Improved body force propulsion model for ship propeller simulation
Introduction
It is very important for the ship design stage to predict and assess the self-propulsion performance of various vessels. In addition, CFD (Computational Fluid Dynamics) is a higher fidelity method based on physical principles and the results are typically more accurate with almost no need for empirical inputs (L. Guo et al., 2018). Compared with experiment study, ship self-propulsion free running CFD simulation not only reduces time and cost, but can provide more information of ship flow, ship wave and other details related to the ship hydrodynamic performance. Usually there are two ways to model the propeller during simulating the free running ship: discretized propeller model and body force propulsion model.
Carrica et al. (Carrica et al., 2010; Castro et al., 2011; Chase and Carrica, 2013) and Song et al. (Song et al., 2020) proposed a method using PI speed controller and discretized propellers that could be used to predict self-propulsion performance for KVLCC, ONRT, KCS and DARPA SUBOFF generic submarine hull in model scale. Zhang et al. (Zhang et al., 2020) had analyzed the hydrodynamic performance and structural response of composite propellers using CFD and FEM and then proposed an objective function for selecting the most suitable material attribute scheme for propeller based on existing propeller theories. The flow around a rotating propeller is complex and transient, so the discretized propeller model requires higher mesh resolution and smaller time step to capture the flow features around propeller blades, which leads to complex meshes, more simulation time and cost. The body-force method makes self-propulsion simulation more easily and quickly when the detailed propeller flow is not essential for some studies like interaction of propeller-hull-rudder system. DURANTE et al. (DURANTE et al., 2013) had compared different body-force models to analyze the propeller unsteady loads in an axial, non-uniform inflow. The models were validated through numerical comparisons with propeller loads predicted by a fully 3-D panel-method BEM solver and represented a good trade-off between accuracy and cost. Villa et al. (Villa et al., 2019) proposed a new procedure to extract the self-propulsion coefficients and the method was proven to be reliable in KCS self-propulsion and maneuver conditions. A simplified hybrid method was proposed by Villa et al. (Villa et al., 2018) to address propeller and rudder interactions with reducing computational efforts and these discrepancies of the body force might be accepted due to the lower influence on the overall ship maneuverability performance. Bradford et al. (Knight and Maki, 2019) trained a semi-empirical algorithm to accurately prescribe the unsteady body force to model the propeller and the predictions of the algorithm had a good match with the CFD results. Saettone et al. (Saettone et al., 2020) selected full-scale KVLCC2 propeller to compare the propeller performance in waves using the quasi-steady and the fully unsteady approach.
The body-force methods can usually be classified into descriptive and iterative body force based on the methods of obtaining the body-force source term. The descriptive body force is based on the propeller open water curve and discretizes the thrust and torque of the propeller using a specified distribution which is first put forward by Hough and Ordway (Hough and Ordway, 1964) . Choi et al. (Choi et al., 2010), Kunihide et al. (Ohashi et al., 2018) and Jin et al. (Yuting et al., 2019) had performed propeller-hull interaction simulations using the body-force method. The results obtained through the method showed that prediction of propeller-hull interaction using CFD method was feasible. However, the vessel velocity or modified vessel velocity is usually used as the advance velocity in this method, so the interaction of the propeller and hull isn't under consideration. But in iterative body-force method, the local instantaneous velocity is used as advance velocity in every iteration step so that the virtual propeller and RANS codes can interact with each other towards a solution and the bidirectional coupling between the local flow field and the virtual propeller can be taken into account. This body-force methods generally originate from some potential flow methods, such as lift-line theory and surface singularity potential flow models. KUM (Kyushu University Method) proposed by Yamazaki (Yamazaki, 1977) is a typical potential flow method based on a simplified QBET (quasi-steady blade element theory) with the finite-bladed propeller model. Tokgoz (Tokgoz, 2015) developed viscous flow method OUM (Osaka University Method), which uses infinite-bladed propeller model coupled with RANS based on the idea of KUM. Ernesto Benini (Benini, 2004) proposed CMBET (combined momentum-blade element theory) method which is intrinsically two-dimensional following the methods of Goldstein (Goldstein and Sydney 1929) and Tachmindji and Milan (Tachmindji and Milam, 1957), and explained that the difference between RANS and CMBET is due to the difference between two-dimensional and three-dimensional airfoil. In addition, CL and CD are vital for the methods based on BET. In the KUM, OUM and CMBET, CL and CD are obtained by empirical formulas, two-dimensional data or potential flow methods and can't incorporate viscous effects.
