Low Reynolds Number Turbulent Flow Past Thrusters Of ... - icmrt
LOW REYNOLDS NUMBER TURBULENT FLOW PAST THRUSTERS OF UNMANNED UNDERWATER VEHICLES Lucia Sileo, University of Basilicata, Italy SUMMARY The three-dimensional turbulent flow past a marine propeller used to actuate an Unmanned Underwater Vehicle (UUV) is investigated. As UUVs are often operating at low speed, this work is focused on the propeller operating at low Reynolds number regime and at off-design conditions. A parallel RANS solver was used, based on a cell-centered, finitevolume method. Following a hybrid mesh generation approach, prismatic cells were generated in the boundary layer where viscous phenomena are dominant, and tetrahedral cells in the remaining regions, while the k-ω model was employed for turbulence closure. A moving reference frame fixed on the propeller blades was used and different values of advance ratio were considered. Pressure and velocity distributions and turbulent quantities were used to analyze the computed flow field. The thrust and torque coefficients, KT and KQ, were selected as global quantities and compared with the available experimental data. The results show a good quantitative agreement with the experimental data. 1. INTRODUCTION The need for high performing underwater vehicle systems results in an increased research activity in advancing the related knowledge and technology. Especially precision automatic position control is required in fulfillment of principal industrial and scientific tasks, as automatic docking and station keeping, precise surveying, inspection, sample gathering, and manipulation. The understanding of the dynamic aspects of the thrusters must be properly considered to obtain results and to precisely control the hovering and the low-speed trajectory. In fact at very low speed, nonlinearities related to the thruster dynamics can be very important and influence the overall system behavior, making very difficult the control of the trajectory. This problem still remains to be solved and in the last few years it is focusing the attention of many studies [1-4]. Propeller and fluid dynamics are usually approximated by a two-dimensional (2-D) second-order nonlinear dynamical system, generally based on experimentally derived data. Even when these data are obtained with precision 3-D fluid velocity instrumentation, two outstanding issues are related to the need of measuring the fluid flow velocity at the actuator disk and to the presence of turbulence and high variance in velocity. In this work a Computational Fluid Dynamics (CFD) method is used to simulate the flow field generated by a rotating marine propeller, with the special perspective of an underwater vehicle application. CFD methods solving the Reynolds Averaged Navier-Stokes Equations (RANSEs) have been introduced and increasingly applied since a decade ago. Such methods offer the possibility of a detailed investigation of the full threedimensional viscous and turbulent flow around a propeller in different operational conditions, including off-design conditions. As only limited information is generally available for such conditions and detailed flow measurements are lacking, accurate numerical simulations can be even more useful, as CFD methods are especially suited to perform detailed investigations of complex three-dimensional flows.
Session C
The flow past a marine propeller is a very challenging problem in CFD and in the last few years remarkable improvements in numerical modeling of viscous flows around marine propellers have been obtained. Various numerical simulation approaches, usually applying inviscid methods (panel methods, boundary elements, etc.) have been used for decades for studying marine propeller geometries, but only recently, due to the rapid advances in computer power and in parallelization capabilities, different CFD methods, and in particular RANSEs solvers, are increasingly applied to simulate the full three-dimensional viscous and turbulent flow for various propeller geometries [5-12]. In these cases structured grids were used, and computational results were obtained for steady flow in open water conditions, with uniform inflow and non-cavitating conditions. The use of unstructured mesh is suitable for accuracy improvements, for future extensions to unsteady and cavitating flows, and for investigations of the hullpropeller interaction [13-15]. Also Large Eddy Simulation (LES) approaches began to be used to analyze marine propeller flows [16], but the computational time and resources required are considerably higher than those for RANS methods. 2. METHODOLOGIES In this section the generation of the computational grid around the propeller geometry is described, followed by the main strategy used for the calculation and the setting up of the numerical parameters directly related to the solving procedure. 2.1 PROPELLER MODEL In the present work, a three bladed thruster, used to actuate Romeo [17], an underwater vehicle designed by the RobotLab of Istituto per l'Automazione Navale (IAN) of Genoa, is considered. The propeller has a diameter D=0.16 m and three blades, characterized by sharp angles, as it was designed to be encapsulated in a duct, to improve its efficiency and to guarantee a symmetric behavior either in forward or in backward conditions. The propeller geometry is shown in Fig. 1(a).
