Three-dimensional water entry of a solid body: A particle image velocimetry study

Understanding and predicting the hydrodynamic loading experienced by a solid body during water impact is critical for researchers and practitioners in naval engineering. While two-dimensional (2D) water entry problems have been extensively investigated, experimental data on 3D fluid–structure interactions during water impact are rather limited. Here, particle image velocimetry (PIV) is utilized to study the free fall vertical impact of a solid body, modeling a ship hull, on an otherwise quiescent fluid. Planar PIV is used to measure the velocity field on multiple cross-sections along the length and width of the model. These data are combined to infer the 3D velocity field in the entire fluid. The 3D velocity field is then utilized to reconstruct the pressure field by integrating the incompressible 3D Navier–Stokes equations in a time-varying domain, where both the free surface and the fluid–solid interface evolve in time. By evaluating the pressure field on the wetted surface of the model, we estimate the hydrodynamic loading during water entry. Experimental results demonstrate the central role of 3D effects on both the flow physics and the hydrodynamic loading. As the cross-sectional velocity decreases away from the mid-span, we observe a robust increase in the axial velocity component. This translates into a complex spatio-temporal dependence of the hydrodynamic loading, which is initially maximized in the vicinity of the pile-up and later increases toward the keel. Due to the deceleration of the model during the impact and the increase in the wetted surface, the hydrodynamic loading close to the mid-span in the early stage of the impact is considerably larger than the ends. The 3D flow physics is used to study the energy imparted to the fluid during the impact, which we find to be mostly transferred to the risen water, consisting of the pile-up region and the spray jet. Our methodology can be implemented for the analysis of other solid bodies with multiple geometric curvatures, and our experimental results can be utilized for the validation of 3D mathematical models of water entry.     

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.     

Experimental and computational study of the flow induced by a plasma actuator

A complementary experimental and computational study of the flow field evoked by a plasma actuator mounted on a flat plate was in focus of the present work. The main objective of the experimental investigation was the determination of the vector force imparted by the plasma actuator to the fluid flow. The force distribution was presently extracted from the Navier–Stokes equations directly by feeding them with the velocity field measured by a PIV technique. Assuming a steady-in-mean, two-dimensional flow with zero-pressure gradient, the imbalance between the convective term and the momentum equation’s right-hand-side terms reveals the desired resulting force. This force-distribution database was used afterwards as the source term in the momentum equation. Furthermore, an empirical model formulation for the volume-force determination parameterized by the underlying PIV-based model is derived. The model is tested within the RANS framework in order to predict a wall jet-like flow induced by a plasma actuator. The Reynolds equations are closed by a near-wall second-moment closure model based on the homogeneous dissipation rate of the kinetic energy of turbulence. The computationally obtained velocity field is analysed along with the experimental data focussing on the wall jet flow region in proximity of the plasma actuator. For comparison purposes, different existing phenomenological models were applied to evaluate the new model’s accuracy. The comparative analysis of all applied models demonstrates the strength of the new empirical model, particularly within the plasma domain. In addition, the presently formulated empirical model was applied to the flow in a three-dimensional diffuser whose inflow was modulated by a pair of streamwise vortices generated by the present plasma actuator. The direct comparison with existing experimental data of Grundmann et al. (2011) demonstrated that the specific decrease of the diffuser pressure corresponding to the continuous forcing was predicted correctly.     

Experimental PIV/V3V measurements of vortex-induced fluid–structure interaction in turbulent flow—A new benchmark FSI-PfS-2a

