Effect of Operational Conditions on the Cavitation Inception Speed of Naval Propellers

Transcription

1 25 th Symposium on Naval Hydrodynamics St. John s, Newfoundland and Labrador, CANADA 8-3 August 24 Effect of Operational Conditions on the Cavitation Inception Speed of Naval Propellers T.J.C. van Terwisga,2, D.J. Noble 3, R. van t Veer, F. Assenberg, B. McNeice 4, P.F. van Terwisga 5 ( MARIN, The Netherlands, 2 Delft University of Technology, 3 Defence R&D Canada - Atlantic, 4 Royal Australian Navy, 5 Royal Netherlands Navy) ABSTRACT A propeller analysis package for time domain simulations is described that permits evaluation of the effects of variable operating conditions on propeller cavitation inception in a seaway. The package is based on linear seakeeping and propeller lifting surface theories and is combined with a simulator that models the dynamic response of conventional twin propeller and ship engine systems. It is developed in a cooperative project by the Canadian, Netherlands and Australian Navies and MARIN. In this paper, the simulation tool is applied to a representative naval ship and propeller design to illustrate the effect of sea state, heading and propeller control strategy on the cavitation inception speed. In the sample case examined, the effect of sea state on cavitation inception speed in bow quartering seas is shown to agree with previous full-scale observations and measurements, predicting a cavitation inception speed in sea state 6 of only some 36% of that in sea state 2. A range of propeller control strategies is examined to show that operating propellers using a constant thrust coefficient and ship speed control strategy can produce a cavitation inception speed that is some 29% higher in following seas at sea state 4 than obtained with a commonly used propeller shaft speed control algorithm. For bow quartering waves in the same sea state, no significant difference in inception performance could be found using the same controller settings. Optimization of the controller for each direction to waves is likely to improve inception speeds for headings other than following seas as well. INTRODUCTION To minimize the ship's underwater acoustic signature, propeller design for naval ships is typically governed by an optimization process aimed at achieving the highest possible ship speeds for inception of cavitation. In present day practice, this design optimization is performed under assumptions of ideal operating conditions with the ship moving at constant forward speed on a straight course in calm seas. Staff requirements, the propeller design condition, and design evaluation criteria are all aimed at an optimized design for these conditions. Even the acoustic evaluation of propellers in full-scale sea trials is typically performed in deep, sheltered waters, with results providing no indication of the degradation in acoustic performance obtained in actual service conditions. Observations in previous sea trials have typically revealed significant reductions in cavitation inception speeds relative to design expectations during normal operations in a seaway or during maneuvers. In actual service, a ship will typically not sail in calm water on a perfectly straight course due the presence of oblique waves in a seaway and currents. The ship will maneuver to sail a specific course or to fulfill specific tasks, and will also accelerate or decelerate at certain times. The ship will foul, generating increases in resistance, and will also experience variable added resistance due to wind and waves that change the loading condition of the propellers. Current propeller design practices and operational procedures are often found to be severely lacking due to neglect of the effects of realistic operating conditions. These effects can now be made amenable to analytical evaluation and optimization through the use of currently available ship-propellerengine simulation tools. To assess the effects of in-

2 service operating conditions on the cavitation performance of naval ship propellers, the Canadian, Netherlands and Australian Navies have jointly participated with MARIN in a Cooperative Research Navies (CRN) Project that has the following objectives: to determine the most important factors contributing to the degradation in propeller cavitation performance during normal operations such as maneuvering and sailing in a seaway (problem definition). to evaluate available methods for predicting the most important effects and assemble an analysis package that can be used to predict cavitation performance under these conditions (software development). to formulate strategies for operational guidance on existing ships and suggest improvements for the design of new propellers and ship control systems in order to control and maximize the operational window for cavitation free operation under service conditions (operational and design strategies). This paper provides an update to the progress of work in this CRN Project reported previously in a paper presented at the 24 th Symposium on Naval Hydrodynamics in Fukuoka, Japan [Kuiper et al. 22]. That paper investigated the changes in the fullscale propeller inflow of a Fremantle Class Patrol Boat of the Royal Australian Navy between a straight run and a turn at constant rudder setting based on LDV measurements. Results were also provided for the effect of the measured inflow changes on propulsion and cavitation predictions with a lifting surface code. For this particular ship, changes to the transverse inflow velocity components were found to have a dominant effect on the power absorption and cavitation performance of the propellers. Development of tools for the prediction of ship propeller and engine performance under realistic operating conditions will help to meet the growing demand by navies for integrated system evaluation by means of modeling and simulation. These tools can provide important input for evaluating the effectiveness of tactics and decoys in torpedo defense and anti-aircraft simulations. The simulation tools can be applied to evaluate the effect of optimal control of propeller cavitation and engine loads on resulting acoustic and IR signatures. In the following sections of this paper, results from full-scale observations on a geographic survey vessel are provided to demonstrate the significance of operational conditions on propeller cavitation performance. The philosophy and structure of the PEASE simulation tool are then described in detail, including the computation and validation of some key results obtained for the unsteady wake field in waves. An example of the use of the simulation tool will then be provided to illustrate the effect of sea state, heading and the Propeller Control Algorithm (PCA) on cavitation inception speed. The selected ship and propeller design for this example are considered representative of contemporary naval ships. Although the ship and propeller particulars are not provided, the results of numerical simulations in a seaway are presented and their implication for the control and optimization of propeller cavitation performance under in-service conditions is discussed. IMPORTANCE OF OPERATIONAL CONDITIONS ON CAVITATION INCEPTION The importance of operational conditions on the cavitation inception behaviour of a propeller is illustrated here with full scale observations made on board of the Hydrographic Survey Vessel, HM Tydeman (see Figure ). Figure HM Tydeman This is a survey vessel of the Royal Netherlands Navy, with which cavitation inception tests have been conducted in both sheltered waters and open sea. Calm water inception tests were conducted in the Sognefjord (Norway) and inception tests in waves were conducted in open sea with significant wave heights of approximately 3.5 m and an observed period of 6 s. Wave height and direction were estimated by the crew and later confirmed by hindcasting. The tests in calm water were conducted in ideal conditions: No waves, straight course, minimal rudder motions, no wind and no traffic. 2

