Quasi-Steady Two-Quadrant Open Water Tests for the Wageningen Propeller C- and D-Series

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1 Twenty-Ninth Symposium on Naval Hydrodynamics Gothenburg, Sweden, 26-3 August 202 Quasi-Steady Two-Quadrant Open Water Tests for the Wageningen Propeller C- and D-Series Jie Dang, Joris Brouwer, René Bosman and Christiaan Pouw (MARIN, 2 Haagsteeg, 6708PM Wageningen, The Netherlands) ABSTRACT The Maritime Research Institute Netherlands (MARIN) has recently started a Joint Industry Project (JIP) on controllable pitch propeller (CPP) series called the Wageningen Propeller C- and D-series, after the successful development of the famous Wageningen B-series which are used by designers and engineers worldwide. The B-series comprise the open water characteristics of conventional fixed pitch propellers (FPPs) designed for merchant ships with various numbers of blades and blade area ratios at different pitch. For several of these propellers, also the four-quadrant characteristics were published by MARIN in the sixties and seventies of the last century. Today many ships are equipped with CPPs. Also used widely are the ducted CPPs, both for ships and offshore structures. The off-design performance of the CPPs is not only of importance for ships powering performance, but also for e.g. dynamic positioning and manoeuvring of those vessels. Due to a lack of systematic information for the CPPs in such cases, the B-series data are often used instead, both for the estimation in an early design stage and also as the final data delivered for specific new CPP designs, simply because there is no other systematic data available rather than the B-series data. However, the characteristics of CPPs differ substantially from those of FPPs. There is a high demand for developing CPP series with full off-design information - the complete twoquadrant open water characteristics at all possible pitch settings. In order to reduce the cost, a quasi-steady propeller open water test technique has been developed and thoroughly studied under support of this JIP, which reduced the tank test time by a factor of 8 to 0. This method ensures the affordability of the tests for the C- and D-series, and therefore the whole JIP. In addition to the propeller thrust and torque, the propeller blade spindle torque is also provided as systematic data in propeller series for the first time. NOMENCLATURE hydrodynamic pitch angle [ o ] D propeller diameter [m]; drag [N] I, I a mass moment and added mass moment of inertia [kgm 2 ] k reduced frequency[-]; Fourier harmonics [-] m, m a mass and added mass [kg] n propeller shaft rotational rate [/s] angular acceleration [/s 2 ] P propeller pitch [m] Q propeller shaft torque [Nm] Q blade propeller blade spindle torque [Nm] R propeller radius [m] T propeller thrust [N] test run period [s] V a propeller advance speed [m/s] linear acceleration [m/s 2 ] INTRODUCTION The Maritime Research Institute Netherlands (MARIN), former Netherlands Ship Model Basin (N.S.M.B.), started to develop the well-known Wageningen Propeller B-series right from the establishment of this institute in 932 (Kuiper 992). The first series were published by van Lammeren (936) and Troost (938 and 940), followed by a long period of further developments and expansions of the series over more than 40 years. A major review of the available data was given by van Lammeren et al (969 and 970). The B-series had been further extended to 6 and 7 bladed propellers in the 970 s. Totally, 20 series with more than 20 propellers were tested over that period. Systematic series have also been developed for ducted propellers since 954 (van Manen 954). A major amount of data of the K a -series were published by Oosterveld (970). In the meantime, other systematic propeller series were also developed worldwide, such as the Taylor, Gawn and MAU series. However, none of the these series is so extensive as the B-series which have found widespread applications. Besides that the propeller characteristics (the thrust and the torque) of the series in design operation conditions have been made available by model tests between J=0 and K T =0, fourquadrant open water characteristics of some of the propellers in the B-series and in the K a ducted propellers series were also made available in the 980 s (MARIN report 984) for offdesign conditions. Table provides an overview of the propellers in the B-series where their 4-quadrant open water characteristics are available. For the K a -series, only K a 4-70 propellers in 9A and 37 ducts have been published.

