An Experimental Investigation of Cavitation Inception and Development on a Two-Dimensional Hydrofoil

2000 ◽  
Vol 44 (04) ◽  
pp. 259-269
Author(s):  
J.-A. Astolfi ◽  
J.-B. Leroux ◽  
P. Dorange ◽  
J.-Y. Billard ◽  
F. Deniset ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Velocity Distribution ◽  
Cavity Length ◽  
Pressure Coefficient ◽  
Sudden Change ◽  
Leading Edge ◽  
Cavitation Number ◽  
Cavity Surface ◽  
Cavitation Inception ◽  
Flow Visualizations

The cavitation inception (and desinent) angles at given cavitation numbers, the velocity distribution, and the resulting pressure coefficient, together with the sheet cavity lengths developing on a hydrofoil surface, have been investigated experimentally for a Reynolds number ranging between 0.4 × 106 and 1.2 × 106. It is shown that the cavitation inception (and desinent) angle decreases progressively when the Reynolds number increases and tends to be close to the theoretical (inviscid) value when the Reynolds number is larger than 0.8 × 106. The magnitude and the position of the minimum surface pressure coefficient, inferred from the velocity distribution measured at the leading edge, were shown to be dependent upon the Reynolds number as well. An investigation of the cavitating flow velocity field upstream of the cavity and on the cavity surface showed that the pressure in the cavity was very close to the vapor pressure. The detachment location of the cavity was found to occur very close to the leading edge (at about one hundredth of the foil chord for both Re = 0.4 × 10® and Re = 0.8 × 106). The length cavities measured from flow visualizations exhibited a sudden change for a Reynolds number passing from 0.7 × 106 to 0.8 × 106 with a given angle of incidence (α= 6 deg) and cavitation number (σ = 1.3). Photographs of the sheet cavity show that the cavity length can be inferred also from the extent of the region for which the pressure coefficient is close to the cavitation number. It was shown to have the values l/c 0.03 for Re = 0.4 × 106 and l/c ~ 0.06 for Re = 0.8 × 10® and σ = 1.8 with the latter value very close to the value obtained from flow visualizations. Photographs of the cavity show that the increase of the cavity length is coupled to the migration, towards the leading edge, of a transition point on the cavity surface when the Reynolds number increases.

Effect of Hydrofoil Planform on Tip Vortex Roll-Up and Cavitation

1995 ◽  
Vol 117 (1) ◽  
pp. 162-169 ◽  
Author(s):  
D. H. Fruman ◽  
P. Cerrutti ◽  
T. Pichon ◽  
P. Dupont
Keyword(s):  
Reynolds Number ◽  
Incidence Angle ◽  
Pressure Coefficient ◽  
Tangential Velocity ◽  
Leading Edge ◽  
Velocity Profiles ◽  
The Other ◽  
Tip Vortex ◽  
Trailing Edge ◽  
Cavitation Inception

The effect of the planform of hydrofoils on tip vortex roll-up and cavitation has been investigated by testing three foils having the same NACA 16020 cross section but different shapes. One foil has an elliptical shape while the other two are shaped like quarters of ellipses; one with a straight leading edge and the other with a straight trailing edge. Experiments were conducted in the ENSTA, Ecole Navale and IMHEF cavitation tunnels with homologous foils of different sizes to investigate Reynolds number effects. Hydrodynamic forces as well as cavitation inception and desinence performance were measured as a function of Reynolds number and foil incidence angle. Laser Doppler measurements of the tangential and axial velocity profiles in the region immediately downstream of the tip were also performed. At equal incidence angle and Reynolds number, the three foils show different critical cavitation conditions and the maximum tangential velocity near the tip increases as the hydrofoil tip is moved from a forward to a rear position. However, the velocity profiles become more similar with increasing downstream distance, and at downstream distances greater than one chord aft of the tip, the differences between the foils disappear. The rate of tip vortex roll-up is much faster for the straight leading edge than for the straight trailing edge foil and, in the latter case, a significant portion of the roll-up occurs along the foil curved leading edge. The minimum of the pressure coefficient on the axis of the vortex was estimated from the velocity measurements and correlated with the desinent cavitation number for the largest free stream velocities. The correlation of data is very satisfactory. At the highest Reynolds number tested and at equal lift coefficients, the straight leading edge foil displays the most favorable cavitation desinent numbers.

