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Types of cavitation: sheet cavitation
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Types of cavitation: sheet cavitation

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Types of cavitation: sheet cavitation Types of cavitation: sheet cavitation Document Transcript

  • Chapter 6Types of cavitation: SHEETCAVITATION Figure 6.2: Sketch of 2-dimensional sheet cav- itation later. Without diffusion the pressure in the sheet cavity will be close to the equilibrium vapor pressure and the surface of the cavityFigure 6.1: Sheet cavitation on a propeller can be considered as a free surface.blade at full scaleObjective: Description of the appearanceand behavior of sheet cavitation 6.1 2 Dimensional sheet cavitation In two dimensions a sheet cavity can be An example of sheet cavitation on a ship sketched as in Fig. 6.2propeller is given in Fig. 6.1. Sheet cavitation occurs when there is a Sheet cavitation is a region of vapor which strong low pressure peak at the leading edgeremains approximately at the same position of the foil and sheet cavitation therefore hasrelative to the profile or propeller blade. In its leading edge close to the leading edge ofthis way it seems attached to the foil. The the foil.surface of sheet cavitation can be very glossy,at least at model scale, but at full scalethe surface is often not transparent, as in 6.1.1 The cavity leading edgethe outer radii on Fig. 6.1. In this Figurethe sheet cavity is attached to a strongly The fact that the surface of a sheet cavity iscavitating tip vortex, which will be treated a constant pressure surface has consequences 37
  • 38 G.Kuiper, Cavitation in Ship Propulsion, June 21, 2012 there are no nuclei in that region. Although some measurement indicate the existence of such a small region, it is more probable that the location of C is such that the radius of the cavity leading edge is large and the pres- sure outside the cavity remains very close to the vapor pressure. This makes the region S- C a constant pressure region. Hoekstra [20] found from RANS calculations that in this re- gion a significant production of vapor takes place, which could make that the streamlines are not coinciding with the free surface. It is not clear yet if this is physical or a conse- quence of the cavitation model in the RANS calculations. Williams et al [64] point out thatFigure 6.3: Leading edge structure of a 2D the definition of cavity length is different whensheet cavity the leading edge is taken from points S or C. For thin foils such as used in ship propellers and airplanes the distance S-C is very shortfor the streamlines at the beginning and at and the precise structure of the leading edgethe closure of the cavity, as shown in Fig 6.3. of the cavity is unimportant.At the beginning or leading edge of the cavity Note that the flow separation at the leadingthe constant pressure means that the stream- edge of the cavity (point S) is cavity induced.lines separate tangentially from the surface of At a higher pressure without cavitation no sep-the foil in point S(assuming that the foil is a aration may occur!smooth surface). Tangential separation, how-ever, means that there is a region just down-stream of the separation location where the 6.1.2 The trailing edge of thecavity is very thin. So thin that the surface cavitytension becomes recognizable and results in acurved surface, making the leading edge of the More important is the structure at the trailingcavity in point C instead of S. edge of the cavity. A constant pressure along the free surface requires a smooth attachment The curvature at the leading edge of the cav- of the streamline to the foil. This does notity depends on the surface tension between va- happen in general. Instead some fluid will re-por and water, and on the location of point C. enter the cavity, creating a so-called re-entrantThe angle at the separation point depends on jet.Fig 6.4the contact angle between water, vapor andthe surface material. Due to viscosity of thefluid a circulation will occur inside the red re- 6.1.3 Shedding of clouds bygion. sheet cavitationAs a consequence of the surface tension thepressure in the red region upstream of the sep- As a result the two-dimensional cavitating flowaration location will be below the vapor pres- over a foil is never steady, as is illustrated insure. This would mean that there is fluid be- Fig. 6.5.tween point S and C with a pressure below When the cavity becomes shorter at a higherthe vapor pressure. This is only possible when pressure the shedding becomes less violent,
  • June 21, 2012, Sheet Cavitation39Figure 6.4: Leading edge structure of a 2Dsheet cavity Figure 6.6: High Speed Video:Shedding of cloud cavitation behind a short two- dimensional sheet cavity. The presence of a re-entrant jet makes that this cavity cannot remain stable. It gradually fills with fluid. As a result part of the cavity, or sometimes even the whole cavity, is separated from the foil and is shed as cloud cavitationFigure 6.5: High Speed Video:Shedding with the fluid, as sketched in Fig. 6.7of cloud cavitation behind a long two-dimensional sheet cavity. When the re-entrant jet is 2-dimensionalbut remains present. (Fig. 6.6) it means that the jet is directed upstream. In principle the red streamline in Fig 6.4 is A strong upstream re-entrant jet can eventhe cavity surface and it is a constant pressure reach the leading edge and in such a casesurface at the equilibrium vapor pressure. The the whole sheet cavity detaches from theexistence of a re-entrant jet means that there is foil,as is shown in Fig. 6.8, while a newa streamline just outside the re-entering fluid sheet is formed at the leading edge. Notewhich ends in a stagnation point P (the blue that this occurs in steady inflow!. This is astreamline in Fig. 6.4). Outside that stream- very violent unsteady behavior of the cavity,line the flow continues over the foil surface (the which leads to a violent implosion of the cloud.green streamline).
