DYNAMIC STALL AND CAVITATION OF STABILISER FINS AND THEIR INFLUENCE ON THE SHIP BEHAVIOUR Guilhem Gaillarde, Maritime Research Institute Netherlands (MARIN), the Netherlands SUMMARY The lifting characteristics of stabiliser fins and their efficiency are evaluated most of the time with a static and steady approach. Usually the same is applied in numerical simulations, both in the frequency or time domain. Although this approach can be assumed to be correct when the fins are working at low angle of attack in mild sea conditions, strong non-linearity appears when reaching their limits in rougher sea conditions. Non-linearity originates from dynamic effects on lift and drag, stall or cavitation. When stall occurs while sailing, the degradation in roll motion of the vessel is such that the fins can hardly recover their lift until lower waves are encountered. Hysteresis loops are then observed in the lift slope curve. At large fin angle of attack and high ship speed cavitation will also occur, resulting in lift degradation. In the present paper experimental investigation on the dynamic behaviour and characteristics of lift and drag is presented. Results of cavitation tunnel tests are presented and compared with experimental data obtained with a freerunning model in waves, both for a high aspect ratio and a low aspect ration fin. The results of these experiments will be used in the future to obtain a more accurate description of lift characteristics under dynamic conditions and thus a more accurate prediction of roll motions. Nomenclature A amplitude of oscillation [deg] c average chord length of the fin [m] l span length of the fin [m] S lateral surface foil (projected area) [m 2 ] Lpp Length between perpendicular [m] M pitching moment [Nm] L lift [N] D drag [N] C M pitching moment coefficient = M/(½ρV 2 Sc) [-] C L Lift coefficient = L/(½ρV 2 S) [-] C D drag coefficient = D/(½ρV 2 S) [-] g acceleration of gravity = 9.8 [m/s 2 ] h fin axis submersion [m] k reduced frequency =ωc/(2v) [-] P A ambient pressure in cavitation tunnel at pitch axis[pa] P atmospheric pressure [Pa] P v vapour pressure [Pa] Re Reynolds number = Vc/ν [-] Fn Froude number = V S / g. LPP [-] t dimensional time [s] t' non dimensional time [-] T period of oscillation [s] V test section velocity [m/s] V S ship speed [m/s] α ν kinematic viscosity of water [m 2 /s] ρ density of water [kg/m 3 ] σ 2 cavitation number = (P-P v+ ρ gh)/( V ) [-] ω angular frequency [s - ] 2 INTRODUCTION The lifting characteristics of stabiliser fins and their efficiency are evaluated most of the time with a static and steady approach. Usually the same is applied in numerical simulations, both in the frequency or time domain. Lift degradation due to stall is sometimes used in numerical models. Although this approach can be assumed to be correct when the fins are working at low angle of attack in mild sea conditions, strong non-linearity appears when reaching their limits in rougher sea conditions. When working in a real environment and especially at high speed, the lift and stall of the fins is subject to dynamic effects. When stall occurs while sailing, the degradation in roll behaviour of the vessel is such that the fins can hardly recover their lift until lower waves are encountered. Hysteresis loops are then observed in the lift slope curve. This effect was shown previously in a number of experimental studies, mainly conducted for aircraft or helicopter applications, see references ()-(7). This effect was also measured on stabiliser fins during seakeeping tests conducted with a free running model sailing in stern-quartering seas (8). At large fin angle of attack and ship speed above 25 knots, cavitation will also occur. Non-linear effect due to cavitation, resulting in lift degradation, was investigated on a T-foil in a cavitation tunnel. The set-up allowed the fin to oscillate at different frequencies and amplitudes in order to simulate unsteady flow conditions. The results were presented and discussed in (9). Also, scale effects were investigated and presented in (). This study showed that for hydrofoils with laminar section types and relatively high aspect ratio, scale effects on lift in an unsteady flow are rather small, while in steady flow condition scale effect can be relatively larger.