3 Cavitation inception was determined from visual observations with the MARIN CAVOBS system. This comprises a digital camera that is triggered with the shaft frequency, thus collecting pictures of a particular blade s passage. A description of the system is given by Verkuyl et al. (2). Inception was determined by establishing when the worst performing blade showed cavitation over some 3% of the time. Cavitation inception was determined for both sheet cavitation and tip vortex cavitation. The figures quoted in this paper refer to tip vortex cavitation inception, as it was the first type of cavitation to occur. After cavitation inception had been determined for calm water conditions, straight course ahead, similar tests were conducted for turning circles, applying rudder angles of and 2 deg to both port and starboard. Figure 2 presents the results of the cavitation inception tests for calm water conditions. This figure shows that a reduction in cavitation inception speed of some 5% occurred for rudder angles of ±2 deg. water condition. For head seas, the cavitation inception speed even reduces to zero. These trials results illustrate clearly the importance of sea state and heading on cavitation inception speed. They also underline the relevance of the current study, which ultimately aims at the design and operation of the ship and propulsion system in such a way that significant reductions in radiated noise are attained. Cav. Inception Speed CIS [kts] Calm water Following seas Stern Qrtrng seas Beam seas Bow qrtrng seas Head seas 8 7 dg Figure 3 Effect of sea state 5 on inception speed Cav. Inception Speed CIS [kts] dg PS dg PS Figure 2 Effect of a turn on inception dg SB 2 dg SB Cavitation inception measurements in waves are rare. During the Tydeman trials, weather conditions worsened and the position of the ship in open sea, provided a good environment to explore the effect of sea state and heading on cavitation inception. In an average sea state of 4 to 5, five series of inception measurements have been recorded for the following headings; head waves, bow quartering waves, beam seas, stern quartering waves and following waves. Figure 3 presents the results. It is shown that in following seas, the inception speed increases by some 7% above the calm sea value. In the other headings, cavitation inception occurs at significantly lower speeds when compared to the calm OBJECTIVES AND SCOPE Having illustrated the importance of sea state and heading on cavitation inception, this paper aims to demonstrate the adverse effects of ship operations on a straight course in a seaway on propeller cavitation performance through the use of a simulation package named PEASE (Propeller Evaluation and Analysis in a Service Environment). This package consists of linear ship seakeeping and propeller lifting surface components in combination with a simulator that solves the equations of motion, and models the dynamics and control of a complete twin-screw, propeller-engine system in the time domain. The paper also describes results for a representative naval ship design that indicate how the degradation in propeller cavitation performance is affected by sea state, heading and propeller control strategy. In simulating propeller performance on a straight course in a seaway with an emphasis on cavitation inception, it is necessary to obtain a sufficiently adequate prediction of the instantaneous operating point of the propeller. This implies that accurate predictions are needed of the parameters that determine cavitation inception for a given propeller: A prediction model for the effects of maneuvering on cavitation inception is currently under development. 3