A Scaling Law for Cavitation Inception in Circular Jet Flows

2007 ◽  
Author(s):  
Brian A. Edge ◽  
Eric G. Paterson ◽  
Mario F. Trujillo
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Scale Effects ◽  
Scaling Law ◽  
Pressure Coefficient ◽  
Cavitation Number ◽  
Scaling Relations ◽  
Length Scale ◽  
Cavitation Inception ◽  
Dynamic Head

The historical data for circular jets indicates that the incipient cavitation number increases with the diameter of the jet. This trend is not explained by the classic cavitation theory which expects incipient cavitation number to remain constant regardless of the jet diameter, flow parameters, or water quality. This paper explores the origins of cavitation scale effects and explains the correlation between the incipient cavitation number, jet diameter, and nuclei size. This is accomplished through turbulence-resolving CFD simulations of the jet flow field at three length scales and Rayleigh-Plesset bubble dynamics for three nuclei sizes. The numerical simulations show that incipient cavitation number (σi) changes significantly as the size of the jet is altered while the Reynolds number and the value of the minimum pressure coefficient are held constant. Larger nuclei bubbles (100μm) exhibit an increase in σi with jet diameter, while moderate (50μm) and small (10μm) nuclei bubble exhibit a decrease in σi as jet diameter increases. The value of σi associated with a small jet was similar for all nuclei sizes. As the jet increased in size, the disparity between the values of σi associated with each nuclei size was found to increase substantially. The equilibrium form of the Rayleigh-Plesset equation was used to derive a correction to the classic theory of cavitation inception. This correction is a function of initial nuclei size and the dynamic head of the flow. As either the nuclei properties or dynamic head of the fluid change, the magnitude of the correction term will also change. This correction to the classic cavitation theory was used to make predictions of how σi will change as length scale and Reynolds number are altered. These equilibrium predictions were found to be in good agreement with the numerical simulations of cavitation inception for large and moderate (100μm and 50μm) nuclei bubbles. Comparisons with the small (10μm) nuclei bubbles indicate that the inertial terms are quite significant for these bubbles, resulting in large discrepancies between the full numerical solution and the equilibrium predictions. In general, the equilibrium scaling relations show that as the length scale of a flow is held constant and the Reynolds number is increased, σi will converge to −CPmin. The scaling relations also show that when Reynolds number is held constant and the length scale of a flow is increased, σi will depart from −CPmin.

Steady Performance of a Flexible Hydrofoil Near a Free Surface

1990 ◽  
Vol 34 (04) ◽  
pp. 302-310
Author(s):  
Salwa M. Rashad ◽  
Theodore Green
Keyword(s):  
Mathematical Model ◽  
Free Surface ◽  
Cavity Length ◽  
Leading Edge ◽  
Cavity Flow ◽  
Cavitation Number ◽  
Deformation Characteristics ◽  
Flow Depth ◽  
Lift And Drag ◽  
The Galerkin Method

A linearized cavity-flow theory is used to develop a mathematical model to study the steady characteristics of a flexible hydrofoil near a free surface. The Galerkin method is employed to account for the mutual interaction between the fluid and structure forces. Cheng and Rott's method [1]2 is used to derive general expressions for the deformation characteristics in steady flow of an arbitrarily shaped hydrofoil, with a clamped trailing edge and free leading edge. From the analysis it is possible to determine the lift and drag coefficients, cavity length, and the foil steady deformation for any given specific foil shape, cavitation number, angle of attack, flow depth/chord ratio and rigidity. Sample numerical results are given, and the effects of flexibility and the proximity of the free surface are discussed. Chordwise flexibility tends to increase drag and decrease lift coefficients. This effect is more serious near the free surface. A slight increase of the thickness near the leading edge diminishes the flexibility effects.

