THREE DIMENSIONAL MULTIPHASE COMPUTATIONAL FLUID DYNAMICS ANALYSIS OF VENTILATED SUPERCAVITATION

For some vehicles travelling through water, it is advantageous to cover the vehicle in a supercavity for the sake of reducing the drag acting on it. The method of artificial ventilation is most effective for generating and dominating the supercavity. This paper focuses on the numerical simulation of flow field around three dimensional body. The method is based on the multiphase computational fluid dynamics （CFD） model combined with the turbulence model and the full cavity model. The flow field of cavity is simulated by solving the compressible Navier-Stokes equations. The fundamental similarity parameters of ventilated supercavitaty flows that include cavitation number, Froude number, ventilation rate and drag coefficient are all investigated numerically in the case of steady flow and gravity field. We discuss the following simulations results in section 3： The variations of the cavitation number and the supercavity＇s relative diameter with ventilation rate （subtopic 3.1）; The drag coefficient versus the cavitation number （subtopic 3.2）; Deformation of supercavity axis caused by gravitational effect for three different fixed Froude numbers-2.8, 3.4, 4.2 （subtopic 3.3）. In subtopic 3.2, we give the comparison results of the drag reduction ratio among numerical simulation and experiment conducted in hydrodynamic tunnel and towing tank respectively. In subtopic 3.3, we summarize our discussion of gravitational effect on the axis deformation of supercavity as follows： In the case of smaller Froude number, the inclination of the cavity axis increases monotonously with increasing horizontal length, and reaches its maximal value at the end of supercavity; This deformation can be almost completely negligible when the Froude number Fr〉7. The comparisons with the experimental data in the hydrodynamic tunnel and the towing tank indicate that the present method is effective for predicting the flows around ventilated supercavity; that the numerical results is in good agreement with the experimental ones and that the maximal value of the drag reduction ratio can reach 88% compared with that the condition of fully-wetted.

Study on hysteresis phenomenon in the acceleration phase of supercavitation vehicle

This paper aims to explore cavity shape variation regularity in the acceleration phase of supercavitat- ing vehicle. According to the theory of Homogenous Equilibrium Flow,with Mixture Multiphase Model,by setting up the flow speed at the inlet boundary as a function of time,this study carried out the experiments for the supercavitation vehicle's numeral model and obtained the variation regularity of cavity shape,the viscous drag coefficient and the cavity hysteresis time when the supercavitating vehicle was in the phase of acceleration. Results show that when the vehicle is in the phase of acceleration,at the same cavitation number,the cavity size decrease with the increase of acceleration. With the decrease of cavity number,the effect of acceleration on cavity shape is smaller,but the viscous drag increases along with the increase of acceleration. On the condition when the velocity reaches equality uniform status,the cavity hysteresis decreases as the acceleration becomes smaller. On the condition of the same acceleration,the cavity hysteresis time decreases as the velocity increases.

Numerical study on morphological characteristics of rotational natural supercavitation by rotational supercavitating evaporator with optimized blade shape

In view of the supercavitation effect, a novel device named the rotational supercavitating evaporator (RSCE) has been designed for the desalination. In order to improve the blade shape of the rotational cavitator in the RSCE for the performance optimization, the blade shapes of different sizes are designed by utilizing the improved calculation method for the blade shape and the validated empirical formulae based on previous two-dimensional numerical simulations, from which the optimized blade shape with the wedge angle of 45° and the design speed of 5 000 r/min is selected. The estimation method for the desalination performance parameters is developed to validate the feasibility of the utilization of the results obtained by the two-dimensional numerical simulations in the design of the three-dimensional blade shape. Three-dimensional numerical simulations are then conducted for the supercavitating flows around the rotational cavitator with the optimized blade shape at different rotational speeds to obtain the morphological characteristics of the rotational natural supercavitation. The results show that the profile of the supercavity tail is concaved toward the inside of the supercavity due to the re-entrant jet. The empirical formulae for estimating the supercavity size with consideration of the rotation are obtained by fitting the data, with the exponents different from those obtained by the previous two-dimensional numerical simulations. The influences of the rotation on the morphological characteristics are analyzed from the perspectives of the tip and hub vortices and the interaction between the supercavity tail and the blade. Further numerical simulation of the supercavitating flow around the rotational cavitator made up by the blades with exit edge of uniform thickness illustrate that the morphological characteristics are also affected by the blade shape.