4 The time dependent inflow velocity field in which the propeller operates. The time dependent ambient pressure. The time dependent propeller rotation rate and ship speed. The unsteady wake field entering the propellers is built up from the calm water nominal wake field and the unsteady wake field caused by the seaway and the hull s response. In the current PEASE model, ship motions are first computed in the frequency domain using linear seakeeping theory for a given steady ship speed. The ship motion velocities and disturbance potentials that contribute to the resulting inflows to each propeller are then added to the calm-sea nominal wake field to provide a series of inflow velocity distributions at discrete time steps during a simulation run. In the current model, the ship motions in a seaway are decoupled from the propellership dynamics. The computation of the ambient pressure in a seaway is less straight-forward than it is for calm water conditions. The time derivative of the potential function in the Bernoulli equation, normally neglected in steady state calm water considerations, can no longer be neglected. To determine the instantaneous ship speed and propeller rotation rate, the equations of motion of the ship in the longitudinal direction and the rotor dynamics of the propeller-engine system are solved at each time step. The engine dynamics are modelled by a generic PID controller, hereafter referred to as the Propeller Control Algorithm or PCA. This algorithm can be programmed to enforce various propeller control strategies, such as operation at constant rpm, constant torque, constant power, etc., and thus determine the instantaneous operating point of each propeller. Having defined the propeller operating conditions, a detailed propeller analysis can be made for each time step using lifting surface theory to derive surface pressure distributions on propeller blades and to determine whether and where cavitation occurs. Cavitation performance in operational conditions can then be evaluated using the percentage of time during which the propeller is observed to be free of cavitation. STRUCTURE OF PEASE SIMULATION TOOL Having described the philosophy behind the timedomain simulation package PEASE, this section will focus on the structure and the elements used in the package. A data flow chart of the PEASE simulator is presented in Figure 4. First, the seakeeping characteristics of the ship at an average ship speed in a given sea state and heading are computed in the frequency domain. This is done with the linear seakeeping program PRECAL (Van't Veer, 23). This program is used to provide the three components of the seakeeping-induced velocities in the propeller plane. In a subsequent step, the frequency domain wake velocities from PRECAL are converted into time domain velocities by a program named WAVECAL, that uses a random phase angle distribution to realize a wave train. The resulting wake velocities are then added to the nominal wake field obtained from steady state model testing in calm water. Figure 4 Data flow chart of the PEASE suite of programs In the next step, the ship speed and the propeller rotation rate for both propellers (in a twin screw arrangement) are computed by the time domain simulator (PEASE simulator). To this end, the equations of motion for the longitudinal ship dynamics and the propulsion system rotor dynamics are solved simultaneously for both propellers. A time-averaged 4

5 total resistance as a function of speed is available, together with the propeller s open water torque characteristic. The Propeller Control Algorithm (PCA) determines the reaction from the combined engine and engine control system to changes in engine operating point. A simple PID controller is used for this system, requiring three control coefficients K p, K i and K d that are defined for proportional, integration and differentiation components, respectively. The result of this block of the simulator is the instantaneous ship speed and propeller rotation rate. The above elements feed subsequently into the lifting surface program ANPRO (Van Gent, 975), which calculates the detailed surface pressures over the propeller blade. Also, the instantaneous thrust calculated by ANPRO is fed back to the simulator for the computation of the longitudinal ship dynamics in the next time step. With the detailed pressure distribution now available, it is assessed whether and where cavitation occurs on the blade. To this end, a simple cavitation criterion is applied, where cavitation is said to occur whenever the local pressure is lower than the vapor pressure of seawater. A complication in the determination of cavitation inception arises for contemporary naval propellers due to the fact that tip vortex cavitation usually occurs first with increasing speed. This type of cavitation is not modelled in current lifting surface theory. To account for this deficiency, a correction is made by adjusting the ambient pressure until the computed sheet cavitation results are obtained at the ship operating point for tip vortex cavitation inception observed at full scale (in ideal, calm water conditions). The adequacy of this correction is expected to worsen as operating conditions deviate further from ideal conditions, due to differences in the variation of inception characteristics of tip vortex cavitation with the propeller operating condition. However, for a first assessment of cavitation inception in off-design conditions, the current correction is considered to provide a satisfactory result. The input data sets needed for this analysis are thus the geometrical data for both the ship s hull and the propeller, operational data (sea state, heading and average ship speed), nominal wake field data in steady-state, calm water conditions and data defining the Propeller Control Algorithm. Unsteady Wake Field Following the assumptions of linear theory, the total wake field is assumed to be a summation of the steady (calm water) wake field and the unsteady seakeeping components (the contributions from the waves and the ship motions). Aalbers and Van Gent (984) validated this approach with measurements, showing that the velocity components due to waves and ship motions can be linearly superimposed onto the nominal wake field. Both the steady and unsteady wake field will be divided into components that can be assessed independently. The total effective wake field in the propeller plane that can be used as input for the propeller analysis, is based on the following separation of flow components: V = V + V eff eff { total} { calm water} { waves} () = V + V + V + V + V + V t n int i d r cw cw wi wi wi sm The subscript cw in equation () indicates calm water components, the subscript wi indicates wave induced components and the subscript sm indicates ship motion induced velocities. The total calm water flow field is defined as a summation of three components: the nominal flow field V, the propeller induced flow, V i and the n cw int propeller flowfield related to interaction effects, V cw. The preferred wake field to be used for a propeller analysis is the so called effective wake field, which is the total wake field minus the propeller induced velocities: V = V V = V + V (2) eff tot i n int cw cw cw cw cw Typically, the total and induced flow field are not available, and the effective wake field is built up from the nominal wake field and the propeller-wake interaction component, for which a code is available (Van Gent and Hoekstra, 985). n The nominal flow field, V cw, is the flow field caused by the ship s hull and appendages without propellers fitted. This wake field is considered to be time independent. Possible unsteady flow phenomena such as the effect of vortices shed by the hull are time i averaged. The propeller induced flow field, V cw, is solely due to the propeller action in a given wake field. This part is caused by the loading or force distribution on the blades and provides a propeller-induced velocity that is dependent on the blade s angular position. The resulting contribution to the wake field is therefore periodic at blade rate. The propeller-wake int interaction component, V cw, is the wake field introduced to account for interaction effects that are lost by the breakdown into separate small components. Phenomena that are included here are the effect of propeller suction on the incoming hull flow and on the vorticity distribution. cw 5

