Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.

Properties of sound attenuation around a two-dimensional underwater vehicle with a large cavitation number

Due to the high speed of underwater vehicles, cavitation is generated inevitably along with the sound attenuation when the sound signal traverses through the cavity region around the underwater vehicle. The linear wave propagation is studied to obtain the influence of bubbly liquid on the acoustic wave propagation in the cavity region. The sound attenuation coefficient and the sound speed formula of the bubbly liquid are presented. Based on the sound attenuation coefficients with various vapor volume fractions, the attenuation of sound intensity is calculated under large cavitation number conditions. The result shows that the sound intensity attenuation is fairly small in a certain condition. Consequently, the intensity attenuation can be neglected in engineering.

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.

Orifice plate cavitation mechanism and its influencing factors

The orifice plate energy dissipater is an economic and highly efficient dissipater. However, there is a risk of cavitaion around the orifice plate flow： In order to provide references for engineering practice, we examined the cavitation mechanism around the orifice plate and its influencing factors by utilizing mathematical analysis methods to analyze the flow conditions around the orifice plate in view of gas bubble dynamics. Through the research presented in this paper, the following can be observed： The critical radius and the critical pressure of the gas nucleus in orifice plate flow increase with its initial state parameter r0 ; the development speed of bubbles stabilizes at a certain value after experiencing a peak value and a small valley value; and the orifice plate cavitation is closely related to the distribution of the gas nucleus in flow. For computing the orifice plate cavitation number, we ought to take into account the effects of pressure fluctuation. The development time of the gas nucleus from the initial radius to the critical radius is about 107-10-5 s; therefore, the gas nucleus has sufficient time to develop into bubbles in the negative half-cycle of flow fluctuation. The orifice critical cavitation number is closely related to the orifice plate size, and especially closely related with the ratio of the orifice plate radius to the tunnel radius. The approximate formula for the critical cavitation number of the square orifice plate that only considers the main influencing factor was obtained by model experiments.

A numerical model for cloud cavitation based on bubble cluster

The cavitation cloud of different internal structures results in different collapse pressures owing to the interaction among bubbles. The internal structure of cloud cavitation is required to accurately predict collapse pressure. A cavitation model was developed through dimensional analysis and direct numerical simulation of collapse of bubble cluster. Bubble number density was included in proposed model to characterize the internal structure of bubble cloud. Implemented on flows over a projectile, the proposed model predicts a higher collapse pressure compared with Singhal model. Results indicate that the collapse pressure of detached cavitation cloud is affected by bubble number density.

STUDIES ON PROPERTIES OF FLOW CAVITATION NUMBER AND MINIMUM PRESSURE COEFFICIENT IN SHORT CLOSED CONDUITS

For a short closed conduit with smooth (streamline pattern) boundary, the comparison of minimum pressure coefficient at boundary, - Cpm , which obtained from model tests, with flow cavitation number a is possible to describe the property of preventing cavitation in the closed conduit.In this paper, analytical results show that the ratio σ/ - Cpm decreases with increasing Reynolds number Re, when the configuration of the conduit is designed, and this ratio approaches a constant when Re = 106 or so. The model test data for five engineering cases of the short closed conduit with various configuration indicates that the analytical results are reliable. Therefore, the value of the ratio σ/ - Cpm corresponding to that of Reynolds number in model (Re)m ≥106 must be taken so as to correctly describe the cavitation property of the studied conduit. The condition of Lr ≥ 10-4[(Re)p]2/3 should be satisfied ( Lr is model length scale; (Re)p is Reynolds number in prototype) when the model is designed by Froude criterion of similarity.

THE WALL EFFECT ON VENTILATED CAVITATING FLOWS IN CLOSED CAVITATION TUNNELS

For ventilated cavitating flows in a closed water tunnel, the wall effect may exert an important influence on cavity shape and hydrodynamics, An isotropic mixture multiphase model was established to study the wall effect based on the RANS equations, coupled with a natural cavitation model and the RNG k-ε turbulent model. The governing equations were discretized using the finite volume method and solved by the Gauss-Seidel linear equation solver on the basis of a segregation algorithm. The algebraic multigrid approach was carried through to accelerate the convergence of solution. The steady ventilated cavitating flows in water tunnels of different diameter were simulated for a conceptual underwater vehicle model which had a disk cavitator. It is found that the choked cavitation number derived is close to the approximate solution of natural cavitating flow for a 3-D disk. The critical ventilation rate falls with decreasing diameter of the water tunnel. However, the cavity size and drag coeflicient are rising with the decrease in tunnel diameter for the same ventilation rate, and the cavity size will be much different in water tunnels of different diameter even for the same ventilated cavitation number.

