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The latest Wärtsilä’s propeller designs come as a result of the extensive use of Computational Fluid Dynamics (CFD) in the design process. Numerical methods are also applied more and more to develop more fuel efficient modern hull designs. With the application of numerical simulations (see Figure 1), it has become possible to make the analyses for true full scale dimensions, thereby eliminating the use of semi-empirical scaling methods.

The conventional maritime industry approach is to optimize hull resistance and propeller performance separately. The bare hull resistance is minimized by the naval architect, and the propeller thrust is maximized for a given power by the propeller designer. Once both designs are combined (ship + propeller) the actual performance of the system is found. Due to the action of the propeller, the actual bare hull resistance increases, which is often considered as being an inevitable loss of overall performance. Modern numerical flow simulations specifically address this issue.

*Fig. 1 - Numerical flow simulation of the propeller and hull.*

#### OPTI Design FP and CP propeller design process

The use of numerical simulations in the design process enables the introduction of a completely new approach in the design of propellers. This new approach is described in Figure 2, which illustrates both the conventional approach, based on model scale testing, and the new approach based on full scale numerical flow simulations.

- The different steps in the conventional approach are represented in the blue boxes:
- Model scale ship resistance and self-propulsion measurements with stock propeller
- Propeller open water performance measurements
- Self-propulsion measurements with the actual designed propeller and extrapolation to full scale performance

The initial measurements provide the inflow velocity distribution to the propeller (wake field), which is important input for the propeller design process. Based on the powering prediction of the ship with a stock propeller, selection of the actual propeller diameter can be made. For this diameter selection the so-called B-series are often used. These B-series are based on a large set of model scale propeller performance measurements that date back to just after World War II. Nowadays, there is realisation that the actual full scale performance can differ rather significantly from the B-series predictions.

The use of full scale numerical flow simulations for vessel and propeller designs is one of the key features of the new OPTI Design approach. The different steps in the OPTI Design philosophy are shown in the orange boxes:

- Full scale bare hull calculation to determine hull resistance and wake field
- Selection of the optimum propeller diameter based on available full scale B-series polynomials
- Propeller design process based on standard design tools, making use of decades of experience
- Full scale propeller performance evaluation in open water with CFD
- Full scale propulsion calculation with hull and propeller to determine the interaction factors and thus the propeller performance in behind ship condition
- An impact analysis can be carried out to evaluate the effects of geometric variations of the propeller

These actions are defined to get firstly, the most accurate input for the design process and secondly, to check the performance of both the propeller in open water and the propeller in behind ship condition with the focus on the actual (full) scale. It can be seen from the diagram, that a final model scale test can still be part of the OPTI Design process.

*Fig. 2 - Flow chart of the OPTI Design and conventional propeller design processes.*

#### Development of numerical methods

During the past two decades, the development of numerical methods has made huge progress. Nowadays, the effects of viscous flow can be taken into account for engineering applications, which means that accurate bare hull resistance predictions and propeller open water performance calculations are feasible. Based on current technology, the viscous flow simulations (also denoted as RANS (Reynolds-Averaged Navier-Stokes)) can take the effects of the free surface along the hull, and the dynamic sinkage and trim of the vessel into account. Moreover, the accuracy of the calculations can compete with the accuracy of the model scale resistance measurements. Now that confidence in the numerical methods has been established, the step towards actual full scale geometries can be made. In this way the need for the semi-empirical extrapolation methods, as used in the model tests, will diminish.

The following step in the development of the numerical simulations is the propulsion calculation, whereby the ship and the propeller are analyzed together. The propeller performance is then derived from fully transient moving mesh simulations with sliding interfaces. In these simulations, the propeller position is adjusted for every time step, which gives the time dependent solution of the flow. The propeller thrust and torque are calculated for each time step in this approach.

The added value of the numerical simulations is found in the extensive options of flow visualization (see, for example, Figure 1) and post-processing. With these means of data analysis, it is possible to get new insights on the actual occurring flow phenomena, such as the interaction phenomena. It is also possible to determine the contribution of drag on the different components and appendages on the hull so as to get an indication of their contribution to the total resistance.

*Fig. 3 - Comparison of calculated and measured bare hull resistance on model scale.*

#### Full scale hull resistance and wake field

The value of the numerical simulations is, to a large extent, based on the achieved accuracy of the simulations. Validation of the methods is, therefore, one of the key elements in the implementation process of CFD. At Wärtsilä, a multi-year project on the method development for propeller performance predictions, thruster load determination, and ship hull resistance calculations, among others, has been executed.

A typical result of the validation work is shown in Figure 3, where the calculated bare hull resistance on model scale is compared with the experimental data from the model basin. The agreement between the calculations and the measurements is very good over the whole range of analysed ship speeds.

Calculations of the vessel resistance at actual full scale have been made as well. Though a direct comparison with full scale resistance is not possible, a good agreement has been found with the results of the semi-empirical extrapolation methods.

