Numerical investigation on the gas entrainment of ventilated partial cavity based on a multiscale modelling approach

Ventilated cavitation which is acknowledged as an efficient drag reduction technology for underwater vehicle is characterised by the very disparate length and time scales, posing great difficulty in the application of this technology. A multiscale numerical approach which integrates a sub-grid air entrainment model into the two-fluid framework is proposed in this paper to resolve the complex flow field created by ventilated cavity. Simulations have been carried out for the partially ventilated cavity underneath flat plate, with special efforts putting on understanding the gas entrainment at the cavity tail and the bubble dispersion process downstream. The flow parameters including the void fraction, the bubble velocity and the bubble size distributions in and downstream of the ventilated cavity are fully investigated. Comparisons between the numerical results with the experimental data are in satisfactory agreement, demonstrating the potential of the proposed methodology. The ventilation rate effect on the cavity shape and bubbly flow parameters are further investigated, obtaining the law of bubble dispersion and the bubble size evolution. This research not only provide a useful method for the investigation on the multiscale multiphase flow, but also give insight on understanding the combined drag reduction mechanism resulted from large-scale cavity and microbubbles.     

Numerical research on drag reduction by ventilated partial cavity based on two-fluid model

This paper presents a numerical study on the drag reduction mechanism created by a ventilated partial cavity and its associated effects by the downstream dispersed microbubbles. A semi-empirical approach is introduced to model the discrete interface of the ventilated cavity and its complex gas leakage rate induced by the local turbulent shear stress. Based on the Eulerian–Eulerian two-fluid modeling framework, a population balance approach based on MUltiple-SIze-Group (MUSIG) model is incorporated to simulate the dynamical effects of bubbly flow along the test body. Particular attention is also directed to grasp a better understanding of the size evolution of microbubble and its associated effects on drag reduction. Model predictions are validated against three experimental measurements carried out in a high-speed water tunnel by Schauer (2003) and Wosnik et al. (2005). Close examination of the flow structures, gas void fraction distributions and its resultant density ratio provides valuable insights on the complex physical phenomenon, helping to consolidate idea to maximize the drag reduction for ventilated cavitating vehicles.     

Study of air-ventilated cavity under model hull on water surface

The use of air cavities beneath ship hulls can lead to significant drag reduction. A study of air-ventilated cavities under a simplified hull has been undertaken. Experiments with a 56-cm-long stepped-hull model were carried in an open-surface water channel at flow velocities 28–86 cm/s. The air-cavity parameters were measured at different model positions. Different cavity forms, a strong growth of the cavity length with the flow velocity, and an optimal trim angle for the largest air-cavity area were identified. Numerical studies were conducted using a linear potential-flow method and the finite-volume viscous code Fluent. The computationally inexpensive three-dimensional potential-flow modeling predicted air-cavity shapes and provided qualitative agreement with the measured average length of the air cavity. Two-dimensional viscous modeling reasonably predicted macroscopic features and viscous effects in the air-cavity flow, while exaggerated the mixed-phase flow regions.     

Ships with ventilated cavitation in seaways and active flow control

Bottom ventilated cavitation has been proven as a very effective drag reduction technology for river ships and planning boats. The ability of this technology to withstand the sea wave impact usual for seagoing ships depends on the ship bottom shape and could be enhanced by some active flow control devices. Therefore, there is the need in numerical tools to estimate the effects of bottom changes and to design such devices. The fundamentals of active flow control for the ship bottom ventilated cavitation are considered here on the basis of a special model of cavitating flows. This model takes into account the air compressibility in the cavity, as well as the multi-frequency nature of the incoming flow in wavy seas and of the cavity response on perturbations by incoming flow. The numerical method corresponding to this model was developed and widely manifested with an example of a ship model tested in a towing tank at Froude numbers between 0.4 and 0.7.The impact of waves in head seas and following seas on cavities has been studied in the range of wavelengths from 0.45 to 1.2 of the model (or ship) length. An oscillating cavitator-spoiler was considered as the flow controlling devices in this study. The oscillation magnitude and the phase shift between cavitator oscillation and the incoming waves have been varied to determine the best flow control parameters. The main results of the provided computational analysis include oscillations of cavity surface, of the pressure in cavity and of the moment of hydrodynamic load on the cavitator. The major part of computations has been carried out for the flap oscillating at the frequency coinciding with the wave frequency, but the effect of a frequency shift is also analyzed.     