6 The total unsteady flow field can be decomposed into the incoming undisturbed waves together with the diffracted and the radiated wave velocities and into the flow velocities induced by the ship motions in 6 degrees of freedom. The additional wake velocity field induced by i the undisturbed incoming wave is denoted V wi. The undisturbed incoming waves will partly be reflected by the hull, and thereby generate a diffracted wave d system, leading to a diffracted flow field V wi. As the ship sails through the seaway, it carries out translations and rotations, giving rise to a wave system that is radiated by the hull. The corresponding radiated r velocity field is denoted V wi. The above seakeeping components are described in a frame of reference steadily moving with the average ship speed. The motions of the propeller, due to the global 6 degrees of freedom ship motions, relative to this reference frame introduce additional velocities. If the velocity of the propeller plane due to ship motions is described by V sm, the corresponding flow field experienced by the propeller is given by: t Vsm = V sm (3) The resulting total effective wake field in the propeller plane that is input for the propeller analysis is now obtained as the sum of the individual components as expressed in equation (). Ambient Pressure The calculation of the pressures in the propeller plane has a direct effect on the calculation of the cavitation inception number. Since the cavitation number incorporates the ambient pressure, it is necessary to determine the pressures in the propeller plane accurately. The pressure in an unsteady potential field defined by the total velocity potential Φ, such as in the case of a propeller operating in a seaway, can be determined from the Bernoulli equation: Φ 2 p = ρ 2 ρ( φ φ Vs ) ρgz+ p a (4) t where φ is the total disturbance potential, incorporating both steady and unsteady terms. It can be seen from equation (4) that the pressure is built up from three contributions: First of all, the static pressure p s, given by ρ gz + p a, where p a is the atmospheric pressure. In this case, the earth fixed reference system is used to determine the (vertical) z- position, taking the effect of the ship motions on the position in the propeller plane under the calm water plane into account. Secondly, the dynamic term 2 ρ φ φ V, due to the inflow ( ) 2 s velocities in the propeller plane. Finally, the transient pressure term to the potential flow field. ρ Φ t, due On the free-surface wave elevation a dynamic and kinematic boundary condition should be satisfied, prescribing the pressure on the water surface equal to the atmospheric pressure and the flow velocity direction of the water particles. Using the Bernoulli equation, the surface elevation ζ is found to be: Φ ( 2 ζ = φ φ V s ) (5) g t 2g In the present version of the PEASE code, the second term on the right hand side of eq. (5) is neglected, resulting in the following expression for the unsteady potential contribution in the pressure: Φ ρ = ρ gζ t (6) In a linearized model, it is justified to neglect the φ. φ term. 2 The neglect of the Vs term implies that there is no pressure recovery in the wake of the hull. In reality, pressure recovery will be somewhere in between zero (strong viscous dissipation of energy) and the full dynamic pressure (for potential flow). The ratio of the pressure recovery can be determined for example from a RANS analysis of the flow about the hull. The above treatment simplifies the assessment of the unsteady pressure, and although incorrect, it is typically used in linear theory without introducing serious inaccuracies. This approach however, will require further validation. Propeller Rotation Rate and Ship Speed The propeller rotation rate and the ship speed are obtained by solving the equations of motion of the longitudinal translational motion of the ship system and the rotating motion of the propeller-engine system. The equation of motion of the propeller-ship system is given by: 6

7 dv + a = tot R (7) dt S ( M M ) T ( t) where: M = displacement mass of the ship system M a = added mass of the ship in longitudinal direction, that is typically frequency dependent. This mass is given a constant value for the frequencies under consideration T tot = total thrust from all propellers V S = ship speed R = total instantaneous hull resistance. This resistance is given a time averaged value, built up from a calm water contribution and a time averaged drag in waves. A more realistic model predicting a time varying drag in waves is currently being implemented. t = thrust deduction value (time averaged) It is realized that the resistance fluctuations in waves might have an important effect on instantaneous propeller loading and therefore on cavitation inception. Work is currently defined to include an algorithm that includes this time dependency of the added resistance in waves in a future version of PEASE. The equation for the rotating motion of the propeller-engine system is given by: dω j IP = MDEj Qj (8) dt where: I P = polar moment of inertia of the complete rotary system. This includes propeller, shaft, gearbox and rotating part of the engine. When a Power Take Off is used, the moment of inertia of this generator should be included as well. ω = shaft rotation rate j M = torque delivered by the prime mover DEj (often a diesel engine). The magnitude of this torque is currently controlled by the Propeller Control Algorithm. Four different PCAs are used in this study, which are elaborated in the following. Q j = torque exerted by the propeller on the shaft system at the thrust bearing. It includes bearing losses. Subscript j indicates the shaft system location (e.g. starboard or port). For a twin screw configuration, we now have three equations with three unknowns, viz.: ω, ω 2 and V S. The other parameters have to be given as input to the simulator. The determination of the time dependent values of propeller torque Q j, thrust T j and engine torque M DEj is now described. The propeller thrust T j is determined from the propeller analysis by the lifting surface code ANPRO. This analysis is also made for the detection of cavitation inception. Contrary to the thrust, the instantaneous propeller torque Q is determined from the measured open water characteristics and the instantaneous nominal wake fraction. The measured open water characteristics for torque are preferred because of the greater uncertainty in the computed torque compared to the thrust calculated by ANPRO. The instantaneous propeller torque is consequently determined from the open water torque coefficient: 2 5 Qj = KQj ρω 2 jd (9) 4π ω j where KQj = f VS,( wjn ), and wjn is the 2 π nominal instantaneous wake fraction for shaft system j. The engine torque is determined by the PCA as described below. Apart from the PCA, the above set of differential equations needs to define limits and initial values to find a unique solution. To this end, the time averaged estimates of ship speed and propeller rotation rate V S and n provide the initial values. An important constraint for the engine is its operational envelope, which is often expressed in terms of torque and engine rotation rate (see Figure ). Propeller Control Algorithm A generic block diagram, representing the shippropeller-engine system is depicted in Figure 5 (Stapersma, 2). This diagram shows the relation between the translational motion dynamics of the shippropeller system and the rotational motion dynamics of the propeller-engine system. In the upper left part of the Figure 5, the Propulsion Control Algorithm is depicted, representing the Command, the Engine Control System and the Engine. Pitch control is left out of consideration here. The propeller operates with a fixed pitch setting. Four different control strategies are implemented in this PCA, each controlling the diesel engine torque delivered to the propeller: 7

