Shape optimization of two-dimensional cavitators in supercavitating flows, using NSGA II algorithm

The reduction of energy consumption of high speed submersible bodies is an important challenge in hydrodynamic researches. In this paper, shape optimization of two-dimensional cavitators in supercavitating flows is studied. A two dimensional supercavitation potential flow passes a symmetric two dimensional cavitator, which is placed perpendicular to the flow in a channel of infinite length and immediately a cavity is formed behind the cavitator. This is because of the generation of a gas or vapor cavity between the body and the surrounding liquid due to the change in a high speed flow direction passing the cavitator. Drag force acting on this supercavitating body dictates the thrust requirements for the propulsion system, to maintain a required cavity at the operating speed. Therefore, any reduction in the drag force, by modifying the shape of the cavitator, will lead to decrease this force. This study concentrates on the optimization of two dimensional cavitators in order to decrease drag coefficient for a specified after body length and velocity in a potential flow. To achieve this goal a multi-objective optimization problem is defined to optimize cavitator shapes in supercavitating flow. The so-called NSGA II (Non-dominated Sorting Genetic Algorithm) algorithm is used as an optimization method. Design parameters and constraints are obtained according to supercavitating flow characteristics and cavitator modeling and objective functions are generated using Linear Regression Method. The obtained results are compared with other classic optimization methods, like the weighted sum method, for validation.     

Numerical Study on Characteristics of Supercavitating Flow Around the Variable-Lateral-Force Cavitator

A control scheme named the variable-lateral-force cavitator, which is focused on the control of lift force, drag force and lateral forces for underwater supercavity vehicles was proposed, and the supercavitating flow around the cavitator was investigated numerically using the mixture multiphase flow model. It is verified that the forces of pitching, yawing, drag and lift, as well as the supercavity size of the underwater vehicle can be effectively regulated through the movements of the control element of the variable-lateral-force cavitator in the radial and circumferential directions. In addition, if the control element on either side protrudes to a height of 5% of the diameter of the front cavitator, an amount of forces of pitching and yawing equivalent to 30% of the drag force will be produced, and the supercavity section appears concave inwards simultaneously. It is also found that both the drag force and lift force of the variable-lateral-force cavitator decline as the angle of attack increases.     

Limiting heave response of a wave energy device by draft adjustment with upper surface immersion

Many studies have been published concerning the influence of the immersed shape (in still water) of a floating body on its response and power capture from ocean waves. With a few notable exceptions, much of this analysis has assumed small amplitude motion and linear models have been employed to predict response. The form of the upper surface of such a body has received little attention. Here, we show how the shape of the upper (top) surface of a floating body can be designed to ensure that the response amplitude of the body is within a specified value. This is of considerable importance to the survivability of wave energy devices. The approach used is to achieve a large increase of both natural period and hydrodynamic damping for only a small change of float mass. These two factors impose a hydrodynamic limit on the displacement which may be exploited to avoid the ‘end-stop’ problem often encountered in wave device design. To demonstrate the change of response, experimental measurements are presented of the response of an axisymmetric float with rounded base and conical upper surface with rounded perimeter due to a range of regular, irregular and focused wave conditions. Power extraction is not considered since the mechanically undamped response represents the worst case. In contrast to a simple, straight-sided axisymmetric float, a smaller change of mass is required to satisfy a particular response amplitude limit. Although a significant reduction is not expected, hydrodynamic damping may reduce with increasing physical scale, and this remains to be quantified.     

水下滑翔器整体外形设计及水动力性能分析

对水下滑翔器的整体外形设计与水动力性能进行研究。在Slocum等几种典型水下滑翔器样机的基础上,对滑翔器的主体和附体进行一体化设计,得到阻力最小的新型水下滑翔器构型设计。利用CFD方法对水下滑翔器进行模拟仿真,通过分析对比五种主体构型,得到了比较合理的主体线型,然后用正交设计方法和曲线拟合法对附体进行了优选工作,最后得到了性能更优的整体载体外形。模拟仿真实验表明,滑翔器在8°左右攻角航行时,具有最大的升阻比;和Slocum等经典样机相比,新的载体具有更好的水动力性能。通过上述研究工作,也可以缩短水下滑翔器研制周期,降低设计成本,并为水下滑翔器的更优设计提供了有力的技术指导和参考。     

Modeling and Simulation of Supercavity with Inertial Force in the Horizontal Curvilinear Motion