In the present paper, further investigation on the dynamic behaviour and characteristics of lift and drag is presented. Results of tests performed with regular and irregular fin oscillations in a cavitation tunnel are presented, for low and high aspect ratio fins. Irregular fin oscillations were based on measurements performed during seakeeping model tests where strong lift degradation and large roll behaviour were observed. Results of cavitation tunnel tests with irregular unsteady flow are then compared with experimental data obtained with a free-running model in waves. The aim of the study is first to check the validity of the lift and drag coefficients derived from free sailing seakeeping tests, with low Reynolds and high cavitation number conditions. This point is particularly important to assess the validity of the roll behaviour obtained from seakeeping tests with relatively small model as at high speed the roll damping provided by fin stabilisers is largely prominent. The second goal of this study is to gather enough information to prepare a numerical model for dynamic lift and drag and apply it in time domain simulations. The results can also be used to optimise the control algorithm of lifting surfaces, as developed in (), in order to avoid situation with strong non-linear characteristics of the lift. 2 TESTS IN CAVITATION TUNNEL 2. EXPERIMENTAL SET-UP Two stabiliser fins were manufactured. The fist one is a typical high aspect ratio fin, retractable, that was previously used during seakeeping tests for a 8 m high speed Ro-Ro ferry having a calm water speed of 35 knots. The tests were conducted at that time with a model of scale to 4. The fin for test in cavitation tunnel was manufactured at scale to 25. The section profile is a NACA 65-2, the main dimensions on full scale and a drawing of the fin are shown in figure. Profile: NACA 65-2 span: 4.4 m chord: 2.25 m aspect ratio:.95 area: 9.9 m 2 The second fin is a low aspect ratio fin typically used in modern motor yacht design. The relatively extreme low aspect ratio and high eccentricity allow the fin to work also at zero speed to reduce roll. Similar fin was used during free sailing seakeeping tests for a 83. m yacht. The vessel speed was in the order of 6 knots. Profile: NACA 64-8 Modified (flatten) trailing edge and tip plate span:.4 m aspect ratio:.49 chord: 2.85 m area: 4. m 2 axis at 8% of chord length from trailing edge seakeeping tests performed with :6 scale cavitation tunnel tests performed with :6 scale Figure 2: Drawing and main particulars of the low aspect ratio fin These fins have a deadrise angle of 2 to 45 deg with respect to the horizontal when fixed on the hull. The fins were mounted horizontally on the wall of the test section of MARIN s Large Cavitation Tunnel. Turbulence of the flow over the fins was induced by strips at the leading edge and at 4% of the chord length with carborundum grains with an average diameter of about 6 µm. The forces (normal and tangential to the chord of the fin) and moment on the fin were measured by a 3-component balance. The forces were projected parallel and perpendicular to the flow direction, in order to provide the lift and the drag. Figure 3 shows the sign convention as used in the presented results. L axis at 6% of chord length from trailing edge seakeeping tests performed with :4 scale cavitation tunnel tests performed with :25 scale D M α flow Figure : Drawing and main particulars of the high aspect ratio fin Figure 3: Sign convention for delivered results
observed on the profile had the same characteristics as the one observed on full scale at a speed of 34 knots. The following table 2 shows the test conditions used for the low aspect ratio fin. Cavitation tunnel a 59.6 3.2 5.8 ) [-] Re [-] V [m/s] b 3.55 6. 5 3.8 ) equivalent full scale speed 4) in [kn] 4 24 SMB Full scale 47 3.2 5 2.6 2) 3.55 2. 7 8.23 3) 6 6 Table 2: Test conditions for low aspect ratio fin Photograph : High aspect ratio fin in cavitation tunnel TEST CONDITIONS Steady and unsteady flow conditions were realised at high and low cavitation number. Tests with the same Reynolds number as during free sailing seakeeping tests were conducted. The resulting high cavitation number did not allow of course any cavitation observation and the aim was more to repeat the tests in a more confine set-up than in the large new Seakeeping and Manoeuvring Basin (SMB). Then, the same tests were repeated with the full-scale cavitation number that showed a large amount of cavitation. The following table gives a summary of the conditions in which the tests were conducted. Cavitation tunnel [-] Re [-] V [m/s] a b 4.7 5.47.4 5 6. 5.36 ) 5.95 ) equivalent full scale speed 4) in [kn] 3.2 57.8 ) 2) 3) 4) c.95 6. 5 5.95 ) SMB Full scale 25.94.4 5 3.5 2).947 3.4 7 7.5 3) 3 RESULTS FOR HIGH ASPECT RATIO FIN 3. STEADY CONDITION A selection of results are shown in the following, showing the influence of the different parameters on the measured lift, drag and moment. In Figure 4, the lift coefficient is shown in conditions a, b and c. Up to 2 deg the linear relation is relatively well followed in each condition. At higher angles of attack stall will occur. The effect of stall is stronger at low flow velocity and without cavitation. For a high flow velocity (conditions b and c) the effect of cavitation is clearly shown with a lift degradation of about 5%, for angles comprised between 5 and 25 deg. At 3 deg the lift coefficient is similar with and without cavitation..8 57.8 34 34 test section flow velocity in cavitation tunnel speed of the model during seakeeping tests in the SMB full scale ship speed according Froude s law of similitude Table : Test conditions for high aspect ratio fin The condition a has the same Reynolds number as during the tests in the SMB. In view of the high value of, no cavitation was observed. The test condition b is similar to condition c but with a higher pressure. The aim was to keep a high speed and observe stall at large incidence but also eliminate cavitation. The test condition c has the same cavitation number as the full-scale condition. In those tests, the cavitation 2.2 The program comprised series of static angle tests, harmonic oscillation tests at different amplitudes and frequencies and irregular oscillations corresponding to time traces of fin angles measured during free sailing seakeeping tests..6.4.2 o condition a o condition b x condition c 2 3 Figure 4: Effect of test condition on static lift coefficient 4