The investigation of the bidirectional coupling between a fluid flow and a structure motion is a growing branch of research in science and industry. Applications of the so-called fluid–structure interactions (FSI) are widespread. To improve coupled numerical FSI simulations, generic experimental benchmark studies of the fluid and the structure are necessary. In this work, the coupling of a vortex-induced periodic deformation of a flexible structure mounted behind a rigid cylinder and a fully turbulent water flow performed at a Reynolds number of Re=30 470 is experimentally investigated with a planar particle image velocimetry (PIV) and a volumetric three-component velocimetry (V3V) system. To determine the structure displacements a multiple-point laser triangulation sensor is used. The three-dimensional fluid velocity results show shedding vortices behind the structure, which reaches the second swiveling mode with a frequency of about 11.2 Hz corresponding to a Strouhal number of St=0.177. Providing phase-averaged flow and structure measurements precise experimental data for coupled computational fluid dynamics (CFD) and computational structure dynamics (CSD) validations are available for this new benchmark case denoted FSI-PfS-2a. The test case possesses four main advantages: (i) the geometry is rather simple; (ii) kinematically, the rotation of the front cylinder is avoided; (iii) the boundary conditions are well defined; (iv) nevertheless, the resulting flow features and structure displacements are challenging from the computational point of view. In addition to the flow field and displacement data a PIV-based force calculation method is used to estimate the lift and drag coefficients of the moving structure.     

波浪环境中垂直射流紊动特性的实验研究

利用粒子图像测速技术PIV(particle imagevelocimetry)对有限水深规则波浪环境下垂直射流紊动特性进行了实验研究. 应用相位分析法从测量数据中分离出速度脉动项,用4种不同波高的波浪研究波高对射流紊动特性的影响,对紊动量的分布以及大小进行了分析. 结果表明波高对射流的紊动特性有显著影响,并且对流项对波高的变化较紊动扩散项更为敏感,紊动扩散项量值约是对流项的$1/8\sim1/3$, 在时均化的N-S方程中起的作用不可忽略.      

Scaling investigation of plasma-induced flows over curved and flat surfaces: Comparison to the wall jet

The present investigation deals with Dielectric Barrier Discharge (DBD) induced jets flowing over curved surfaces and studied in the framework of a circulation control application, carried out by acting near the rounded trailing-edge of an airfoil. These jets are characterized experimentally via Particle Image Velocimetry (PIV) in quiescent air conditions. The study assesses the evolution of these flows in terms of self-similarity of the mean flow and of its turbulent components. DBD wall jets evolution in the streaming direction is also analyzed through the rate of spread and the maximum velocity decay evolution as commonly done for fluidic wall jets, and also through several normalized quantities deriving from different length and velocity scales. A comparison with a canonical flow, such as the classical wall jet flowing over plane or curved surfaces, is made in order to find out the similarities and the discrepancies between these two flows. Results reveal that DBD wall jets and canonical fluidic wall jets show comparable properties in the diffusion zone. Compared to the plane DBD wall jet, centrifugal forces are responsible of the greater spread of curved DBD wall jets and are likely the source of instabilities leading to their transitional state. The momentum flux of the induced jet and the radius of curvature of the surface are two relevant scales for DBD induced flows developing over curved surfaces.     

Dynamics of swirling jet flows

Experimental investigations of near-field structure of coaxial flows are presented for four different configurations: coaxial jets without rotation (reference case), outer flow rotating only (OFRO), inner-jet rotating only (IJRO) and corotating jets (CRJ). The investigations are performed in a cylindrical water tunnel, with an independent rotation of two coaxial flows. Laser tomography is used to document the flow field, and photographs are shown for different configurations. Time mean velocity profiles obtained by PIV, with and without swirl, are also presented. The dynamics of the swirling jets in the initial region (i.e. near the exit of the jets) is described. The effects of azimuthal velocity and axial velocity ratio variations on flow dynamics are examined. The appearance and growth of the first instabilities are presented and compared with some theoretical results, as is the influence of the rotation (inner or outer) on the dominating structures.     

Oscillations of the fluid flow and the free surface in a cavity with a submerged bifurcated nozzle

The free surface dynamics and sub-surface flow behavior in a thin (height and width much larger than thickness), liquid filled, rectangular cavity with a submerged bifurcated nozzle were investigated using free surface visualization and particle image velocimetry (PIV). Three regimes in the free surface behavior were identified, depending on nozzle depth and inlet velocity. For small nozzle depths, an irregular free surface is observed without clear periodicities. For intermediate nozzle depths and sufficiently high inlet velocities, natural mode oscillations consistent with gravity waves are present, while at large nozzle depths long term self-sustained asymmetric oscillations occur.For the latter case, time-resolved PIV measurements of the flow below the free surface indicated a strong oscillation of the direction with which each of the two jets issue from the nozzle. The frequency of the jet oscillation is identical to the free surface oscillation frequency. The two jets oscillate in anti-phase, causing the asymmetric free surface oscillation. The jets interact through a cross-flow in the gaps between the inlet channel and the front and back walls of the cavity.     

