Hydrodynamic forces of contra-rotating ducted propeller with large pitch-diameter ratio

CHINESE JOURNAL OF SHIP RESEARCH,VOL.11,NO.5,OCT 2016 DOI:1969/j.issn.1673-3185.2015.007 27 http:// english.ship-research.com Translated from:mei Lei,ZHOU Junwei,NI Haoliang. Hydrodynamic forces of contra-rotating ducted propeller with large pitch-diameter ratio[j]. Chinese Journal of Ship Research,2016,11(5):42-47,54. Hydrodynamic forces of contra-rotating ducted propeller with large pitch-diameter ratio MEI Lei, ZHOU Junwei, NI Haoliang School of Naval Architecture and Ocean Engineering, Harbin Institute of Technology at Weihai, Weihai 264209, China Abstract: A Single Rotor (SR) ducted propeller and two Contra-Rotating (CR) ducted propellers with different pitch-diameter ratios are designed on the basis of the cascade theory, and the numerical simulation of the flow field is carried out using commercial CFD software. The upstream rotor pitch-diameter ratios of the two CR ducted propellers are 1.451 and 2.108 respectively, and the pitch-diameter ratios of the downstream rotors are designed according to the principle of eliminating the swirl flow. The simulation results show that both the thrust coefficient and the torque coeffi cient of the CR ducted propellers are improved significantly with the increase of pitch-diameter ratio, while the efficien cy increases slightly and the maximum efficiency point of the propeller offsets to the right. Compared to the SR propel ler, the CR ducted propeller can maintain higher propulsion efficiency at a higher pitch-diameter ratio. Key words: propeller; Contra-Rotating (CR) ducted propeller; large pitch-diameter ratio; propulsion efficiency CLC number: U664.33 0 Introduction Over the past decade, ships have been developing in the direction of being large-scale and high-pow er. In order to meet the requirements of high-speed and high-thrust performance, as well as to ensure that the propeller gets high efficiency, ducted propel ler is an option [1]. The ducted propeller can increase the flow through the per unit time and reduce the contraction of the wake, thus decreasing the propeller's loading coefficient and improving the propulsion efficiency. In addition, contra-rotating propulsion form is an alternative because the propel ler aft can reduce or even eliminate the swirl flow in the wake and absorb the rotational energy imparted to the water by the forward propeller, thus to improve the efficiency [2-3]. Combining characteristics of duct ed propeller and contra-rotating propeller, a new pro peller, namely, Contra-Rotating (CR) ducted propel ler could be constructed to improve its performance further. At present, the conventional hydrodynamic design methods of propeller are the lifting line method and the lifting surface method [4-5]. As for the combined propellers like contra-rotating propeller, there is an unsteady interference velocity between the forward and aft propellers, with the interference between the duct and the propeller in the design of CR ducted propeller. Therefore, its calculation method is more complex and difficult. As a kind of turbo machine, the design of CR duct ed propellers can adopt the cascade theory [6] besides the traditional methods, despite that this method has been rarely applied in ducted propellers. But accord ing to previous study of the authors, this theory can be better used to guide the design of ducted propel ler [7-8]. Based on the pre-study on CR ducted propel ler, the difference of the efficiency of CR rotor and Received:2016-03 - 08 Supported by:national Natural Science Foundation of China (51309070); Fund of Shandong Science and Technology Agency (2013GGA10065); Natural Science Foundation of Shandong Province (ZR2012EEQ004) Author(s):MEI Lei, female, born in 1981, Ph. D., lecturer. Research interests: increasing efficiency and reducing noise of composite propeller, design and constrcution of composite high speed boats. E-mail: mlsmile81@163.com ZHOU Junwei (Corresponding author), male, born in 1981, Ph. D., associate professor. Research interest: hydrodynamics of ship propulsion turbine. E-mail: zhou_junwei@foxmail.com