8 Engine control system Propeller Control Algorithm Command Propulsion control system θ Pitch control system θ controlling the engine on C T alone is not sufficient to maintain a constant ship speed. This is caused by the indifference of the thrust coefficient to variations in ship speed. The error functions used in PCA4 are thus defined as: Engine/ controler n Mshaft 2π Ip Mdt n Mprop Propeller Torque n Vs n Va J = nd n Va Propeller Thrust Vs w Fprop m Fdt Vs Fship Sea keeping disturbances Ship resistance Vs e = C C CT ji T SP Tji ( ) e = V V VS i SSP S( i ) M = K e + K e + DE ji pct CT ji pvs VSi K e dt+ K ict CT ji dct de CT ji dt () Figure 5 Generic block diagram of the ship-propellerengine system PCA = constant propeller rotation rate PCA2 = constant power PCA3 = constant torque PCA4 = constant thrust coefficient C T and ship speed A generic PID controller is used for all four algorithms. The torque at time step i for each engine is consequently determined from a correction to the torque obtained in the previous time step: de j DE ji = p ji + i ji + d () M K e K e dt K dt where: e j = error between some user defined set point SP and some measured process variable for shaft system j K p = controller proportional coefficient K i = controller integration coefficient K d = controller differentation coefficient Subscript j refers to the shaft system and, except for K i, subscript i to the time step. The error function for the constant rotation rate is defined by: e ji = ωsp ω j( i ) where: e ji = error of shaft system j at time step i ω SP = set point of propeller rotation rate ω ji ( ) = actual propeller rotation rate of shaft system j at time step i- The constant thrust coefficient strategy requires multiple error functions to be used because e V S i It is noted here that the error in ship speed is only reflected in the proportional part of the error function. The integral and differential parts of the error function for the speed have been omitted. In representing the engine command and the engine system as one element in the block diagram, it is implicitly assumed that the engine reacts instantaneously to the new fuel rack setting that is determined by the PID control system. However, this would likely be a valid assumption since the combustion process has a much shorter reaction time than the shaft system. VALIDATION OF UNSTEADY WAKE FIELD VELOCITIES The validation of a simulation tool that is itself composed of several complex components can be cumbersome. However, the validation is still an essential process that is required to define the limitations and applicability of the tool. A proper validation requires reliable data sets that preferably allow for an end-to-end uncertainty analysis. Such an analysis would assist in directly quantifying the uncertainty of the final results. Most often, however, such data sets are not available and an overall estimate of the uncertainty must be obtained from only partial validation studies. Validation obviously is partly driven by opportunity, with data sets typically only being available for portions of the simulation code. One of the effects expected to play an important role in cavitation inception in a seaway is the unsteady ship wake field induced by the waves. The wake field velocity variations affect the propeller operating condition in two ways: on the one hand, they affect the propeller pressure distribution and resulting blade loading variations directly, while on the other hand, through variations in thrust and thus ship speed, they again affect the loading variations indirectly. Partial validation of these unsteady velocities can be conducted with the availability of a unique data 8