Concerning drag coefficient, the same results are obtained at high flow velocity with and without cavitation, as shown in Figure 5, for angles of attack exceeding 2 degrees. At lower angle of attack a relatively large difference is observed. It may be attributed to cavitation, as large cavitation sheet was already observed at degrees angle of attack (see photograph 2). The tests with low flow velocity (and Reynolds number) tend to overestimate the drag coefficient at large angles of attack. 2 deg Drag coefficient [-].8.6.4 Photograph 3: Steady condition, 2 deg, o condition a o condition b x condition c.2 2 3 =.95 3 deg 4 Figure 5: Effect of test condition on static drag coefficient Apparently the strongest increase in cavitation extent and change in character of the cavitation occurs between 5 and degrees angle of attack. Photographs 3 and 4 shows that almost the complete fin is covered by cavitation above α = degrees. The video recordings show furthermore that this cavitation is shed periodically in large clouds. A tip vortex cavitation is already observed at low angle of attack and increases when increasing the angle of attack. Photograph 4 also shows the backside of the fin while cavitating at 3 degrees angle of attack. -3 deg deg sheet cavitation tip vortex cavitation Photograph 2: Steady condition, deg, Photograph 4: Steady condition, +3 and -3 deg, =.95 =.95
3.2 UNSTEADY CONDITION Figure 6 shows a comparison of the results obtained in steady and unsteady condition. The unsteady condition is shown for harmonic oscillations with amplitudes of 2 and 3 degrees. Dynamic effects of lift, drag and moment coefficients are clearly observed. The graphs above represent the condition a (no cavitation and low Reynolds number). The bottom graph represents the condition c (cavitation and higher Reynolds number)..5.5 A classical clock-wise rotating loop (or hysteresis loop) is observed in unsteady condition. The Figures only show one period of the time trace and the loop was smoothen for clarity of the presentation. The original time trace and hysteresis loop presents strong vibrations caused by the periodic shedding of sheet cavitation. Vibrations are already observed at degrees angle of attack. The following Figure 6 also suggests that in cavitating condition c the dynamic effect is smaller than in noncavitating condition a. This conclusion is not fully correct as the condition a was also performed at lower Reynolds number and lower section flow velocity. A comparison of conditions b and c show that the characteristics of unsteady lift and drag are rather similar. Another important observation is the fact that during unsteady oscillation the higher the value of maximum angle of attack, the higher the angle of attack reached before the beginning of flow separation (stall), and the larger the hysteresis loop. 2 3 4. Figure 7: Effect of oscillating frequency on hysteresis loop Figure 7 shows one hysteresis loop obtained in noncavitating condition at an equivalent full scale oscillating periods of 9 and 2 seconds and 3 degrees angle amplitude. These two periods were selected as being rather typical natural roll period of vessels. No clear differences are observed between the two tests. The same conclusion applies for the tests performed in cavitating condition. 3.3 UNSTEADY CONDITION WITH IRREGULAR SIGNAL A time trace of fin angle measured during seakeeping tests with a free-running model was applied to the fin in the cavitation tunnel. The effective angle of attack of the flow on the fin was not measured. condition a condition c Figure 6: Comparison between steady and unsteady harmonic oscillation at low and high Reynolds and cavitation number harmonic oscillation 3 deg amplitude harmonic oscillation 2 deg amplitude steady angle
During tests in the SMB, the angle of attack will originate from the ship speed, the mechanical angle of attack of the fin, the velocities induced by ship motions, the wave orbital velocities and diffracted waves orbital velocities. The tests were performed in a relatively mild sea state with a high ship speed. Ship motions were moderate, apart from roll that exceeded 3 degrees in some occasion. Based on the assumption that the wave orbital velocities and diffracted wave velocities would be relatively small compared to the other components, only the ship speed was taken as inflow condition, corrected for the ship velocity (in heave, roll and pitch). The latter correction proved to be very small in that case. A view of the time trace in cavitating condition is shown in Figure 8, as well as the variations of the lift and drag coefficients. The time was scaled according to Froude s law of similitude. An additional test was performed with scaling further the time with keeping an equivalent reduced frequency k. The effect was to multiply the time scale by a factor 2.57, resulting in a longer test duration and lower fin oscillation periods. The effect on the character of lift and drag was relatively small, as shown by a detail of the time trace with stall occurrences in Figure 9. In order to compare the two time traces, the time scale were modified to allow direct comparison. Figure 8: Time traces of angle of attack, lift, drag and moment coefficients during unsteady irregular condition
