Hydrodynamic characteristics of marine composite propeller blade using a numerical approach

M L P Kishore, Vijay K Singh, R K Behra, Chandra S Saran, Manikant Paswan, Kapil Kumar Department of Mechanical Engineering, ICFAI University, Telangana, India National Project Implementation Unit-Ministry of Human Resource and Development, MMMUT, Uttar Pradesh, India Department of Mechanical Engineering, NIT Rourkela, Odisha, India Department of Mechanical Engineering, Government College of Engineering, Odisha, India Department of Mechanical Engineering, NIT Jamshedpur, Jharkhand, India


INTRODUCTION
Since 19 th century, screw propellers have secured a position in the ship hydrodynamics as the best propulsion system despite of several developments in the propeller design and propulsion system due to its suitable use and higher efficiency over a long period of time. With the rapid advancements in technology, the determination of principal dimensions like ship size, speed for the design of ship using numerical methodbased tools has gained much importance. These numerical applied computational methods have gained the closed form of solutions with analytical or experimental methods. The use of Wageningen B-series as base series for marine propeller blades proved desirable for various applications of ocean engineering. Although much research has been done on the optimal design and applications of such series, the baseline lies in determining the open water characteristics of these blades to assess the suitability in underwater conditions. A normal procedure is to design a propeller is based on the diagrams obtained from the open water test of the model series. The marine propeller design and determination of optimum diameter can be made using the data from the polynomials of developments in the technology of computers, great improvements occurred in the propeller's design followed by its analysis. The application of computers reduced the time and effort involved to carry out number of experiments in towing tanks by designing the performance of propellers with a just few design parameters and considered to be one of the most effective techniques for analysis of fluid flow parameters. The design of marine propeller was done [1], systematic propeller series and implemented numerical relations in the design of propeller blade (B-series) under various loading conditions. A three-dimensional hydrofoil in a water tunnel has been investigated with respect to its' fluid-structure interaction (FSI), Shiliang HU et al [2] using the Finite volume method (FVM) and Finite element method (FEM). The propeller efficiency (open water and body) for single and twin-screw ships was computed [3], using several advanced coefficients definitions. The comprehensive description of the state of art can be found [4], where the flow across a propeller examined experimentally in open water channels keeping the flow conditions uniform.
The flow field and physical parameters subjected to a propeller simultaneously was analysed [5] using computational fluid dynamics (CFD) technology. While dealing with the turbulent shock wave and break wave to take care nonlinearity, they applied the Navier stokes equation has been applied to the solver. The thrust and torque performance of the marine propeller blade at different rotational speed has been estimated using CFD and found a good relevance with the experimental results reported [6,7]. A series of marine propeller have tested under open water experimentation and the obtained hydrodynamic characteristics was compared with that of the numerical results [8], A performance test was carried out [9] for 79 propellers in the diameter range of 9 to 11 inch along with the measurement of thrust as well as torque in the propeller speed range 1500-7500 rpm with respect to its' diameter. The complementation of combined blade-momentum element-theory for the propellers which are light/moderately loaded was illustrated [10]. The hydrodynamic characteristics for the propellers (conventional metallic) of various sizes was determined [11,12] using cavitation and tunnel test.
Most of these research work had been carried out either by analytically or numerically in viscid or fully viscous/boundary layer technique [13]. With the effects of turbulence flow taking into consideration and flow field estimation with no-slip boundary conditions are out of important RANS (Reynolds average Navier stokes equation) with appropriate turbulence model is used to predict the flow characteristics of propeller blade according to [14]. A CFD based lifting line surface theory was used [15,16] for visualizing the flow pattern around the merchant's ship propeller. The viscous equation solution for the flow pattern was implemented [17]. A ship propeller design (SPD) computer code developed and employed for many propulsors (propeller rudder system and contra rotating propeller [18][19][20][21][22]. The hydrodynamic analysis of marine propeller was performed using this SPD code based on boundary layer theory. A coupled boundary element method along with the finite element method was applied to determine the numerical solution for the flexible propellers (composite) [23]. A numerical analysis was carried out [24] in the case of propellers of large-scale surface. The open water characteristics was computed along with the analysis of cavitation problem [25] using computer code (solaga). Senthil et al [26] obtained the open water characteristics of propeller (B-series) using CFD simulation. Later on, the CFD analysis of propeller (contra-rotating) was performed by Das et al [27]. Das and Jaykumar [28] predicted the hydrodynamic characteristics of a contrarotating propeller by validating the computed results with the experimental data. [29] Studied an autonomous underwater vehicle in the case of hull propulsor interaction by performing the computational analysis and experimental validation. Krishna et al. [30] presented the acoustic characterization of a Benchmark Marine propeller using CFD. The numerical prediction was made [31] for the forces acting on propellers (podded and open), working under the abnormal flow situations. Subramanian and Senthil [32] implemented a scheme for the optimization of the propeller by coupled LM and RANS solver methods. Application of CFD for the prediction of performance characteristics in marine propeller can be found in Kimura et al. [33], Takshi and Jun [34], Choong et al. [35]. A mechanical prototype of (OWC) Oscillating conversion Chamber device was built and studied using CFD simulator [36]. A comprehensive study on bend-twist coupling of composite propeller blades in order to improve the hydrodynamic efficiency was presented by Das and Kapuria [37].
The objective of the present study is to perform the Computational fluid dynamics simulation for the flow around the B-series Wageningen propeller using an unstructured mesh-based Reynolds-averaged Navier stokes equation method. The computed results are validated with the standard B-series data in order to test the efficacy of the present method. A moving reference frame approach is selected using the K-ɛ model and employed for turbulence closure. The global quantities such as thrust and torque coefficients along with open water efficiency (KT, KQ, and o) are determined in addition to pressure contours on the blade surfaces. The deviation in solution has been found from 5 to 15% in the case of thrust and 10-20% in the case of torque. Pressure estimation is usually quite accurate with 5-8% variation.

