Numerical Investigation of the Angle of Attack Effect on Cloud Cavitation Flow around a Clark-Y Hydrofoil

Cavitation is a prevalent phenomenon within the domain of ship and ocean engineering,predominantly occurring in the tail flow fields of high-speed rotating propellers and on the surfaces of high-speed underwater vehicles.The re-entrant jet and compression wave resulting from the collapse of cavity vapour are pivotal factors contributing to cavity instability.Concurrently,these phenomena significantly modulate the evolution of cavitation flow.In this paper,numerical investigations into cloud cavitation over a Clark-Y hydrofoil were conducted,utilizing the Large Eddy Simulation(LES)turbulence model and the Volume of Fluid(VOF)method within the OpenFOAM framework.Comparative analysis of results obtained at different angles of attack is undertaken.A discernible augmentation in cavity thickness is observed concomitant with the escalation in attack angle,alongside a progressive intensification in pressure at the leading edge of the hydrofoil,contributing to the suction force.These results can serve as a fundamental point of reference for gaining a deeper comprehension of cloud cavitation dynamics.

Numerical Simulation of the Flow around Two-dimensional Partially Cavitating Hydrofoils

In the present study, a new approach is applied to the cavity prediction for two-dimensional （2D） hydrofoils by the potential based boundary element method （BEM）. The boundary element method is treated with the source and doublet distributions on the panel surface and cavity surface by usethe of the Dirichlet type boundary conditions. An iterative solution approach is used to determine the cavity shape on partially cavitating hydrofoils. In the case of a specified cavitation number and cavity length, the iterative solution method proceeds by addition or subtraction of a displacement thickness on the cavity surface of the hydrofoil. The appropriate cavity shape is obtained by the dynamic boundary condition of the cavity surface and the kinematic boundary condition of the whole foil surface including the cavity. For a given cavitation number the cavity length of the 2D hydrofoil is determined according to the minimum error criterion among different cavity lengths, which satisfies the dynamic boundary condition on the cavity surface. The NACA 16006, NACA 16012 and NACA 16015 hydrofoil sections are investigated for two angles of attack. The results are compared with other potential based boundary element codes, the PCPAN and a commercial CFD code （FLUENT）. Consequently, it has been shown that the results obtained from the two dimensional approach are consistent with those obtained from the others.

The influence of surface roughness on cloud cavitation flow around hydrofoils

The aim of this study is to investigate experimentally the effect of surface roughness on cloud cavitation around Clark-Y hydrofoils. High-speed video and particle image velocimetry(PIV) were used to obtain cavitation patterns images(Prog. Aerosp. Sci. 37: 551–581, 2001), as well as velocity and vorticity fields. Results are presented for cloud cavitating conditions around a Clark-Y hydrofoil fixed at angle of attack of α = 8? for moderate Reynolds number of Re = 5.6 × 10~5. The results show that roughness had a great influence on the pattern, velocity and vorticity distribution of cloud cavitation. For cavitating flow around a smooth hydrofoil(A) and a rough hydrofoil(B), cloud cavitation occurred in the form of finger-like cavities and attached subulate cavities, respectively. The period of cloud cavitation around hydrofoil A was shorter than for hydrofoil B.Surface roughness had a great influence on the process of cloud cavitation. The development of cloud cavitation around hydrofoil A consisted of two stages:(1) Attached cavities developed along the surface to the trailing edge;(2) A reentrant jet developed, resulting in shedding and collapse of cluster bubbles or vortex structure. Meanwhile, its development for hydrofoil B included three stages:(1) Attached cavities developed along the surface to the trailing edge, with accumulation and rotation of bubbles at the trailing edge of the hydrofoil affecting the flow field;(2) Development of a reentrant jet resulted in the first shedding of cavities. Interaction and movement of flows from the pressure side and suction side brought liquid water from the pressure side to the suction side of the hydrofoil, finally forming a reentrant jet. The jet kept moving along the surface to the leading edge of the hydrofoil, resulting in large-scale shedding of cloud bubbles. Several vortices appeared and dissipated during the process;(3) Cavities grew and shed again.

