The design of propeller and propeller boss cap fins (PBCF) by an integrative method*

MA Cheng (马骋), CAI Hao-peng (蔡昊鹏)

Institute of Naval Academy of Armament, Beijing 100161, China, E-mail: 13901138354@163.com

QIAN Zheng-fang (钱正芳)

Institute of Naval Academy of Armament, Beijing 100161, China

Department of Ship Engineering, Naval University of Engineering, Wuhan 430033, China

CHEN Ke (陈科)

Institute of Naval Academy of Armament, Beijing 100161, China

The design of propeller and propeller boss cap fins (PBCF) by an integrative method*

MA Cheng (马骋), CAI Hao-peng (蔡昊鹏)

Institute of Naval Academy of Armament, Beijing 100161, China, E-mail: 13901138354@163.com

QIAN Zheng-fang (钱正芳)

Institute of Naval Academy of Armament, Beijing 100161, China

Department of Ship Engineering, Naval University of Engineering, Wuhan 430033, China

CHEN Ke (陈科)

Institute of Naval Academy of Armament, Beijing 100161, China

(Received January 21, 2014, Revised March 10, 2014)

Generally, after a marine propeller design, the propeller boss cap fins (PBCF) design concerns with an optimal selection of model test results, without a due consideration of the interaction between the PBCF and the propeller. In this paper, the PBCF and the propeller are considered as a whole system with their design as an integrative process, in which the concept of the increased loading in the blade root is incorporated. The load distribution on the blade becomes well-proportioned due to the increased loading in the blade root, and it is advantageous to the reduction of the vibratory force and the blade tip vortex. The blade root area is stronger in withstanding forces, and is not easy to be vibrated, therefore, the increased loading there is beneficial to the noise reduction. The disadvantage of the increased loading in the blade root is the generation of the hub vortex behind the boss cap, but the hub vortex can be broken up by the energy saving hydrodynamic mechanism of the PBCF. The integrative design method introduced in this paper can provide a higher efficiency for propellers under the same design conditions. In this paper, an integrative propeller and PBCF design method including the theoretical design and the numerical optimization design is proposed, based on the potential flow theory, the CFD tools, the improved particle swarm optimization algorithm, and the model tests. A propeller with the PBCF is designed based on the method of integrated increased loading in the blade root for a cargo vessel in this paper. The cavitation tunnel model test results show that the propeller and the PBCF thus designed enjoys a higher efficiency, and the design method is effective, reliable and practical.

propeller boss cap fins (PBCF), integrative design, increased loading in blade root

Introduction

The propeller boss cap fins (PBCF) is an effective energy saving device, which can recover the energy loss due to the propeller hub vortex in the propeller down stream flow and eliminate the low-pressure area behind the boss cap. A PBCF consists of some small planar fins fitted on the propeller boss cap, and it rotates together with the propeller. Since the PBCF is designated as a novel energy saving device in 1987, its effectiveness is confirmed by both model and full scale tests[1-4]. The statistical analysis of a large amount of actual vessel voyage data indicates that 3%-7% efficiency gains can be achieved[5]. Figure 1 shows a PBCF installed on a ship.

The PBCF energy-saving mechanism, the flow field around the PBCF, and the design method of the PBCF, were extensively studied since the 1990s, especially since the concept of “EEDI” was suggested[5-12].

The hydrodynamic mechanism of the PBCF can be summed up as follows: (1) the propeller thrust increases by the disappearance of the low-pressure area behind the boss cap due to breaking up of the hub vortex, (2) the total propeller torque decreases because the force acting on the fin reacts as the inverse torque by the rectification of the downstream flow from the propeller blade trailing edge.

Generally speaking, the PBCF design concerns an optimal selection of model test results for a fixed propeller, without due consideration of the interaction between the PBCF and the propeller. In this paper, the PBCF and the propeller are considered as a whole system, which is designed in an integrative process. In order to achieve better efficiency, based on the hydrodynamic mechanism of the PBCF, the concept of the increased loading in the blade root is incorporated in the design. An integrative design process of a propeller with the PBCF for a cargo vessel is presented, and the model test results show that the propeller with the PBCF designed by the integrative method enjoys a higher efficiency under the design conditions.

1. Traditional design method of pbcf

1.1 Optimal selection of model test results

To combine the empirical design with the model test validation is a widely used PBCF design method in engineering applications. A series of geometric parameters of the PBCF are selected empirically, and they are optimized to serve as the design output according to the model test results of the PBCF. This method is simple and practical, also the model test results are reliable, and so an appropriate design scheme can thus be established. However, this method can not ensure the most efficient use of the PBCF, because the choice is based on limited samples, depending largely on one’s experience. In addition, the optimal selection based on the model test results will have the disadvantage of the model test itself, such as the scale effect.