  • 40 G.Kuiper, Cavitation in Ship Propulsion, June 21, 2012Figure 6.7: Sketch of shedding of cloud cavi- Figure 6.9: Cavity surface flow and reflectedtation in 2D re-entrant flow entrant flow the re-entrant flow is ”reflected” against the cavity trailing edge, as is sketched in Fig 6.9. This reflexion can be understood, because the trailing edge of the cavity is a con- stant pressure line. There is no reversion of the flow along the trailing edge. So only the flow component perpendicular to the trailing edge of the cavity is reversed.Figure 6.8: Shedding of cloud cavitation on a The reflection of the re-entrant flow against2-dimensional foil the trailing edge of the cavity has serious con- sequences for shedding. When the cavity trail-6.2 Three-dimensional ing edge is convex the re-entrant flow will con- verge, as is sketched in Fig. 6.10. shedding of cloud cav- This leads to a strong upward flow in the itation centerline of the convergent re-entrant flow, with shedding as a result. A schematic form ofIn general the re-entrant jet is not 2- the shedding is that a wedge shaped openingdimensional, even not on a 2 dimensional foil, is formed in the cavity. Although the struc-as can be seen in Fig. 6.6. Sometimes there ture of the re-entrant flow is unknown, it seemsis a large part of the sheet which detaches, that the collision at the centerline cuts off thebut generally the shedding has a smaller scale. downstream part of the cavity and this cut-offThis is because the trailing edge of the cavity spreads quickly in spanwise direction, leadingis not a straight line. There are disturbances in to the wedge-shaped hole in the cavity.the cavity length and this leads to curvatures The part of the cavity downstream of the open-in the trailing edge. In such a case the re- ing is shed with the flow. It often contains ro-
  • June 21, 2012, Sheet Cavitation41 Figure 6.12: Shedding of a vortical cavity be- hind a three-dimensional sheet cavity in steadyFigure 6.10: Converging re-entrant flow due to inflowa concave cavity trailing edge Figure 6.13: Shedding behind a two- dimensional cavity in steady inflow cavity has a concave trailing edge at the lo- cation of the shedding and the re-entrant flow will not converge, but spread out inside the cavity. However, at both ends of the concave region there is a convex location again and the shedding will repeat itself on a different scale. This mechanism is also present in ”two-Figure 6.11: Schematic shedding of a vortical dimensional” cavities, where smaller oscilla-cavity due to converging re-entrant flow tions of the trailing edge of the cavity cause lo- cal shedding. An example is given in Fig. 6.13.tation, so it has the characteristic of a short Such small scale shedding was also observedcavitating vortex (Fig 6.11). in the video of Fig 6.6. Cavitation frees dis- A picture of such a shedding is shown in solved air from the fluid and after collapse of aFig. 6.12. cavity there is always free air left. A stream of In this figure the cavity was strongly 3- free air bubbles is therefore always present indimensional, which was caused by the twisted the wake of cavitation. The three-dimensional;shape of the foil ([16]). The remaining sheet shedding on a small scale behind a 2 dimen-
  • 42 G.Kuiper, Cavitation in Ship Propulsion, June 21, 2012sional sheet cavity can explain that the stag- same length scale lshed is used. However,nation pressure (at the location P of Fig. 6.4 when the Strouhal number remains based onis not present (although it is also very difficult the maximum cavity length and the relevantto measure). length is the shedding length, this results in an increase of the theoretical Strouhal number by the ratio llshed . cav6.2.1 Shedding frequenciesA feature that can be measured in this com- Another questionable assumption in theplex flow is the shedding frequency. This shed- determination of the theoretical Strouhalding frequency is generally more pronounced number is the velocity of the re-entrant flow.at strong , more or less two-dimensional, cav- Very little is known experimentally about thisitation, where the re-entrant flow is reaching value. It seems reasonable that viscosity willthe leading edge. When the shedding is caused slow the re-entrant flow down. In that caseat the leading edge the relevant length scale is the time required for one shedding increasesthe cavity length lcav . The shedding frequency and the Strouhal number decreases.is therefore often made non-dimensional as theStrouhal number: For two dimensional configurations a value of the Strouhal number of around 0.25 has f ∗ lcav been reported (e.g. [10], [3]), but values of 0.11 St = (6.1) V to 0.40 have also been reported 2 . A difficulty is the definition of the cavity length, which where