Thermodynamic Effect on a Cavitating Inducer—Part I: Geometrical Similarity of Leading Edge Cavities and Cavitation Instabilities

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Jean-Pierre Franc ◽  
Guillaume Boitel ◽  
Michel Riondet ◽  
Éric Janson ◽  
Pierre Ramina ◽  
...  
Keyword(s):  
Transit Time ◽  
Cavity Length ◽  
Cold Water ◽  
Rotation Speed ◽  
Leading Edge ◽  
Cavitation Number ◽  
Thermodynamic Effect ◽  
Cavity Closure ◽  
Cavity Development ◽  
Onset Of Cavitation

The thermodynamic effect on a cavitating inducer is investigated from joint experiments in cold water and Refrigerant 114. The analysis is focused on leading edge cavitation and cavitation instabilities, especially on alternate blade cavitation and supersynchronous rotating cavitation. The cavity length along cylindrical cuts at different radii between the hub and casing is analyzed with respect to the local cavitation number and angle of attack. The similarity in shape of the cavity closure line between water and R114 is examined and deviation caused by thermodynamic effect is clarified. The influence of rotation speed on cavity length is investigated in both fluids and analyzed on the basis of a comparison of characteristic times, namely, the transit time and a thermal time. Thermodynamic delay in the development of leading edge cavities is determined and temperature depressions within the cavities are estimated. Thresholds for the onset of cavitation instabilities are determined for both fluids. The occurrence of cavitation instabilities is discussed with respect to the extent of leading edge cavitation. The thermodynamic delay affecting the occurrence of cavitation instabilities is estimated and compared with the delay on cavity development.

scholarly journals Optimization for Cavitation Inception Performance of Pump-Turbine in Pump Mode Based on Genetic Algorithm

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Ran Tao ◽  
Ruofu Xiao ◽  
Wei Yang ◽  
Fujun Wang ◽  
Weichao Liu
Keyword(s):  
Genetic Algorithm ◽  
Pressure Drop ◽  
Cfd Simulation ◽  
Pressure Coefficient ◽  
Leading Edge ◽  
Algorithm Optimization ◽  
Pump Mode ◽  
Local Flow ◽  
Cavitation Inception ◽  
Blade Thickness

Cavitation is a negative factor of hydraulic machinery because of its undesirable effects on the operation stability and safety. For reversible pump-turbines, the improvement of cavitation inception performance in pump mode is very important due to the strict requirements. The geometry of blade leading edge is crucial for the local flow separation which affects the scale and position of pressure drop. Hence, the optimization of leading edge shape is helpful for the improvement of cavitation inception performance. Based on the genetic algorithm, optimization under multiple flow rate conditions was conducted by modifying the leading edge ellipse ratio and blade thickness on the front 20% meanline. By using CFD simulation, optimization was completed with obvious improvements on the cavitation inception performance. CFD results show that the pressure drop location had moved downstream with the increasement of the minimum pressure coefficient. Experimental verifications also got an obvious enhancement of cavitation inception performance. The stability and safety was improved by moving the cavitation inception curve out of the operating range. This optimization is proved applicable and effective for the engineering applications of reversible pump-turbines.

An Experimental Investigation of Cavitation Inception and Development on a Two-Dimensional Eppler Hydrofoil

1999 ◽  
Vol 122 (1) ◽  
pp. 164-173 ◽  
Author(s):  
J.-A. Astolfi ◽  
P. Dorange ◽  
J.-Y. Billard ◽  
I. Cid Tomas
Keyword(s):  
Reverse Flow ◽  
Pressure Coefficient ◽  
Large Angle ◽  
Separated Flow ◽  
Leading Edge ◽  
Angle Of Incidence ◽  
Two Dimensional ◽  
Velocity Measurements ◽  
Cavitation Inception ◽  
Minimum Pressure