MATHEMATICAL FORMULATION 2.1. Governing equations
For the practical design consideration and performance analysis point of view empirical relations along with diagrams are presented for B-series propeller. The parameters contained for design of a propeller blade include the power delivered (PD), the number of blades blade area ratio, advanced speed, number of propeller revolutions pitch ratio and the diameter D, by systematically changing the advanced speed or propeller revolutions the performance characteristics are investigated among probable solutions. The variable parameters representing this series are the propeller blade number, the blade area ratio and the pitch ratio.
The dimensionless characteristics are expressed as The Wageningen B-series being a general series expressed with open water diagrams obtained from open water or model tests where the , , 0 , curves are showed with constant blade number, blade area ratio and pitch ratios.

Flow simulation
The above governing equations have been converted to the algebraic equations which can be solved numerically using control volume technique of Fluent. This control volume technique consists of governing equations about each control volume yielding discrete equations and conserve the quantities on the basis of control volume. The standard wall functions used are based on the proposal of Launder and spangling and have been found quite reliable for propeller flows. The standard K-Ɛ model has been used.

NUMERICAL ILLUSTRATION
The computational domain was created for the scaled model propeller with a hub surrounded by a fluid domain shown in Figure 1(a, b). The inlet was prescribed at 3D upstream exit at 4D downstream solid surfaces on the blades and hub centred at the origin of the coordinate system followed by the alignment with uniform inflow. A hybrid mesh was generated inside the domain using hyper mesh 11.0 shown in Figure 1(d). Initially the blade surfaces were meshed with smaller triangular element while the inner region was filled approximately with growing triangular element and finally the domain region was filled with tetrahedral elements. The number of cells used in the mesh is about 583451. The 3D flow (viscous and incompressible) was solved using the FLUENT 6.3.26 code. The fluid continuum was chosen and assigned with the properties of water. A moving reference frame is assigned to fluid which has the same rotational velocity as that of propeller. The wall interface of the propeller blade and hub were assigned a relative Int J Adv Appl Sci ISSN: 2252-8814  Hydrodynamic characteristics of marine composite propeller blade using a numerical … (Vijay K Singh) 23 rotational velocity of zero with respect to the adjacent cell zone. A uniform velocity was prescribed at inlet. The magnitude of velocity was adjusted to obtain appropriate advanced coefficients (J). At outlet outflow boundary condition was set. The far boundary (far-field) was taken as inviscid wall and assigned an absolute rotational velocity of zero. Fluent 6.3. Has been used for the computation of Flow through propeller (B-series). The simulation has been carried out to determine the propeller's open water characteristics with different varying advanced ratios in the range of 0.2-1.4 as the requirement 0 for the performance of the propeller in this operational range. The discretized fluid structure interaction can be seen in the Figure 2 where the propeller blade is surrounded by the tetrahedral element. The pressure distribution and rotational speed variation across the propeller blade can be observed in the Figure 3 and Figure 4 respectively. The comparison of presently Computed hydrodynamic characteristics responses of thrust coefficient ( ), torque coefficient ( ) and open water efficiency ( 0 ) with that of the standard B-series data are presented in the Figure 5. It can be seen that the present hydrodynamic characteristics responses follow the same trend i.e. linear decreasing as in the standard B-series data after reaching to the 65 % of the advanced coefficient (J). The variation in the open water characteristic can be realised with respect to the advanced coefficient (J) in the Figure 6. The specification for the B-series propeller and the solver settings for the flow simulation are presented in the Table 1 and Table 2 respectively. Table 3 provide the more transparency in the numerical responses of the open water characteristics with the advanced coefficient (J) which was difficult to realise in the Figure 5. The variation in the Open Water Characteristics of B-Series Propeller with the varying rotational speed and the advanced velocity is shown in the Table 4 and Table 5 respectively. It is observed that all these responses show a significant decrement with a marginal change in the rotational speed and the advanced velocity.

CONCLUSIONS
The limiting streamlines and the path lines of the propeller blade, as well as the pressure distribution on the blade surface, represent its' flow characteristics more accurately. In absence of validation while employing the results if this CFD simulation solution generally tends to overestimate and the discrepancy increases with increasing propeller load i.e. decreasing (J). The deviation in solution may range from 5 to 15% in the case of thrust, 10-20% in case of torque. Pressure estimation is usually quite accurate with 5-8% variation. The tabular data of pressure distribution over the propeller blade may be used for further structural analysis. Maximum open water efficiency for computational result is 60.1% which is the instant exactly at the specific operating conditions which shows that the obtained computational results are up to the mark. In order to achieve a close form solution, tetrahedral element mesh has been replaced with hexahedral element mesh. There is a wide future scope of the present research work in finding more suitable method of combining blade and hub of a propeller within the block along with the refinement of mesh.

ACKNOWLEDGMENTS
Authors express their sincere regard to the National Institute of Technology, Rourkela-273010, Odisha and National Project Implementation Unit-Ministry of Human Resource and Development, Govt of India, for providing consistent support and encouragement in performing the present study.