1.2 Theoretical design method

In the 1990s, the theoretical design method of the PBCF was proposed[6,11], based on the potential flow theory, including the lifting line and lifting surface model. In this method, the PBCF is regarded as a turbine or tandem installed behind the propeller, and the induced velocity of the propeller is taken into account in the design. However, the propeller and the PBCF are considered as two separate parts, with the propeller geometry being fixed during the design of the PBCF, so the effect of the PBCF upon the propeller is not duly considered. The theoretical design method of the PBCF is not used widely in the engineering applications.

2. An integrative design method of propeller and PBCF

In considering the energy saving mechanism of the PBCF, it is reasonable to assume that the stronger the PBCF’s ability to break up the hub vortex, the more energy might be saved. Therefore, if the load on the inner radius of the propeller is increased, the efficiency of the PBCF will rise accordingly, and the energy saving potential of the PBCF can be employed sufficiently. Besides, the increased loading on the blade root brings other advantages. For example, the bladeload moves to the inner radius properly, and the consequently modified well-proportioned radial load distribution is advantageous to the reduction of the vibratory force and the blade tip vortex. As the blade root area is stronger in withstanding external forces, it would not be easy to be vibrated, therefore, the increased loading is beneficial to the noise reduction.

In this paper, the potential flow theory including the lifting line and lifting surface theory is used as a preliminary design method. Then, viscous flow CFD tools are used to simulate and analyze the flow field around the propeller and the PBCF. And the improved particle swarm optimization (PSO ) algorithm[12]is selected to adjust both the propeller and the PBCF slightly. After that, model tests results of the design output serve as a validation and modification method for the integrative design work. The iterations of each design part finally form the design method for the propeller with the PBCF. The integrative design procedure can be expressed by the flow chart as shown in Fig.2.

2.1 Determination of propeller’s main parameters

In the general case of a marine propeller design, the design conditions or constraints should be given, including the type of the ship, the design velocity of the ship, the revolution number of the propeller, the load factor or power factor (thrust or engine power), the wake fraction, the thrust deduction fraction and so on. Those design requests can be obtained by the prototype ship and thruster, by empirical formulas, or by the performance calculation tools.

According to the design conditions or constraints, the diameter and the blade number of the propeller can be decided and the contour of the propeller blade can be properly chosen, based on the designer’s experience or with the help of design charts.

2.2 Determination of circulation distribution type

The propeller radial circulation distribution type plays an important role in the propeller design process; it determines the hydrodynamic load distribution of the propeller. The increased loading in the blade root is the key to tap the energy-saving potential of the PBCF and is closely related with the hydrodynamic mechanism of the PBCF. Besides, the increased loading on the blade root brings other advantages such as the reduction of the vibratory force, the alleviation of the blade tip vortex, and the noise reduction.

In this paper, the propeller circulation distribution curve is described by B-spline, and the designer can easily move the control points of B-spline to change the curve shape while keeping the curve smooth. Furthermore, moving the control points smoothly in the local zone around the propeller blade root, the circulation distribution curve shape round the blade root will not change.

In the general case, the propeller blade root zone is in the size of the propeller hub (around0.2R ) or up to0.5R in the radial length, whereRdenotes the radius of the propeller. Figure 3 shows the circulation distribution curve of the increased loading in the blade root. The circulationΓis non-dimensionalized with the propeller radiusR and the upstream flow Vsas follows

2.3 Lifting line and lifting surface design method for propeller

Since the design of a marine propeller is an important part in the design of a ship, a large number of studies have been carried out. However, until now, almost all theoretical design methods for marine propellers are based on the lifting line theory or the lifting surface theory.

In the lifting line theory, the propeller blade is replaced by a bound vortex line (the lifting line). Designers can obtain the radial circulation distribution and the hydrodynamic pitch angle distribution of the propeller through the propeller lifting line design method.

In the lifting surface theory, the singularities are continuously distributed on the reference surface of the propeller to form a lifting surface. By the design methods based on the lifting surface theory, the camber surface of the propeller and the attack angle of the blade sections can be obtained, and the effect of the thickness of the propeller blade also can be included.

In this paper, a method[13]to determine the circulation distribution using the variational calculus is selected as the lifting line design method. And a numerical discrete lifting surface method[14]is used. More details about the lifting line and lifting surface design methods can be found in the references[13,14].

2.4 CFD analysis of flow field

The three-dimensional incompressible viscousReynolds-Averaged Navie-Stokes (RANS) equations for steady flow are applied to calculate the flow field around the propeller with the PBCF.