超空泡射弹的结构优化与稳定性分析

Stability is the key issue for kinetic-energy supercavitating projectiles.Our previous work established a six degrees of freedom(DOF)dynamic model for supercavitating projectiles.However,the projectile’s structure did not meet our current design specifications(its sailing distance could reach 100 m at an initial speed of 500 m/s).The emphasis of this study lies in optimizing the projectile’s configuration.Therefore,a program was developed to optimize the projectile’s structure to achieve an optimal design or the largest sailing distance.The program is a working optimal method based on the genetic algorithm(GA).Additionally,the convergence standard and population producing strategy were improved,which greatly elevated the calculation speed and precision.To meet design specifications,the improved GA was combined with the 6DOF model,which establishes a dynamic optimization problem.The new projectile’s structure was obtained by solving this problem.Then,the new structures’dynamic features were compared with the ideals proposed in this paper.The criterion of stability,which is called weakened self-stability,was redefined based on the results.The weakened self-stability is the optimal stability for an actual kinetic projectile motion,and it is instructive for the design of supercavitating projectiles in the future.

UNDERWATER ACOUSTICS AND CAVITATING FLOW OF WATER ENTRY

The fluid mechanics of water entry is studied through investigating the underwater acoustics and the supercavitation.Underwater acoustic signals in water entry are extensively measured at about 30 different positions by using a PVDF needle hydrophone.From the measurements we obtain (1)the primary shock wave caused by the impact of the blunt body on free surface;(2)the vapor pressure inside the cavity;(3)the secondary shock wave caused by pulling away of the cavity from free surface;and so on.The supercavitation induced by the blunt body is observed by using a digital high-speed video camera as well as the single shot photography.The periodic and 3 dimensional motion of the supercavitation is revealed.The experiment is carried out at room temperature.

HYDRODYNAMIC BEHAVIOR OF AN UNDERWATER MOVING BODY AFTER WATER ENTRY

An experimental study was conducted to investigate the water entry phenomenon. A facility was designed to carry out the tests with the entry veloci- ties of around 352 m/s. Visualization, pressure ineasurement, velocity measurement and underwater impact test were performed to investigate the hydroballistic behav- ior of the underwater moving body, the underwater flow field, the supercavitation, etc.. This study shows that the motion of a high-speed underwater body is strongly three-dimensional and chaotic. Furthermore, it is found that the distribution of the trajectory deflection of the underwater projectile depends on the depth of water. It is also found by measuring the deformation on a witness plate submerged in water, that the impact energy of an underwater projectile is reduced as it penetrates deeper into water.

Breakup of Cavitation Bubbles within the Diesel Droplet

Supercavitation in the diesel nozzle increases the instability of droplets in part due to the two-phase mixture, while the effect of cavitation bubbles on the instability of drops is still unclear. In order to investigate the breakup of cavitation bubbles within the diesel droplet, a new mathematical model describing the disturbance growth rate of the diesel bubble instability is developed. The new mathematical model is applied to predict the effects of fluids viscosity on the stability of cavitation bubbles. The predicted values reveal that the comprehensive effect of fluids viscosity makes cavitation bubbles more stable. Compared with the viscosities of air and cavitation bubble, the diesel droplet＇s viscosity plays a dominant role on the stability of cavitation bubbles. Furthermore, based on the modified bubble breakup criterion, the effects of bubble growth speed, sound speed, droplet viscosity, droplet density, and bubble-droplet radius ratio on the breakup time and the breakup radius of cavitation bubbles are studied respectively. It is found that a bubble with large bubble-droplet radius ratio has the initial condition for breaking easily. For a given bubble-droplet radius ratio （0.2）, as the bubble growth speed increases （from 2 m/s to 60 m/s）, the bubble breakup time decreases（from 3.59 gs to 0.17 ps） rapidly. Both the greater diesel droplet viscosity and the greater diesel droplet density result in the increase of the breakup time. With increasing initial bubble-droplet radius ratio （from 0.2 to 0.8）, the bubble breakup radius decreases （from 8.86 trn to 6.23 tm）. There is a limited breakup radius for a bubble with a certain initial bubble-droplet radius ratio. The mathematical model and the modified bubble breakup criterion are helpful to improve the study on the breakup mechanism of the secondary diesel droplet under the condition of supercavitation.

Analysis on Velocity Characteristics of Cavitation Flow Around Hydrofoil

The time-averaged velocity distributions in flows around a hydronautics hydrofoil were measured by using a digital particle image velocimeter(DPIV) system.The results show that the velocity distribution in the whole flow field depends on the development of cavitation structures with the decreasing of cavitation number.The high-fluctuation region with lower velocity relates to the cavitation area.The lowest velocity distribution in the cavity core becomes more uniform,and its influence becomes smaller gradually as moving to downstream.The main-stream velocity distribution is even,then fluctuate and even at last.In the supercavitation stage,the fluid velocity in the cavitation region,corresponding to the front of the hydrofoil's suction surface,has a distribution close to the main stream,while the fluid velocity in other cavitation area is lower.

