LES study of the wake features of a propeller in presence of an upstream rudder

Highlights

• Large-Eddy Simulation is adopted for studying rudder-propeller interaction.

• Three incidence conditions of the upstream hydrofoil are considered.

• In the near wake hub and tip vortices weakly affected by the upstream disturbance.

• Faster breakdown of the smaller vortices shed from the suction side of the blades.

• Separation on the hydrofoil leading to higher turbulence within the propeller wake.

Abstract

Large-Eddy Simulations were carried out on a notional submarine propeller in presence of a disturbance at the inflow, associated to the wake of an upstream hydrofoil, mimicking a rudder. Three orientations of the hydrofoil were simulated, equivalent to angles of incidence of $\alpha =0^{\circ },$ $\alpha ={10}^{\circ }$ and $\alpha ={20}^{\circ },$ respectively. Results were also compared with the open-water configuration, featuring the same propeller in isolated conditions. Present computations demonstrate that the topology of the largest coherent structures, that are the tip vortices and the hub vortex, is practically unchanged across the three cases with different inflow perturbations. In the near wake, for $\alpha =0^{\circ }$ and $\alpha ={10}^{\circ }$ turbulent fluctuations within the propeller wake were increased only locally, at the azimuthal positions corresponding to the wake of the hydrofoil. In contrast, for $\alpha ={20}^{\circ },$ featuring separation over the suction side of the hydrofoil and thus a wider disturbance at the propeller inflow, turbulence within the core of the tip vortices was affected also at azimuthal positions away from the ingested perturbation. For the same condition also the wake axis demonstrated a stronger destabilization of the hub vortex, compared to the cases with milder disturbances, with about a four fold increase of turbulent kinetic energy, relative to the open-water condition. Downstream of the destabilization of the wake system, increasing values of turbulent kinetic energy were associated to growing incidence angles of the upstream hydrofoil.

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).