The benefits of combined hull form and propeller optimisation

1 The benefits of combined hull form and propeller optimisation Joy Klinkenberg * , John Huisman, Bram Starke and Evert-Jan Foeth Maritime Research Institute Netherlands (MARIN), The Netherlands Abstract. A new approach is demonstrated for the combined performance optimisation of both hull form and propeller. The approach is based on optimizing power rather than minimising the resistance. Consequently, the interaction between propeller and hull form is incorporated in the approach, including optimisation of propeller parameters. Calm-water hull-form optimisation is part of many design processes for new-built vessels. Most investigations focus on reducing the resistance contributions of both forebody and afterbody. Sometimes, also the thrust-deduction factor is studied, often using an actuator disk approach. As a next step, the propeller is optimised after the hull has been designed, using the nominal wake and propeller clearance obtained from the resistance-based optimised hull. This method does not account for the mutual interaction between the propeller and the hull. The present approach has been developed to find the best combination of hull form and propeller, to achieve higher total efficiency. A test case of an aft-ship optimised vessel for resistance only and in combination with an integrated propeller optimisation is presented to show its potential. The optimisation is performed using a Surrogate Based Global Optimisation with parameters defining the hull form and the propeller geometry. The starting point in the propeller optimisation is an F-series propeller and during the optimisation the propeller design pitch is adjusted to maintain a fixed rotation rate. The propeller optimisation focuses on propeller efficiency, cavitation volume and propeller-induced pressure fluctuations on the aftbody. Using the propeller optimiser PropArt in combination with the viscous flow solver ReFRESCO for the hull and the BEM code PROCAL for the propeller, the balance is found between propeller thrust and hull resistance. The results show that the combined optimisation results in different optimal hull forms when optimising with the propeller. Keywords: Optimisation, hull form, propeller, RaNS-BEM. 1 Introduction In ship design, one aims for minimizing ship resistance or required engine power. However, due to e.g. time constraints and computational costs, the optimisation is often split between hull form optimisation for resistance followed by a separate propeller optimisation. This can be regarded as a reasonable first approach as in general the influence of the hull on the propeller is much larger than the influence of the propeller on the hull. The influence of the propeller on the hull form can be accounted for with for instance an actuator disc approach or alternatively a boundary element method when a basic propeller design is available, see for instance [1]. In many studies the propeller geometry is then fixed and does not respond to changes in the hull form. In the current paper, the effect of the propeller on the hull and rudder is taken into account in an optimisation. This paper introduces a methodology where the hull form and the propeller geometry are optimized simultaneously to achieve the best combination possible. First, the numerical code and methods are introduced and the coupling procedure between the codes is discussed. This procedure is then shown in an optimisation for a General Cargo vessel for resistance and power to show the additional gain that can be obtained when propeller-hull interaction is included. * Correspondence to: [email protected] 16th International Symposium on Practical Design of Ships and Other Floating Structures PRADS 2025 Ann Arbor, MI, USA, October 19th – 23rd 2025 2 2 Numerical Methods 2.1 The viscous-flow (RaNS) solver for the hull The RaNS solver used for the viscous flow around the hull is ReFRESCO [2]. It solves the multiphase unsteady incompressible RaNS equations, complemented with a turbulence model (k-ω-SST in the present paper) and volume fraction transport equations for different phases. The equations are discretized using a finite-volume approach with cell-centered collocated variables. The implementation is face-based, which permits grids with elements consisting of an arbitrary number of faces, and h-refinement (hanging-nodes). The code is parallelized using MPI and sub-domain decomposition and runs on Linux workstations and HPC clusters. The momentum and pressure equations can be solved in a segregated or coupled approach. The code is targeted at and optimized for hydrodynamic applications. It has been applied, verified and validated for various flows, including cavitating flows and propellers [2] [3]. 