9 set of wave-induced wake field velocities. Aalbers and Van Gent (984) performed unsteady velocity measurements with Laser Doppler Velocimetry (LDV) for 8 positions in the propeller disk (Figure 6) in regular head waves of m wave amplitude. They found wave induced wake field variations up to 2% of the maximum wake deficit (w max@r=.88 ) per unit wave amplitude. This implies that unsteady wake field variations up to some 23% of the maximum wake fraction w max can occur in sea state 4, with a 4% chance of exceeding the maximum. These wake velocity variations can significantly affect cavitation inception. be sufficiently well predicted to provide a realistic simulation of the effect of a seaway on cavitation inception. uxa / (wmax A) AXIAL Velocity, pnt (8 deg) PRECA L Experiments.5.5 WAVE FREQUENCY [rad/s] uxa / (wmax A) AXIAL Velocity, pnt 4 (24 deg) PRECAL Experiments.5.5 WAVE FREQUENCY [rad/s] AXIAL Velocity PHASE, pnt (8 deg) AXIAL Velocity PHASE, pnt 4 (24 deg) 8 8 PRECAL PRECAL Experiments Experiments 9 9 PHASE [deg].5.5 PHASE [deg] WAVE FREQUENCY [rad/s] -8 WAVE FREQUENCY [rad/s] Figure 6 Positions in propeller plane for which velocity measurements were conducted Figure 7 shows a comparison of measured and computed velocities at points and 4 in the propeller disk as a function of the wave frequency. Both the amplitude of the wake velocity variation and the phase angle (relative to the wave at the CG) are given. Error bars about the experimental velocity amplitudes indicate the estimated uncertainty in the measurements. The general trend in this comparison (which holds for most positions in the propeller disk) is that the computations are within the estimated experimental uncertainty of some 25% (with 95% reliability for wave frequencies lower than approximately.8 rad/s). The deviation is larger for higher frequencies however. The prediction of the phase angle is satisfactory. It is noteworthy to mention that the scatter in results is larger for the top position of the propeller plane. This effect is attributed to the flow distortion generated by the appendages and the complicated viscous dominated wake this gives. The Response Amplitude Operators (RAOs) of the calculated ship motions for surge, pitch and roll are in good agreement with the experimental values. The RAO values of the local wake velocities seem to Figure 7 Comparison of measured and computed axial velocities in position and 4 of the propeller plane; Comparison of amplitudes (upper half) and phase angles (lower half). The prediction for the top location is good, while the velocities in point 4 are over-predicted by PRECAL. This can be attributed to the influence of the shaft and brackets at which location (2 deg) there is a clear decrease of the flow velocities in the measurement. The influence of these appendages is not accounted for in PRECAL. The prediction for the shorter waves is less accurate than for longer waves. Although in long waves the absolute surge motions increase, the relative surge motions decrease as the ship follows the wave contour. The wave velocity due to the incident wave dominates the flow field. In shorter waves the diffraction effects become more important and since these cancel the incident wave the measurements become very sensitive to local disturbances. EFFECT OF SEA STATE, HEADING AND PROPULSION CONTROL ON CAVITATION INCEPTION A CASE STUDY The effect of Propeller Control Algorithm (PCA), sea state and heading on cavitation inception have been studied with the previously described simulation tool. Four PCAs have been studied, involving constant 9

10 propeller rotation rate, constant power, constant torque and a combined constant thrust coefficient (C T ) and speed. Most of the simulations were conducted for sea state 4 and a heading angle of degrees (following waves). The effect of sea state was investigated for a heading of 35 degrees (bow quartering waves), where the effect of sea states 2 and 6 were additionally studied. The effect of heading was studied only for sea state 4 (at headings and 35 degrees). A review of the combinations of PCA, sea states and heading angles considered is given in Table. Table Matrix of simulation conditions Heading Sea state PCA,2,3, PCA,2 PCA,2 PCA,2 8 Note: PCA = propeller rotation rate control PCA2 = power control PCA3 = torque control PCA4 = thrust coefficient C T and speed control The control coefficients used in the PCAs were chosen by a trial and error process, until stable convergence was reached for the sea state 4, heading deg condition. These coefficients were subsequently used for all other conditions, pertaining to that PCA. For each simulation case, a period of 9 s is simulated using the same wave realization. The starting condition, specified by ship speed V S and n, is estimated based on time averaged values. The ship velocities are non-dimensionalized by a sea state and heading dependent reference velocity (V ref (SS,H)). This reference velocity represents the calculated propeller inception speed, based on time averaged values of added resistance in waves and instantaneous wake velocities. These inception speeds resulted from initial work, where ship speed and propeller rotation rate were kept constant. The non-dimensional inception speed changes reported here thus represent the separate effect of including the ship and propeller dynamics only, unless indicated otherwise. For each simulation case, a statistical analysis of the simulation has been made. In order to prevent start-up effects from biasing the statistics, the first s were omitted from the data on which a statistical analysis was performed. Important statistical data that were collected are: - ship speed V S - propeller rotation rate n - thrust coefficients K T and C T - quasi propeller advance coefficient J, based on average ship speed - cavitation number σ n For each of these parameters, the time averaged value and the standard deviation were determined. In addition, the minimum and maximum value were determined for ship speed, propeller rotation rate and thrust coefficient C T. The statistical analysis furthermore produced the number of cavitation events on the propeller, where cavitation was considered present whenever the local pressure coefficient was smaller than the cavitation number at any position on the blade. A distinction was made between pressure side and suction side cavitation. In this way, the percentage of the time that the blades were free of cavitation on each side was obtained. The Cavitation Inception Speed (CIS) in a seaway can be determined from the statistical cavitation data when, for a given sea state and heading combination, a number of different ship speeds have been simulated. Plotting the percentage of time free of cavitation versus the average ship speed VS then shows an almost linear relation, the percentage cavitation free decreasing with increasing speed. An example of this process is presented in Figure 8 for sea state 4, heading and all four PCAs. The CIS is now defined as the maximum speed where the propeller is % of the time free of cavitation, given by the intersection between the former relation and the % free of cavitation line. Perc. time free of cav Vs [-] PCA-rpmcontr PCA2-Pcontrol PCA3-Torque-control PCA4-Ct/V control Figure 8 Non-dimensional cavitation inception speed for four Propulsion Control Algorithms at sea state 4, heading