2 Table Overview of B-series with four-quadrant open water characteristics (pitch ratio P/D of the propellers are listed in the table). A E /A 0 [%] Z=3.0 Z= , 0.6, 0.8.0,.2, Z=5.0 Z=6.0 Z=7.0 Different from fixed pitch propellers (FPPs), controllable pitch propellers (CPPs) are well-known for their advantage for full power utilization at any circumstances: accelerating and stopping; rapid manoeuvring; dynamic positioning (DP); etc. For these reasons, CPP are widely used for multi-purpose vessels where their propulsors are often used in off-design conditions. In order to predict the performance of a CPP in off-design conditions, people have to either carry out dedicated and expensive measurements for a specific propeller design, such as often done for navy vessels (Hampton 980, Queen 98), or rely on the estimated values from the existing four-quadrant open water data from the B-series (Roddy et al 2006), which were primarily designed for merchant ships with FPP blade forms. Scarce information is available in the public domain for the complete two-quadrant open water characteristics of CPPs, especially when the propeller blades are deflected away from its design pitch (Yazaki 962, Chu et al 979). In the Wageningen series book (Kuiper 992), off-design information is only available for two CPPs in ahead and astern conditions, one with a design pitch ratio of zero and the other of one. With the booming business in oil exploration in recent years, accurate prediction of the off-design performance of a propulsor becomes more important than ever, especially in the requirements for DP operations. Dedicated tests for each propeller design is unaffordable for most of the projects, while the existing limited information is far than enough. There is a strong demand on developing new contemporary CPP series with complete information of their off-design performance. In addition to these, a CPP blade has a completely different blade form as an FPP. This is because more practical issues need to be considered for a CPP, such as: that the blades must be able to pass each other from positive pitch to negative pitch; that the blade has to sit on the blade foot between bolt holes; that the blade overhang at the blade root is not preferable to prevent stress concentration; that the blade tip must not touch the inner side of a duct at any deflected pitch angles for the ducted CPPs; etc. Within all of these, one of the important and unique thing is the blade spindle torque of CPPs (Pronk 980), where very limited information can be found (Chu et al 979, Ito et al 984, Jessup et al 2009, Koushan 20). To the knowledge of the authors, there is also no CPP series with systematic information on the propeller blade spindle torque at all possible blade pitch settings (from full positive pitch to full negative pitch and over the complete two quadrants). With the strong demands from the industries and by taking into account the fact that CFD calculations (Chen and Stern 999) are not yet accurate enough and needs still to be validated against model test results, from the beginning of 20 MARIN started to consider, together with the universities and the industries, the possibilities of developing a new CPP series. In September 20, a Jointed Industry Project (JIP) was officially launched, which is called the Wageningen Propeller C- and D-series for both open and ducted CPPs. Here the C stands for controllable and the D stands for ducted. Conducting propeller series tests for the complete two quadrants, especially at different pitch settings for CPPs (typically more than 0 pitch settings are needed between full positive and full negative pitch), is not affordable at the present economic situation. New test technology needs to be developed in order to reduce the cost significantly. This is made possible by the rapid development of sensor technology in the past decades, which makes dynamic measurement possible at higher frequencies with rapid response. This leads to the idea of a quasi-steady test technique for propeller open water characteristics. Quasi-steady test techniques have been already used for the propulsion tests in the towing tank of MARIN for some years (Holtrop and Hooijmans 2002, Verhulst and Hooijmans 20). However, quasi-steady propeller open water test has never been explored in the past. Under support of the Wageningen C- and D-series JIP, a pilot study has been successfully carried out, which proves that the quasi-steady test results are as accurate as the conventional steady test results, while reduces the test time by a factor of 8 to 0. The results of the pilot study is presented in this paper, with detailed discussions on the test set-up, the sensors, the test procedure, the data analysis and the results, including also the uncertainty analysis. FACILITY, TEST SET-UP AND INSTRUMENTATION The model tests for the study have been carried out in the Deep Water Towing Tank (DT) of MARIN, which measured 250m long, 0.5m wide and 5.5m deep. The detailed description of the facility can be found on MARIN web site. An open water test set-up, as sketched below in Figure, has been used for the present study. This test set-up has a very slender POD body and a thin strut. The propeller shaft is driven by a toothed-belt through the hollow strut, connecting the propeller shaft to the electric motor shaft above on the towing carriage. Figure A sketch of the open water test set-up with test cap. 2

3 Dedicated sensors have been designed and manufactured to measure the propeller thrust, the torque on the shaft and also the blade spindle torque on one blade the key blade. The blade transducer is special designed and capable to measure the spindle torque on the key blade with a negligible disturbance of the thrust and torque forces which provide bending moments on the transducer at the same time. All the sensors are shown in Figure 2. After the placement of the strain gauges and soldering lacquer threads for the blade transducer, the transducer is coated with a special watertight coating which stays flexible to avoid hysteresis and creep. When this process is done, the transducer is tested in water for three days to check if the transducer is still watertight. After three days, the insulation value should be more than 500 MΩ otherwise the measurements can be disturbed. The signals from the sensors are transmitted by cables through the hollow shaft to the other end of the test set-up and are sent to the carriage through slip-rings. This open water test set-up is equipped with only an eight-channel slip ring set. Normally this is enough for the thrust and torque measurements - four channels for the excitation voltage of the two strain gauge bridges and four channels for the signals. For the present three sensors, the excitation voltage is shared. The other six channels are used for the signals of the three sensors. anodized surface, in order to reduce the influence of the mass and mass moment of inertia on the measurements. Two photo s of the propeller with the blades fitted to the instrumented hub are shown in Figure 3 where the key blade is bolted to the blade sensor which can be easily identified on the photo by the gaps between the blade foot and the hub (the blade facing the reader in the photo on the left is the key blade). Figure 3 MARIN stock propeller blades No. 726R fitted to the measuring hub with blade sensor, at design pitch. The inside space of the hub has been fully used to accommodate the blade spindle torque sensor and no shaft hole with keyway is able to be made through the hub. The propeller is hence mounted on one end of the hub by flange directly on the thrust and torque sensors without any friction of sealing and bearings. In order to have control on the accuracy of the blades, the mounting method and the CPP pitch setting, the propeller has been optically scanned at its design pitch. The results are compared to the theoretical geometry and the deviations are shown in Figure 4 and 5. The major deviations are seen as a kind of small inclination due to the structure of the two halves of the hub. The pitch at 0.7R is judged as accurate enough and attention needs to be put on the adjustment of the pitch settings between test runs. Figure 2 Propeller shaft thrust and torque sensors and the blade spindle torque sensor A four-bladed controllable pitch propeller model No. 726R from the stock of MARIN has been chosen for the present study. The propeller model is made in such a way that three of the blades are directly clamped by the two-halves of the hub with four bolts (see Figure 2) while the key blade is bolted to one end of the blade spindle torque sensor and the other end of the sensor is clamped also by the two halves of the hub. By loosening the bolts on the hub, the pitch of each blade can be adjusted and set to different pitch settings, including the key blade. This is usually done on the MARIN s pitch adjustment table. This selected stock propeller is a typical controllable pitch propeller (CPP) with contemporary blade design for high power density and high speed vessels with comfort requirements. Both the propeller blades and the hub are made of aluminium with Figure 4 Deviations (in mm) of the stock propeller from its theoretical geometry, pressure side, results of optical scan. 3