2.2 The potential-flow (BEM) solver for the propeller For the analysis of the flow passing the propeller, a boundary element method (BEM) is used that solves the incompressible potential flow equations for lifting and non-lifting bodies. The method, designated PROCAL, is being developed within MARIN’S Cooperative Research Ships (CRS) for the unsteady analysis of cavitating propellers operating in a prescribed hull wake. It has been validated for open water characteristics, shaft forces, sheet cavitation inception and extent and hull-pressure fluctuations. 2.3 The RANS-BEM coupling procedure The steady RANS solver and the unsteady boundary element method are coupled in the following way [4] : • A RANS computation is made for the hull without propeller. This provides the ship resistance and the nominal wake field at the propeller plane. • In this wake field a first propeller computation is made using the BEM, iteratively updating the propeller RPM to a prescribed thrust coefficient. This provides a thrustand loading distribution. This unsteady loading distribution, in a ship-fixed coordinate system, is averaged in time for all blade positions to produce a steady, but axially, circumferentially and radially non-uniform force distribution. This force distribution is interpolated onto the RANS grid. • Finally, the viscous-flow computation is restarted from the previous solution, imposing the loading distribution from the BEM as a force field acting on the flow. This yields a new total wake field, from which we then subtract the induced velocities coming from the BEM to obtain a first estimate of the effective wake field. An iteration is performed between both methods until changes in the RPM and torque coefficients as well as the effective inflow to the propeller have become negligibly small. 3 Figure 1 Flow chart of the RANS/BEM coupling procedure. 2.4 The optimizer (PropArt) PropArt is a toolbox developed by MARIN for day-to-day propeller design work [5, 6]. Within PropArt, an optimisation workflow manager is present that couples the propeller geometry with PROCAL, along with thirdparty optimisation toolboxes for the automated design of propellers. PropArt typically balances the propeller efficiency by noise and vibration and cavitation erosion risk. It uses a parametric description of the propeller and tries to find the most optimal propeller within the given input and settings. Within each optimisation round, a series of PROCAL computations is performed. The results from PROCAL are converted into new objectives and constraints for PropArt. The result of the optimisation study is a Pareto front. The iteration towards self-propulsion can either be done by changing the RPM of the propeller or, with a fixed RPM, by changing the pitch of the propeller. The latter has the preference because the ship’s engine and propeller rate are known and fixed. Changing the RPM would unintentionally also include the effect of rotation rate on the optimisation results. Therefore, for the current workflow, PropArt is used to iteratively update the pitch of the propeller towards self-propulsion at a prescribed rotation rate. Additional advantages of including the propeller in the optimisation is that many things can be optimized for, apart from resistance and wakefield quantities only. Besides power, also the cavitation volume (variations), the tip vortex strength (ETV model), the integrated fluctuating force on the aft ship and the amplitude of the pressure pulses on the hull are assessed. PROPART 4 2.5 Optimisation process The optimisation in this paper is based on a Surrogate-Based Global Optimisation (SBGO) using a Design of Experiments (DoE) and is extensively described in [7] and [8]. A schematic overview of the several processing steps is given below. The optimisation process starts with the parent, or initial, hull form. Then several base variants of the parent hull form are defined, based on the analysis of the CFD results on the parent hull (e.g. pressure distribution, wave making resistance and wakefield). Each of these base variants is expected to improve the results either individually, or in combination with other variants. In the study presented in this paper we have six base variants, which have been linearly combined and sampled to form the DoE, using Latin Hypercube Sampling (LHS). All hull forms within this DoE