LES study of the wake features of a propeller in presence of an upstream rudder
Introduction
Underwater vehicles propellers are typically installed in the wake of upstream rudders, which are utilized for maneuvering. Rudders, especially at high angles of attack, generate perturbations on the flow ingested by the propeller. To date, the impact of such perturbations on the propeller wake is not well documented via either high-fidelity computations or experiments. The most advanced computational studies in the literature on propellers adopt the Large-Eddy Simulation (LES) methodology. Early LES simulations dealing with submarine propellers are due to Di Felice et al. [8] and Alin et al. [1], who both computed the flow around the INSEAN E1619 propeller. In particular, Di Felice et al. [8] adopted a wall-modeling strategy to carry out LES computations on body-fitted grids composed of 4.5 million finite volumes. Alin et al. [1] and Liefvendahl et al. [16] reported finer grids, up to 13 million volumes, but still the limited resolution of the computational mesh restricted the analysis to the near wake flow, up to 0.58 diameters downstream of the propeller plane. The qualitative agreement on the mean flow statistics from the Laser Doppler Velocimetry (LDV) measurements by Di Felice et al. [8] was good, while turbulence was damped by lack of resolution. Additional LES studies on propellers, using computational grids at least an order of magnitude larger than above, were reported in the literature more recently. However, as before, they still deal with the less computationally demanding open-water configuration [5], [13], [14], [15], [27], [32]. We should mention that Schroeder et al. [32] and Balaras et al. [5] also considered a configuration featuring an upstream disturbance. The notional INSEAN E1619 propeller was simulated in the wake of a NACA0018 hydrofoil at 0 incidence, relative to the free-stream. Computations were carried out using LES, coupled with an Immersed-Boundary (IB) method, on a staggered cylindrical grid. Results demonstrated that the narrow wake generated by the hydrofoil in those incidence conditions was not able to affect significantly the wake of the INSEAN E1619 propeller. In the work by Posa et al. [27] the INSEAN E1658 propeller (a modification of the INSEAN E1619) was simulated via the same Navier-Stokes solver as in Schroeder et al. [32] and Balaras et al. [5]. Comparisons of the velocity statistics with the experiments by Felli and Falchi [9] were very satisfactory, demonstrating the accuracy of the solver in this class of applications. Good agreement with measurements was also reported by Kumar and Mahesh [15] and Keller et al. [13], 14], who simulated the DTMB 4381 marine propeller in open-water conditions using an LES unstructured solver. It is worth noting that additional LES studies on propellers are available in the literature, but they deal with the crashback condition, with the propeller generating a thrust directed along the direction opposite to that of advancement. Examples can be found in Verma et al. [34] and Jang and Mahesh [12]. Implicit LES (ILES) was also adopted to study cavitation phenomena affecting the working conditions of marine propellers [2], [3], [6], [18].
Simulations of propellers operating as part of an appended underwater vehicle have also been reported. An early study is due to Alin et al. [1], who carried out LES of the self-propelled DARPA suboff [11], equipped with the INSEAN E1619 propeller. They utilized body-fitted grids composed of a total number of finite volumes equal to about 40 million, in the framework of a grid deformation and regeneration strategy to handle the propeller motion, relative to the body of the submarine. Liefvendahl and Tröeng [17] studied via LES the loads over the blades of the INSEAN E1619 propeller, working again at the tail of the DARPA suboff, using the same strategy adopted by Alin et al. [1]. The computations utilized approximately 8 million finite volumes, exploiting wall-modeling to tackle the boundary layer. However, results on the wake development were not reported. Wall-modeled LES computations on body-fitted grids were performed by Norrison et al. [21] and Petterson et al. [22] on the self-propelled fully-appended Joubert model, with both seven-bladed and five-bladed propellers. Petterson et al. [22] considered also non-zero yaw conditions. Computations were carried out on grids up to 350 million finite volumes. Posa and Balaras [25], using a finite-differences approach, simulated via LES/IB the fully-appended DARPA suboff, equipped with a modified INSEAN E1619 propeller, on a cylindrical grid composed of about 3 billion nodes. This study, however, was not focused on rudder/propeller interaction and did not consider non-zero yaw conditions.
To overcome the prohibitive cost of a parametric study involving the full system as in the examples discussed above, in the present work we report LES of a simplified configuration: the INSEAN E1658 propeller operating within the wake of a hydrofoil. Three incidence conditions were simulated, producing different levels of disturbance at the propeller inflow. The paper is structured as follows: methodology (Section 2), computational setup (Section 3), results, including validation, visualization of instantaneous realizations of the solution, phase-averaged and time-averaged statistics (Section 4) and conclusions (Section 5).
Section snippets
Methodology
In the present computations the filtered Navier-Stokes equations in non-dimensional form are considered: where Eq. (1) stands for the conservation of mass and Eq. (2) for the conservation of momentum. There indicates filtered quantities, associated to the scales resolved by the computational grid. Thus, and are the filtered velocity vector and pressure, respectively, while t stands for time. ∇( · ), ∇ · ( · ) and ∇2( · ) represent the gradient,
Geometry and computational setup
The INSEAN E1658 submarine propeller was simulated in presence of an upstream rudder. It is a seven-bladed propeller studied in open-water conditions via Particle Imaging Velocimetry (PIV) experiments by Felli and Falchi [9] and via LES computations by Posa et al. [26], [27], using the same solver adopted in the present study. The agreement between the computations and the experiments was excellent.
The upstream rudder was mimicked by a hydrofoil, having a NACA0020 cross-section, as the fins of
Results
In this section we will first report comparisons of the flow statistics with the experiments by Felli and Falchi [9] to establish the accuracy of the computations. Then, analysis of the wake structure is conducted via: i) instantaneous realizations of the solution; ii) time-averages; iii) phase-averages. Time-averages were computed using all available instantaneous realizations of the flow. Collection of the statistics was started after wake establishment, in order for the solution to be
Conclusions
Large-Eddy Simulations were performed on the INSEAN E1658 propeller with an upstream hydrofoil, mimicking a rudder, for three orientations, equivalent to incidence angles of 10∘ and 20∘ (cases C00, C10 and C20, respectively). Comparisons were presented across those cases and with the results in open-water conditions reported by Posa et al. [27]. The same methodology was validated by Posa et al. [27] with the present level of resolution of the computational grid and the same propeller
Acknowledgments
AP was supported by the European Union Horizon 2020 research and innovation programme HOLISHIP “Holistic Optimisation of Ship Design and Operation for Life Cycle”, under grant agreement n. 689074. EB was partially supported by the Office of Naval Research Grant N00014-18-1-2671, monitored by Dr. Ki-Han Kim. The Authors are grateful to Michael Brown (Naval Surface Warfare Center, Carderock Division, Maryland), for generating the Lagrangian grid of the INSEAN E1658 propeller. We acknowledge PRACE
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