4 At propeller off-design conditions, the propeller hydrodynamic pitch angle is often used, instead of the advance ratio J, to define the operation condition of the blades, Under this definition, a complete set of two-quadrant open water characteristics of a controllable pitch propeller covers the range -90 o +90 o. A quasi-steady open water test is, in principle, an unsteady model test by continuously varying the advance speed and/or the rotational rate in order to obtain the steady state performance of a propeller. For the present study, we have proposed the following four test runs in order to cover the complete two quadrants, as numbered in Table 2. Figure 5 Deviations (in mm) of the stock propeller from its theoretical geometry, suction side, results of optical scan. The test setup after mounting the propeller is shown by the photo in Figure 6. During the tests, the shaft is immersed under the water surface with a distance according to ITTC (2008) standard procedure. Figure 6 The instrumented test set-up, connected to the towing carriage before immersing into the water. QUASI-STEADY TEST PROCEDURE & ASSUMPTIONS In a conventional propeller open water test from J=0 to K T =0, the propeller shaft rotational rate is often kept constant while the advance speed of the propeller varies, as recommended by the ITTC (2008). During propeller fourquadrant open water tests, both the advance speed and the shaft rotational rate have to vary and change directions, because only a finite towing speed of the carriage can be achieved. However, most controllable pitch propellers will never rotate reversely, except for some special applications e.g. a CPP connected to a diesel-electric drive system. This practice has been also used here during the model tests, where only one rotational direction (positive rotational direction) has been tested. Therefore, only two-quadrant (the first and the fourth quadrant) open water characteristics have been studied and discussed in this paper for the quasi-steady test technique. Extending this technique to the full four-quadrant tests should be straightforward. Table 2 Quasi-steady test runs for the complete 2-quadrant open water characteristics of a controllable pitch propeller. run shaft rotational rate advance speed range constant +n max 0 to +V a max to 0 0 o to ~+30 o to 0 o 2 0 to +n max to 0 constant +V a max +90 o to ~+30 o to +90 o 3 constant +n max 0 to -V a max to 0 0 o to ~-30 o to 0 o 4 0 to +n max to 0 constant -V a max -90 o to ~ -30 o to -90 o This proposal makes it possible to test the complete twoquadrant open water characteristics of a propeller in only 4 test runs, using 2 runs by varying the towing speed of the carriage and 2 runs by varying the shaft rotational rate. From the first two runs - No. and No. 2, the results in the first quadrant for from 0 to +90 degrees can be obtained. From the last two runs - No. 3 and No. 4, the results in the fourth quadrant for from 0 to -90 degrees can be obtained. Two forms of variations of the carriage (advance) speed and the propeller rotational rate have been considered and thoroughly investigated in the present study. They are the sinusoidal variations and the trapezoidal variations as sketched in Figure 7. Figure 7 Two forms of variations sinusoidal & trapezoidal. The advantage of the sinusoidal variations is that all of its higher derivatives are smooth functions of time. However, it has a high rate of change at its two shoulders. The trapezoidal variations have the advantage of a (±) constant rate of change for the speed or the rotational rate over the whole range of one test run, but may suffer from the non-continuity of their derivatives at the beginning and end, and also in the top region. 4