The model scale and full scale bare hull resistance calculations provide the velocity distribution at the location of the propeller. This is called the ship’s wake field. This is always one of the key input data sets for the propeller designer. The industry has come to recognize that the measured wake field at model scale is not fully representative of the actual inflow to the propeller on the ship itself. A comparison between the calculated wake field at model scale and at full scale is shown in Figure 4. Due to the low velocity region in the top part, the propeller loading is increased, which may lead to more cavitation. The actual cavitation behaviour of the propeller on the ship might differ, which results in less noise and lower pressure pulses. These benefits can be turned into more efficient propeller designs thanks to an enlarged design envelope. A strong non-uniform velocity distribution requires compromises in the design at the cost of efficiency. Thus, the more disturbances there are present, the lower the propeller efficiency will be.

*Fig. 4 - Comparison of model scale (left) and full scale wake field.*

#### Propeller performance determination

The numerical simulation of a propeller offers other challenges than those of the hull resistance simulations. The complex 3D shape of the propeller blades with their subtle, though critical details at the leading and trailing edges of the blades, have to be taken properly into account. The first propeller performance CFD calculations at Wärtsilä date from a decade ago, so there is considerable experience available on this topic.

Over the years, the focus has been on achieving both high accuracy of the simulations, as well as clear process descriptions, in order to get perfect repeatability of the calculations. The performance of a propeller is often presented in an open water diagram, in which the dimensionless advance speed of the water is presented on the horizontal axis, and the thrust produced and the torque absorbed by the propeller are presented on the vertical axis. The propulsive efficiency is defined as the resistance times the advance speed divided by the shaft power. An example of the open water performance calculations on model scale and full scale is shown in Figure 5. In this diagram, the results from the model scale experiments are also shown. It can be seen that the differences between model scale and full scale are larger than the deviations between measurements and calculations. Hereby showing the relevance of a full scale approach.

The lack of proper correlation between model scale and full scale has long been acknowledged within the industry. The International Towing Tank Conference (ITTC) has developed a correction formula for the propeller thrust and torque. This conventional method for propeller performance scaling (ITTC’78) is used by many model basins. More recent studies have shown that this method is not valid for every type of propeller design. For more conventional, simple designs the method is fairly accurate, but for more advanced (modern) designs with some skew and rake, completely different trends have been found. In order to take the full benefits of design features such as tip rake into account, full scale performance calculations are required.

In the case of ducted propellers, such as a propeller with an HPN as shown in Figure 6, no scaling procedures are available at the model basins. In general, this results in rather pessimistic performance predictions for ducted propulsion systems. A typical full scale example, which can be used for validation, is the bollard pull sea trial. In such tests, a vessel is connected to shore with a cable, in which the maximum pull force at zero speed can be measured. In such conditions, the actual hull resistance is negligible due to the lack of forward speed. Comparisons of the measured pull force with full scale CFD results have proven that the Reynolds scale effects for ducted propellers are present and significant in most cases.

*Fig. 5 - Open water performance diagram of propeller for model scale and full scale.*

*Fig. 6 - Numerical flow simulation of a propeller in HPN at full scale.*

#### Optimum propeller diameter selection

The key feature of the OPTI Design propeller process is the application of full scale numerical flow simulations. As discussed previously, the use of actual full scale dimensions in the simulations will have an impact on the wake field, which determines to a certain extent the design envelope of the propeller with respect to cavitation behaviour and pressure pulses. Another important parameter, with respect to fuel efficient designs, is the selection of the optimum propeller diameter and RPM. The conventional method to select these particulars is based on the model scale Wageningen B-series. This is a set of polynomials of a large range of propellers with different numbers of blades, blade area ratios, and pitch. The performance of these propellers was determined shortly after World War II in the Marin model basin. With the model scale polynomials, the optimum diameter and RPM can be determined for a specific ship. Recently, a new set of full scale polynomials has been developed based on full scale CFD simulations of the B-series propellers. This data is the property of Wärtsilä. With these full scale polynomials, the selection of the optimum diameter and RPM can be based on the actual full scale input.

A comparison has been made of the diameter selection based on the model scale and full scale polynomials. The results are shown in Figure 7, where the normalized efficiency is plotted against the normalized diameter. The starting point is the currently selected propeller (100%-diameter), based on model scale. Based on the model scale curve, it seems that the propeller has indeed the optimum diameter. However, if the actual full scale curve is used in the selection process, then a larger propeller would be selected.

It should be noted, that besides the efficiency gain due to the optimum diameter selection, also a clear difference in efficiency due to Reynolds scaling effects is visible in this diagram.

*Fig. 7 - Optimum diameter selection based on model scale and full scale propeller performance data.*

*Fig. 8 - Numerical flow simulation of a vessel with FPP and EnergoPac rudder.*

#### Conclusions

The new way of working, based on full scale numerical flow simulations, eliminates numerous issues that are part of model scale testing procedures. Full scale bare hull resistance calculations provide proper data of the actual inflow velocity distribution to the propeller. This gives the propeller designer the best starting point for the design process and reduces the compromises, which have to be made to get acceptable cavitation behaviour and pressure pulses.

The use of the full scale B-series polynomials, which are exclusive Wärtsilä property, can give a different optimum propeller diameter, which results in improved propulsive efficiency and consequently, more fuel efficient ship operation.

The versatility of the numerical simulations also enables the integration of energy saving devices, such as HPN-nozzles and EnergoPac rudder configurations in the OPTI propeller design cycle (Figure 8).

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