f is the shedding frequency (in HZ) is inherently unsteady when shedding occurs.and V is the incoming velocity. In most cases the maximum cavity length wasWhen the re-entrant jet reaches the leading taken. Foeth ([16]) found no relation betweenedge of the cavity and causes shedding there, the cavity length and the cavitation index andthe situation is as given in Fig. 6.4. In for his cavity shape (Fig. 6.12). The Strouhalthat case some sort of theoretical shedding number (again based on the maximum cavityfrequency can be derived. The flow velocity at length) he found was less than 0.2. However,the cavity surface can be estimated assuming √ that was on a three-dimensional cavity , wherepotential flow as V 1 + σ. Assuming that multiple sheddings occurred during a cycle, asthe re-entrant flow has the same velocity, the will be discussed next.time required for one shedding is 2 ∗ √lcav . V( 1+σ)The theoretical Strouhal number in that case √is St = 0.5 1 + σ. 1 A weak point is the 6.2.2 Shedding behind a three-assumption that the shedding takes place over dimensional sheet cavitythe maximum cavity length. When the realshedding occurs over a fraction of the maxi- In three dimensional cavities the shape of themum cavity length, this theoretical Strouhal trailing edge affects the convergence of the re-number is not changed when the length scale entrant flow. This leads to a strong spanwiseof the cavity length lcav is replaced by an component of the re-entrant flow (called sidearbitrary shedding length lshed , as long as entrant jets by Foeth in [16]). The mechanismin the definition of the Strouhal number the of shedding, as described above, may become more complex, as is shown in the high speed 1 There is something to say for the assumption that 2the velocity of growth after √ shedding goes with the Note that Arndt mentions a theoretical coefficientvelocity V instead of with V 1 + σ. In that case the of 0.25 instead of 0.5, but the argument was not givenshedding time is T = lcav ∗ (1 + √1+σ ) V 1 in [3]
  • June 21, 2012, Sheet Cavitation43Figure 6.14: High Speed Video:Shedding of Figure 6.15: High Speed Video:Shedding ofcloud cavitation behind a three-dimensional cloud cavitation at the tip of a rectangu-sheet cavity in steady inflow. lar foil. Courtesy: Gongzheng Xin, CSSRC, Wuxi,Chinavideo of Fig. 6.14. In this case the cavity was made three This generally results in a very complexdimensional, so that the shape of the trailing shedding pattern, in which repeatable struc-edge was no longer a line, but a curve. This tures can only distinguished with difficulty.was done using a twisted foil, which had the An example is the shedding pattern of aheaviest loading in the centerline and very sheet cavity at the rectangular tip of a foil.little or no loading at the tunnel walls. This (Fig. 6.15). The inflow is steady.arrangement shows more clearly the effect The regular pattern is sharply illustrated byof converging re-entrant flow. The shedding a single picture out of this collapse: Fig. 6.16.mechanism as described above occurs repeat- This picture also shows that in this caseingly. After a shedding in the cenbterline the roughness has been used to generate sheettwo resulting cusps also generate shedding cavitation. At the leading edge the sheet stilland so on. At the same time the shedding consists of local spots, which merge furtherdoes not involve the whole re-entrant flow. downstream. Due to this merging the cavityA diverging re-entrant flow persists after a behaves as a single sheet (for a discussion onshedding, so the complete shedding period these phenomena see also [59].of the cavity contains multiple local shed-dings. The fact that the shed cavity contains A three-dimensional cavity can be madevorticity is illustrated by the complex vortex completely steady at the trailing edge whenpattern, which is visible in between of the the re-entrant flow is deflected and does notlocal sheddings. These connecting vortices cause shedding. This is e.g. the case on a pro-become also visible because they tend to peller blade in Fig. 6.17. At the inner radii ofcavitate in the core. the sheet a triangle is visible. This is the re- entrant flow, which reflects against the trail-
