characterize dynamic contact lines. Highlighted are three important conclusions from the experimental results that should be prominent in the development of new theoretical models for this flow. First, the velocity along the streamline configuring the liquid–fluid interface is remarkably constant within a distance of a couple of millimeters from the contact line. Second, the relative velocity of the liquid–fluid interface, defined as the ratio of the velocity along the interface to the velocity of the solid surface, is independent of the solid surface velocity. Third, the relative interface velocity is a function of the dynamic contact angle.     

Characteristics of flow field and water concentration in a horizontal deadleg

Deadlegs are defined as the inactive portion of the pipe where the flow is stagnant. Corrosion in deadlegs occurs as a result of water separation due to the very low flow velocity. The present work provides an investigation of the effect of deadleg geometry and average flow velocity on flow field and oil/water separation in deadlegs. The investigation is based on the solution of the mass and momentum conservation equations of an oil/water mixture together with the volume fraction equation for the secondary phase. A fluid flow model based on the time-averaged governing equations of 3-D turbulent flow has been developed. An algebraic slip mixture model is utilized for the calculation of the two immiscible fluids (water and crude oil). The model solves the continuity and momentum equations for the mixture, and the volume fraction equation for the secondary phase utilizing an algebraic expression for the relative velocity. Flow visualization experiments were conducted in order to validate the numerical procedure. Good agreement was obtained between the calculated and measured flow patterns. Results are obtained for different lengths of the deadleg. The considered fluid mixture contains 90% oil and 10% water (by volume). The inlet flow velocity ranges from 0.2 to 10 m/s and the deadleg length to diameter ratio (L/D) ranges from 1 to 10. The results showed that the size of the stagnant fluid region increases with the increase of L/D and decreases with the increase of inlet velocity. The results also indicated that the water volumetric concentration increases with the increase of L/D and influenced by the deadleg geometry.     

Modified control grid interpolation for the volumetric reconstruction of fluid flows

Complex applications in fluid dynamics research often require more highly resolved velocity data than direct measurements or simulations provide. The advent of stereo PIV and PCMR techniques has advanced the state-of-the-art in flow velocity measurement, but 3D spatial resolution remains limited. Here a new technique is proposed for velocity data interpolation to address this problem. The new method performs with higher quality than competing solutions from the literature in terms of accurately interpolating velocities, maintaining fluid structure and domain boundaries, and preserving coherent structures.     

An advanced off-axis holographic particle image velocimetry (HPIV) system

Holographic PIV (HPIV) is the most promising candidate for the next generation full-field velocimetry that can measure high spatial resolution instantaneous three-dimensional (3D) velocity fields. To explore the maximum performance capabilities of HPIV including spatial resolution, off-axis holography based HPIV has become a major direction of development. A fully automated off-axis HPIV system based on an injection-seeded dual-pulsed YAG laser and 3D data processing software has been implemented in the laser flow diagnostics lab (LFD). In our system, 90-degree particle scattering, dual reference beams, in situ reconstruction/data processing, and 3D velocity extraction based on a fast “concise cross correlation” (CCC) algorithm are utilized. The off-axis HPIV system is tested for an acoustically excited air jet and the wake of a surface-mounted tab in a water channel flow, giving instantaneous 3D velocity fields for both flows. Experimental data of instantaneously measured 3D flow structures using this technique show great promise. Received: 12 August 1998/Accepted: 20 October 1999     

Time-resolved PIV measurements of the interaction of polystyrene beads with near-wall-coherent structures in a turbulent channel flow

Time-resolved PIV measurements were performed in a dilute particle-laden flow tracking near-neutrally buoyant polystyrene beads and the velocity field of a near wall turbulent boundary layer. Data were taken in a vertical light sheet aligned in the streamwise direction at the center of a horizontal, closed loop, transparent square water channel facility. In addition, low speed measurements were performed characterizing the effects of the dispersed phase on mean and turbulence flow quantities. Reynolds shear stress slightly differed from clear water conditions whereas fluid mean and rms values were not affected. A case study for several beads revealed a clear relation between their movement and near-wall coherent structures. Several structures having 2D vorticity signatures of near-wall hairpin vortices and hairpin packets, directly affected bead movement. A statistical analysis showed that the mean streamwise velocity of ascending beads lagged behind the mean fluid velocity and bead rms values were higher than fluid ones. Particle Reynolds numbers based on the magnitude of the instantaneous relative velocity vector peaked near the wall; values not exceeding 100, too low for vortex shedding to occur. Quadrant analysis showed a clear preference for ascending beads to reside in ejections while for descending beads the preference for sweeps was less.