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Fig. 1: (a) Propeller geometry [18], (b) simplifications, and (c) computational domain. The CAD drawing of the propeller was provided by the RobotLab [18], then the geometry file was imported using the pre-processor Pro-Surface [19]. Further corrections and simplifications were necessary for the numerical modeling, i.e. the blades were simply mounted on an infinitely long cylinder, which serves as the hub and shaft, to avoid the stagnation point on the hub close to the propeller, as it is shown in Fig. 1(b). The computational domain was identified with a cylinder surrounding the propeller and aligned with the hub axis, as shown in Fig. 1(c). If D is the propeller diameter, the inlet was set 4D upstream, the outflow 6D downstream, while the diameter of the lateral cylindrical boundary is 5D. Uniform inflow is aligned with the Z-axis of the coordinate system, whose origin is placed on the solid surface of the propeller and located on the central axis of the domain. The Pro-Star Auto-Meshing [19] was used for the mesh generation. The surfaces on the hub/shaft and blades were triangulated and optimized for tetrahedral meshing. Ten layers of prismatic cells were attached to the blades and hub surface, and the remaining domain was filled with tetrahedral cells. The final hybrid mesh is composed of about two million cells. The height of the first cell adjacent to the solid surface is approximately 0.0001 D, which is 1 to 30 in terms of y+ for all surfaces.
as the Z-axis and aligned with the inflow velocity vector W0: for forward conditions they have both a negative component on the Z-axis while, for the crashback condition, the direction of the inflow velocity vector was kept constant but ω has a positive component, as the rotation occurs in the opposite direction. The boundary conditions were set in an infinite domain and then they do not reproduce properly the experimental conditions in the water tunnel, leading to an over-prediction of the non-dimensional thrust and torque. In fact it has been seen that the water tunnel results are generally lower than the respective tow-tank values [16]. The present computations were carried out on a rotating frame fixed on the propeller blades. In fact, when a domain rotates at a constant angular velocity, the analysis can be simplified if the problem is analyzed in a coordinate system which rotates together with this domain. The setting of a rotating domain makes no influence in Comet with respect to the specification of boundary velocities, in fact they are given in the same way as in the case of a stationary domain [20]. The steady-rotating reference frame source terms, i.e., the centrifugal and the Coriolis force terms are simply added to the RANS equations derived in the inertial frame. A second order discretization scheme was used for the spatial differencing of the convective terms. As a steady solution is expected to occur, at least for standard forward conditions, a pseudo-transient procedure was used first, as described in [15], to yield a reasonable initial dependent variable field for the subsequent unsteady simulation. This procedure is particularly useful in situations where the mass flow rate through the solution domain is not known in advance. The standard Wilcox' k-ω model [21] was used for turbulence closure. In Comet the use of wall functions depends from the resolution of the mesh: if the first grid point is in the viscous sub-layer (y+
Session C
The flow past a marine propeller is a very challenging problem in CFD and in the last few years remarkable improvements in numerical modeling of viscous flows around marine propellers have been obtained. Various numerical simulation approaches, usually applying inviscid methods (panel methods, boundary elements, etc.) have been used for decades for studying marine propeller geometries, but only recently, due to the rapid advances in computer power and in parallelization capabilities, different CFD methods, and in particular RANSEs solvers, are increasingly applied to simulate the full three-dimensional viscous and turbulent flow for various propeller geometries [5-12]. In these cases structured grids were used, and computational results were obtained for steady flow in open water conditions, with uniform inflow and non-cavitating conditions. The use of unstructured mesh is suitable for accuracy improvements, for future extensions to unsteady and cavitating flows, and for investigations of the hullpropeller interaction [13-15]. Also Large Eddy Simulation (LES) approaches began to be used to analyze marine propeller flows [16], but the computational time and resources required are considerably higher than those for RANS methods. 2. METHODOLOGIES In this section the generation of the computational grid around the propeller geometry is described, followed by the main strategy used for the calculation and the setting up of the numerical parameters directly related to the solving procedure. 2.1 PROPELLER MODEL In the present work, a three bladed thruster, used to actuate Romeo [17], an underwater vehicle designed by the RobotLab of Istituto per l'Automazione Navale (IAN) of Genoa, is considered. The propeller has a diameter D=0.16 m and three blades, characterized by sharp angles, as it was designed to be encapsulated in a duct, to improve its efficiency and to guarantee a symmetric behavior either in forward or in backward conditions. The propeller geometry is shown in Fig. 1(a).