Effect of Injection Angle on Artificial Cavitation Using the Design of Experiment Method

Using the supercavitation phenomenon is necessary to reach high velocities underwater. Supercavitation can be achieved in two ways: natural and artificial. In this article, the simulation of flows around a torpedo was studied naturally and artificially. The validity of simulation using theoretical and practical data in the natural and artificial phases was evaluated. Results showed that the simulations were consistent with the laboratory results. The results in different injection coefficient rates, injection angles, and cavitation numbers were studied. The obtained results showed the importance of cavitation number, injection rate coefficient, and injection angle in cavity shape. At the final level, determining the performance conditions using the Design of Experiment (DOE) method was emphasized, and the performance of cavitation number, injection rate coefficient, and injection angle in drag and lift coefficient was studied. The increase in injection angle in the low injection rate coefficient resulted in a diminished drag coefficient and that in the high injection rate coefficient resulted in an enhanced drag coefficient.

Motion stability and control of supercavitating vehicle with variable cavitation number

Cavitation number and speed are capable of variation during the motion of supercavitating vehicle underwater,for example,under the condition of accelerated motion stage and external disturbance.The dynamic model and control challenge associated with the longitudinal motion of supercavitating vehicle with variable cavitation number and speed have been explored.Based on the principle of cavity expansion independence the properties of cavity and the influence on planning force of body were researched.Calculation formula of efficiency of the fin was presented.Nonlinear dynamics model of variable cavitation number and speed supercavitating vehicle was established.Stabilities of the open-loop systems of different situations were analyzed.The simulations results of open-loop systems show that it is necessary to design a control method to control a supercavitating vehicle.A gain schedule controller with guaranteed H∞ performance was designed to stabilize the dive-plane dynamics of supercavitating vehicle under changing conditions.

Dynamic Characteristics of Supercavitating Flow Around a Hydrofoil

Supercavitation dynamic characteristics around a hydrofoil are studied with both high-speed visualization and drag and lift measurements. In the supercavitation condition, the cavitation area covers the entire surface of the foil. There is a distinct interface between the main flow and the supercavitating flow regions. The cavitating region is filled with cavitation bubble and water mixture. Small fluctuations of the interface are observed, which indicates that even a relative smooth surface is formed in this state, the interface is unsteady. The minimum drag is to be obtained in the supercavitation condition.

Global approximation based adaptive RBF neural network control for supercavitating vehicles

A global approximation based adaptive radial basis function（RBF） neural network control strategy is proposed for the trajectory tracking control of supercavitating vehicles（SV）.A nominal model is built firstly with the unknown disturbance.Next, the control scheme is established consisting of a computed torque controller（CTC） for the practical vehicle and an RBF neural network controller to estimate model error between the practical vehicle and the nominal model. The network weights are adapted by employing a Lyapunov-based design. Then it is shown by the Lyapunov theory that the trajectory tracking errors asymptotically converge to a small neighborhood of zero. The control performance of the proposed controller is illustrated by simulation.

Influence of Ramjets’ Water Inflow on Supercavity Shape and Cavitator Drag Characteristics

Water ramjets using outer water as an oxidizer have been demonstrated as a potential propulsion mode for underwater High Speed Supercavitating Vehicles (HSSVs) because of their higher energy density, power density, and specific impulse, but water flux changes the shapes of supercavity. To uncover the cavitator drag characteristics and the supercavity shape of HSSVs with water inflow for ramjets, supercavitation flows around a disk cavitator with inlet hole are studied using the homogenous model. By changing the water inflow in the range of 0-10 L/s through cavitators having different water inlet areas, a series of numerical simulations of supercavitation flows was performed. The water inflow flux of ramjets significantly influences the drag features of disk cavitators and the supercavity shape, but it has little influence on the slender ratio of supercavitaty. Furthermore, as the water inlet area increases, the drag coefficient of the cavitators' front face decreases, but this increase does not influence the diameter of the supercavity's maximum cross section and the drag coefficient of the entire cavitator significantly. In addition, with increasing waterflux of the ramjet, both the drag coefficient of cavitators and the maximum diameter of supercavities decrease stably. This research will be helpful for layout optimization and supercavitaty scheme design of HSSVs with water inflow for ramjets.

