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Modelling and Simulation of Moored-Floating Structures Using the Tension-Element-Method 系泊-浮式结构的张力单元法建模与仿真
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-77776
T. Martin, A. Kamath, H. Bihs
The application of a discrete mooring model for floating structures is presented in this paper. The method predicts the steady-state solution for the shape of an elastic cable and the tension forces under consideration of static loads. It is based on a discretization of the cable in mass points connected with straight but elastic bars. The successive approximation is applied to the resulting system of equations which leads to a significant reduction of the matrix size in comparison to the matrix of a Newton-Raphson method. The mooring model is implemented in the open-source CFD model REEF3D. The solver has been used to study various problems in the field of wave hydrodynamics and fluid-structure interaction. It includes floating structures through a level set function and captures its motion using Newton and Euler equations in 6DOF. The fluid-structure interaction is solved explicitly using an immersed boundary method based on the ghost cell method. The applications show the accuracy of the solver and effects of mooring on the motion of floating structures.
本文介绍了离散系泊模型在浮式结构中的应用。该方法预测了考虑静载荷作用下弹性索的形状和张力的稳态解。它是基于索在质量点上的离散化,这些质量点与直但有弹性的杆相连。将逐次逼近应用于所得到的方程组,与牛顿-拉夫逊方法的矩阵相比,矩阵大小显著减小。系泊模型在开源CFD模型REEF3D中实现。该求解器已用于波浪流体力学和流固耦合领域的各种问题的研究。它通过水平集函数包含浮动结构,并使用牛顿和欧拉方程在6DOF中捕获其运动。采用基于鬼胞法的浸入边界法明确求解了流固耦合问题。应用表明了求解器的准确性以及系泊对浮体运动的影响。
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引用次数: 5
Adaptive Grid Refinement for Two-Phase Offshore Applications 海上两相应用的自适应网格优化
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-77309
P. V. D. Plas, A. Veldman, H. Seubers, J. Helder, K. Lam
In the past, the CFD simulation method ComFLOW has been successfully applied in a wide range of offshore applications, involving wave simulations and impact calculations. In many of these calculations the area of interest comprises a small part of the domain and remains fixed in time, which allows for efficient grid refinement by means of grid stretching or static local refinement. However, when trying to accurately resolve the surface dynamics and kinematics of irregular and breaking waves, the resolution requirements are strongly time-dependent and difficult to predict in advance. Efficient grids can only be obtained by means of time-adaptive refinement. A Cartesian block-based refinement approach is followed which allows for efficient grid adaptation, with moderate overhead. An array-based data structure is employed which exploits the semi-structured nature of the Cartesian block grid. Currently we are testing the method with the simulation of lifeboat drops in regular and irregular wave conditions. This poses several challenges such as accurately imposing the incoming waves and modifying the absorbing boundary conditions to support two-phase flow. To reduce the wall-clock time, the simulation method has been parallelized.
在过去,CFD模拟方法ComFLOW已经成功地应用于广泛的海上应用,包括波浪模拟和冲击计算。在许多这样的计算中,感兴趣的区域只占域的一小部分,并且随着时间的推移保持固定,这允许通过网格拉伸或静态局部细化的方式进行有效的网格细化。然而,当试图准确地解析不规则波和破碎波的表面动力学和运动学时,分辨率要求具有强烈的时间依赖性,难以提前预测。有效的网格只有通过时间自适应细化才能得到。遵循基于笛卡尔块的改进方法,允许有效的网格适应,开销适中。采用了基于数组的数据结构,利用了笛卡尔块网格的半结构化特性。目前,我们正在对该方法进行测试,模拟救生艇在规则和不规则波浪条件下的下降。这就提出了一些挑战,如准确施加入射波和修改吸收边界条件以支持两相流。为了减少挂钟时间,仿真方法进行了并行化处理。
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引用次数: 4
Numerical Analysis of Debris Containment Grid Fluid-Body Interaction 碎片围护网格流-体相互作用的数值分析
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-78106
Eduardo Tadashi Katsuno, Gustavo de Goes Gomes, Felipe Santos de Castro, J. Dantas
Debris containment grid is an important part of hydroelectric power plant, since it retains objects, preventing damage to the turbine. In the case of the Santo Antonio hydropower plant, located in the Amazon rainforest, in the north of Brazil, the most significant debris are logs. This paper aims to analyze the interaction between several log boom modules (type of debris containment grids developed specifically for containing logs) present in a debris containment line present in Santo Antonio hydropower plant, as well as its interactions with the fluid, varying the advance velocity and side-slip angle. The analysis of the fluid-body interaction is performed using CFD software with Finite Volume Method approach. The problem is divided into steps. Firstly, one log boom module is simulated with several velocities and side-slip flow angle, obtaining a relation between forces, moments and movements. Next, in order to save the expected computational cost, the module is analyzed and compared through the porosity approach. Finally, the analysis of a line with several log boom modules, including the interaction between each module, is carried out. The results of the simulations will allow to perform an analysis of the line stability, obtaining the forces, moments and movements of each log boom module, observing its influence in the log boom line. With a fluid-body hydrodynamic analysis of several modules in a line, data are provided for a structural analysis. Since the porosity approach is used to reduce the computational cost, this paper also contributes to similar cases, with a main interest in larger scales of forces and movements.