5 For the first quadrant (test runs No. and No. 2), the towing carriage is travelling in the normal towing direction, which we call the positive direction as shown in the sketch in Figure 8. Figure 8 Sketch of test set-up for the first quadrant tests. For the fourth quadrant (test runs No. 3 and No. 4), we have studied the following two possibilities. One is shown in the sketch in Figure 9 with exactly the same set-up used for the first quadrant test but towed by the carriage in the reverse direction. The advantage of this method is that the whole set-up remains the same as for the first quadrant, except for the towing direction of the carriage. The drawback is that the flow goes first over the open water test POD housing and strut before it reaches the propeller. The influence of the wake from the strut needs to be studied carefully. -Va Figure 9 Sketch of test set-up for the fourth quadrant tests option The other way of carrying out the fourth quadrant tests is to reversely install the propeller on the shaft (in fact, to fit each blade with 80 o deflection angle, see Figure 6) and to reverse the shaft rotational direction too, as shown in the sketch in Figure 0. By doing so, the propeller is in the upstream of the POD and the strut. The drawback is that the test cap is in the downstream of the propeller slip stream. The drag of the test cap is not easily subtracted from the measured thrust on the propeller shaft in order to obtain the pure propeller blade thrust from the measurements. In addition, reversely-fitting the propeller will result in more uncertainties to the system and the test results. It also costs extra preparation time. Figure 0 Sketch of test set-up for the fourth quadrant tests option 2 +n -n +n +Va reversely fitted propeller (each blade deflects 80 o ) +Va In order to make the quasi-steady open water test technique valid, the following assumptions have been made. The basis of the assumptions will be discussed in the following sections in more detail. The test results will further prove the validity of these assumptions. An open or ducted propeller consists basically of lifting surfaces (the blades and the duct). When varying the advance ratio of the propeller, the angle of attack of the flow to the propeller blades varies, resulting in a change of the strength of the bounded vortex. The fact is that if the varying of the shaft rotational rate or the towing speed is infinitely slow, meaning that, then, This means, unsteady steady. Practically, the variation of the shaft rotational rate and the towing speed of the carriage cannot be infinite slow. So we need the following assumption with regard to the unsteadiness of the flow. Assumption I: The variation of the shaft rotational rate and the variation of the towing speed is so slow that the hysteresis effect due to the unsteadiness of the flow is very limited. Therefore averaging the increasing and decreasing (V a and n) parts of the test results at the same value represents the steady state test result at this value, assuming the deviations are linear. The viscous effects of the fluid should also be considered during the tests. Around the propeller design condition, the correct simulation of the viscous effects is ensured by a high shaft rotational rate so that the Reynolds number of the propeller blade is higher than a critical value, as we often do for conventional propeller open water tests. At off-design conditions, due to the high angle of attack and also the separation of the flow on the blade, Reynolds effects become less dominant, and thus a somewhat lower shaft rotational rate would be allowed. The extreme situations are at +90 o and -90 o of the hydrodynamic inflow pitch angle, where the rotational rate of the shaft has to be zero. The biggest influence of the viscous effects on the quasisteady test technique can be the hysteresis effect due to flow separation and re-attachment at off-design conditions. The flow separation and re-attachment usually do not occur at the same advance ratio during increasing compared to decreasing the towing speed or the shaft rotational rate. These effects can be clearly seen in the later sections of this paper with the test results. To make the quasi-steady test technique valid, we need 5

6 the following additional assumption with regard to the flow separation at off-design conditions. Assumption II: In the instable regime where the flow separates and re-attaches, the average of the increasing and decreasing (V a and n) parts of the test results at the same value represents the steady state test result at this value in this regime. HYSTERESIS EFFECTS Three hysteresis effects have been identified during a quasi-steady propeller open water test. They are the hysteresis effect due to the mass and mass moment of inertia of the propeller, including also the added mass effects; the hysteresis effect due to the unsteady hydrodynamic flow around the propeller, mainly the vortex shedding to the propeller wake, both spanwise and also chordwise; and the hysteresis effect due to flow separation and re-attachment. Mass and mass moment of inertia Since the way to increase the carriage speed or the shaft rotational rate in the increasing part is the same as in the decreasing part, both for sinusoidal and also for trapezoidal variations, the rate of change (acceleration or deceleration) are exactly the same, but with a different sign. The hysteresis effects of this part cancels perfectly with each other. However, large hysteresis effect should be prevented. This can be achieved by using light materials for the propeller, such as aluminium. This part of the hysteresis effect is seen as the additional thrust and torque on the shaft resulting from the acceleration and deceleration, where m and I are the mass and the mass moment of inertia, respectively, where subscript p denotes the propeller and a denotes the added mass effect. For stock propeller No. 726R and by using the maximum acceleration and deceleration during the present tests, these additional thrust and torque are estimated and listed in Table 3 for indication. Table 3 Thrust and torque levels due to acceleration and deceleration mass and mass moment of inertia effects. Indicative values for Propeller 726R unit T ~ ±0.05 N Q ~ ±0.0 Nm Compared to the hydrodynamic thrust and torque levels of this model propeller during the tests, these values are rather small although it is not negligible. Even if a bronze propeller is tested by using the present test technique, no large hysteresis effect is expected. Attention may need to be paid when a quasisteady test technique is used for open water tests of the total unit performance of an azimuth thruster or a podded propulsor (POD). Due to the total mass and the added mass of a thruster or a POD, the hysteresis effect can be much larger. Unsteady flow Since an open propeller or a ducted propeller consists of mainly lifting surfaces, the hysteresis effect due to unsteadiness of the flow comes mainly from the memory effect of the wake system. The hydrodynamic unsteadiness is governed by the Strouhal number and can be expressed as the reduced frequency for the present study, where is the period of one test run with sinusoidal or trapezoidal variations. For the present model tests with stock propeller No. 726R and with the achievable longest period of each test run in the DT of MARIN, the reduced frequency k is around to These values are regarded as very small which will not result in any significant unsteady force and moment to the system that will finally be measured by the sensors. Flow separation and reattachment The largest hysteresis effect can be expected from the flow separation and reattachment at off-design conditions because the hydrodynamic forces and moments differ significantly for flows with and without separation. It is difficult to quantify the influence of the flow separation and reattachment. However, experience from model tests of e.g. oscillating fins (fin stabilizer) and unsteady azimuthing tests of thrusters or POD shows that the average values of the hydrodynamic forces and moments does represent the steady state test values. Observation and analysis of the raw data signals of steady tests also show that a strong oscillating flow in the regime of separation and reattachment results in the measured forces and moments jumping between the values of flows with and without separation. This effect will be clearly shown later in the section on the test results of this paper (see Figure 23), which occurs mainly in the area close to = +90 o and around = -0 o to -60 o at design pitch setting. When the pitch is deflected, the area will also be shifted. PROPERTY OF SENSORS AND CENTRIFUGAL FORCE Natural frequency and sensor properties Good sensor properties are important factors to guarantee the quality of the measurements. Two requirements are often working against each other - the static accuracy and the dynamic response. For accurate static measurements, sensors need to be elastic enough. However, the sensors must also be 6