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.     

On the Capability of PIV-Based Wall Pressure Estimation for an Impinging Jet Flow

A PIV-based pressure estimation methodology is used to compute the wall pressure from the velocity field of a turbulent impinging jet flow. A simplified formulation (2D-2C) is applied to velocity fields issued from PIV data. The ability of the method to qualitatively estimate the wall pressure signature of a 3D unsteady impinging jet flow using only two velocity components in a plane is demonstrated. Nevertheless, the 2D flow assumption used in the context of planar measurements involves an underestimation of the wall pressure values all along the radial direction. The formulation based on the full integral formalism (3D-3C), computed from DNS data without any assumption on the flow, provides a reference solution. The contributions of the surface and volume integrals to the pressure coefficient are assessed. It is shown that the most important contribution to the wall pressure comes from the volume integral. Then the underestimation observed for the simplified formulation is mostly linked with the assumptions considered for the source term computation. The effect of each assumption is quantitatively analysed with the help of the DNS data and some ways to improve the simplified methodology are finally proposed.     

A method for automatic estimation of instantaneous local uncertainty in particle image velocimetry measurements

The uncertainty of any measurement is the interval in which one believes the actual error lies. Particle image velocimetry (PIV) measurement error depends on the PIV algorithm used, a wide range of user inputs, flow characteristics, and the experimental setup. Since these factors vary in time and space, they lead to nonuniform error throughout the flow field. As such, a universal PIV uncertainty estimate is not adequate and can be misleading. This is of particular interest when PIV data are used for comparison with computational or experimental data. A method to estimate the uncertainty from sources detectable in the raw images and due to the PIV calculation of each individual velocity measurement is presented. The relationship between four error sources and their contribution to PIV error is first determined. The sources, or parameters, considered are particle image diameter, particle density, particle displacement, and velocity gradient, although this choice in parameters is arbitrary and may not be complete. This information provides a four-dimensional “uncertainty surface” specific to the PIV algorithm used. After PIV processing, our code “measures" the value of each of these parameters and estimates the velocity uncertainty due to the PIV algorithm for each vector in the flow field. The reliability of our methodology is validated using known flow fields so the actual error can be determined. Our analysis shows that, for most flows, the uncertainty distribution obtained using this method fits the confidence interval. An experiment is used to show that systematic uncertainties are accurately computed for a jet flow. The method is general and can be adapted to any PIV analysis, provided that the relevant error sources can be identified for a given experiment and the appropriate parameters can be quantified from the images obtained.     

An efficient and accurate approach to MTE-MART for time-resolved tomographic PIV

The motion-tracking-enhanced MART (MTE-MART; Novara et al. in Meas Sci Technol 21:035401, 2010) has demonstrated the potential to increase the accuracy of tomographic PIV by the combined use of a short sequence of non-simultaneous recordings. A clear bottleneck of the MTE-MART technique has been its computational cost. For large datasets comprising time-resolved sequences, MTE-MART becomes unaffordable and has been barely applied even for the analysis of densely seeded tomographic PIV datasets. A novel implementation is proposed for tomographic PIV image sequences, which strongly reduces the computational burden of MTE-MART, possibly below that of regular MART. The method is a sequential algorithm that produces a time-marching estimation of the object intensity field based on an enhanced guess, which is built upon the object reconstructed at the previous time instant. As the method becomes effective after a number of snapshots (typically 5–10), the sequential MTE-MART (SMTE) is most suited for time-resolved sequences. The computational cost reduction due to SMTE simply stems from the fewer MART iterations required for each time instant. Moreover, the method yields superior reconstruction quality and higher velocity field measurement precision when compared with both MART and MTE-MART. The working principle is assessed in terms of computational effort, reconstruction quality and velocity field accuracy with both synthetic time-resolved tomographic images of a turbulent boundary layer and two experimental databases documented in the literature. The first is the time-resolved data of flow past an airfoil trailing edge used in the study of Novara and Scarano (Exp Fluids 52:1027–1041, 2012); the second is a swirling jet in a water flow. In both cases, the effective elimination of ghost particles is demonstrated in number and intensity within a short temporal transient of 5–10 frames, depending on the seeding density. The increased value of the velocity space–time correlation coefficient demonstrates the increased velocity field accuracy of SMTE compared with MART.     