are computed: first a nominal computation and thereafter a computation including Actuator Disc (AD) and a computation including propeller with RaNS-BEM. For the latter, the propeller geometries are all based on the Wageningen F-series Each of these three computations result in certain possible objectives, listed inTable 1 and described below. All objective data is gathered together to perform the SBGO for one or more of these objectives. For this, the program Dakota [9] is used, using Kriging, see [7] and [8] for more details on the optimisation process. A Pareto front is constructed of which a few hulls on the front are then also computed to verify the predictions of the surrogate model l. The final hull forms are then analyzed resulting in the choice of the optimal hull form. The first objectives are obtained with nominal computations: the resistance and the nominal wakefield can be extracted. From the wakefield we obtain the wake fraction w. Furthermore, we also would like an indication of the wakefield quality. For that purpose, the Wake Object Function (WOF) can be used. The Wake Object Function, WOF, is a measure of the non-uniformity in the wake field, see e.g. [10], [11] and is defined as follows: 𝑊𝑂𝐹=∫ ∫ |𝜕𝛽 𝜕𝜃|𝑓(𝜃,𝑟)𝑑𝜃𝑟𝑑𝑟 𝜃 𝑅𝑃 𝑅𝐻 ∫ ∫ 𝑓(𝜃,𝑟)𝑑𝜃𝑟𝑑𝑟 𝜃 𝑅𝑃 𝑅𝐻 (1) In which β is the angle of attack, as computed: 𝛽=𝑎𝑟𝑐𝑡𝑎𝑛( 𝑢 𝜔𝑟 𝑅𝑃−𝑣𝑡) (2) Where u is the axial velocity in the wake field, Rp the propeller radius, RH the radius of the hub, vt the tangential velocity field, ω the rotation rate of the propeller. f(θ,r) is a weighing function which could be used to put more emphasis on variations of β in a specific part of the propeller plane, for example around the wake peak. In this paper, this function is set to f(θ,r) = 1. The WOF can be used as an indicative value of improving or worsening the wake field quality and can only be used relatively between wakes in an optimisation. A lower value of the WOF would indicate a better wakefield quality with less variation in the angle of attack. 5 The second set of objectives comes from computations with an actuator disc (AD). The actuator disc mimics the thrust in axial direction at the propeller location, where the actuator disc force balances with the resistance. The computation with actuator disc results in the total thrust, but also an estimation of the power can be extracted [11]: 𝑃𝐷=∫ 𝑢1∆𝑝𝑑𝐴1 (3) 𝐴1 With A1, the area of the actuator Disc, Δp the pressure jump over the actuator disc induced by the body forces of the actuator disc and u1 the local flow velocity in the actuator disc. This PD includes the hull efficiency and part of the open water efficiency: the ideal efficiency. The last objectives are obtained with the RaNS-BEM computations: the total delivered power, including the open water efficiency. Besides the power, the cavitation volume and the integrated hull pressure fluctuation are objectives that could be optimized for; in this paper we use the hull pressure fluctuations as objective. Instead of objectives, these could also be used as constraints, e.g the pressure fluctuation should not exceed a certain value. Additional constraints are monitored such as margins against erosive cavitation and the general risk on cavitation erosion as assessed based on the dynamic shape of the sheet cavitation following the EROCAV observation handbook [12] Finally, hydrostatic data per variant in the DoE is collected to impose for example constraints on displacement, LCB position or KM-value. Table 1: List of possible objectives for each of the three methodologies. These are explained in more detail in Section 2.5 Nominal Computation Actuator Disc Computation RaNS-BEM Computation Resistance (R) Resistance (Thrust deduction) (R) Resistance (Thrust deduction) (R) Wake fraction (w) Power (P) Power (P) Wake Object Function (WOF) Cavitation volume Tip vortex strength Integrated pressure pulses 3 General Cargo vessel One testcase with a general cargo vessel is shown here to show the methodology and its potential in hull form optimisation. The hull form is taken from the Leanships [13] EU project, with the main particulars given in Table 2 and the propeller in Table 3. Within Leanships, one work package investigated the influence of propeller diameter on efficiency and power. For the current study a subset of the hull form base variants was chosen for which we expect to have an influence on hull propeller interaction. In Figure 1, the Parent hull lines are given in blue, while the base variants are given in red. Base variant A removes the tunnel. Variant B and Variant C change