碎片围护网是水电厂的重要组成部分,它能截留物体,防止水轮机受损。在位于巴西北部亚马逊雨林的圣安东尼奥水电站中,最重要的碎片是原木。本文旨在分析圣安东尼奥水电站碎屑围护线中存在的几个原木吊杆模块(专门为容纳原木而开发的碎屑围护网格类型)之间的相互作用,以及它与流体的相互作用,改变前进速度和侧滑角。采用有限体积法,利用CFD软件进行了流-体相互作用分析。这个问题分为几个步骤。首先,对一个具有不同速度和侧滑流角的原木臂架模块进行了仿真,得到了力、力矩和运动之间的关系。其次,为了节省预期的计算成本,通过孔隙度法对模块进行分析比较。最后,对一条具有多个原木吊杆模块的线路进行了分析,包括各模块之间的相互作用。模拟的结果将允许对管线稳定性进行分析,获得每个原木吊杆模块的力、力矩和运动,观察其对原木吊杆管线的影响。通过对一条直线上多个模块的流体力学分析,为结构分析提供了数据。由于孔隙度方法用于减少计算成本,因此本文也有助于类似的情况,主要关注更大尺度的力和运动。
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引用次数: 2
A 3D Coupled Fluid-Flexible Multibody Solver for Offshore Vessel-Riser System 海洋船舶隔水管系统三维耦合流-柔性多体求解器
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-78281
V. Joshi, P. S. Gurugubelli, Y. Law, R. Jaiman, Peter Francis Bernad Adaikalaraj
Precise position and motion control of offshore vessels is often challenging, especially in harsh environment due to highly nonlinear dynamic loads from free-surface ocean waves and currents. In addition, coupled nonlinear effects of risers and mooring cables connected to the vessel can lead to unexpected responses, thus justifying the significance of modeling these nonlinear coupled effects for safer and cost-effective design and operation of offshore structures. In this study, a fully coupled multi-field fluid-structure-interaction (FSI) solver is developed to simulate the wave- and flow-induced vibration of the flexible multibody system with constraints (viz., vessel-riser system) in a turbulent flow. The structural domain with multibody systems is solved using nonlinear co-rotational finite element method, whereas the fluid domain is solved using Petrov-Galerkin finite element method for moving boundary Navier-Stokes solutions. A partitioned iterative scheme based on non-linear interface force corrections is employed for coupling of the turbulent fluid-flexible multibody system with nonmatching interface meshes. Delayed Detached Eddy Simulation (DDES) via the Positivity Preserving Variational (PPV) method is employed for modeling turbulence effects at high Reynolds number. The free-surface ocean waves are modeled by the Allen-Cahn based phase-field method. We address two key challenges in the present variational coupled formulation. Firstly, the coupling of the incompressible turbulent flow with a system of nonlinear elastic bodies described in a co-rotated frame. Secondly, the two-phase coupling based on the phase-field approach to model the air-water interface. We then present the dynamics of coupled vessel-riser system studied in harsh environmental conditions with a view of developing a robust station keeping system. The proposed fully-integrated methodology based on the first principles of variational continuum mechanics removes many assumptions and empirically assigned parameters (e.g. drag and inertia coefficients) for modeling the surrounding fluid flow at high Reynolds number.