11 Effect of Propeller Control Algorithm The present study shows that the Propeller Control Algorithm (PCA) has an important effect on the Cavitation Inception Speed (CIS) for sea state 4, heading (following seas), as presented in Figure 8. This graph shows that the propeller rotation rate control (PCA) produces the worst CIS. The best control algorithm appears to be the constant C T / ship speed control (PCA4), resulting in a CIS that is some 29% higher than that of PCA. Power control (PCA2) and torque control (PCA3) show a similar intermediate performance. Contrary to the important effect that the PCA has on the inception speed in following seas, its effect becomes negligible for bow quartering seas as can be seen in Figure 3. This difference in effectiveness of the PCA is ascribed to the much higher wave encounter frequency in bow quartering seas, which is typically a factor of 5 higher for bow quartering waves than for following seas (zero up-crossing periods Tup = 4 s versus Tup = 2 s respectively). The effectiveness of the control system in coping with such different time scales depends on its frequency characteristics and the dynamic characteristics of the ship-propeller-engine system. In the present study, the PID coefficients (or gains) have been chosen to obtain a good behaviour of the complete system in following seas. These coefficients have subsequently been used for the controller in bow quartering seas. It is likely that a better selection of coefficients is achievable that will behave better over a wider frequency range. Considering that the frequency characteristics of the control system will also necessitate a closer look at the frequency characteristics of the driving engine and its control system, this issue will need further attention in subsequent work. Figure 9 shows the dynamic cavitation inception diagrams that result from the propeller analysis at every time step considered for the rpm control (PCA), power control (PCA2) and thrust coefficient / ship speed control (PCA4). sigma_n sigma_n sigma_n constant rpm control Kt [-] constant Power control Kt [-] Constant C T and V S control Kt [-] cav. free cav. s.s. cav p.s. calm water cav. free cav. s.s. cav p.s. calm water cav. free cav. s.s. cav p.s. calm water Figure 9 Dynamic cavitation inception Diagrams for three Propeller Control Algorithms (PCA,2 and 4) in sea state 4, heading and V S =.93 The calculated calm water inception "bucket" has been added to these dynamic inception diagrams for reference purposes. This latter diagram is also constructed with the propeller analysis code ANPRO, where the same cavitation inception criterion is used. The calm water diagram is constructed by analyzing the propeller at a number of different propeller rotation rates. For each propeller rotation rate, the advance velocity is varied and thus the propeller thrust

12 coefficient KT. In this way, both pressure side and suction side cavitation inception could be detected. Although the average ship speed is the same for all three simulations, there is a clear difference in number of cavitation events. It is observed that the PCA determines the orientation of the operational region (indicated by a cigar shaped area of operating points) of the propeller in the cavitation inception diagram. Clearly, the PCA4 fits best within the calm water cavitation inception bucket. Another noticeable observation is the difference between calm water inception and dynamic inception in a seaway. Since the same computer code ANPRO has been used to determine cavitation inception, the difference must be caused by dynamic effects in the wakefield and the dynamic pressure. Clearly, the determination of the operating point using the thrust coefficient K T and cavitation number is no longer sufficient to discriminate between cavitating and cavitation free operations. This discrepancy is likely to be caused by the spatial and time varying wake field. Another possible source is a variyng cavitation number caused by dynamic effects in the ambient pressure. An understanding of the precise mechanisms of these effects could possibly be exploited in the Propeller Control Algorithm to further delay cavitation inception in dynamic conditions. It appears from this analysis that the most successful control system aims at confining the operational area to a narrow band at essentially a constant thrust coefficient K T. The problem with such an algorithm is that there is hardly a change in thrust coefficient for different ship speeds, so that an algorithm is needed that combines both the thrust coefficient and the ship speed in one error function. PCA4 is a first attempt at defining such an algorithm. The ultimate control system would limit the operational area to a single operating point within the cavitation bucket. Figure presents the operating regions in the engine torque-rpm diagram. The red line in these diagrams represents the static engine limits, produced by the engine manufacturer. If the PCAs are to be judged from the point of view of engine management, PCA4 also seems to offer the best possibility of not exceeding the engine limits during operation. M engine [Nm] M engine [Nm] M engine [Nm] constant rpm control n [rps] constant Power control n [rps] constant C T and speed control n [rps] Figure Engine operating regions for three Propeller Control Algorithms (PCA,2 and 4) p4 - MF ss4 head, Vs=.92, PIDn=constant Max eng. torque p4 - MF ss4 head, Vs=.92, PIDP=constant Max eng. torque p4 - MF ss4 head, Vs=.94, PID Ct=c, V=c Max eng. torque 2