71
Fig. 1: (a) Propeller geometry [18], (b) simplifications, and (c) computational domain. The CAD drawing of the propeller was provided by the RobotLab [18], then the geometry file was imported using the pre-processor Pro-Surface [19]. Further corrections and simplifications were necessary for the numerical modeling, i.e. the blades were simply mounted on an infinitely long cylinder, which serves as the hub and shaft, to avoid the stagnation point on the hub close to the propeller, as it is shown in Fig. 1(b). The computational domain was identified with a cylinder surrounding the propeller and aligned with the hub axis, as shown in Fig. 1(c). If D is the propeller diameter, the inlet was set 4D upstream, the outflow 6D downstream, while the diameter of the lateral cylindrical boundary is 5D. Uniform inflow is aligned with the Z-axis of the coordinate system, whose origin is placed on the solid surface of the propeller and located on the central axis of the domain. The Pro-Star Auto-Meshing [19] was used for the mesh generation. The surfaces on the hub/shaft and blades were triangulated and optimized for tetrahedral meshing. Ten layers of prismatic cells were attached to the blades and hub surface, and the remaining domain was filled with tetrahedral cells. The final hybrid mesh is composed of about two million cells. The height of the first cell adjacent to the solid surface is approximately 0.0001 D, which is 1 to 30 in terms of y+ for all surfaces.
as the Z-axis and aligned with the inflow velocity vector W0: for forward conditions they have both a negative component on the Z-axis while, for the crashback condition, the direction of the inflow velocity vector was kept constant but ω has a positive component, as the rotation occurs in the opposite direction. The boundary conditions were set in an infinite domain and then they do not reproduce properly the experimental conditions in the water tunnel, leading to an over-prediction of the non-dimensional thrust and torque. In fact it has been seen that the water tunnel results are generally lower than the respective tow-tank values [16]. The present computations were carried out on a rotating frame fixed on the propeller blades. In fact, when a domain rotates at a constant angular velocity, the analysis can be simplified if the problem is analyzed in a coordinate system which rotates together with this domain. The setting of a rotating domain makes no influence in Comet with respect to the specification of boundary velocities, in fact they are given in the same way as in the case of a stationary domain [20]. The steady-rotating reference frame source terms, i.e., the centrifugal and the Coriolis force terms are simply added to the RANS equations derived in the inertial frame. A second order discretization scheme was used for the spatial differencing of the convective terms. As a steady solution is expected to occur, at least for standard forward conditions, a pseudo-transient procedure was used first, as described in [15], to yield a reasonable initial dependent variable field for the subsequent unsteady simulation. This procedure is particularly useful in situations where the mass flow rate through the solution domain is not known in advance. The standard Wilcox' k-ω model [21] was used for turbulence closure. In Comet the use of wall functions depends from the resolution of the mesh: if the first grid point is in the viscous sub-layer (y+