海上船舶的精确定位和运动控制往往具有挑战性,特别是在恶劣环境下,由于自由海面海浪和洋流的高度非线性动态载荷。此外,与船舶相连的隔水管和系泊电缆的耦合非线性效应可能导致意想不到的响应,因此,对这些非线性耦合效应进行建模对于更安全、更经济地设计和运行海上结构具有重要意义。在本研究中,开发了一个完全耦合的多场流固耦合(FSI)求解器来模拟具有约束的柔性多体系统(即容器-隔水管系统)在湍流中的波动和流致振动。多体系统的结构域采用非线性共旋转有限元法求解,流体域采用Petrov-Galerkin有限元法求解,运动边界采用Navier-Stokes解。采用一种基于非线性界面力修正的分段迭代方法对具有非匹配界面网格的湍流-柔性多体系统进行耦合。采用保正变分(PPV)方法进行延迟分离涡模拟(DDES),模拟高雷诺数湍流效应。采用基于Allen-Cahn的相场方法对自由海面海浪进行了模拟。我们解决了当前变分耦合公式中的两个关键挑战。首先,在共旋转框架中描述了不可压缩湍流与非线性弹性体系统的耦合。其次,采用基于两相耦合的相场法对气-水界面进行建模。然后,我们介绍了在恶劣环境条件下研究的耦合容器立管系统的动力学,以期开发一个鲁棒的站保持系统。该方法基于变分连续介质力学第一原理,消除了对高雷诺数下周围流体流动建模的许多假设和经验分配参数(如阻力系数和惯性系数)。
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引用次数: 5
CFD Simulations of Multi-Directional Irregular Wave Interaction With a Large Cylinder 大圆柱体多向不规则波相互作用的CFD模拟
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-77511
Weizhi Wang, A. Kamath, H. Bihs
Ocean waves are random by nature and can be regarded as a superposition of a finite number of regular waves travelling in different directions with different frequencies and phases. Cylinder-shaped objects are commonly present in most coastal structures. An irregular bottom topography has a significant influence on the wave behaviours and therefore the wave forces on the coastal structures. A numerical approach that is able to calculate the wave forces on a cylinder in a multi-directional irregular wave field over an irregular bottom is desired. As Computational Fluid Dynamics (CFD) is able to represent most of the wave behaviour with few assumptions, it is considered to be an attractive option to address these issues. The open-source CFD wave model REEF3D has shown good performances in simulating wave propagation over irregular bottoms and a good prediction of wave forces on a cylinder in a uni-directional wave field, yet the ability to calculate the wave force in a multi-directional irregular sea needs to be validated. Therefore, this paper attempts to simulate the multi-directional random sea interaction with a large cylinder using REEF3D and validate the results. A novel approach of multi-directional irregular wave generation method in a CFD-based numerical wave tank is introduced. Only even-bottom tanks are considered in this study, leaving the irregular bottom simulation for future studies. Furthermore, among many factors that influence the wave forces, this paper focuses particularly on the effect of the wave steepness. The effects of wave steepness in regular waves, uni-directional irregular waves and multi-directional irregular waves are investigated. Goda’s JONSWAP frequency spectrum and the frequency-independent Mitsuyasu directional spreading function are used to generate the multi-directional irregular waves. The wave forces due to the multi-directional irregular waves in the numerical tank are compared with experimental data. The performance of the CFD simulation is analysed and discussed.