Three-dimensional wave patterns in long air cavities on a horizontal plane

Significant drag reduction of large displacement vessels can be achieved by applying multi-wave air cavities arranged on the hull bottom. Waves generated on the air–water interface of air cavities impose requirements on the dimensions of a hull recess that accommodates the air cavity. An approximate model for calculating wave patterns in the critical upstream part of long air cavities in a simplified, horizontal-plane geometry is presented in this paper. The influence of the recess planform boundaries and other factors on the wave patterns is studied parametrically. Some hydrodynamic aspects of multi-wave air cavities are discussed.     

An iterative scheme for two-dimensional supercavitating flow

In the present research, supercavitating potential flow is studied numerically by the boundary element method (BEM). Using the advantages of BEM, an iterative algorithm has been introduced to capture cavity boundary in two-dimensional symmetric flows. In this algorithm, the cavity length is known and used to find the related cavitation number and cavity profile. In order to obtain finite length cavities, a cusped cavity closure model has been employed. Applying this cavity closure model, it is possible to change the cavity closure profile and its specified length. By comparing the results of the present analysis with previous analytical and numerical solutions as well as the experimental data, it can be concluded that the present iterative numerical algorithm is reliable and can be applied with BEM or other numerical methods to predict the characteristics of a supercavitating flow. Moreover, the feasibility of the cavity capturing in a flow field with low cavitation number is especially attractive.     

Dynamic and diffusive growth of microbubbles near a two-dimensional hydrofoil

A technique for predicting the bubble growth along a two-dimensional hydrofoil with traveling bubble cavitation is presented. The method is based on the dynamic response of ambient microbubbles to the flow field and the subsequent diffusion of dissolved air into the flow field cavities. The bubble growth model is divided into three components, including the prediction of 1) the hydrofoil surface pressure distribution, 2) the ambient microbubble response to the pressure distribution, and 3) the diffusive mass flow rate. The hydrofoil velocity and pressure field is determined by two-dimensional thin airfoil theory. The microbubble response to the pressure field is given by the Rayleigh-Plesset equation with the addition of a mass diffusion term. The diffusion of dissolved gasses into the cavitation bubbles is determined by a solution to the steady-state diffusion equation under spherically symmetric convective flow. Results are given for the bubble wake of a NACA 66-006 (a = 0.8meanline) hydrofoil with traveling bubble cavitation. The effect of the relative velocity of the cavitation bubbles with respect to the surrounding water is investigated as well as the significance of the mass diffusion term in the Rayleigh-Plesset equation.     

Model test of the surface and submerged vehicles with the micro-bubble drag reduction

This study is based on the effective experiment observation and measuring technology to discuss the interaction influence between liquid turbulent boundary layer and a crowded group micro-bubbles. It is in order to understand and quantify the micro-bubbles clouds inside the turbulent boundary layer to eliminate the capacity of skin friction drag. Whenever the micro-bubbles are over supplied, pile up effect happened which makes micro-bubbles to integrate to each other as a large-size air film. Although they still have the drag reduction effect, the efficiency of drag reduction slowed down at this transition period. In the experiment of vertical type circulating water tunnel, when 1 μm porous medium is at 7 m/s flow speed, the C_v value at 0.056 has the best drag reduction efficiency of 26%. While 10 μm porous medium is at the same flow speed, the drag reduction efficiency is only around 23%.     