To make a curvilinear motion in the horizontal plane is one of the most contents for realizing the maneuverability of the supercavitating vehicle. It is significant to achieve the controllability and maneuverability of the vehicle in three dimensions both theoretically and practically on research. Models of angle of attack, gravity and inertial force effects on the supercavity in the horizontal curvilinear motion are established, respectively. The supercavity is simulated based on these models in combination with Logvinovich model and the unsteady gas-leakage rate model at the given ventilation rate, and the effect of the inertial force on it is analyzed numerically. Results show that the maximum deviation of the center line of the cross section of supercavity towards the outward normal direction of its trajectory increases as the cavitation number or curvature radius decrease and always occur in the tail because of the increase of inertial effects along the axis of supercavity from the cavitator when other models and flow parameters are constant for the given trajectory curvature. For the variable curvature, the supercavity sheds due to its instability caused by the time-varying angle of attack. The deviation increases along the length of supercavity if the curvature remains the same sign.     

Modeling and Simulation of Supercavity with Inertial Force in the Horizontal Curvilinear Motion简

To make a curvilinear motion in the horizontal plane is one of the most contents for realizing the maneuverability of the supercavitating vehicle. It is significant to achieve the controllability and maneuverability of the vehicle in three dimensions both theoretically and practically on research. Models of angle of attack, gravity and inertial force effects on the supercavity in the horizontal curvilinear motion are established, respectively. The supercavity is simulated based on these models in combination with Logvinovich model and the unsteady gas-leakage rate model at the given ventilation rate, and the effect of the inertial force on it is analyzed numerically. Results show that the maximum deviation of the center line of the cross section of supercavity towards the outward normal direction of its trajectory increases as the cavitation number or curvature radius decrease and always occur in the tail because of the increase of inertial effects along the axis of supercavity from the cavitator when other models and flow parameters are constant for the given trajectory curvature. For the variable curvature, the supercavity sheds due to its instability caused by the time-varying angle of attack. The deviation increases along the length of supercavity if the curvature remains the same sign.     

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.     

Hydrodynamics of A Flexible Riser Undergoing the Vortex-Induced Vibration at High Reynolds Number

This study proposed a method to obtain hydrodynamic forces and coefficients for a flexible riser undergoing the vortex-induced vibration (VIV), based on the measured strains collected from the scale-model testing with the Reynolds numbers ranging from 1.34E5 to 2.35E5. The riser is approximated as a tensioned spatial beam, and an inverse method based on the FEM of spatial beam is adopted for the calculation of hydrodynamic forces in the cross flow (CF) and inline (IL) directions. The drag coefficients and vortex-induced force coefficients are obtained through the Fourier Series Theory. Finally, the hydrodynamic characteristics of a flexible riser model undergoing the VIV in a uniform flow are carefully investigated. The results indicate that the VIV amplifies the drag coefficient, and the drag coefficient does not change with time when the CF VIV is stable. Only when the VIVs in the CF and IL directions are all steady vibrations, the vortex-induced force coefficients keep as a constant with time, and under “lock-in” condition, whether the added-mass coefficient changes with time or not, the oscillation frequency of the VIV keeps unchanged. It further shows that the CF excitation coefficients at high frequency are much smaller than those at the dominant frequency, while, the IL excitation coefficients are in the same range. The axial distributions of the excitation and damping region at the dominant frequency and high frequency are approximately consistent in the CF direction, while, in the IL direction, there exists a great difference.     

Drag Optimization of A Planing Vessel Based on the Stability Criteria Limits

China Ocean Engineering - One of the important phases of designing a craft is stability analysis and optimization of the drag force in cruise speed. In this research the longitudinal and lateral...     

Tension and Drag Forces of Flexible Risers Undergoing Vortex-Induced Vibration

This paper presents the results of an experimental investigation on the variation in the tension and the distribution of drag force coefficients along flexible risers under vortex-induced vibration (VIV) in a uniform flow for Reynolds numbers (Re) up to 2.2×10⁵. The results show that the mean tension is proportional to the square of the incoming current speed, and the tension coefficient of a flexible riser undergoing VIV can be up to 12. The mean drag force is uniformly and symmetrically distributed along the axes of the risers undergoing VIV. The corresponding drag coefficient can vary between 1.6 and 2.4 but is not a constant value of 1.2, as it is for a fixed cylinder in the absence of VIV. These experimental results are used to develop a new empirical prediction model to estimate the drag force coefficient for flexible risers undergoing VIV for Reynolds number on the order of 10⁵, which accounts for the effects of the incoming current speed, the VIV dominant modal number and the frequency.     