海浪本质上是随机的,可以看作是有限数量的规则波以不同的频率和相位向不同方向传播的叠加。圆柱状物体通常存在于大多数海岸结构中。不规则的海底地形对波浪行为有重大影响,因此对海岸结构的波浪力也有重大影响。需要一种能够在不规则底部上的多向不规则波场中计算圆柱体上波浪力的数值方法。由于计算流体动力学(CFD)能够在很少的假设下表示大多数波浪行为,因此它被认为是解决这些问题的一个有吸引力的选择。开源CFD波浪模型REEF3D在模拟不规则海底波浪传播和预测单向波场中圆柱体波浪力方面表现良好,但在多向不规则海中波浪力的计算能力有待验证。因此,本文尝试使用REEF3D模拟大型圆柱体的多向随机海面相互作用,并对结果进行验证。介绍了一种基于cfd数值波槽的多向不规则波生成方法。本研究只考虑了均匀底槽,将不规则底槽的模拟留到以后的研究中。此外,在影响波浪力的诸多因素中,本文重点讨论了波浪陡度的影响。研究了波浪陡度对规则波、单向不规则波和多向不规则波的影响。利用Goda的JONSWAP频谱和与频率无关的Mitsuyasu定向扩散函数产生多向不规则波。对数值槽内多向不规则波作用下的波浪力与实验数据进行了比较。对CFD仿真的性能进行了分析和讨论。
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引用次数: 9
Full-Scale Reynolds Number VIV Testing of Tri-Helically Grooved Drill Riser Buoyancy Module 三螺旋槽钻隔水管浮力模块全尺寸雷诺数VIV测试
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-78605
Collin Gaskill, Jie Wu, Decao Yin
A newly developed Tri-Helically Grooved drilling riser buoyancy module design was tested in the towing tank of SINTEF Ocean in June 2017. This new design aims to reduce riser drag loading and suppress vortex-induced vibrations (VIV). Objectives of the test program were two-fold: to assess the hydrodynamic performance of the design allowing for validation of previous computational fluid dynamics (CFD) studies through empirical measurements, and, to develop a hydrodynamic force coefficient database to be used in numerical simulations to evaluate drilling riser deformation due to drag loading and fatigue lives when subjected to VIV. This paper provides the parameters of the testing program and a discussion of the results from the various testing configurations assessed. Tests were performed using large scale, rigid cylinder test models at Reynolds numbers in the super-critical flow regime, defined as starting at a Reynolds number of Re = 3.5 × 105 – 5.0 × 105 (depending on various literatures) and continuing until Re = 3 × 106. Towing tests, with fixed and freely oscillating test models, were completed with both a bare test cylinder and a test cylinder with the Tri-Helical Groove design. Additional forced motion tests were performed on the helically grooved model to calculate lift and added mass coefficients at various amplitudes and frequencies of oscillation for the generation of a hydrodynamic force coefficient database for VIV prediction software. Significant differences were observed in the hydrodynamic performance of the bare and helically grooved test models considering both in-line (IL) drag and cross-flow (CF) cylinder excitation and oscillation amplitude. For the helically grooved model, measured static drag shows a strong independence from Reynolds number and elimination of the drag crisis region with an average drag coefficient of 0.63. Effective elimination of VIV and subsequent drag amplification was observed at relatively higher reduced velocities, where the bare test model shows a significant dynamic response. A small level of expected response for the helically grooved model was seen across the lower range of reduced velocities. However, disruption of vortex correlation still occurs in this range and non-sinusoidal and highly amplitude-modulated responses were observed.
2017年6月,新开发的三螺旋槽钻井隔水管浮力模块设计在SINTEF Ocean拖曳箱中进行了测试。这种新设计旨在减少隔水管阻力载荷并抑制涡激振动(VIV)。测试计划的目的有两个:一是通过经验测量来评估设计的水动力性能,从而验证之前的计算流体动力学(CFD)研究;二是开发一个水动力系数数据库,用于数值模拟,以评估钻井隔水管因阻力载荷和疲劳寿命而产生的变形。本文提供了测试程序的参数,并讨论了各种测试配置评估的结果。试验采用超临界流态雷诺数下的大型刚性圆柱体试验模型进行,定义为从雷诺数Re = 3.5 × 105 - 5.0 × 105(取决于各种文献)开始,一直持续到Re = 3 × 106。采用固定和自由摆动两种试验模型,分别采用裸试验缸和三螺旋槽试验缸进行拖曳试验。在螺旋槽模型上进行了额外的强迫运动试验,计算了不同振荡幅度和频率下的升力系数和附加质量系数,为涡激振动预测软件生成了水动力力系数数据库。考虑直线(IL)阻力和横流(CF)圆柱体激励和振荡幅值,裸槽和螺旋槽试验模型的水动力性能存在显著差异。对于螺旋槽模型,实测静阻力与雷诺数无关,消除了阻力危机区,平均阻力系数为0.63。在相对较高的减速速度下,观察到有效消除了VIV和随后的阻力放大,其中裸测试模型显示出显着的动态响应。在降低速度的较低范围内,螺旋槽模型的预期响应水平很小。然而,在这个范围内仍然会出现涡旋相关的破坏,并且观察到非正弦和高度振幅调制的响应。
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引用次数: 2
Development of a Lifting-Line-Based Method for Preliminary Propeller Design 基于升力线的螺旋桨初步设计方法的发展
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-77995
J. R. Chreim, M. Pimenta, J. Dantas, G. Assi, Eduardo Tadashi Katsuno
A novel formulation for marine propellers based on adaptations from wing lifting-line theory is presented; the method is capable of simulating propellers with skewed and raked blades. It also incorporates the influence of viscosity on thrust and torque from hydrofoil data through a nonlinear scheme that changes the location of the control points iteratively. Several convergence studies are conducted to verify the different aspects of the numerical implementation and the results indicate satisfactory convergence rates for Kaplan, KCA, and B-Troost propellers. It is expected that the method accurately describes thrust, torque, and efficiency under the moderately loaded propeller assumption.