the contour and thickness of the gondola, with the idea that both affect wake fraction and thrust deduction. Variant D changes the propeller position upwards, while Variant E moves the propeller further aft. Finally, Variant F changes the buttock lines. For the computations with propeller, some initialization is required to set the input for the computations. In a real optimisation, these input parameters should be selected with care and might also be different per design variant. In the current simplified testcase the diameter is constant, and the rotation rate is taken from the Leanships project and set at 120 rpm. Table 2: Main particulars of general cargo vessel Length between perpendiculars 214.70 [m] Breadth moulded 23.74 [m] Design draught moulded 8.00 [m] Displacement volume moulded 34318 [m3] 6 Table 3: Main particulars of the propeller Propeller diameter 6.0 [m] Boss-diameter ratio 0.2 [-] Number of Blades 4 [-] Rotation rate at Vs = 17.0kn 120 [rpm] Blade area ratio 0.548 [-] Variant A: Removing the tunnel Variant B: Contour Gondola Variant C: Gondola thickness Variant D: Propeller position upwards Variant E: Propeller Further Aft Variant F: Buttock lines Figure 2: The hull form base variants as used in the testcase. Blue: the Parent hull form, red: the base variants. From these base hull forms, seventy linear combinations are made for the DoE via Latin Hypercube Sampling method, chosen to be domain space-filling, as also discussed in [7] and [8]. 7 4 Results Several objectives will be compared to investigate the influence of different objectives to the final optimal hull form. The first part shows the results without changing the propeller position and the power as computed with both Actuator Disc and with RaNS-BEM are compared. This is followed by an optimization where the propeller position is shifted, and we show the differences in the optimisation between resistance and power. The last section show the results when optimizing for power and for pressure pulses on the hull. 4.1 Fixed propeller position The first step is to analyze the data obtained from DoE where we do not change the propeller position. A surrogate with Kriging is constructed, with the base variants D and E set to zero as variables in the SBGO. To show differences between two methods, the power obtained through the Actuator Disc approach and through RaNS-BEM are compared. The pareto plot is presented in Figure 3 where the results are presented in relative difference compared to the parent hull form for two measures of the delivered power. If the trends for both powers are equal, a linear correlation should exist, which is not true for these results. The pareto front from the surrogate is located on the bottom left of the pareto diagram. Even though both methods predict power, the gains found with the actuator disc are larger compared to those with the RaNS-BEM method. Assuming that the RaNS-BEM method has a higher fidelity, the gains with the AD method are overpredicted. The differences between the pareto front and the checkpoints are relatively large. This could either be due to some inaccuracy of the Surrogate or too few points were computed with the DoE. This is open for further investigation. For the entire pareto front, base variants B, C and F (see Figure 2) are at their maximum values which results in a ship with a small gondola and some change to the buttock lines. Table 4 shows the results of hulls (a) and (b): The wake fraction reduces, the wake becomes less uniform and consequently, also the cavitation volume and hull pressure fluctuation level increases. Interestingly, the most gain in power with RaNS-BEM is in case the tunnel is removed, while the most gain in power with only an Actuator Disc is where the tunnel is partially kept. The results also show that by using a stock propeller like the Wageningen F-series, the pressure pulse is more than twice as high as commonly accepted. This indicates the need for a custom optimized propeller design for this particular ship, especially due to the tunnel shape. Nevertheless, by keeping the propeller geometry consistent, the influence of the hull design on the cavitation properties is made visible. Figure 3: Result of the computations with the Power obtained from the actuator disc on the horizontal axis and the Power obtained from the RaNS-BEM computations where the propeller position is not allowed to change. The blue dots denote the computed Design of Experiments; the orange squares the pareto diagram obtained from the SBGO. The blue triangles show the final computations on two optima (the 2 extremes) from the Pareto plots. 