7 Value Response (log) Value Value stiff enough so that the natural frequency of the system is high enough to ensure that the sensors do measure physical phenomena. A sketch is shown in Figure for a typical response of a sensor system to the impact source which is shown as a step function in the small graphs. Both the amplifying effect in the area close to its natural frequency f n of the system and the damping effect in the high frequency range should be avoided. Source Response Source Response Time t X Time t X Figure 2 Computer model for finite element analysis of the natural frequency, with assumed added mass of water. Source Response fn Frequency f key blade Time t Figure Sketch of sensor properties on the measured values. A sensor system is a mass-spring-damping system (Hagesteijn et al 202). The natural frequency of the system is not only determined by the sensors itself but also the propeller mass and mass moment of inertia, including the effect of added mass. To determine accurately the effect of added mass of a propeller is difficult. An approximation has been made by adding a ball of water to the blades as shown in Figure 2. In hindsight the added mass effect is likely over-exaggerated by this method providing a conservative estimation on the natural frequency of the system. Some examples of the blade deformations are shown in Figure 3 and Figure 4. The calculated natural frequencies of the system for the first mode are listed in Table 4. Since the shaft rotational rate is around 900RPM, meaning 5Hz, these natural frequencies of the propeller and its blades are considered high enough to obtain reliable results. Table 4 Calculated natural frequencies of the sensors with MARIN stock propeller 726R (made of aluminium) Forces / moments Natural frequencies (first mode) Propeller shaft thrust 04.9 Hz Propeller shaft torque 08.4 Hz Blade spindle torque 25.4 Hz Figure 3 Blade deformation in propeller thrust direction (at 04.9 Hz). key blade Figure 4 Blade deformation in blade spindle torque direction (at 25.4 Hz). 7

8 Blade spindle torque caused by centrifugal force In order to remove the spindle torque induced by blade centrifugal force and obtain the pure hydrodynamic torque, one test has been carried out in air for each pitch setting of the propeller by slowly varying the shaft rotational rate. The measured results are filtered and fitted with a quadratic curve. Figure 5 shows the spindle torque correction for the centrifugal force. Because it is a low-pass frequency filter of 0Hz, the gravity effect is clearly seen in the low frequency range from the shaft rotational rate of 0 to 600RPM, although it is much smaller than the effect of the centrifugal force. This is partly because of the light material, aluminium, which is used for manufacturing the blades. These measurements are also checked on every pitch settings by using the CAD model of the blade. Good agreements have been found. Figure 5 Spindle torque measured in the air (centrifugal force induced blade spindle torque) and the correction, filtered at 0Hz. Figure 7 Development of the wake from the strut (first plot) to the propeller disc (last plot), where L pp is the total shaft length of the open water test set-up. TEST SET-UP WAKE FLOW AND HUB CORRECTIONS Figure 6 Flow velocity field on the central plane of the open water test set-up, towed reversely without operating propeller. Wake of the test-setup and CFD calculations For the fourth quadrant with test option, as proposed and shown in Figure 9, the test set-up will be towed in the reverse direction. The influence of the POD and the strut of the open 8