Forces on a smooth submarine pipeline in random waves — A comparative study

Forces on a smooth submarine pipeline, fixed horizontally near a plane boundary, have been investigated under random wave conditions. The submarine pipeline was subjected to Pierson-Moskowitz spectrum (P-M spectrum) at various energy levels. The water particle kinematics were computed based on the linear random wave model and the Morison equation was chosen as the wave force predictor model. The inline hydrodynamic coefficients of drag and inertia were evaluated using two different methods, one in the frequency domain and the other in the time domain. Five mathematical formulations were considered for the analysis of transverse wave forces and these were compared in terms of the correlation coefficient. The transverse force was also analyzed in terms of the transverse root mean square (rms) coefficient. The inline hydrodynamic coefficients of drag and inertia and the transverse rms coefficient were correlated with the Keulegan-Carpenter number or period parameter, the relative clearance of the pipeline from the bed and the depth parameter. Finally, the results of the random wave tests were compared with those of regular waves under similar pipeline conditions.     

A numerical study of second-order springing of an elastic body using higher-order boundary element method (HOBEM)

Second-order springing on an elastic body with forward speed is analyzed by numerical simulations. The boundary-value problem for the velocity potential is solved by means of the direct time-domain higher-order boundary element method (HOBEM). The free-surface boundary condition in the boundary-value problem is approximated on the mean surface up to second order by use of perturbation and Taylor-series expansion methods. The body boundary condition for an elastic body is derived with various quantities which are redefined in the generalized mode. These variables such as mode shape, normal vector, etc. are obtained by using directional derivative and continuum mechanics, and the same mathematical expressions are used to obtain several second-order generalized forces. To validate the numerical results, the second-order hydrodynamic force on the bottom-mounted rigid/elastic cylinders without forward speed is compared with other semi-analytic results. The property of second-order forces on an elastic ship is studied by changing the flexural rigidity and forward speed with elastic response. It is confirmed that the second-order velocity potential is important for a body with forward speed and investigation should be made more on numerical methods for accurate computation of the second-order velocity-potential force with forward speed.     

Hydrodynamic characteristic of synthetic jet steered underwater vehicle

In this paper, the hydrodynamic characteristic of a synthetic jet steered underwater vehicle is studied. The steering motion studied is the lateral motion and the yaw motion. The lateral motion is induced through the in-phase work of this two actuators and the yaw motion is realized through the out-of-phase work. The vehicle studied is REMUS AUV with synthetic jet actuator mounted inside. The hydrodynamic characteristic of the vehicle under different cruising speed is studied. The driving parameters of the SJ actuator keep invariant in different cases. When the two actuators work in phase, the average steering force is smaller than the thrust of the isolated actuator and keeps nearly invariant under different cruising speed. When the two actuators work out of phase, the average steering moment also keeps invariant with cruising speed. The mathematical model of the additional drag of the vehicle, the thrust of the actuator, the steering force as well as the steering moment is given. The velocity distribution is also given to assistant the analysis in this paper. From the analysis given it can be known the steering method based on SJ is realized through position control other than velocity control.     

水下滑翔器主体外形优化设计

对水下滑翔器主体外形的优化设计问题进行研究.首先,在考虑内部机械结构限制的条件下,建立了主体外形优化数学模型,并采用CFX计算了若干主体形状的绕流阻力.在此基础上建立了映射主体外形的尺寸参数与绕流阻力的BP神经网络.然后将建立的神经网络作为优化设计问题的目标函数,采用坐标轮换法对滑翔器主体外形进行了优化设计,确定了尺寸参数的最优解.     

A coupled model of submerged vegetation under oscillatory flow using Navier–Stokes equations

This work presents a new model for wave and submerged vegetation which couples the flow motion with the plant deformation. The IH-2VOF model is extended to solve the Reynolds Average Navier–Stokes equations including the presence of a vegetation field by means of a drag force. Turbulence is modeled using a k–ε equation which takes into account the effect of vegetation by an approximation of dispersive fluxes using the drag force produce by the plant. The plant motion is solved accounting for inertia, damping, restoring, gravitational, Froude–Krylov and hydrodynamic mass forces. The resulting model is validated with small and large-scale experiments with a high degree of accuracy for both no swaying and swaying plants. Two new formulations of the drag coefficient are provided extending the range of applicability of existing formulae to lower Reynolds number.     