提出了一种基于机翼升力线理论的船用螺旋桨新公式;该方法能够模拟具有倾斜和倾斜叶片的螺旋桨。它还通过迭代改变控制点位置的非线性方案,结合了粘度对水翼数据的推力和扭矩的影响。为了验证数值实现的不同方面,进行了几项收敛研究,结果表明Kaplan、KCA和B-Troost螺旋桨的收敛率令人满意。期望该方法能准确地描述中等载荷螺旋桨假设下的推力、扭矩和效率。
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引用次数: 3
Large Eddy Simulation of Cross Flow in Pipe Junction 管交界处交叉流动的大涡模拟
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-77751
Jiajun Chen, Yue Sun, Hang Zhang, D. Feng, Zhiguo Zhang
Mixing in pipe junctions can play an important role in exciting force and distribution of flow in pipe network. This paper investigated the cross pipe junction and proposed an improved plan, Y-shaped pipe junction. The numerical study of a three-dimensional pipe junction was performed for calculation and improved understanding of flow feature in pipe. The filtered Navier–Stokes equations were used to perform the large-eddy simulation of the unsteady incompressible flow in pipe. From the analysis of these results, it clearly appears that the vortex strength and velocity non-uniformity of centerline, can be reduced by Y-shaped junction. The Y-shaped junction not only has better flow characteristic, but also reduces head loss and exciting force. The results of the three-dimensional improvement analysis of junction can be used in the design of pipe network for industry.
管交界处的混合对管网的激励力和流动分布起着重要的作用。本文对交叉管结点进行了研究,提出了一种改进方案——y型管结点。通过对三维管结点的数值计算,提高了对管内流动特性的认识。采用过滤后的Navier-Stokes方程对管道内非定常不可压缩流动进行了大涡模拟。从分析结果可以看出,采用y型结可以降低中心线的涡强度和速度不均匀性。y型接头不仅具有更好的流动特性,而且减小了水头损失和激励力。结点三维改进分析的结果可用于工业管网的设计。
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引用次数: 0
Effect of Secondary Motion on Hydrodynamics of a Cylinder Oscillating in Still Fluid 二次运动对静止流体中圆柱振荡流体力学的影响
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-78443
L. Baranyi, E. Konstantinidis
In this study, we conducted numerical simulations to compute the hydrodynamic forces acting on a circular cylinder undergoing bidirectional oscillations in still fluid. The simulations correspond to the regime of attached laminar two-dimensional flow at low values of the Keulegan-Carpenter number (KC ≤ 5) and Reynolds numbers from 35 to 1000 based on the primary motion of the cylinder. The effect of a secondary motion transverse to the primary motion having twice the frequency and a fifth of the amplitude of the latter is investigated and the results are compared with the corresponding case of unidirectional motion and theoretical predictions from Stokes–Wang theory. The results for unidirectional motion show that the computed force in-line with the motion agree well with theory for KC < 1 and KCRe > 100. The agreement between computations and theory improves as KC decreases and Re increases. The addition of a secondary motion with different phase angles with respect to the primary motion did not have any observable effect on the force acting along the direction of the primary motion compared to that for the same unidirectional motion, although it had a marked effect on the distribution of vorticity around the cylinder. The forces on the cylinder undergoing bidirectional oscillations could be well predicted from Stokes–Wang theory applied in each individual direction for the range of parameters examined in this study. The present study provides insight into the relationship between the generation of vorticity around an oscillating cylinder and the fluid forces acting on it.