9 water test set-up has been studied by using CFD calculations. MARIN s in-house RANS code PARNASSOS has been used for these calculations. All calculations are carried out at -4m/s. The results are shown in Figure 6 and Figure 7. The strongest influence is on the central plan of the test setup behind the strut in the peak of the wake. Figure 6 shows the development of the peak wake flow from the strut when there is no propeller in operation. This is rather similar to the nominal wake of a ship. It is seen that the wake peak reduces rather rapidly after the end of the strut. At about 2 to 3 chord lengths of the strut, the flow deficit is reduced to smaller than 0% of the nominal velocity. In addition, the peak is very narrow as shown in the plots in Figure 7, starting from the strut to the propeller disc. On the propeller disc, the flow deficit is less than 5% in the narrow wake peak. Taking into consideration of the small over speed resulted by the displacement effect of the shaft and the hub, the mean advance velocity on the propeller disc is not really affected by the strut. This concludes that no speed correction is necessary to be applied to all of the reverse towing tests with the present test set-up. Test cap corrections The hydrodynamic drag on the test cap must be subtracted since there is no sensor to measure the force on the cap separately. The drag is determined by a pre-defined drag coefficient, where S is the frontal area of the test cap. To determine the drag coefficient, tests have been carried out by using a dummy hub with the test cap at both positive and negative carriage speeds and at positive and negative shaft rotational rates. It is known that the drag coefficient changes with the Reynolds numbers for difference towing speeds. It is found that the drag coefficient for a negative carriage speed is higher than that for a positive carriage speed, which are both not sensitive to the shaft rotational rate. This can be explained by the fact that the flow at the end of the cap is separated during the reverse towing tests, which results in more pressure drag on the test cap than that in the normal towing direction. Practically, a constant drag coefficient is applied for the whole speed range. For the present test set-up with the test cap, a value of 0.3 has been found for the C D when towing in the normal direction. During the reverse towing with operating propeller, the situation becomes more complicated. When a propeller has a positive pitch setting and rotates in the positive direction, the propeller slipstream is working against the inflow, leaving the test cap in the dead water area of the blocked flow behind the propeller. Even if the propeller blade is set to negative pitch at 0.7R, it is often the case that the blade pitch at the root remains positive. In order to simulate the flow and to find out the influence of the test cap, an additional CFD calculation has been carried out by applying a negative thrust to the flow with an actuator disc model. The results are shown in Figure 8. Indeed, the flow behind the propeller is fully blocked by the operating propeller, leaving a separation zone where the complete test cap is inside. The calculated results also show that the total drag force on the test cap is very small. Based on the investigations above, it is decided to apply the following drag coefficients for the test cap corrections as listed in Table 4, when reverse towing is used. Figure 8 Flow velocity field on the central plane of the open water test set-up, towed reversely with propeller operating against the flow. Table 4 Test cap corrections used for the data analysis Towing condition Drag coefficient C D positive carriage speed 0.3 negative carriage speed 0.00 DATA ACQUISITION, REDUCTION & PRESENTATION The measured propeller shaft thrust and torque, and the blade spindle torque, are non-dimensionalized by the relative velocity at 0.7R radius defined as, with the propeller thrust coefficient defined as, the propeller torque coefficient defined as, and the blade spindle torque coefficient defined as, 9

10 where, the positive directions of the propeller shaft thrust, torque and the blade spindle torque are shown in Figure 9. The positive blade spindle torque is defined as the direction that tends to drive the propeller to a larger pitch. During each open water test run, 5 channels of signals have been sampled and recorded. These are the speed of the carriage V a, the shaft rotational rate n, the propeller shaft thrust T, the propeller shaft torque Q and the blade spindle torque Q blade. All channels have been sampled up to a frequency of khz. Some selected raw data samples are shown in Figure 20 to Figure 22. fitted with one of the following Fourier series, respectively, and the Fourier series coefficients have been determined up to 30 harmonics. (2) Figure 9 Definition of positive directions for the thrust, torque and the blade spindle torque. Figure 20 shows examples of the sampled carriage towing speed variations and the shaft rotational rate variations, following the predefined sinusoidal form variations. It can be seen that both the towing carriage speed and the shaft rotational rate can follow the sinusoidal curve quite well. In the first quadrant when the propeller blade is operating around its design point, no severe flow separation is expected. The measured data show rather stable values as can be seen in the examples in Figure 2 for the thrust and the spindle torque. When the propeller operates in the fourth-quadrant, flow separation and reattachment occurs, resulting in a strong oscillating flow. This is found in the sampled thrust and spindle torque data, as examples show in Figure 22. As the present study is not aimed at the dynamic response of a propeller and its shafting system where higher frequencies play an important role, it is decided to filter the raw data by a low-pass filter with an upper-bound frequency at 0 Hz, which is lower than the shaft frequency in the majority of time in order to remove the possible noise coming from the bearing and the toothed belt. After the filtering of the raw data, the data was further grouped and averaged over each degree of the hydrodynamic pitch angle, forming a set of discrete data sets of 8 elements from -90 to +90 degrees. Thereafter, each set of the data the propeller thrust coefficients, the propeller torque coefficients and the blade spindle torque coefficients has been Figure 20 Typical examples of the sampled carriage speed (top) and shaft rotational rate (bottom), V a max = 4m/s, n max = 00RPM, sinusoidal variations. 0