Numerical study of hydrofoil surface jet flow on cavitation suppression

Cavitation caused vibration and noise of hydraulic machinery. To some extent,cavitation made fatigue damage in advance. Many scholars found that the re-entrant jets were the reasons of the shedding of cavities. To suppress cavitation,based on the idea of blocking the re-entrant jets,a special surface flow structure of 2D hydrofoil was proposed. The through-hole was made in the proper position of the hydrofoil. The incoming flow can outflow from this jet-hole automatically depending on the pressure difference between pressure side and suction side. Re-entrant jet growth can be weakened by optimizing the jet-hole geometry. Based on the standard k-ε turbulence model and Schnerr & Sauer cavitation model,under different cavitation numbers( σ) and jet-angles( β) for NACA0066( 2D) hydrofoil with 8° angles of attack,cavitation field numerical analysis was carried out. The results show that 2D hydrofoil cavitation flow had a strong unsteadiness. Making a jet-hole at the junction between the re-entrant jet and cavity can effectively minimize cloud cavitation. For a certain cavitation condition,optimal jet-angles( β) can be obtained to control cavitation growth. For the same β,the effects of cavitation suppression were changed with different cavitation numbers( σ). Consequently,suitable jet-angle and jet-position could extend the stable operating range of the hydrofoil.

Fluid-structure interaction simulation of three-dimensional flexible hydrofoil in water tunnel

The closely coupled approach combined with the finite volume method （FVM） solver and the finite element method （FEM） solver is used to investigate the fluid-structure interaction （FSI） of a three-dimensional cantilevered hydrofoil in the water tunnel. The FVM solver and the coupled approach are verified and validated by compar- ing the numerical predictions with the experimental measurements, and good agreement is obtained concerning both the lift on the foil and the tip displacement. In the noncav- itating flow, the result indicates that the growth of the initial incidence angle and the Reynolds number improves the deformation of the foil, and the lift on the foil is increased by the twist deformation. The normalized twist angle and displacement along the span of the hydrofoil for different incidence angles and Reynolds numbers are almost uniform. For the cavitation flow, it is shown that the small amplitude vibration of the foil has limited influence on the developing process of the partial cavity, and the quasi two-dimensional cavity shedding does not change the deformation mode of the hydrofoil. However, the frequency spectrum of the lift on the foil contains the frequency which is associated with the first bend frequency of the hydrofoil.

Adaptability research of hydrofoil surface water injection on cavitation suppression

To study the effectiveness of hydrofoil surface water injection on cavitation suppression,the unsteady cavitation flow field around the NACA0066 hydrofoil at attack angle of 6°was simulated by the modified RNG k-εturbulence model combined with the full-cavitation model.The structure of cavitation flow field and the hydrodynamic performance of hydrofoil were analyzed at the cavitation number of 0.85,0.70,0.55,respectively.The results show that barriered by the jet,the momentum of the reentrant jet was reduced;The development of cavitation and the strength of cavity shedding were weakened to some extent.Cavitation suppression effect was very obvious in the cavitation conditions with the cavitation number of 0.7 and above when the injection position was at 37% chord length from the hydrofoil leading edge and the jet-flow ratio kept 0.3.Time-averaged lift and drag coefficient were reduced,and the lift-drag ratio increased in water injection conditions.

CFD Simulation of Mixing in a Stirred Tank with Multiple Hydrofoil Impellers

The mixing process in a stirred tank of 0.476 m diameter with single, dual and triple 3-narrow blade hydrofoil CBY impellers was numerically simulated by using computational fluid dynamics (CFD) package FLU-ENT6.1. The multi-reference frame (MRF) and standard k-ε turbulent model were used in the simulation. The shaft power and the mixing time predicted by CFD were in good agreement with the experiment. The effects of tracer feeding and detecting positions on mixing time were investigated. The results are of importance to the optimum design of industrial stirred tank/reactors.

Simulation of Cavitating Flow around a 2-D Hydrofoil

In order to predict the effects of cavitation on a hydrofoil, the state equations of the cavitation model were combined with a linear viscous turbulent method for mixed fluids in the computational fluid dynamics (CFD) software FLUENT to simulate steady cavitating flow. At a fixed attack angle, pressure distributions and volume fractions of vapor at different cavitation numbers were simulated, and the results on foil sections agreed well with experimental data. In addition, at the various cavitation numbers, the vapor fractions at different attack angles were also predicted. The vapor region moved towards the front of the airfoil and the length of the cavity grew with increased attack angle. The results show that this method of applying FLUENT to simulate cavitation is reliable.

Influences of Lorentz force on the hydrofoil lift

In this paper, Lorentz forces are proved to be able to suppress separation in flows over hydrofoils. Furthermore, a differential equation of pressure distributions on the hydrofoil surface is derived, from which it is found that BVF （boundary vortex flux） σ is a suitable criterion for describing the lift coefficient variations during the electromagnetic control process. According to our numerical results, the periodic variations of lift for a hydrofoil at an attack angle of 17 ° are analyzed and its inherent mechanism is discussed in detail with the concept of BVE On the other hand, the effects of Lorentz force on the hydrofoil＇s lift are investigated both experimentally and numerically for different magnitudes and locations.