Experimental Investigation and Numerical Analysis to Develop Low-Energy Large-Midwater Trawls

Fuel consumption in fisheries is a primary concern because of its effects on the environment and the costs incurred by fishermen. Many studies have been conducted to reduce the fuel consumption in fishing operations. Fuel consumption due to fishing gear during a fishing operation is generally related to the hydrodynamic resistance on the gear. This means that fuel consumption is proportional to the drag created by the towing speed. Based on numerical methods, this study suggests a new approach to reduce fuel consumption in fisheries. The results of the simulation are in good agreement with those of model experiments. The total as well as partial resistance forces on the gear are calculated by simulation. The simulation results suggest improved materials and gear structure for reducing the hydrodynamic forces on the gear while maintaining gear performance. The method for assessing the gear performance involves measuring the height and width of the net mouth. Furthermore, this study investigates the efficiency of a low-energy trawl from an economic point of view. The findings of this study will be useful in reducing greenhouse gas (GHG) emissions in fishing operations, and thereby contribute toward lowering fishing costs by saving fuel.     

Wave forces on submarine pipelines near a plane boundary

Forces induced by regular waves on submarine pipelines resting on as well as near a plane boundary and aligned parallel to wave fronts of the oncoming waves are investigated experimentally. The inline hydrodynamic coefficients of drag and inertia are evaluated through the use of Morison equation and the least squares method. The transverse force is analysed in terms of maximum transverse force and transverse root mean square (r.m.s.) coefficients. The resulting inline and transverse hydrodynamic coefficients are correlated with the period parameter or Keulegan-Carpenter number and relative clearance of the pipeline from the plane boundary. The effect of depth parameter on these coefficients and the correlation between maximum transverse force and transverse r.m.s. coefficients are also reported.     

Wake II model for hydrodynamic forces on marine pipelines including waves and currents

The Wake II model for the determination of the hydrodynamic forces on marine pipelines is extended to include currents and waves. There are two main differences between the Wake II and the traditional model. First, in the Wake II model the velocity is modified to include the pipe's encounter with the wake flow when the velocity reverses. Second, the model uses time dependent drag and lift coefficients. The flow field is assumed to be the linear superposition of regular waves and uniform current and is treated as wave only but in two different phases. The model requires eight empirical parameters that are obtained from comparisons with field data for various Keulegan–Carpenter numbers and current to wave ratios. The effective velocity and the force predictions are compared with field data from Exxon Production Research Company and with the conventional model. The model gives satisfactory results and predicts lift forces that in shape, magnitude and phase relative to the velocity are in very close agreement with measured forces. For the horizontal forces the results are very accurate. A substantial improvement is obtained over the predictions with the conventional model. This work is applicable to the design of submarine pipelines laying on the sea bottom in water depths where waves or waves and currents contribute to the hydrodynamic forces.     

Hydrodynamic Forces on Smooth Inclined Cyh''''nders in Oscillatory Flow

-The hydrodynamic forces on a smooth inclined circular cylinder exposed to oscillating flow were experimentally investigated at Reynolds number (Re) in the range 40000-200000 and Keulegan-Capenter number (KC) in the interval from 5-40. In the test, Re number and KC number were varied systematically. The inertia force coefficient (Cu) and the drag force coefficient (CD) in Morison equation were determined from the measured loads and the water particle kinematics. In this analysis a modified form of Morison equation was used since it uses the normal velocity and acceleration. Thus, the applicability of the Cross Flow Principle was assumed. This principle, simply stated, is as follows: the force acting in the direction normal to the axis of a cylinder placed at some oblique angle with the direction of flow is expressed in terms of the normal component of flow only, and the axial component is disregarded. Both the total in-line force coefficient (CF) and transverse force (lift) coefficient (Cf) were analyzed     

Numerical Study on the Hydrodynamic Characteristics of Biofouled Full-Scale Net Cage

The effect of biofouling on the hydrodynamic characteristics of the net cage is of particular interest as biofouled nettings can significantly reduce flow of well-oxygenated water reaching the stocked fish. For computational efficiency, the porous-media fluid model is proposed to simulate flow through the biofouled plane net and full-scale net cage. The porous coefficients of the porous-media fluid model can be determined from the quadratic-function relationship between the hydrodynamic forces on a plane net and the flow velocity using the least squares method. In this study, drag forces on and flow fields around five plane nets with different levels of biofouling are calculated by use of the proposed model. The numerical results are compared with the experimental data of Swift et al.(2006) and the effectiveness of the numerical model is presented. On that basis, flow through full-scale net cages with the same level of biofouling as the tested plane nets are modeled. The flow fields inside and around biofouled net cages are analyzed and the drag force acting on a net cage is estimated by a control volume analysis method. According to the numerical results, empirical formulas of reduction in flow velocity and load on a net cage are derived as function of drag coefficient of the corresponding biofouled netting.