Cavitation inception and development on a two-dimensional foil with an Eppler E817 cross section issued from an inverse calculus have been experimentally investigated. The foil is theoretically designed to have a wide cavitation-free bucket allowing a large range of cavitation-free angle of incidence (Eppler, R., 1990, Airfoil Design and Data, Springer-Verlag, Berlin). The inception cavitation numbers, the noise level, the velocity distribution, the minimum pressure coefficient, the cavitation patterns (bubble, leading edge “band type” cavitation, attached sheet cavity), together with the sheet cavity length have been experimentally determined. Effects on the velocity field have been studied too with a slightly developed cavitation. For angles of incidence larger than 1 deg, a great difference exists between the inception cavitation number and the theoretical minimum pressure coefficient. However it is in agreement with the measured one obtained from velocity measurements (for 0 deg<α<6 deg). Discrepancy between theory and experiment on scale models is generally attributed to a flow separation at the leading edge. Although there are some indications of a separated flow at the leading edge, the velocity measurements do not show reverse flow with clearly detected negative velocities excepted for a large angle of incidence equal to 10 deg. Concerning sheet cavity development, the length cavity is found to scale as [σ/2α−αiσ]−m with m close to 2, for length cavities that do not exceed half the foil chord and for σ/2α−αiσ larger than about 30. [S0098-2202(00)00201-7]

A numerical nonlinear analysis of the flow around two- and three-dimensional partially cavitating hydrofoils

1993 ◽  
Vol 254 ◽  
pp. 151-181 ◽  
Author(s):  
Spyros A. Kinnas ◽  
Neal E. Fine
Keyword(s):  
Boundary Element Method ◽  
Boundary Conditions ◽  
Boundary Element ◽  
Present Method ◽  
Cavity Length ◽  
Three Dimensional ◽  
Cavitation Number ◽  
Cavity Surface ◽  
Cavity Shape ◽  
Dynamic Boundary

The partially cavitating two-dimensional hydrofoil problem is treated using nonlinear theory by employing a low-order potential-based boundary-element method. The cavity shape is determined in the framework of two independent boundary-value problems; in the first, the cavity length is specified and the cavitation number is unknown, and in the second the cavitation number is known and the cavity length is to be determined. In each case, the position of the cavity surface is determined in an iterative manner until both a prescribed pressure condition and a zero normal velocity condition are satisfied on the cavity. An initial approximation to the nonlinear cavity shape, which is determined by satisfying the boundary conditions on the hydrofoil surface rather than on the exact cavity surface, is found to differ only slightly from the converged nonlinear result.The boundary element method is then extended to treat the partially cavitating three-dimensional hydrofoil problem. The three-dimensional kinematic and dynamic boundary conditions are applied on the hydrofoil surface underneath the cavity. The cavity planform at a given cavitation number is determined via an iterative process until the thickness at the end of the cavity at all spanwise locations becomes equal to a prescribed value (in our case, zero). Cavity shapes predicted by the present method for some three-dimensional hydrofoil geometries are shown to satisfy the dynamic boundary condition to within acceptable accuracy. The method is also shown to predict the expected effect of foil thickness on the cavity size. Finally, cavity planforms predicted from the present method are shown to be in good agreement to those measured in a cavitating three-dimensional hydrofoil experiment, performed in MIT's cavitation tunnel.

Viscous and Nuclei Effects on Hydrodynamic Loadings and Cavitation of a NACA 66 (MOD) Foil Section

1989 ◽  
Vol 111 (3) ◽  
pp. 306-316 ◽  
Author(s):  
Y. T. Shen ◽  
P. E. Dimotakis
Keyword(s):  
Pressure Distribution ◽  
Pressure Coefficient ◽  
Leading Edge ◽  
Full Scale ◽  
Pressure Loading ◽  
Foil Surface ◽  
Negative Minimum ◽  
Cavitation Inception ◽  
Minimum Pressure ◽  
Bubble Cavitation