Effect of leading edge roughness on cavitation inception and development on thin hydrofoil

The cavitation incipience and development of water flow over a thin hydrofoil placed in the test section of high-speed cavitation tunnel were investigated.Hydrofoils with smooth and rough leading edge were tested for different upstream velocities and incidence angles.The observations clearly revealed that cavitation incipience is enhanced by roughness at incidence angle below 2°.This is in line with the former reports,according to whose roughness element decreases the wettability and traps a larger amount of gas.As a result,surface nucleation is enhanced with an increased risk of cavitation.Surprisingly,for higher incidence angles(>3°),it was found that cavitation incipience is significantly delayed by roughness while developed cavitation is almost the same for both smooth and rough hydrofoils.This unexpected incipience delay is related to the change in the boundary layer structure due to roughness.It was also reported a significant influence of roughness on the dynamic of developed cavitation and shedding of transient cavities.

Numerical Simulations of Cavitation Flows around Clark-Y Hydrofoil

Cavitation is a complex flow phenomenon including unsteady characteristics, turbulence, gas-liquid two-phase flow. This paper provides a numerical investigation on comparing the simulation performance of three different models in OpenFOAM-Merkle model, Kunz model and Schnerr-Sauer model, which is helpful for understanding the cavitation flow. Considering the influence of vapor-liquid mixing density on turbulent viscous coefficient, the modified SST k-ω model is adopted in this paper to increase the computing reliability. The InterPhaseChangeFoam solver is utilized to simulate the two-dimensional cavitation flow of the Clark-Y hydrofoil with three cavitation models. The hydrodynamic performance including lift coefficient, drag coefficient and cavitation flow shape of the hydrofoil is analyzed. Through the comparison of the numerical results and experimental data, it is found that the Schnerr-Sauer model can get the most accurate results among the three models. And from the simulation point of water and water vapor mixing, the Merkle model has the best water and water vapor mixing simulation.

Experimental Study on Influences of Surface Materials on Cavitation Flow Around Hydrofoils

In order to resist on the cavitation erosion, many researchers try to change the solidity and tenacity of the coatings, but ignore the influence of surface characteristics of materials on cavitation flow and the interaction with each other. In this paper, high speed visualization system is used to observe the cavitation flow patterns in different stage. After comparing the characteristics of cavitation flow around hydrofoils made of aluminum (Foil A), stainless steel (Foil B) and the hydrofoil painted with epoxy coating (Foil C), the study shows that material has a significant effect on the cavitation flow. Firstly, when the incipient cavitation occurs, cavitation number of Foil A is highest among three hydrofoils, generating horseshoe vortex randomly. For Foil B and Foil C, it shows in the form of free bubbles. When the sheet cavitation occurs, Foil A has the highest cavitation number and shortest period, which is contrary to Foil C. And cavity consists of lots of small finger-like cavities. For Foil B and Foil C, it both constitutes with many bubbles. Compared with the high-density and small-scale cavities over surface of Foil C, the cavity of Foil B has larger scale and less density, which causes a minimal scope of influence of the re-entrant jet and strong randomness. When the cloud cavitation occurs, Foil C has the lowest cavitation number and shortest period. Secondly, compared with aluminum, both of stainless steel and epoxy coating restrains the occurrence and development of cavitation, and stainless steel and epoxy coating performs better than aluminum. For inception and sheet cavitation, stainless steel performs better than epoxy coating and aluminum. For cloud cavitation, epoxy coating performs better than stainless steel and aluminum. The objective of this paper is applied experimental method to investigate the effect of surface materials on cavitation around Clark-Y hydrofoils.

Numerical simulation of cavitation around a Clark-Y hydrofoil with different LES models in OpenFOAM

A finite volume,multiphase solver in the framework of OpenFOAM was used to calculate the flow field of the cavitating flow over the Clark-Y hydrofoil. This solver used Transport Based Equation Model(TEM) to solve the liquid volume fraction,and utilized volume of fluid(VOF) technique to predict the interface between liquid and vapor phases. The simulation was designed to study the cavitation shedding and different fluid characteristics in the cloud cavitation regime when adopting two different Large Eddy Simulation(LES) models,namely,one equation eddy viscosity(one EqEddy) model and Smagorinsky model. It is shown that these two models can be used to study the cavitation shedding dynamics and predict the velocity profiles.