Numerical Study on the Vertical Water Exit of A Cylinder with Cavity

When a high-speed body with cavity passes through water-air free surface and exits water, its mechanical environment and dynamic characteristics change significantly due to the great difference in density and viscosity between water and air. With focusing on this problem, the Computational Fluid Dynamics (CFD) method is applied to perform numerical calculation on the process of this vapor-liquid-gas flow during the water exit of a high-speed cylinder, with the Volume of Fraction (VOF) multiphase flow interface-capturing techniques and the overset grid technology. After the verification and validation of the CFD model through mesh convergence study and a water-entry experiment, cavity evolution and flow characteristics including pressure and velocity distribution during the water exit are analyzed. The effects of different initial velocities on the pressure distribution and drag characteristics of the cylinder are investigated. Calculated results show that the cavity collapse during water exit causes strong pressure fluctuation on the cylinder; when the cylinder exits water enveloped in a supercavity, the pressure distribution on its wall surface and surrounding water region is relatively uniform, and the drag changes gently, and thus the cylinder has good motion stability.

     

Numerical simulation of the motion of an ice keel in a stratified flow

The results of the three-dimensional numerical simulation for the study of the stratification effect and wave processes associated with it on the drag of the underwater part of the hummocked ice are considered. The numerical model is based on the sampling of equations on a rectangular grid using the immersed boundary method that makes it possible to explicitly describe the interaction of moving ice with a stratified flow. The dependence of the drag force on the Froude number was established based on these calculations. This dependence has expressed points of maximum and minimum. The form of this dependence is common for the considered models of ice keels. The obtained estimations of drag force consistent with the known results of laboratory experiments show the need for the construction of parametrizations of the drag coefficient on the ice–ocean boundary, taking into account wave effects.     

Very Large Eddy Simulation of Cavitation from Inception to Sheet/Cloud Regimes by A Multiscale Model

The cavitating flow in different regimes has the intricate flow structure with multiple time and space scales. The present work develops a multiscale model by coupling the volume of fluid(VOF) method and a discrete bubble model(DBM), to simulate the cavitating flow in a convergent-divergent test section. The Schnerr-Sauer cavitation model is used to calculate the mass transfer rate to obtain the macroscale phase structure, and the simplified Rayleigh-Plesset equation is applied to simulate the growing and collapsing of discrete bubbles. An algorithm for bridging between the macroscale cavities and microscale bubbles is also developed to achieve the multiscale simulation. For the flow field, the very large eddy simulation(VLES) approach is applied. Conditions from inception to sheet/cloud cavitation regimes are taken into account and simulations are conducted. Compared with the experimental observations, it is shown that the cavitation inception, bubble clouds formation and glass cavity generation are all well represented, indicating that the proposed VOF-DBM model is a promising approach to accurately and comprehensively reveal the multiscale phase field induced by cavitation.     

高雷诺数下近壁圆柱绕流数值模拟与分析

近壁圆柱绕流问题在海底悬跨管道的研究中具有重要的意义。在绕流阻力、升力以及海底土壤的耦合作用下,海底管道所发生的移位、悬跨等现象对于海底管道的安全运行构成了很大的威胁。正确预测各种绕流条件下管流之间的作用力是保证油气管道安全的首要任务。海底管道在极端海洋环境条件下的管、流相互作用为高雷诺数绕流问题,处于高雷诺数下的绕流模拟比处于低雷诺数下的绕流模拟要复杂很多,它需要更精细的网格以及合适的湍流模型。此文对处于悬跨状态下的海底管道进行数值研究,给出不同间隙比下海流绕流海底管道的流场结构形态,分析了间隙比对绕流阻力和绕流升力的影响,为进一步研究海底悬跨管道的受力和变形提供载荷边界数据。     

Numerical simulation of micro-bubble drag reduction using population balance model