11 Q [Nm] Q [Nm] Figure 2 Typical examples of the sampled thrust (top) and blade spindle torque (bottom) during test run No., at design pitch, n=900rpm, sinusoidal variations. RESULTS AND DISCUSSIONS To verify the quasi-steady propeller open water test technique, two-quadrant open water tests for MARIN s stock propeller No. 726R have been carried out, both by the conventional method as well as by the quasi-steady method. Two typical pitch settings have been investigated, being the design pitch setting and a negative pitch setting by deflecting all blades with -35 o from their design pitch. For the conventional tests, the thrust, torque and the blade spindle torque have been measured from -90 o to +90 o with a step of 0 o. For the quasi-steady tests, both sinusoidal and trapezoidal variations of the speed and the shaft rotational rates have been studied in order to investigate the sensitivity of the results to the test methods. Also done are the tests for the fourth-quadrant with option 2 (Figure 0) where the propeller is reversely fitted to the shaft and the shaft is rotating in the negative direction. Sinusoidal variation at design pitch Figure 22 Typical examples of the sampled thrust (top) and blade spindle torque (bottom) during test run No. 3, at design pitch, n=750rpm, sinusoidal variations. With the sinusoidal variations, both for the advance speed and also for the shaft rotational rate, 4 test runs have been carried out according to the procedure described in Table 2 for the stock propeller No. 726R at the design pitch, where the reverse towing for the fourth quadrant has been used. The sampled results are filtered at 0Hz, calculated into coefficients as defined by Equation 9, 0 and and their curves plotted in Figure 23. Also plotted in this figure are the conventional steady test results by dots (circles, squares and triangles) with their 95% occurrence intervals indicated by the + s. A 95% occurrence interval is the interval where 95% of the sampled signals are within this interval, while 5% are outliers. Also shown in this figure are the dark and light coloured curves for each thrust or torque, representing the accelerating (dark) and decelerating (light) parts of the sinusoidal variations, respectively. Hysteresis effect can be clearly seen between the dark and light coloured curves for each thrust and torque. This occurs mainly in the area close to +90 o and the area around -0 o to -60 o for this pitch setting.

12 Also seen in Figure 23 is that the width of the 95% interval from the conventional steady open water tests at discreet points is rather similar to the fluctuation in amplitude of the measured thrust or torque during the quasi-steady tests. In area where most of the fluctuations have been measured by the quasisteady tests, the widths of the 95% intervals of the conventional steady test are also larger. By fitting the measured data with a Fourier series as given in Equation 2, the complete two-quadrant propeller open water characteristics are expressed by Fourier coefficients up to 30 harmonics. The re-generated thrust and torque coefficients from the Fourier series are plotted in Figure 24, together with the steady measurement points with their 95% occurrence intervals. It is seen that the quasi-steady test results match the conventional steady test results very well CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 23 Comparison of the filtered raw data from quasi-steady tests to the steady test results with their 95% occurrence intervals, sinusoidal variations, at design pitch. One of the most important observations of the results is that only strong hysteresis effects have been found in the area where flow separation occurs. This proves that the hysteresis effects from both the mass, the mass moment of inertia and the unsteadiness of the flow are very small, as analyzed in the previous sections. In addition, the average of the test results in the accelerating and decelerating parts of the tests, even in the area where the flow separates and reattaches, equals to the steady test results. These prove that Assumption I and II made at the beginning of this paper are reasonable and valid assumptions. The same observations were also found for the other pitch settings, for the trapezoidal variations and for the propeller reversely-fitted tests for the fourth quadrant. Sinusoidal variations at negative pitch setting Also investigated in the present study is the quasi-steady tests for negative pitch setting by deflecting the blade pitch angle by -35 o from its design pitch angle. It should be mentioned that at this pitch setting, although the pitch at 0.7R is negative, the pitch at the blade root remains slightly positive. The filtered quasi-steady test measurements are plotted in Figure 25 together with the steady test results with their 95% occurrence intervals. The dark and light coloured curves for each thrust and torque represents the accelerating (dark) and the decelerating (light) parts of the sinusoidal variations, respectively. At this test condition, large fluctuations of the test results are only seen for the blade spindle torque in the area between -40 o to -90 o. No strong hysteresis effect has been found in the whole range of the two-quadrant open water characteristics. After the Fourier fitting of the filtered raw data, the thrust and torque coefficients are regenerated from the Fourier series and plotted together with the conventional steady test results in Figure 26. The quasi-steady test results agree perfectly with the conventional steady test results. 2

13 2.5 0CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 24 Comparison of Fourier series fitted curves to steady test results with their 95% occurrence intervals, sinusoidal variations, at design pitch CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 25 Comparison of filtered raw data from quasi-steady test to steady test results with their 95% occurrence intervals, sinusoidal variations, pitch deflected -35 o from design pitch. 3

14 2.5 0CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 26 Comparison of Fourier series fitted curves to steady test results with their 95% occurrence intervals, sinusoidal variations, pitch deflected -35 o from design pitch CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 27 Comparison of filtered raw data from quasi-steady test to steady test results with their 95% occurrence intervals, sinusoidal variations, at design pitch, propeller reversely fitted to the hub. 4

