Effect of the laminar separation bubble induced transition on the hydrodynamic performance of a hydrofoil

Abstract

The present study deals with the effect of the laminar separation bubble (LSB) induced transition on the lift, drag and moment coefficients of a hydrofoil. A 2D numerical study, based on the SST $\gamma \text{–}{\mathrm{Re}}_{\theta }$ transition model of ANSYS-CFX^®, is conducted on a NACA66 hydrofoil. Angles of attack range from −4°to 14°and the chord-based Reynolds number is $\mathrm{Re}=7.5\times {10}^5$. An experimental investigation is carried out in the French naval academy research institute’s hydrodynamic tunnel based on the measurements of lift, drag and moment. Experiments on a smooth, mirror finished, hydrofoil enable comparison with RANS calculations using the transition model. Experiments with a roughness added on the leading edge enable comparison with RANS calculations using the SST fully turbulent model. For angles of attack below 6°, the LSB triggered laminar to turbulent transition of the boundary layers of the suction and pressure sides is located near the trailing edge of the smooth NACA66. As the angle of attack reaches 6°, the LSB suddenly moves to the leading edge on the suction side while transition is located at the trailing edge on the pressure side. The smooth hydrofoil shows higher $C_L$ and $C_M$ and lower $C_D$ than the rough leading edge one from −4°to 6°. Both experiments lead to the same coefficients from 6°to 14°. The calculations show that both models are in good agreement with their corresponding experiments. Velocity profiles in the vicinity of the LSB at an angle of attack of 2°and pressure coefficients of the calculations using the transition model are compared with published experimental studies and show very good agreement. The SST $\gamma \text{–}{\mathrm{Re}}_{\theta }$ transition model proves to be a relevant, even essential, prediction tool for lifting bodies operating at a moderate Reynolds number.

Introduction

The need for practical RANS-based CFD codes including accurate laminar to turbulent transition models has increased due to the renewed interest in the low to moderate Reynolds number flows. The large increase of investigations in micro-aerodynamics and in micro-hydrodynamics dedicated to drones highlights the important need of valuable transition models at full scale. Performance prediction quality of flight control devices of micro-vehicles such as Autonomous Underwater Vehicles (AUVs), Unmanned Surface Vessels (USVs) or miniature Unmanned Air Vehicles (UAVs) strongly depends on the code capability to accurately model transition. Consideration of transition at model scale is also important to estimate performance of devices based on lifting bodies such as ship appendages (rudders, stabilizers, propulsion systems) or marine current turbines.

CFD investigations need to interact with theoretical and experimental approaches to allow accurate prediction of instantaneous forces on lifting bodies. These forces are very sensitive to flow separation, laminar separation bubble (LSB) and flow reattachment which are strongly influenced by boundary layer laminar to turbulent transition. The latter has been studied theoretically and experimentally for a long time in fluid dynamics. Its modeling is a very challenging task. Data analysis of classical flat plate cases–with or without pressure gradient–and foil cases has given rise to dedicated transition models based on empirical correlations  [1]. However, the absence of laminar to turbulent transition models in the Reynolds-Averaged Navier–Stokes (RANS) CFD codes has been considered as one of their major deficiencies for a long time. CFD calculations were then performed either in laminar regime or in fully turbulent regime. Empirical methods imposing a turbulence model downstream of a transition region or low-Reynolds-number models calibrated taking into account the transition prediction  [2] were sometimes used but with no entire satisfaction.

Recently, transition models based on additional transport equations coupled to linear eddy-viscosity turbulent models have been proposed in the literature  [3] and implemented in RANS-based CFD codes, clearly improving their capabilities as compared to classical fully-turbulent models. This is the case of the correlation-based $\gamma \text{–}{\mathrm{Re}}_{\theta }$ transition model of Menter  [4] validated by the help of flat plates and some industrial test cases. The model is coupled with the Shear Stress Transport (SST) k-$\omega$ turbulence model. Counsil and Goni Boulama propose a validation of Menter’s model  [5] based on the NACA 0012 airfoil for three Reynolds numbers ($5\times {10}^4$, $1\times {10}^5$ and $2.5\times {10}^5$) and three angles of attack (0°, 4°and 8°). Their results show good agreement between calculations with the transition model and experiments for instantaneous and mean flow features. Ducoin et al.  [6] use this model on a NACA66 hydrofoil undergoing transient pitching motions. Numerical and experimental pressure coefficients are compared at several chord locations for both quasi-static and high angular velocities and show good agreement. The inflection point of the $C_p$ curves due to transition is particularly well predicted by the transition model. Lanzafame et al.  [7], after having validated Menter’s model on a 2D S809 airfoil, use it with success on a horizontal-axis wind turbine. A validation of the k–k${}_l$–$\omega$ model of Walters and Cokljat  [8] based on one additional transport equation is carried out by Genç, Kaynak and Yapici  [9]. They compare the k–k${}_l$–$\omega$ model to Menter’s model on a NACA 2415 airfoil at AoA=8° and $\mathrm{Re}=2\times {10}^5$. Their results show that modeling the transition improves the accuracy of the solution for a moderate Reynolds number compared to a fully turbulent calculation. The k–k${}_l$–$\omega$ model seems to be more accurate on the studied configuration.

High accuracy requirements lead to the use of high-density grids. As a consequence, High Performance Computing (HPC) capabilities are required to use single-point eddy viscosity models instead of correlation-based highly empirical approaches only. Conversely, due to another limitation consisting in reasonable calculation times, these models are less time-consuming as compared to fully-realized methods (LES, DNS) which cannot be easily considered on a day-to-day basis for classical engineering applications.

The purpose of this study is to evaluate the capability of the $\gamma -{\mathrm{Re}}_{\theta }$ Menter two-equation transition model  [4] in accurately determining flow characteristics on a NACA 66(mod)-312 hydrofoil in incompressible flow for a moderate Reynolds number ($\mathrm{Re}=7.5\times {10}^5$) at angles of attack ranging from −4°to 14°. The model is based on two additional transport equations, one dedicated to the intermittency $\gamma$ and the other one to the Reynolds number ${\mathrm{Re}}_{\theta }$ based on boundary layer displacement thickness. First, the experimental setup is presented, followed by a description of the model and an overview of the numerical methodology. Then, after a verification procedure dealing with four spatial and four temporal discretizations, results are presented and discussed. A global analysis dealing with lift, drag and moment coefficients is followed by a local analysis based on velocity profiles in the vicinity of the LSB, and on pressure and friction coefficients. Special focus is carried out in the boundary layer on transition location. 3D calculations are run to evaluate the 3D effect inherent in the experiment and complete the 2D calculations. The calculation accuracy improvement due to the consideration of transition effect is highlighted on the basis of validations with measurements carried out at the French naval academy research institute (IRENav).