在这项研究中,我们进行了数值模拟,以计算作用在静止流体中进行双向振荡的圆柱体上的水动力。模拟结果表明,基于圆柱的初始运动,在Keulegan-Carpenter数(KC≤5)和雷诺数(35 ~ 1000)较低的数值范围内,二维层流流场是附着的。研究了频率为主运动的两倍、幅度为主运动的五分之一的二次运动对主运动的横向影响,并将结果与单向运动的相应情况和Stokes-Wang理论的理论预测进行了比较。单向运动的计算结果表明,当KC < 1和KCRe < 100时,计算得到的与运动一致的力与理论吻合较好。随着KC的减小和Re的增大,计算与理论的一致性提高。与相同的单向运动相比,加入与主运动相位角不同的次运动对沿主运动方向作用的力没有任何可观察到的影响,尽管它对圆柱体周围涡度的分布有明显的影响。通过Stokes-Wang理论,可以很好地预测圆柱体上经历双向振荡的力,该理论适用于本研究中检查的参数范围内的每个方向。本研究提供了关于在振荡圆柱周围产生涡度和作用在其上的流体力之间的关系的见解。
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引用次数: 0
Research on Trailing Cavity of Underwater Vehicles Based on Potential Flow Theory 基于势流理论的水下航行器尾空腔研究
Pub Date : 2018-06-17 DOI: 10.1115/OMAE2018-78676
Zeyu Shi, X. Yao, Jiaolong Zhao, Longquan Sun, Yue Tian
In the exceeding water process of underwater vehicles, the existing of trailing cavity will have distinct effects on the hydrodynamic characteristics of vehicles. Recent researches mostly leave gravity effect out of consideration, while the gravity will affect trailing cavity characteristics and then affect the hydrodynamic characteristics of vehicles. In this study, we research the effect of gravity on the trailing cavity of underwater vehicles. Firstly, a complex boundary model which taken partial cavity into consideration is established based on potential flow theory and a program according to this model is written. Because all flow parameter has nothing to do with the radial location, the research problem can be simplified as a two-dimensional problem and studied in polar coordinates. With regularization of the length of the navigation calculation model, infinity to flow velocity and the distance pressure, research domain can be represented by plane in the containing slit. The program is proved to be effective by comparison the results with the data in existing papers. Finally, we calculate the trailing cavity forms of a cone and an underwater vehicle under different cavitation numbers and Froude numbers to study the rules of trailing cavity forms changing with cavitation number and Froude number. Under the same number of Froude, the cavity size of the rear part of vehicle gradually decreases with the increasing cavitation number, and the maximum radius of the cavity equals to the biggest size of the tail radius of the vehicle. Under the same cavitation number bodies, vehicle trailing cavity length gradually increases with the increase of Froude number, but radius of the cavity of the vehicle changed little, the largest radius is equivalent to the tail radius of the vehicle.
在潜航器的过水过程中,尾空腔的存在会对潜航器的水动力特性产生明显的影响。目前的研究大多没有考虑重力效应,而重力会影响尾腔特性,进而影响车辆的水动力特性。在本研究中,我们研究了重力对水下航行器尾腔的影响。首先,基于势流理论建立了考虑局部空腔的复杂边界模型,并根据该模型编写了程序。由于所有流动参数都与径向位置无关,因此可以将研究问题简化为二维问题,在极坐标下进行研究。通过对导航计算模型长度的正则化、对流速和距离压力的无限大,将研究区域用含缝内的平面表示。通过与已有文献数据的比较,证明了该程序的有效性。最后,对不同空化数和弗劳德数条件下锥体和潜航器的尾空腔形态进行了计算,研究了尾空腔形态随空化数和弗劳德数的变化规律。在相同的弗劳德次数下,随着空化次数的增加,车辆后部空化尺寸逐渐减小,空化最大半径等于车辆尾部半径的最大尺寸。在相同空化体数下,随着弗劳德数的增加,车辆尾部空腔长度逐渐增大,但车辆的空腔半径变化不大,最大半径相当于车辆的尾部半径。
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引用次数: 0
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