Flooding Characteristics of Hydrofoil Impeller in a Two- and Three-phase Stirred Tank

The flooding characteristics of hydrofoil impeller were systematically investigated in a two-and three-phase 383 mm i.d. stirred tank operated on air, water and spherical glass beads. The volumetric solid concen-tration Cs was varied from 0 to 25%. And the superficial gas velocity Ug was at the range of 0-0.096 m·s-1. A fast and objective method for identifying flooding point NF is developed based on the statistical analysis of the pressure fluctuation signals. It is found, the effect of solid concentration on the flooding point NF depends on the gas velocity. At the lower gas velocity (Ug = 0.010 m·s-1), the solid concentration has only a minor effect. However, it displays a very significant effect on the flooding point NF at the medium and high gas velocity. The flooding point NF linearly increases with the gas velocity Ug, at lower solid concentration (Cs = 0, 10%). When Cs = 20%, the behavior of NF versus Ug becomes more complex. The correlations of the flooding characteristics in the slurry stirred tank are proposed by considering the solid concentration effect.

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.

The Applicability of Hydrofoils as a Ship Control Device

Centrifugal forces are commonly created when ships turn, which may cause a ship to capsize in a critical situation. A mathematical model has been developed to optimize the stability coefficients for ship, with the aim to prevent capsizing and to increase ship maneuverability in high-speed water craft. This model can be used to develop algorithms for control system improvement. The mathematical model presented in this paper optimized the use of multipurpose hydrofoils to reduce heeling and the trimming moment, maintaining an upright ship’s position and lessening the resistance via transverse force. Conventionally, the trimming and heeling of a ship are controlled using ballast water;however, under variable sea conditions it is sometimes difficult to control a ship’s motion using ballast water. In this case, a hydrofoil would be more stable and maneuverable than a ballast tank controlled vessel. A movable hydrofoil could theoretically be adapted from moveable aerofoil technology. This study proves the merit of further investigation into this possibility.

A Lifting Line Theory for a Three-dimensional Hydrofoil

Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

Analysis of Cavitation Performance of a 2-D Hydrofoil Based on Mixed-iterative Method

In order to study cavitation characteristics of a 2-D hydrofoil, the method that combines nonlinear cavitation model and mixed-iteration is used to predict and analyze the cavitation performance of hydrofoils. The cavitation elements are nonlinearly disposed based on the Green formula and perturbation potential panel method. At the same time, the method that combines cavity shape for fixed cavity length （CSCL） iteration and cavity shape for fixed cavitation number （CSCN） iteration is used to work out the thickness and length of hydrofoil cavitations. Through analysis of calculation results, it can be concluded that the jump of pressure and velocity potentially exist between cavitation end area and non-cavitations area on suction surface when cavitation occurs on hydrofoil. In certain angles of attack, the cavitation number has a negative impact on the length of cavitations. And under the same angle of attack and cavitation number, the bigger the thickness of the hydrofoil, the shorter the cavitations length.

Isoparametric Boundary Element Method Applied to the Rectangular and Delta Hydrofoils near the Free Surface

In this paper, the hydrodynamic characteristics and flow field around rectangular and delta hydrofoils, moving with a constant speed beneath the free surface are numerically studied by means of isoparametric boundary element method （IBEM）. The quantities （source and dipole strengths） and the geometry of the dements are represented by a linear distribution. Two types of three-dimensional hydrofoils （rectangular and delta） are selected with NACA4412 and symmetric Joukowski sections. Some numerical results of pressure distribution, lift, wave-making drag coefficients and velocity field around the hydrofoils are presented. Also, the wave pattern due to moving hydrofoil is predicted at different operational conditions. Comparisons are made between computational results obtained through this method and those from the experimental measurements and other numerical results which reveal good agreement.

Experimental Observations of Cavitating Flows Around a Hydrofoil

The cavitation around a hydrofoil is studied experimentally to shed light on the muhiphase fluid dynamics. Different cavitation regimes are studied by using high speed visualization and particle image veloeimetry（PIV）. As decreasing the cavitation number, four cavitating flow regimes are observed： incipient cavitation, sheet cavitation, cloud cavitation, and supercavitation. From the incipient cavitation to the cloud cavitation, bubbles become more and more. Phenomena with large-scale vortex structure and rear re-entrant jet associated with the cloud cavitation, and subsequent development in the supercavitation are described. The velocity in the cavitation regions in the different cavitation conditions is low compared to that of the free stream. The large velocity gradient is also observed in the cavitating flow region near the surface of the hydrofoil.