The phenomenon of drag reduction by the injection of micro-bubbles into turbulent boundary layer has been investigated using an Eulerian-Eulerian two-fluid model. Multiple-size group (MUSIG) based on population balance models, which resolve a wide range of bubble sizes taking into account the bubble break-up and coalescence have been used for this purpose. The simulated results are compared against the experimental findings of Madavan et al. [1984. Reduction of turbulent skin friction by micro-bubbles. Physics of Fluids 27, 356-363] and also other numerical studies explaining the sophisticated phenomena of drag reduction. For the two Reynolds number cases considered, the buoyancy with the plate on the bottom configuration is investigated, as from the experiments it is seen that buoyancy seem to play a role in the drag reduction. Numerical model employed in the investigation comprises of a micro-bubble laden flow wherein two independent sets of Reynolds averaged Navier-Stokes (RANS) transport equations were used to describe both the phases of the flow. The shear stress transport (SST) turbulence model is used as the turbulent closure for the primary phase and a zero equation turbulence model is used for the micro-bubbles. Change in the mean streamwise velocity profiles, void fraction, turbulence modification and other results are presented and discussed with corresponding change in the gas injection rates. The complex mechanism of drag reduction are scrutinised and explained in context to our numerical findings. Special attentions have been also devoted to divulge the effect of bubble coalescence and break-up caused by random collision and turbulent impact. Numerical results showed good agreement for the skin-friction coefficients against experimental data throughout various air injection rates. The MUSIG model was found to be one of the best candidates to resolve the bubble dynamics in micro-bubble-induced drag reduction problems.     

Deterministic and Stochastic Predictions of Motion Dynamics of Cylindrical Mines Falling Through Water

A physics-based computational model has been developed that is capable of reliably predicting the motion of a 3-D mine-shaped object impacting the water surface from the air, and subsequently, dropping through the water toward the sea bottom. This deterministic model [mine's six-degree-of-freedom dynamics (MINE6D)] accounts for six-degree-of-freedom motions of the body including unsteady hydrodynamic interaction effects. MINE6D allows for physics-based modeling of other hydrodynamic effects due to water impact, viscous drag associated with flow separation and vortex shedding, air entrainment, and realistic flow environments. To demonstrate the efficacy of the model, we compare deterministic MINE6D predictions with tank drops tests and field measurements. MINE6D captures the myriad of complex 3-D motions of cylindrical mines observed in field and laboratory experiments. For relatively simple straight motions, it obtains quantitative comparisons with the field measurements for the kinematics of mines freely dropping in the water including water impact and air cavity effects. In practical applications, the environments are often quite irregular, and the releasing conditions are also with uncertainties. To provide some guidance in understanding and interpreting statistical characterizations of mine motions in practical environments, we perform Monte Carlo simulation using MINE6D. These statistical results are not only the essential input for stochastic bottom impact and burial predictions of mines but also useful for the design of mines.     

Robust design of microbubble drag reduction in a channel flow using the Taguchi method

This study attempts to obtain optimum parametric levels for robust design of the microbubble drag reduction in a turbulent channel flow. This work was carried out experimentally by measuring the frictional resistance on the upper wall of the channel to analyze the efficiency of drag reduction. Considering the mean flow speed as an indicative factor, several controllable factors that influence the effect of microbubble drag reduction were investigated in this work by using the Taguchi method. The controllable factors in this study were the amount of air injected, area of air injection, and microbubble size. For the condition of optimum parametric levels, the effect of drag reduced could reach up to 21.6%.     

On the limiting parameters of artificial cavitation

Artificial cavitation, or ventilation, is produced by releasing gas into the liquid flow. One of the objectives of creating this multiphase flow is to reduce frictional and sometimes wave resistance of a marine vehicle completely or partially immersed in the water. Flows around surface ships moving along the water–air boundary are considered in this paper. It is favorable to achieve a negative cavitation number in the developed cavitating flow under the vessel’s bottom in order to generate additional lift. Cavities, formed in the flow, have limiting parameters that are affected by propulsion and lift-enhancing devices. Methods for calculating these influences and the results of a parametric study are reported.     