Spray features in the near field of a flow-blurring injector investigated by high-speed visualization and time-resolved PIV

In a flow-blurring (FB) injector, atomizing air stagnates and bifurcates at the gap upstream of the injector orifice. A small portion of the air penetrates into the liquid supply line to create a turbulent two-phase flow. Pressure drop across the injector orifice causes air bubbles to expand and burst thereby disintegrating the surrounding liquid into a fine spray. In previous studies, we have demonstrated clean and stable combustion of alternative liquid fuels, such as biodiesel, straight vegetable oil and glycerol by using the FB injector without requiring fuel pre-processing or combustor hardware modification. In this study, high-speed visualization and time-resolved particle image velocimetry (PIV) techniques are employed to investigate the FB spray in the near field of the injector to delineate the underlying mechanisms of atomization. Experiments are performed using water as the liquid and air as the atomizing gas for air to liquid mass ratio of 2.0. Flow visualization at the injector exit focused on a field of view with physical dimensions of 2.3 mm × 1.4 mm at spatial resolution of 7.16 µm per pixel, exposure time of 1 µs, and image acquisition rate of 100 k frames per second. Image sequences illustrate mostly fine droplets indicating that the primary breakup by FB atomization likely occurs within the injector itself. A few larger droplets appearing mainly at the injector periphery undergo secondary breakup by Rayleigh–Taylor instabilities. Time-resolved PIV is applied to quantify the droplet dynamics in the injector near field. Plots of instantaneous, mean, and root-mean-square droplet velocities are presented to reveal the secondary breakup process. Results show that the secondary atomization to produce fine and stable spray is complete within a few diameters from the injector exit. These superior characteristics of the FB injector are attractive to achieve clean combustion of different fuels in practical systems.     

Lagrangian-based investigation of multiphase flows by finite-time Lyapunov exponents

Multiphase flows are ubiquitous in our daily lifeand engineering applications.It is important to investigatethe flow structures to predict their dynamical behaviors effectively.Lagrangian coherent structures(LCS) defined bythe ridges of the finite-time Lyapunov exponent(FTLE) isutilized in this study to elucidate the multiphase interactionsin gaseous jets injected into water and time-dependent turbulent cavitation under the framework of Navier-Stokes flowcomputations.For the gaseous jets injected into water,the highlightedphenomena of the jet transportation can be observed by theLCS method,including expansion,bulge,necking/breaking,and back-attack.Besides,the observation of the LCS revealsthat the back-attack phenomenon arises from the fact that theinjected gas has difficulties to move toward downstream region after the necking/breaking.For the turbulent cavitatingflow,the ridge of the FTLE field can form a LCS to capturethe front and boundary of the re-entraint jet when the adverse pressure gradient is strong enough.It represents a barrier between particles trapped inside the circulation regionand those moving downstream.The results indicate that theFTLE field has the potential to identify the structures of multiphase flows,and the LCS can capture the interface/barrieror the vortex/circulation region.     