A series of experiments has been conducted on a two-dimensional NACA 66 (MOD) foil to examine the effects of viscosity and nuclei on cavitation inception. In this paper the main discussions center on two foil angles having different types of pressure loadings to represent a propeller blade section operating at design and off-design conditions. At one degree design angle of attack the foil experiences a rooftop-type gradually varying pressure distribution. At three degrees off-design angle of attack the foil experiences a sharp suction pressure peak near the leading edge. Cebeci’s viscid/inviscid interactive code is used to compute the viscous scale effects on the development of the boundary layer, lift, drag and pressure distribution on the foil. Chahine’s multibubble interaction code is used to compute the effect of nuclei, test speeds, foil size and foil surface on traveling bubble cavitation. Both computer codes are found to agree satisfactorily with the experimental measurements reported here. Two assumptions commonly used to predict full scale surface cavitation from model tests are examined experimentally and theoretically. The first assumption states that cavitation inception occurs when the static pressure reaches the vapor pressure. On the contrary, the experiments showed that the water flowing over the foil surface sustained significant amounts of tension during inception of midchord bubble cavitation as well as leading edge sheet cavitation. The second assumption states that there is no scale effect on the values of negative minimum pressure coefficient. In the case of a rooftop-type pressure loading, the second assumption is supported by the pressure numerical calculations. However, in the case of a pressure loading with a strong suction peak near the leading edge the value of negative minimum pressure coefficient is as much as 12 to 15 percent lower on a model than at full scale.

High Reynolds Gas-Liquid Two Phase Flow Around a Triangular Body

2014 ◽  
Author(s):  
Pedram Hanafizadeh ◽  
S. Alireza Hojati ◽  
Hamid Eslami ◽  
Navid Latifian
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Void Fraction ◽  
Pressure Coefficient ◽  
Leading Edge ◽  
Industrial Applications ◽  
Measurement Instruments ◽  
Two Phase ◽  
Pressure Drag ◽  
High Reynolds

In many industrial applications, some measurement instruments must be placed in a pipe in which fluid flows. Two phase cross flows around a body have seldom been studied until now and considering these flows can play a significant role in long-term reliability and safety of industrial systems. In this paper drag coefficient, pressure coefficient and void fraction around triangular bodies with different leading edge angles were considered. Also effect of Reynolds number and inlet void fraction on drag coefficient and pressure coefficient has been investigated and flow treatment behind the triangular obstacle has been examined. To achieve this aim, main equations of flow have been developed for investigation of drag coefficient in air-water two phase. Our numerical analyses were performed by a designed and written CFD package which is based on Eulerian-Eulerian approach. Geometries, which have been studied in this article, are triangle, with different leading edge angle. Other parameters such as two phase Reynolds number, free stream void fraction and bubble size were considered, too. Drag coefficient is closely relates to the turbulence and the bubble motion. Since these mechanisms vary over time, we used final value of drag coefficient after convergence. The results showed that drag coefficient is strongly depended of Reynolds number. In this simulation it can be seen that both the drag coefficient and pressure drag coefficient decrease whit increase in two phase Reynolds number and increase with decrease in inlet void fraction.

A Potential-Based Panel Method for the Analysis of a Two-Dimensional Super-or Partially-Cavitating Hydrofoil

1992 ◽  
Vol 36 (02) ◽  
pp. 168-181 ◽  
Author(s):  
C.-S. Lee ◽  
Y.-G. Kim ◽  
J.-T. Lee
Keyword(s):  
Cavity Length ◽  
Cavitation Number ◽  
Panel Method ◽  
Cavity Surface ◽  
Two Dimensional ◽  
Closure Condition ◽  
Surface Pressure Distribution ◽  
Cavity Closure ◽  
Cavitating Hydrofoil ◽  
Method Show

A potential-based panel method is presented for the analysis of a super-or partially-cavitating two-dimensional hydrofoil. The method employs normal dipoles and sources distributed on the foil and cavity surfaces. It is shown that the source plays an important role in positioning the cavity surface through an iterative process. The cavity closure condition is found very effective in generating the cavity shape. Upon convergence, the method predicts the cavitation number together with the lift, drag, and surface pressure distribution for a given cavity length. Systematic convergence tests of the present numerical method show fast and stable characteristics. Good correlations are obtained with existing theories and experimental results for both partially-and supercavitating flows.

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