The SSTk-ωturbulent model is adopted in this paper. The equations are discretized and then solved over grid cells by a finite volume method. The second-order upwind scheme, the second-order center scheme and the first-order implicit scheme serve as the discretization schemes of the convection terms, the diffusion terms and the temporal terms, respectively. The SIMPLE algorithm is selected as the coupled iterative method for the pressure and the velocity. The multi-grid method is used to accelerate the convergence.

The uniform inflow is used to initialize the inlet and the outlet of the calculation region. No-slip wall boundary condition is applied on the surfaces of the propeller and the PBCF. The global calculated region is a concentric cylinder which coincides with the propeller rotating axis. The diameter of the global region is10D , whereDis the propeller diameter. The inlet is6Din length before the propeller and the outlet is set at10D behind the PBCF. The unstructured grids are used in the region of the propeller with the PBCF, while the structured grids are applied in other regions. Figure 4 shows the grid distribution.

2.5 Determination of PBCF’s main parameters

In the PBCF design, the preliminary design output of the propeller is given, and the flow field behind the propeller is calculated by potential methods or CFD tools.

On the basis of analysis of a given propeller and its flow field data, the designer can decide the main parameters of the PBCF by experience, estimation, and historical model test data.

The PBCF main parameters, including the radius, the installed angle, the circumferential location, and the fin shape, can be assigned in the value range as shown in Table 1.

2.6 Lifting line and lifting surface design method for PBCF

According the hydrodynamic mechanism of the PBCF, the downstream flow from the propeller blade trailing edge is rectified by the PBCF, and the propeller efficiency with the PBCF is improved due to the increased thrust and the decreased torque.

The rectification of the flow field behind the propeller is mainly to minimize the tangential velocity. Assuming that the tangential velocity behind the propeller with the PBCF is zero, based on the definition of the circulation, it can be concluded that the circulation of the PBCF is equal to the negative value of the propeller blade root circulation. However, the circulation distribution of the PBCF is different from that of the propeller blade root, for the tip of the PBCF has no circulation. The designer should decide the PBCF circulation distribution type with the help of experience and the existing PBCF geometry. Then, the lifting line and lifting surface design methods are used to obtain the circulation and the chord camber. The lifting line and lifting surface design methods for the PBCF are similar to the methods for the propeller described in Section 2.3.

2.7 Improved PSO algorithm

The particle swarm optimization (PSO) algorithm is an alternative population-based evolutionary computation technique. This derivative free method was shown to be capable of optimizing hard mathematical problems in the continuous or binary space. It was successfully applied to large-scale problems in several engineering disciplines.

However, the PSO algorithm has difficulties in its local searching ability such as it would easily lead into a local solution, the slow local convergence speed and the low convergence accuracy, especially for multi-modal and multi-dimensional problems. A PSO algorithm with the partial mutation strategy (PMPSO)is an improved PSO algorithm aiming at overcoming the difficulties of the standard PSO algorithm.

The PMPSO serves as a numerical optimization tool in this research. During the optimal design process, the diameter, the installed angle and the axial location of the PBCF, and the pitch angle of the propeller blade root, are selected as the design variables, the thrust coefficient Kt, the propeller efficiency with the PBCF and the flow field behind the propeller with the PBCF are set to be the design constraints or design objectives, a multi-stage punishment function is adopted in this optimization problem; and the CFD method is used to calculate the hydrodynamic performance of the whole propulsion unit. More details about the PMPSO and its applications can be found in Ref.[12].

2.8 Model test

The energy-saving gain of the design output should be validated through model tests. And the design method also can be improved based on the model test results if necessary.

The “reverse propeller open test”[15]is conducted in the cavitation tunnel of Shanghai Jiao Tong University in this design process. The tunnel has a circular cross section and a test section of 2.0 m in length, 0.6 m in diameter. The pump power of the tunnel is 400 kw, and the propulsor motor power is 75 kw. The maximum water velocity is 20 m/s, while the minimum cavitation number can reach 0.2. During the model test, the water velocity is fixed at 3.0 m/s, and the revolution speed of the propeller is set to a series of values.

3. Design cases, model test validation and performance analysis

3.1 Design cases

Two design cases of the propeller with the PBCF are named as A and B for a cargo vessel. The PBCF in Case A is designed to match the original propeller of the cargo vessel, and the PBCF and the propeller in Case B are newly designed with the integrative method presented in this paper. Figure 5 shows the radial circulation distribution of both the Case A propeller and the Case B propeller. It can be seen from figure 5 that the propeller in Case B has a larger circulation in the inner radius than that of the Case A propeller. Figure 6 shows the radial circulation distribution of the PBCF in both Cases A and B. It can be seen from Fig.6 that the PBCF in Case B has a larger negative circulation than that in case A, because of the heavier load in the propeller’s blade root in Case B. Moreover, we can see from figure 6 that the circulation drops swiftly in the inner radius for the PBCF in both Cases A and B. Maybe the crescent shape of the PBCF has a significant impact on this type of circulation distribution.