  • 44 G.Kuiper, Cavitation in Ship Propulsion, June 21, 2012Figure 6.16: Regular but complex three di- Figure 6.18: Smooth and steady sheet cavitymensional shedding of a sheet cavity on a foil on a model propeller blade in uniform flowin steady inflow An extreme example of a stable sheet with- out shedding is shown in Fig. 6.18, where the re-entrant flow is fully absorbed by the cavi- tating tip vortex. 6.2.3 Unsteady Sheet cavitation The shedding of sheet cavitation generally is very complex. Fortunately the natural shed- ding of sheet cavitation in steady conditions is not very erosive in many conditions. An exam- ple is the shedding of cloud cavitation behind an irregularly shaped sheet cavity on a ship propeller (Fig. 6.19 The sheet cavity on this propeller extends from the leading edge, which is not completely visible. The trailing edge of the sheet has some strong curvatures due to imperfections of the propeller geometry. The sheet varies in timeFigure 6.17: Steady sheet cavitation at the in- with the blade position, but the sheet is rel-ner radii of a model propeller with visible re- atively steady in comparison to the naturalentrant flow shedding behind the sheet. Thee natural shed- ding at the corner of the sheet trailing edge ising edge and therefore moves outward. At the strong and almost periodical. This is due toouter radii the collected re-entrant flow causes a local converging re-entrant flow at the loca-shedding, but at the inner radii the sheet is tion of the maximum length of the sheet. How-stable. // ever, this type of natural shedding is generally
  • June 21, 2012, Sheet Cavitation45Figure 6.19: Shedding behind an irregularsheet cavity on a full scale propellernot erosive. Erosivity is strongly enhanced byunsteady conditions, which can enhance the Figure 6.20: High Speed Video:Oscillatingshedding process and the implosion. This will sheet cavity. Top view. (courtesy Goran Bark,be discussed in a separate chapter. Now only Chalmers University, Sweden)some physical features of unsteady behaviorwill be mentioned. A varying angle of attack causes an un- tack increases and in this stage the re-entrantsteady cavity on the foil. This means that flow is absent or weak. The trailing edge ofthe sheet cavity has a period of growth and the cavity remains smooth and transparent.a period of decline. Consider the situation as When the angle of attack begins to decreasein Fig. 6.4. When the cavity grows and the the growth of the cavity stops and the re-velocity of point P is about equal to the flow entrant flow emerges. The re-entrant appearsvelocity, the re-entrant jet disappears, because when the growth stops and becomes strongthe pressure in the moving stagnation point is when the cavity begins to shrink. This resultsalso equal to the vapor pressure. In that case in a very strong re-entrant flow neat the trail-the re-entrant jet disappears. Similarly, when ing edge of the sheet, which is converging be-the cavity contracts, the strength (thickness) cause of the shape of the trailing edge. Theof the re-entrant flow will increase and the sharp convergence in the center of the sheetshedding process will become more violent. is clearly visible. Note that the collision of This is illustrated in the following case of re-entrant flow begins in the rear end of thean unsteady sheet cavity on a foil. The an- cavity. The re-entrant flow at the sides has agle of attack of the inflow of this observed foil downstream component due to the angle of thewas varied using another oscillating foil up- cavity trailing edge. this flow will also end upstream of the observed foil, which remained in the rear end of the cavity. The colliding re-steady. The cavity observed is a very smooth entrant flow cuts through the cavity, separat-sheet cavity on the steady foil. The top view ing the two halves of the cavity.// It is remark-is shown in the video of Fig 6.20 (Chalmers able that the implosion of these two halves isUniversity, Department of Naval Achitecture not very violent. Violent implosion occurs inand Ocean Engineering, project 2096). the two clouds which are formed at the center- The sheet cavity grows when the angle of at- line. The violence of the implosion is evident
  • 46 G.Kuiper, Cavitation in Ship Propulsion, June 21, 2012Figure 6.21: High Speed Video: Oscillatingsheet cavity. Side view. (courtesy Goran Bark,Chalmers University, Sweden)from the rebound which occurs. This implo-sion is assumed to be erosive, but the precisemechanism there is not yet well understood. The collision of the re-entrant jet causes anupward flow in the centerline of the sheet cav-ity. The strength of this upward flow is illus-trated by the side view of the same oscillatingcavity, as shown in Fig. 6.21. The vertical velocity is highest near thetrailing edge of the sheet. This is also theregion of the violent collapse. So it seemsthat the main collapse, and subsequent riskof erosion, comes from the bubble cloud whichis generated by the colliding re-entrant flow.This has to be investigated further. In thissimplified case the cloud generated by theupwards directed re-entrant flow is separatedfrom the implosion of the two glassy parts oneach side of the cavity. It makes the eventsinvolved more clear, but it should be kept inmind that generally the phenomena are muchmore complex.