8 Table 4: List of results for the parent hull form and hull forms (a) and (b) from Figure 3. Both the differences in power are given (on the two rightmost columns) as well as some information on the wakefield, cavitation and pressure pulses. Propeller height [m] w [-] WOF [-] Cavitation Volume [m3] Pressure Pulse [kPa] 1st harmonic ΔP RaNSBEM ΔP AD Parent 3.0 0.304 0.0765 0.069 12.4 Hull a 3.0 0.270 0.0843 0.083 14.4 -2.0 -3.2 Hull b 3.0 0.267 0.0822 0.083 14.3 -1.6 -3.4 4.2 Resistance and power The next step includes changing the propeller position. To show differences between the optimization methods, the objectives that are initially investigated and optimized for, are the nominal resistance and the resulting power obtained from the RaNS-BEM computations. The results are shown in Figure 4 and show some gains compared to the parent hull form. The differences between the pareto front and the checkpoints are much smaller compared to the ones in the previous section. The figure shows that the optimisation for power with RaNS-BEM results in a different optimum compared to the optimized hull form for resistance. The optimal hull form for resistance only might actually be worse in power (hull a), or having a smaller decrease in power (hull b) compared to the optimal hull forms in power (hull c) that shows a smaller gain in nominal resistance. The lines plans of these hull forms are given in Figure 5. For powering, a tunnel is more beneficial, while also the gondola is larger to have larger wake fraction. Figure 4: Result of the computations with the nominal resistance on the horizontal axis and the Power obtained from the RaNS-BEM computations. The blue circles denote the computed Design of Experiments, the orange squares the pareto diagram obtained from the SBGO. The blue triangles show the final computations on three optima from the Pareto plots (2 extremes and an intermediate result) 9 Hull a Hull b Hull c Figure 5: Linesplan of the optimal hull forms from Figure 4. Not visible, but the propeller height increases for hull form a to its maximum value, for (b) in the middle, and hardly any change in (c). The propeller is positioned somewhat further aft for all three cases. So far, we have only investigated computed power and resistance and no other objectives. If we take the three hull forms [a, b and c] for further investigations, we can dive into more detail where the changes are derived from. Could we maybe already foresee the optimal hull form for powering, solely based on a nominal computation? If that is true, it would be much cheaper to perform. As mentioned earlier, from the nominal computation, also the wake fraction is extracted from the computations as well as the wake object function. These results, for the parent hull and the three hull variants, are shown in Table 5 below. The wake fraction decreases from the parent hull form to hull forms (b) and (c); the WOF is similar, but slightly smaller for hull form (c). A smaller wake fraction would imply that the hull efficiency is smaller and thus one could arrive at the conclusion that these hull forms are worse. However, the opposite is true in this case: a smaller wake fraction seems to improve the predicted power. It could also be expected that the Wake Object Function and Cavitation Volume follow a similar trend: when the wakefield is smoother, less cavitation and lower pressure pulses are expected. However, due to changes in propeller operating point, this does not always hold. The wakefields themselves are shown in Figure 6 and differ quite significantly between the Parent hull and hull (a). The wake peak is deeper compared to that of the parent hull (Ux/Vs=0.362 vs Ux/Vs=0.403) and also the Wake Object Function is significantly larger. The propeller is located higher; the cavitation volume is larger and especially the pressures pulses are significantly higher due to a smaller hull clearance. Hull form (b) also has a deeper wake peak (Ux/Vs=0.373), but hull (c) with a wake peak of Ux/Vs==0.390 has a smaller gradient, made clear with the lower WOF. Hull form (c) is therefore better for cavitation volume and pressure pulses, compared to hull (b). However, the parent hull form has the smallest pressure pulses and cavitation volume, because the propeller position has shifted upwards in all other cases, which appears to be better in terms of power. This implies that the new method is necessary when the propeller is shifted towards the hull and when pressure pulses are of interest in the optimisation.