The open water test (OWT) is carried out in towing tanks to assess the hydrodynamic performance of propellers. These tests are always performed at a model scale since open water tests at full-scale would be expensive and there are no testing sites where such large-scale tests would be feasible. Nowadays, computational fluid dynamics (CFD) is successfully used by many researchers for the assessment of ship propulsion performance. Farkas et al. [
1] used numerical simulations for the prediction of the nominal wake in the case of a bulk carrier. The authors noticed significant scale effects in both integral values of nominal wake and circumferential averaged non-dimensional axial velocity distribution. Jang et al. [
2] employed numerical simulations of OWT at model scale to assess the influence of pitch motion on the propeller performance. The authors demonstrated that the pitch motion of the ship has a dominant effect on the variation of the propeller performance resulting in the sinusoidal pitch motion of the propeller. Sun et al. [
3] used CFD to investigate the vibration and noise reduction effects of an energy-saving device. The obtained results showed that the considered energy-saving device can improve propulsion efficiency and reduce the radiation noise intensity. Multiple different scaling methods have been developed for the extrapolation of the model scale to full-scale results. Helma et al. [
4] presented an overview of the different scaling methods and assessed their influence on the full-scale results. The authors divided the scaling methods into statistical, analytical, CFD methods, and a combination of the listed methods. Helma [
5] developed a scaling procedure for unconventional propeller designs called the
method utilizing the equivalent profile concept. The author showed that the method works well with all propeller geometries since it is independent of the blade loading distribution. It is also important to point out that it needs the results from only one set of open water curves. Extrapolation performed by any of the scaling methods provides accurate and reliable results [
6], but experimental OWT is cost-intensive and time-consuming. CFD is a reasonable alternative to towing tank tests since it is a versatile tool that can be used to predict ship hydrodynamic characteristics in model and full-scale [
7]. The authors showed in [
7] that the numerical results of the ship resistance in calm water varied from −10% to 4% compared to sea trials data. Mikkelsen and Walther [
8] validated the results from the self-propulsion numerical simulations against the results obtained from the sea trials. They showed that the discrepancy between the results can be further lowered using the modified wall functions for the simulation of the surface roughness. The difference between the obtained delivered powers is largely affected by propellers operating at higher Reynolds numbers in full-scale simulations [
9]. Another problem with extrapolation to full-scale is the fact that the scaling methods are not accurate enough for unconventional propellers [
10]. Multiple authors addressed this issue by simulating the flow around the full-scale propellers with unconventional geometries such as tip-modified propellers [
5,
11,
12]. The hydrodynamic analysis of a tip-loaded propeller was performed using the boundary element method to evaluate the propeller-induced hull pressures in [
13]. The predicted hull pressures are in good agreement with the ones obtained in the cavitation tunnel and with unsteady RANS equations at the design and moderately loaded conditions. Dong et al. [
12] studied the influence of PPTC-II propeller’s tip rake on the scale effects by conducting numerical simulations in full-scale and model scale as well as modifying the propeller geometry with and without the tip rake. The authors compared the results with the ones obtained using the ITTC-1978 method and concluded that the ITTC method must be updated to predict the scale effects on the thrust and torque coefficients more precisely. Li et al. The study by [
10] also concluded that ITTC should develop new scaling methods for unconventional propellers. Chen et al. [
14] studied the open water hydrodynamic performance of a high skew submarine propeller E1619 and concluded that the difference between the predicted torque coefficient using the ITTC 1978 method and the ones obtained by numerical simulations is not negligible. Furthermore, they concluded that the law of scale effect cannot be analyzed using only two models and that several different scales must be considered. Owen et al. [
15] investigated the effect of biofouling on the propeller open water performance using numerical simulations at the model scale where multiple methods for propeller rotation modeling were used, i.e., the moving reference frame (MRF) method and sliding mesh (SM) approach. Minor discrepancies between the open water results obtained from the two methods were shown; thus, the authors decided to retain the MRF method since it is computationally less expensive. The same method was used in [
16,
17] since it lowers the computational time, and the convergence is faster than using the overset mesh (OM) method. Mikkelsen et al. [
18] also used the MRF method for open water simulations; however, in the case of self-propulsion simulations, the MRF method was used only to initialize the flow around the propeller followed by the SM method for the rest of the simulation. A comparison of SM and OM methods was given in [
19] for the case of a rotating vertical axis turbine. The authors showed that by increasing the number of cells the results converge faster using the OM method at the cost of 10% higher computational time. Wang et al. [
20] used a single-run procedure and OM method to determine the open water curves. The results were compared to the experimental results performed by IIHR (available at the Tokyo 2015 CFD Workshop [
21]) and an overall agreement between the results was shown. Bekhit and Lungu [
22] performed numerical simulations of resistance and self-propulsion tests with and without the rudder as well as OWT. The obtained results were compared with experimental results, showing an average error of about 3% for the thrust coefficient and 7% for the torque coefficient. Lungu [
23] in his later study performed numerical simulations of the resistance, open water, and self-propulsion tests of a 3600 TEU containership, where he showed a 5% difference between the measurements and numerical predictions of thrust and torque coefficients. Farkas et al. [
24] compared two methods for assessing the influence of biofouling on the open water propeller characteristics. The verification and validation study were performed for three full-scale propellers and satisfactory agreement was achieved. These results were compared with the results obtained using a propeller performance prediction method for fouled surfaces. The impact of hard fouling on the ship hydrodynamic performance was assessed in [
25], where the authors conducted full-scale CFD simulations of OWT for three propellers and validated the results using the towing tank results. Farkas et al. [
26] investigated the effects of biofilm on ship propulsion characteristics. The authors demonstrated the significant impact of biofilm on the ship hydrodynamic performance highlighting the importance of kee** the hull clean. Dogrul [
27] investigated the scale effects of a self-propelled submarine where he compared the extrapolated numerical results with the results from full-scale simulations. Gonzalez-Adalid et al. [
28] conducted model scale and full-scale numerical simulations for the determination of the performance of two unconventional propellers with the transition model. Good agreement was shown between the results obtained from the fully turbulent, full-scale simulations and the sea trial data. Baltazar et al. [
29] also performed the numerical simulations with the transition model at the model scale, but in addition, the paint test results were used for the validation study. The authors showed an increase in thrust of 2–4% when using the transition model. Moran-Guerrero et al. [
30] used an improved Gamma Reynolds Theta
correlation-based model for transition prediction, which considers the crossflow effects. Pawar and Brizzolara [
31] used the same transition model to simulate the OWT of an open and ducted propeller to assess the discrepancies between experimental and numerical results.
The focus of this study is the investigation of the scale effects of the open water propeller performance. The numerical simulations are conducted for multiple scales ranging from model scale to full-scale. First, the verification study is conducted using the grid convergence index (GCI) method, and the results of the numerical simulations are presented. The rest of the paper is organized as follows: the numerical model and the grid generation are described within Methods section. The results are presented and briefly discussed in the Results section and discussion followed by the conclusions from the present study in the last section.