In this paper, the new body force model follows OUM and CMBET, with however, an important difference regarding the acquisition of CL and CD. The basic idea of this method is BEMT (Blade element momentum theory) based on infinite-bladed propeller model coupled with URANS. CL and CD closer to the actual ones will be obtained directly from CFD. Then functions of CL and CD will be used in BEMT to predict thrust and torque. The key objective of this study is to develop a new body-force method which coupled BEMT with the RANS solver which will improve the accuracy and reliability for ship propulsion simulation. KP505 propeller model was used for this study. The lift coefficients CL and the drag coefficients CD of different radius sections on the propeller blade are obtained from the CFD simulation for open water characteristics of the propeller. The multivariate regression method is used to get the fitting curve of CL, CD and propeller parameters. Then the recommended range of the time step and the thickness of the body domain for the new body-force method are given. The reliability of the new body-force method are studied for the open water performance. All simulations are carried out by HUST-Ship RANS solver in this paper. RANS equations are discretized by finite difference method and solved by PISO algorithm. Computations have been made using structured grid with overset technology.
Section snippets
Governing equations
All computations are carried out by HUST-Ship RANS solver in this paper. It solves unsteady incompressible RANS equations:In which, is Reynolds time-averaged velocity component, is the time-averaged pressure and is Reynolds stress tensor. To simulate the thrust and torque of the discretized propeller, the body-force source term is added to momentum equation. is dimensionless
The geometry of propellers
The open water characteristics of KP505 are available from Gothenburg 2010 (Gothenburg, 2010). The main parameters of the KP505 model are presented in Table 1.
Computational domain and boundary conditions
Boundary conditions are set according to previous studies (Chen et al., 2018; Wei et al., 2018): The front and rear ends of computational domain along the X axis are set to the inlet and exit boundary condition respectively; The two sides and top are both selected as Farfield #2 (zero pressure gradient) and the bottom is Farfield #1(zero
New body force model
Based on discretized propeller model simulation results, the blade is divided into several parts to get the CL and the CD on each section. In addition, the hydrodynamic performance sensitivity analysis on blade divisions is also discussed for the verification of the numerical method. Then CL and CD will be used for predicting the KT and KQ of the propulsion model based on the BEMT using the relationships between the performance of the propeller sections (CL and CD) and the influencing factors
Simulation of open water characteristic using new body force model
Before comparing the new body force model with discretize propeller model, the uncertainty analysis for the new body force model were conducted.
New body force model with wake flow
In this section, simulation of propeller behind hull using the new body force model would be conducted at first. According to the self-propulsion test data, the incoming flow velocity and rotating speed are set to 2.2 m/s and 9.5 r/s respectively. The results of the new body force model would be compared with the results of the discretized propeller model to verify the effectiveness of the new body force model.
Then self-propulsion simulation using new body-force method for KCS would be
Conclusions
In the present study, a new body force model is developed for propulsion model technology. The feasibility of the new body force model were studied for open water characteristics and wake flow conditions. The reliability of the new body force model was proven in simulations of open water and propeller behind hull. By analyzing the CFD results and comparing with the EFD data. The conclusions are following as:
- 1
This method uses the direct coupling of BEMT and RANS so that the iteration loop to
Declaration of Competing Interest
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and company. We confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.
Acknowledgements
This research was sponsored by the Advanced Research Common Technology Project of CHINA CMC (41407010401, 41407020502). The essential support is greatly acknowledged.
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