15 The reverse towing method for the fourth quadrant open water characteristics, as shown in Figure 9, has been used for the fourth quadrant tests of the propeller at this negative pitch setting. Propeller reversely fitted for 4 th quadrant As also proposed for the fourth quadrant open water tests - option 2 (Figure 0), fitting the propeller reversely to the shaft and rotating the shaft in opposite direction can be used too. This method has been tried, by keeping the hub as it is while rotating each blade 80 o on the CPP hub, as shown by the photo in Figure 6. The test results are plotted in Figure 27. When comparing Figure 27 to Figure 23 in the fourth quadrant, a clear difference can be seen. This difference is seen also at bollard condition although it is rather small. This difference is believed to be caused by the test cap which is in the slipstream of the propeller when the propeller is reversely fitted. The flow in the slipstream of a propeller is so complicated that the drag and torque on the test cap cannot easily and accurately be subtracted. In addition, deflecting the propeller blades by turning each blade 80 o may result in additional uncertainties to the pitch setting of the propeller. In general, reversely fitting the propeller on the shaft is not advised unless the drag and torque on the test cap is able to be measured by a separate sensor independently. Trapezoidal variations Until now, only tests with sinusoidal variations have been discussed in detail. However, during the study, the same amount of tests with trapezoidal variations have been carried out as well. The test results at the design pitch setting are shown in Figure 28 while the test results at the negative pitch setting by deflecting the blades with -35 o are plotted in Figure 29, together with the conventional steady test results. By comparing Figure 28 and Figure 29 to Figure 23 and Figure 25, respectively, it is seen that the test results are very close to each other. Further investigations show that the only deviations occur in the region where the derivatives of the variations are not continuous. However, the deviations are within the uncertainties of the test itself. This concludes that the quasi-steady open water test is not very sensitive to the variation in form of the towing carriage speed and of the shaft rotational rate. Making a perfect variation of the towing carriage speed or the shaft rotational rate is therefore not necessary. However, in order to prevent discontinuity of the variations and their derivatives, smooth variations, e.g. sinusoidal variations, are recommended rather than a method such as the trapezoidal method CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 28 Comparison of filtered raw data from quasi-steady test to steady test results with their 95% occurrence intervals, trapezoidal variations, at design pitch. 5

16 UNCERTAINTY ANALYSIS In order to indicate the uncertainty involved in the measurements performed, so-called occurrence intervals are presented in most of the figures around the steady measurements by + symbols. These intervals do not represent the confidence of the mean value itself, but are a very good indication of the stability of the flow and therefore provide an indication on the validity of the presented values in various regimes. The interval denoted by the + symbols is the 95% occurrence interval. This means that during a steady measurement of approximately 0 seconds on model scale, 95% of all samples are within this interval. Prior to establishing the 95% occurrence interval, all signals are filtered using a 0 Hz model scale low pass filter. This is done to subtract noise created by bearings, the carriage and drive belt of the set-up. The signals which are left after filtering contain only relatively low frequent components, which are assumed to be a result of hydrodynamic forces only, except for the blade spindle torque where the centrifugal force effect will be subtracted later on. Signals treated in this manner provide a lot of information. For example in Figure 23, the regime from = 0 o to 60 o shows both a very smooth quasi-steady signal and a very small occurrence interval. This regime spans from bollard pull to the normal working area and beyond. The smooth lines and the very small occurrence intervals tell us that the flow over the propeller is very stable. Starting from = 60 o, a small hysteresis effect can be identified in the quasi-steady measurement lines which starts to grow rapidly beyond = 80 o. The light coloured curves indicate increasing during the test and the dark coloured curves indicate decreasing during the test. The hysteresis above = 80 o is very likely due to the flow separation and reattachment, locally over the blades of the propeller CQ Prop CT Prop /0CQ Prop /CT Prop Beta [deg] Figure 29 Comparison of filtered raw data from quasi-steady test to steady test results with their 95% occurrence intervals, trapezoidal variations, pitch deflected -35 o from design pitch. Below = 0 o a small hysteresis effect seems visible as well, but below = -0 o the flow becomes rapidly unstable. The quasi-steady measurements show very large fluctuations in this area, especially around = -30 o. In this region the advance velocity is reversed while the rotation rates are relatively high, resulting in flow reversal and large turbulence. Again the quasisteady measurements show a very good agreement with the occurrence intervals of the steady tests. In order to judge the accuracy of the results further, the Fourier solution of the quasi-steady results has been compared to the 95% confidence interval resulting from variance analysis of the conventional steady test results. Variance analysis uses the auto covariance of a signal to determine how likely that a found mean value is in the neighbourhood of the actual mean value. The actual mean value can never be found since the measurement time for that needs to be infinite, neglecting other sources of uncertainties (Bendat and Piersol 200). For now it is stated that the measured signal itself is assumed to be true (ignoring calibration uncertainty sources etc.) and the task is to find the true mean. To do this, the 6

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