Computational study of different venturi and orifice type hydrodynamic cavitating devices

This paper reports optimization of various geometrical parameters of two types of hydrodynamic cavitation reactors （HC） such as venturi type and orifice type. Mostly orifice and venturi nozzles are used as HC reactor, a simple valve can also be used to cause cavitation which depends on geometry and area of opening. Different operating and geometrical parameters such as divergence angle, throat height/diameter to length ratio, number of holes and inlet pressure to the cavitating device were selected to study the inception, growth and dynamics of cavities. In this work, a comprehensive computational fluid dynamics simulation is performed to numerically investigate the 3-D flow behaviors within HC reactors using cavitational model with standard κ - ε Turbulence model. The study of different geometries of venturi type HC reactor （like slit, circular and elliptical） shows that 1：1 of the ratio of throat height/diameter to length and 6.5% of divergence angle is an optimum geometry for best cavitational activity. In case of orifice, 1：3 of the ratio of diameter to length is best for cavitation and an increase in the total flow area increases the cavitational yield.

THE COMPARATIVE STUDY OF VENTILATED SUPER CAVITY SHAPE IN WATER TUNNEL AND INFINITE FLOW FIELD

In order to understand the difference of ventilated supercavity in water tunnel and infinite flow field, 3-D numerical simulations are carried out to obtain the ventilated supercavity in above mentioned conditions based on RANS equations, using the finite volume method and SST turbulence model in the framework of the two fluid multiphase flow model. The numerical method adopted in this article for the infinite flow field and water tunnel experiments is validated by comparing results with those of empirical formulas and experimental data. On this basis the difference between water tunnel experiments and infinite flow field is studied, including the influence of the route loss and the blocking effect in the water tunnel. Finally, some suggestions are made for water tunnel experiments.

HYDRAULIC CHARACTERISTICS OF PLUG ENERGY DISSIPATER IN FLOOD DISCHARGE TUNNEL

The hydraulic characteristics of three types of plugs, namely, the single plug, the stepped plug and the gradually contracted plug were studied by means of experimental and numerical simulations. Main research findings are as follows. For the single plug, the pressure recovery lengths inside and after the plug range from 0.63-1.05 times and 2.02-2.84 times of the tunnel diameter, respectively. For the stepped plug, the lengths are 0.24-0.32 times and 1.62-2.84 times of the tunnel diameter, respectively. The best ratio of the inlet diameter to the outlet diameter of the gradually contracted plug can be expressed by a linear function. The relationship between the head loss coefficient and the area contraction ratio is obtained. The incipient cavitation numbers of different plugs are experimentally and numerically determined, and the incipient cavitation numbers are expressed by a formula. Model experiment with scale of 1：50 was carried out on a pressure tunnel with three-stage gradually contracted plugs. The results show that this type of energy dissipater is suitable for spill tunnels of high head （nearly 200 m） and large flow rate （nearly 2500 m^3/s）.

CAVITATION CHARACTERISTICS OF HIGH VELOCITY FLOW WITH AND WITHOUT AERATION ON THE ORDER OF 50m/s

Experimental study of cavitation characteristics with and without aeration was conducted at the flow velocity 50m/s in the non-circulating type water tunnel in the Hydraulics Laboratory at Zhejiang University of Technology. Variations of pressure and cavitation number with air concentration, pressure waveforms as well as cavitation erosion level of concrete specimen with and without aeration were obtained. The effects of cavitation control by aeration were analyzed.

AN EXPERIMENTAL INVESTIGATION OF PRESSURE AND CAVITATION CHARACTERISTICS OF HIGH VELOCITY FLOW OVER A CYLINDRICAL PROTRUSION IN THE PRESENCE AND ABSENCE OF AERATION

This article experimentally investigated the pressure and cavitation characteristics of high velocity flow over a surface irregularity with and without aeration in a non-circulating water tunnel system. The surface irregularity is a cylindrical protrusion made of stainless steel of 6 mm diameter and 2 mm height. Pressures with and without aeration were measured with MPX400D pressure transducers and real-timely acquired by a SINOCERA YE6263 data acquisition system. Variations in flow regimes with and without aeration were observed. Pressure profiles and their variations with air concentration upper and lower cylindrical protrusion on the invert and obvert walls were determined. Variations of cavitation number with air concentration lower cylindrical protrusion were analyzed. Also, cavitation numbers in the presence and absence of aeration were compared.

Hydraulic Characteristics of Multi-Stage Orifice Plate

Energy dissipater of multi-stage orifice plate, as a kind of effective energy dissipater with characteristics of high energy dissipation ratio and low cavitations risk, has become welcomed more and more by hydraulics researchers. The relationship between the contraction ratio of upper stage orifice plate and the lower one's under the principle of equal-cavitation characteristics, and the reasonable distance between upper stage orifice plate and the lower one under the condition of complying with this principle, are two important factors to be considered for multi-stage energy dissipater design. In the present paper, these two factors were analyzed by theoretical consideration and numerical simulations, and solving methods were put forward. The conclusion in this paper was proved to be reasonable by model experiment.