Computational and Empirical Investigation of Propeller Tip Vortex Cavitation Noise

In this study, non-cavitating and cavitating flow around the benchmark DTMB 4119 model propeller are solved using both viscous and potential based solvers. Cavitating and non-cavitating propeller radiated noises are then predicted by using a hybrid method in which RANS(Reynolds-averaged Navier-Stokes) and FWH(Ffowcs Williams Hawkings) equations are solved together in open water conditions. Sheet cavitation on the propeller blades is modelled by using a VOF(Volume of Fiuld) method equipped with Schnerr-Sauer cavitation model.Nevertheless, tip vortex cavitation noise is estimated by using two different semi-empirical techniques, namely Tip Vortex Index(TVI, based on potential flow theory) and Tip Vortex Contribution(TVC). As the reference distance between noise source and receiver is not defined in open water case for TVI technique, one of the outputs of this study is to propose a reference distance for TVI technique by coupling two semi-empirical techniques and ITTC distance normalization. At the defined distance, the starting point of the tip vortex cavitation is determined for different advance ratios and cavitation numbers using potential flow solver. Also, it is examined that whether the hybrid method and potential flow solver give the same noise results at the inception point of tip vortex cavitation.Results show that TVI method based on potential flow theory is reliable and can practically be used to replace the hybrid method(RANS with FWH approach) when tip vortex cavitation starts.     

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.     

带有侧摩擦和底摩擦的绕岛理论

绕岛理论来自于Sverdrup理论,被广泛用于估计和分析通过岛屿之间海峡的输运情况。以往的研究得到了带有侧摩擦或底摩擦的单岛理论或多岛理论。本文在线性情况下考虑了风驱动环流下的解析模型。在同时考虑侧摩擦和底摩擦的情况下,推导出了岛屿周围输运流函数的解析解,并给出了通过岛屿之间通道的流量输运。其结果与Wajsowicz相似,但摩擦常数表示不同的值。从解析解上看,摩擦常数与侧摩擦和底摩擦之间的关系比较复杂,为了推导出它们之间的相互作用原理,本文在正压β平面上随机选取了一些侧摩擦和底摩擦的值。结果表明,在构成摩擦常数方面,侧摩擦和底摩擦近似呈线性关系。我们研究了宽度对通道输运值的影响,结果表明摩擦在一定宽度内提高了流量,这种现象和只考虑侧摩擦时比较相似。本文也比较了在不同深度下的流量,发现当水平涡粘性系数和底部拖曳系数固定时,水深越大,输运减少率越小。为了进一步揭示侧摩擦和底摩擦耗散的联合作用,在两个岛屿的情况下,本文在不同宽度的通道中与Wajsowicz的只考虑底摩擦或侧摩擦的模型进行了比较。结果表明,当通道比较窄,尤其是在小于Munk边界层厚度时,侧摩擦的作用大于底摩擦。当通道宽度远大于Munk边界层厚度时,底摩擦的作用大于侧摩擦。将模型应用到印尼贯穿流,得到大约20%的输运减少量。     

The influence of suspended cohesive sediments on boundary-layer structure and erosive activity of turbulent seawater flow

Velocity and suspension measurements in the logarithmic layer of hydraulically smooth turbulent tidal flow from the North Sea are reported. The data were not compatible with the assumption of Newtonian flow for the experimental seawater—clay suspension.Laboratory measurements were initiated with mud and seawater from the North Sea in which the boundary-layer structure of this two-phase flow was measured down into the viscous sublayer. The dilute seawater—clay suspension was a mixture of illite, kaolinite and chlorite minerals with concentrations less than 380 mg/l and exhibited turbulent drag reduction.By reviewing flow measurements of other authors it is suggested that turbulent drag reduction occurs on a geophysical scale if the flows transport cohesive sediments. It is proposed that drag reduction is caused by dynamic interaction between turbulent shear strain in the flow and deformation of aggregates.As a consequence, the values of the critical friction velocity $\text{u}{}_{\mathrm{<mtext>1\; </mtext><mtext>crit</mtext>}}$ and of erosion rates must be reviewed for cohesive bottom materials. Normally they were obtained under the assumption of a Newtonian flow structure which is not applicable if the flow transports cohesive sediments.To detect the occurrence of drag reduction in geophysical boundary layers (hydraulically smooth), flow measurements must be performed down into the viscous sublayer. The adequate velocity sensors must have a diameter of ?1 mm.