13 Effect of Heading The effect of heading in a seaway has been studied by simulating the ship in a sea state 4 in both following waves (heading deg) and in bow quartering waves (heading 35 deg). The effect of these simulations on the cavitation behaviour is plotted in Figure. constant rpm control cav. free 2 H, PCA-rpmcontrol sigma_n cav. s.s. cav p.s. calm water H, PCA2-Pcontrol H,PCA4'- Ct control H35, PCA-rpmcontrol Perc. time free of cav H35, PCA2-Pcontrol Kt [-] constant Power control Vs [-] Figure Effect of heading on cavitation inception Speed. All ship speeds are normalized with V ref (4,) sigma_n cav. free cav. s.s. cav p.s. calm water It is noted that there is no significant difference in cavitation inception speed for the two distinct PCAs in bow quartering waves, as opposed to the results obtained in following waves. Furthermore, the rate of cavitation events increases faster in following waves than in bow quartering waves, suggesting stronger inflow variations on the propeller in following waves. Figure 2 shows the cavitation inception diagrams in bow quartering waves for PCA and PCA2, controlling rpm and power respectively. It is remarkable in these plots that the power control algorithm appears unable to orient the operational region more into the cavitation free bucket. As for following sea diagrams in Figure 9, a significant difference is also obtained between calm water inception (indicated by the light blue line) and dynamic inception for bow quartering waves. Kt [-] Figure 2 Effect of Propeller Control Algorithm on cavitation inception for bow quartering waves, sea state 4 Effect of Sea State Other than the baseline case of sea state 4, two additional sea states have been considered for bow quartering waves; Sea states 2 and 6. Similar to the lack of effect the PCAs have on CIS in bow quartering waves in sea state 4, Figure 3 shows that there is hardly any difference between the two PCAs tested for sea states 2 and 6. 3

14 Perc. time free of cav Vs [-] SS4, PCA-rpmcontrol SS4, PCA2-Pcontrol SS2, PCA-rpmcontrol SS2, PCA2-Pcontrol SS6, PCA-rpmcontrol SS6, PCA2-Pcontrol Figure 3 Effect of sea state on cavitation inception speed at bow quartering waves (H35 deg) and various PCAs. All ship speeds are normalized with V ref (4,35). The effect of sea state on CIS appears to be significant, however, which is a confirmation of the conclusions found in the previous phase of the CRN Project. The non-dimensional speeds cited in Figure 3 all refer to the calculated inception speed for sea state 4, heading 35 deg in an earlier phase of the Propellers in Service project, where a constant speed and constant propeller rotation rate were imposed. The deviation of the inception speed value from unity in sea state 4 is a measure of the effect of the dynamic simulation. CONCLUSIONS AND RECOMMENDATIONS Conclusions This paper presents results of a simulation model for estimating the effects of operational conditions on propeller cavitation inception performance. The results are obtained from a prototype analysis package for simulating naval ship operations in a seaway. This simulation tool has a number of aspects that are not yet complete and therefore will require further development and validation. The step by step approach followed currently in developing this complex simulator allows for a regular evaluation of its progress. As such, this paper can be regarded as one of a series of milestones reached in achieving the goals of this project. The important effect of sea state on Cavitation Inception Speed, as found for example in the sea trials of HM Tydeman described earlier in this paper, is qualitatively confirmed with the current PEASE simulator. The inception speed in bow quartering waves in sea state 6 is only some 36% of the inception speed in sea state 2. It is further demonstrated that the dynamic characteristics of the propeller control system, modeled here as a generic PID controller, have an important effect on the cavitation inception speed. A constant thrust coefficient algorithm produced a cavitation inception speed that is some 29% higher than a commonly used propeller rpm control algorithm in following seas at sea state 4. For bow quartering waves in the same sea state, no significant difference could be found in inception speed when the controller settings are unchanged from those used in following seas. It is noted that during the current phase of the project, it became clear that the time-dependency of the added resistance in waves is significant and is likely to affect the outcome of the simulations. Work has been done to derive an algorithm for estimating the unsteady added resistance in waves, reported in Van't Veer (22). This algorithm is yet to be implemented in the PEASE simulator. A few remarks need to be made with regard to the Propeller Control Algorithm or PCA: - The coefficients in the PID controller have been selected for stable operation without a proper optimization of the coefficients. The coefficients have been determined only for following seas in sea state 4, and have been applied unchanged throughout the rest of the study. Optimization of the controller is likely to improve the results for other conditions. - In optimizing the Propeller Control Algorithm, due attention needs to be given to the characteristics of the prime mover, i.e. the diesel engine. The dynamic cavitation inception limits occur significantly earlier in terms of thrust coefficient or in terms of cavitation number than is the case for steady state inception in calm water. The difference in inception must be caused by variations in the wake field and dynamics in the ambient pressure. Recommendations It is recommended that an improved formulation for the time dependent added resistance in waves be implemented in the PEASE simulator, which currently uses a constant time averaged value. Little attention has been given to the proper selection and optimization of the control coefficients in the Propeller Control Algorithm. Most of the attention was given to the following seas condition in sea state 4. This has likely resulted in the PCA not showing a significant effect on Cavitation Inception Speed in bow quartering waves. More attention needs to be given to the optimization of the control system 4