Flame liftoff height dependence on geometrically modified bluffbodies in a vitiated flow

In this study, the improvement of liftoff height of bluffbody-stabilized, partially premixed methane flames and the change of flow field in the recirculation zone of bluffbodies, of variously modified base geometries, are investigated in a high temperature (~1,315 K) vitiated flow. The basic geometry of the bluffbody consists of a two-dimensional rectangular body with a rounded nose with fuel jets being discharged from the body at several locations upstream of the base. Flame liftoff height measurements are characterized by CH chemiluminescence, while the three-dimensional flow field is determined using stereo particle image velocimetry (PIV). The lowest liftoff height is observed when the geometric modifications from the original rectangular bluffbody base are carried out such that the base has three-dimensional local cavities together with two-dimensionally modified geometries. PIV measurements show that the improvement of liftoff height is primarily attributed to an intense recirculation induced by multi-dimensional vortex structures in the presence of the two- and three-dimensionally modified base.     

Velocity and surface pressure measurements in an open cavity

Subsonic flow of approximately Mach 0.2 over cavities with L/D ratios of 5.16 and 1.49 were studied experimentally using particle image velocimetry (PIV), surface pressure measurements, and hot-wire measurements. The incoming boundary layer was turbulent in both cases. The PIV data was analyzed to yield mean flow characteristics, vorticity field information, and two-point statistics for the velocity field. The hot-wire data was combined with surface pressure measurements to detail the correlations between velocity and pressure fluctuations. An analysis of the correlation between surface pressure measurements shows contrasting characteristics for the two cavity aspect ratios. The PIV data was combined with surface pressure measurements through the application of quadratic stochastic estimation to predict the time-dependent behavior of the velocity field. An examination of the results supports the existence of different cavity flow modes, as has been suggested in much of the literature.     

Flow behavior of high-temperature flue gas in the heat transfer chamber of a pilot-scale coal-water slurry combustion furnace

The flow characteristics of high-temperature flue gas are important in the heat transfer of coal-water slurry（CWS） combustion furnaces.The flow field of a 250 kg/h vertical-type slag tap cyclone furnace was non-intrusively investigated,using two-dimensional particle-image velocimetry（2D PIV）.The method was verified using traceable fly ash particles in high-temperature flue gas.The flow field of the flue gas was analyzed with a time-averaged method,based on which the effects of excess air ratio and loading were investigated.The flue gas separated by a gas separator maintained good rigidity near the furnace wall,rather than eroding the heating surface.Numerical simulations validated the reliability of PIV under the actual circumstances within the furnace.This study provides guidelines for applying 2D PIV in analyzing flue gas in thermal test boilers.     

侧向多喷口干扰复杂流动数值模拟研究

采用具有高分辨率的NND格式,通过数值求解N-S方程对典型外形多喷口侧向喷流复杂干扰流动进行了数值模拟. 为了提高计算效率,采用了LU-SGS隐式算法. 采用分块对接网格技术,生成高质量的贴体计算网格,精确模拟喷口截面. 对比分析了不同计算格式、限制器形式、网格拓扑及流动形态(层流与湍流)对喷流干扰流场结构和压力分布特性的影响,研究和分析了喷口附近流场的涡系结构、波系结构和喷流干扰引起的气动力特性. 在上述研究的基础上,针对典型飞行器外形的侧向喷流干扰特性进行了详细的数值模拟,得到了喷口参数(喷口位置、数目等)及来流条件对喷流干扰流场结构、气动力特性的影响规律,并对其流动机理进行了相应的分析. 研究表明,发展的针对多喷口侧喷干扰的数值计算方法是成功的,可以应用于飞行器侧向喷流干扰的流场结构分析及气动力特性数值预测.      

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      

Development and structure of a gravity current head

A new approach for 2-dimensional flow field investigation by PIV has been developed for measurements with high spatial resolution without the well known directional ambiguity. This feature of the technique is especially important for measurements in flows with reversal regions or strong turbulent motion as in-cylinder engine measurements. The major aim of the work was to achieve the benefits of cross correlation PIV image evaluation at reasonable cost and under application of common single wavelength double pulsed laser systems as they are mainly used for PIV experiments. The development of the technique is based on polarization rotation of the light scattered by the seeding particles by means of a ferroelectric liquid crystal half wave plate (FLC).Measurement samples from low turbulent jets and the flow in the wake of a cylinder are being presented.