Adaptive robust controller for supercavitating vehicle using guaranteed cost theory

Regarding to the problems that supercavitating vehicles have special characteristics from traditional underwater vehicles,robust control problem was studied in this paper for the supercavitating vehicles with mismatched uncertainties.The nonlinear dynamic model was improved.For mismatched uncertainties,the robust sliding mode function was proposed based on guaranteed cost theory,and sufficient condition for the existence was given in terms of linear matrix inequality (LMI).Continuous sliding mode controller was designed,with an adaptive technology which was used to estimate the unknown upper bound of mismatched uncertainties.Meanwhile,upper bound of parameter uncertainties was not required.Simulation results demonstrated that the system responds rapidly and has good robust stability.Due to application of guaranteed cost theory,the controlled plant is not only stable but also guarantees an adequate level of performance.Therefore,it provides theoretical references for further study on control problems of supercavitating vehicles.

Quadratic and cubic eddy-viscosity models in turbulent supercavitating flow computation

Quadratic and cubic non-linear eddy-viscosity turbulence models(NLEVM) with low Reynolds number(Re) correction were presented to provide better description of anisotropic turbulence stresses in the numerical prediction of supercavitating flows,which are accompanied with large density ratio and large-scaled swirling flow structures.The applications of the NLEVM were carried out through a self-developed cavitation codes,coupled with a cavitation model based on the transport equation of liquid phase.These NLEVM were verified capable of capturing more accurate macroscopic shape and hydrodynamic property of supercavity by the benchmark problems of supercavities over simple objects.Finally,the cubic NLEVM was further applied to the numerical prediction of supercavitating flow around a complex submerged vehicle.The corresponding cavitation behaviors were explored in detail to provide beneficial experience for further research.

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.

PERTURBATION SOLUTION TO 3-D NONLINEAR SUPERCAVITATING FLOW PROBLEMS

A 3-D nonlinear problem of supercavitating flow past an axisymmetric body at a small angle of attack is investigated by means of the perturbation method and Fourier-cosine-expansion method. The first three order perturbation equations are derived in detail and solved numerically using the boundary integral equation method and iterative techniques. Computational results of the hydrodynamic characteristics and cavity shapes of each order are presented for nonaxisymmetric supercavitating flow past cones with various apex-angles at differ- ent cavitation numbers. The numerical results are found in good agreement with experimental data.

Adaptive Controller Design for Dynamic Maneuvers of High Speed Underwater Vehicles

The control synthesis of the high-speed underwater vehicle faces many technical challenges due to its inherent structure and surrounding operational environment.In this paper,the dynamical behavior is firstly described through a bifurcation analysis to give some insights for robust control synthesis.Then a novel adaptive fractional-order sliding mode controller(AFOSMC)is realized to effectively manipulate the supercavitating vehicle against payload changes,nonlinear planing force,and external disturbances.The fractional order(FO)calculus can offer more flexibility and more freedom for tuning active control synthesis than the integer-order counterpart.In addition,the adaptation law has been presented to directly handle the payload change effects.The stability of the controlled vehicle system is proven via Lyapunov stability theory.Next,the dynamic performance of the proposed controller is verified through extensive simulation results,which demonstrate the control accuracy with faster responses compared with existing integer-order controllers.Finally,the proposed fractional order controllers can provide higher performance than their integer order counterparts with control algorithms.

Cavity Flow Pattern Design for Supercaviting Torpedo

The flow pattern design of supercaviting torpedo,like the shape design of conventional bedewed torpedo,occupies an important position in torpedo system design.In this paper,the flow pattern design issues were studied systematically.A set of design criteria and main design requirements were proposed,and the design method and procedure were established.Moreover,the determination method of necessary parameters of cavitator and ventilated system for desired cavity flow pattern was given.Considered the speed and pressure disturbances in the torpedo navigation,a concept named margin design was proposed to solve the supercavitation deformation and instability caused by the disturbances.

Impact Dynamics of Supercavitating Projectile with Fluid/Structure Interaction

As supercavitating projectiles move at high speed, the periodic impacts ("tail-slap") on the interior surface of the cavity generally occur due to disturbances. The interactions between the projectile and the water/cavity interface are the sources of structural vibrations, which affect the guidance of the vehicle and undermine the structural reliability. The Fluid/Structure Interaction calculation procedure of the tail-slaps of supercavitating projectile is established, and the dynamic behaviours of the projectile operating in tail-slap conditions with and without considering Fluid/Structure Interaction are obtained and compared. The responses of the projectile riding a reducing cavity are studied, and the effect of Fluid/Structure Interaction is also analyzed. The results show that the angular velocity of projectile increases as the body slowing down, and the amplitude of the elastic displacement response decreases at the beginning and increases when the cavity size is close to the diameter of the tail of projectile. The effect of Fluid/Structure Interaction reduces the amplitudes and frequencies of the impact loads and the vibration responses of the body, and when the speed is higher, the effect is more apparent.