.75.5.25.25.5.75 45 455 46 465 47 time [s]. Figure 9: Effect of scaling with reduced frequency k When angles of attack are lower than degrees, the lift and drag coefficients obtained from the tests in the SMB are very similar to those obtained in cavitation tunnel with a correct scaling of cavitation number and relatively higher Reynolds number. This also means in other words that the lift and drag measured in the SMB are correct. The same conclusion applies then for the derived motions, and roll in particular. When stall and cavitation occur at larger angles of attack, discrepancies are observed. The tests in the SMB seem to overestimate the lift degradation due to stall. A reason could be that the formation of cavitation decreases the effect of separation on the fin. These observations are shown in Figure, with a time trace of lift coefficient in both cases as a function of time and as a function of angle of attack. 3.4 COMPARISON WITH FREE RUNNING TESTS The test condition c in cavitation tunnel is then compared with the results of free sailing seakeeping tests performed in the MARIN new Seakeeping and Manoeuvring Basin. The results of these tests were presented in (8). The comparison is shown in the following Figures and. Concerning drag, the tests in the SMB also tend to overestimate the extreme values, compared with tests in cavitation tunnel with cavitating condition. Surprisingly, cavitation seems to limit the sudden increase in drag at large angle of attacks. These observations are shown in Figure. Other effects such a variation of fin submergence with free running tests and local wave orbital velocities are difficult to evaluate, but may play a role in the differences observed between the tests..5.5 Drag coefficient [-].75.5.25 455 462.5 47 time [s].5.5 seakeeping basin cavitation tunnel Drag coefficient [-] 455 462.5 47 time [s].8.6.4.2 seakeeping basin cavitation tunnel 4 2 2 4 Figure : Comparison of lift coefficient between cavitation tunnel and free sailing seakeeping tests 4 2 2 4 Figure : Comparison of drag coefficient between cavitation tunnel and free sailing seakeeping tests
3.5 RESULTS FOR LOW ASPECT RATIO FIN The results of tests with a low aspect ratio fin were somewhat different as no cavitation was observed. The relatively high cavitation number is due to the low operational velocity of vessels equipped with such fins. The following figures highlight the main results obtained with low aspect ratio fins and will be developed further in the future, typically for semi-displacement motor yacht applications..5.5 4 2 2 4.6.4.2 4 2 2 4 Figure 2: Steady and unsteady lift and drag obtained in cavitation tunnel tests The tests showed that the lift and drag generated by fin stabiliser during free sailing tests are similar to those measured in cavitation tunnel with correct cavitation number scaling. The fact that no cavitation was observed during the tests and that no stall was present for this type of profile explain this conclusion. 4 CONCLUSIONS The present set of model tests confirm the fact that both cavitation and stall affect the performance of high aspect ratio fins when sailing at high speed and when angles of attack are larger than degrees. Above degrees angle of attack, the effect of cavitation is clearly present with a lift degradation of about 5%. At 3 degrees the lift coefficient becomes similar with and without cavitation. During unsteady oscillation the higher the value of maximum angle of attack, the higher the angle of attack reached before the beginning of flow separation (stall), and the larger the hysteresis loop. When angles of attack are lower than degrees, the lift and drag coefficients obtained from the tests in the SMB are very similar to those obtained in cavitation tunnel with a correct scaling of cavitation number and relatively higher Reynolds number. At angles of attack greater than degrees, the tests in the SMB tend to overestimate the lift degradation due to stall. A reason could be that the formation of cavitation decreases the effect of separation on the fin. Also the drag can be overestimated when the fins reach large angles of attack. The discrepancies can be attributed to the differences in Reynolds number and cavitation number. It should be kept in mind however that other parameters such as local flow velocities due to ship motions or wave orbital velocities (present in reality and during seakeeping tests) may also play a relatively large influence. 5 FURTHER DEVELOPMENT Further development and comparison will be made with the set of tests performed in cavitation tunnel. The results obtained will be used to increase the accuracy of ship motion prediction, especially for roll in stern-quartering seas. Deterministic simulations will be used to reproduce the model tests and obtain more insight in the mechanism yielding non-linear large roll angles. The tests will also be used to try to optimise fin control algorithms. 6 REFERENCES. Ericsson, L.E., Reding, J.P., Dynamic stall at high frequency and large amplitude, J. Aircraft, Vol.7, No.3, March 98. 2. Mc Croskey, W.J., Pucci, L., Viscous-inviscid interaction on oscillating airfoils in subsonic flow, AIAA Journal, Vol.2, No.2, February 982. 3. Walker, J.M., Helin, H.E and Strickland, J.H., An experimental investigation of an airfoil undergoing large-amplitude pitching motions, AIAA Journal, Vol.23, No.8, August 985. 4. Hoerner, S.F. and Borst, H.V., Fluid dynamic lift, 2nd ed., Hoerner Fluid Dynamics, 985.
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