Table 2 shows a parameter comparison between Cases A and B. The main difference of Cases A and B is the propeller pitch ratio in the inner radius and the installed angle of the PBCF. For the convenience of comparison in this paper, the other parameters of the propeller such as the diameter, the blade number, the area ratio, the skew, the rake, the thick distribution, and the blade section are set to same values.

3.2 Model test validation

To validate the energy saving effect of the inte-grative design method, the reverse propeller open test is conducted in the cavitation tunnel of Shanghai Jiao Tong University to compare the hydrodynamic performance of design Cases A and B. The tests are carried out both with and without the PBCF for Cases A and B. The diameter of the propeller model is 0.25 m. The advance coefficient is set to a value from 0.3 to 0.8. And the Reynolds number is around 1.35×106, which is greater than the ITTC recommended minimum value.

Figure 7 shows the comparison of the hydrodynamic performance between Cases A and B for both with and without the PBCF. The results of model tests indicate that the efficiency gains of the propeller with the PBCF can reach 2.9% in case A while 4.1% in Case B under the design condition (around J=0.44). The propeller and the PBCF in Case B designed by the integrative method has a higher efficiency than that in Case A designed by the “PBCF matching fixed propeller” method in a wide range of advance coefficients.

The model cavitation test results show that, in both Cases A and B, the hub vortex may be broken up. Figure 8 shows the comparison of the cavitation visualization results between the original propeller without the PBCF and the design Case B. It can be seen that the hub vortex disappears in the design Case B, moreover, in the heavy loaded working condition (J=0.30), the hub vortex is not generated. Therefore, it can be concluded that the propeller and the PBCF in design Case B match well, and the integrative design method is effective and reliable.

3.3 CFD analysis

The CFD simulations by Fluent are carried out in both Cases A and B with or without the PBCF in the model scale. Table 3 shows the simulation results with each component of thrust(KT )and torque (10KQ).

From Table 3, it can be seen that the negative thrust of the boss cap is reduced significantly in both Cases A and B when the PBCF is installed, due to breaking up of the hub vortex by the PBCF. The negative thrust and the negative torque of the PBCF in Case B are larger than those in case A. Moreover, the negative torque of the Case B PBCF is much larger than in Case A while the negative thrust of the case B PBCF is a little larger than in case A, it can be concluded that the increased loading in the blade root may lead to this phenomenon advantageous to increase the efficiency.

It is easy to observe from this table that the efficiency of the Case A propeller without the PBCF is higher than that in Case B, while the efficiency of the Case B propeller with the PBCF is higherthanthatinCase A, the explanation may be that a propeller with increased loading in the blade root is not a “good” one in the viewpoint of efficiency, but a propeller with the PBCF designed by the integrative method is a better option.

3.4 Vibration and noise analysis

The vibration and noise performance of the design Cases A and B can be indirectly evaluated through the modal analysis. The first order natural frequency in air in both Cases A and B can be analyzed by the software ANSYS[16]. Then, the first order natural frequency in water will be modified by Eqs.(2) and (3) as follows[17]:

In those equations,fwateris the natural frequency in water,fairis the natural frequency in air,Mbis the equivalent mass of the blade and Mwis the added mass due to water.

Figure 9 shows the mesh and the constraints for the modal analysis. Assume that the propeller material is ZQAL12-8-3-2, the material property of which is listed in Table 4. The first order natural frequency in water in both Cases A and B is 30.3 Hz and 38.6 Hz, respectively. From those data we can conclude that the design Case B has a higher first order natural frequency and is not easier to be excited during its running, for the vessel hull has a much lower natural frequency. Therefore, the design Case B has a better vibration and noise performance.

4. Conclusions

In order to consider duly the interaction between the PBCF and the propeller, and to tap the energy-saving potential of the PBCF to the utmost extent, in this paper, an integrative propeller and PBCF design method including the theoretical design and the numerical optimization design is proposed. The design method is based on the concept of increased loading in the blade root, the lifting line and lifting surface theory, the CFD tools, the improved particle swarm optimization algorithm, and the model tests.

The results of the model test and the CFD simulation show that the propeller and the PBCF designedby the integrative method enjoy a higher efficiency, and this method is effective, reliable and practical.

The integrative design method might be helpful for further study of the “EEDI standard” or the “green propulsion”.

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10.1016/S1001-6058(14)60066-4

* Project supported by the National Natural Science Foundation of China (Grant No. 51079158).

Biography: MA Cheng (1963-), Male, Ph. D., Professor

CAI Hao-peng,

E-mail: cdcaisiqi@gmail.com