28 single rotor with the same total thrust will be dis cussed in this paper, and hydrodynamic performanc es of CR ducted propeller with different pitch-diame ter ratios (P/D) are compared and analyzed. 1 Design of ducted propeller In this paper, based on the Single Rotor (SR) duct ed propeller 19A/Ka4-55, the CR ducted propeller is designed to conduct a comparative study on perfor mances of the two propellers. This paper intends to explore performance differences of the CR rotor and single rotor with the same total thrust. In order to make them comparable, the settings in the design stage are as follows: 1) The same airfoil shape and disk ratio are adopt ed in both CR ducted propeller and SR ducted pro peller. 2) The elongated duct in the CR ducted propeller will be used in the SR one and the differential pres sures before and after the rotor are the same, that is, the two thrusts are the same under the ideal actuat ing disk assumption. The SR ducted propeller and the CR one are both in equal-pitch distribution to simplify the design and ensure that there is no overlarge pitch angle θ S at the root of the blade. Moreover, the pitch distribu tion is re-designed with the cascade theory. Consid ering that the greater the radius of the conducted pro peller is, the stronger its performance ability is, the pitch will be calculated at the position with the maxi mum radius, rather than the position of R (R is the blade radius) or 5R used by the traditional propellers. Specific designs of the SR ducted propel ler and the CR one are as follows 1.1 Cascade theory According to the cascade theory, the work of im peller will completely convert to total pressure ener gy in the internal flow without considering the fric tion loss, that is, the relation between the total pres sure rise Dp before and after the, the linear velocity U of blade element and the tangen tial induced velocity DV θ can be expressed as Dp = ρudv θ (1) where the linear velocity U refers to tangential ve locity of the blade element at the radius r, and it can be expressed as U = ωr ; the tangential induced ve locity DV θ refers to the tangential velocity compo nent of the rotor at the outlet; and ρ is the water density. The calculation equations of the pitch angle θ S of the SR ducted propeller, θ 1 and θ 2 of the CR duct ed propeller's forward and aft propellers respective ly, and the pitch-diameter ratio of the blade tip are θ S = arctan U - DV θ V Z V Z θ 1 = arctan U - DV θ (2) θ 2 = arctan V Z U P/D = π tan θ (3) where V Z is the axial velocity at the position of the in the duct. In accordance with the requirements of thrust de sign, differential pressures Dp before and after the rotor can be calculated according to the following for mula, and the unit is Pa. Dp = 4T π(d 2 - d 2 ) = 4K ρn 2 T D 4 = 100 739.83(4) π(d 2 - d 2 ) where T is thrust of the propeller; K T is the thrust coefficient of propeller; and n is the rotational speed. 1.2 Design scheme of CR ducted propellers Owing to the front and rear rows of rotors, perfor mance ability of the CR ducted propeller is far better than that of the SR one because the load on the for mer will be significantly reduced in requests of the same advance speed, rotating speed and thrust. To compare performances of the two in the same ad vance speed and thrust, we must change the load co efficient of the CR ducted propeller, which is achieved by reducing the rotating speed in this pa per. After the rotating speed is reduced, the rotor pitch of the CR ducted propeller is significantly in creased, and then the effects of increasing the pitch on hydrodynamic performance of the CR ducted pro peller will be discussed further. In this paper, two design principles are proposed to redistribute the rotor load of the CR ducted propel ler, which are respectively introduced as follows. Scheme 1: Equal tangential induced velocity at the outlet. The aim of this scheme is to ensure that the con tra-rotating rotor in the first stage and the single ro tor share the same upstream and downstream flow fields. The total pressure rise is evenly distributed to the forward and aft propellers to keep the tangential induced velocities DV θ of the front propellers at the

29 outlet of both the SR and the CR ducted propellers unchanged. According to Eq. (1), the rotating speed of the front and aft propellers of the CR ducted pro peller becomes 1/2 that of the SR one. The pitch-di ameter ratio of the CR ducted propeller at the blade tip can be calculated according to Eq. (2) and Eq. (3), which can be used to determine the pitch angle at each radius of the blade. Scheme 2: Equal work ratio. With the nondimensionalized pressure rise of the blade element at the tip, it can be obtained that: ρudv θ ρu 2 = c (5) After simplification, it can be obtained: DV θ U = c (6) This ratio c is defined as the work ratio of the blade element, so at any radius location: Dp = ρudv θ = ρu cu = cρu 2 (7) The total pressure rise Dp of the CR propeller is equally distributed to the front and back rotors, and to keep it the same with that of the single rotor, the rotating speed of the corresponding propellers of the CR propeller should be 1 peller. 1.3 Design results 2 of the SR ducted pro are shown in Fig. 1 and Fig. 2, respectively. Table 2 1.0 Pitch angle distribution of single rotor(sr) and contra-rotating(cr)ducted propeller SR θ S 1.026) 47.435 39.236 33.156 28.564 25.015 22.211 19.948 18.089 Fig.1 θ 1 2.108) 65.906 59.194 53.302 48.191 43.782 39.982 36.701 33.856 CR1 θ 2 2.000) 64.768 57.858 51.854 46.696 42.285 38.512 35.274 32.482 θ 1 1.451) 56.999 49.111 42.735 37.593 33.422 304 27.170 24.794 Single rotor ducted propeller CR2 θ 2 1.414) 56.319 48.376 41.997 36.880 32.744 29.366 26.573 24.235 Design requirements of the SR ducted propeller are shown in Table 1. Table 1 Main design parameters of SR Parameter Inflow velocity VA /(m s -1 ) Rotor diameter D/m Rotating speed n/(r min -1 ) Hub diameter ratio d/d Thrust coefficient KT Value 14.0 Based on the pre-study on 19A elongated duct, when the ratio of the 's velocity to the inflow velocity is about 1.4, the maximum efficiency of the propeller can be achieved. As the inflow veloc ity of the propeller is 14 m/s in this paper, the ap proximate throat velocity is selected as V Z = 20 m/s. Table 2 shows the distribution of pitch-diameter ratio P/D and pitch angle θ S at the blade tip of the CR ducted propeller with the different radial posi tions in two schemes. CR1 and CR2 respectively represent the CR ducted propellers obtained from schemes 1 and 2 while SR is the single rotor ducted propeller. The completed single rotor ducted propel ler SR and the contra-rotating ducted propeller CR1 1.0 1 200 0.18 2 Numerical calculation The meshing of the outer flow field of the propel ler can be divided into two parts: the rotation domain and the static domain, and the flow field is dis cretized by multi-block structured grids to ensure good grid orthogonality and computational conver gence. As the propeller runs in the uniform advance, the flow field showed the characteristic of rotational periodicity. In addition, only 1/4 of the flow field is simulated to improve the computational efficiency, that is, the meshing is performed only in the single flow channel (Fig. 3). The range of the whole static domain includes areas which are 5 times of the pro peller diameter at the upstream of, 15 times of the diameter at the downstream, and 10 times of the radius in the radial direction. The rota Fig.2 Contra-rotating ducted propeller

30 tion domain grids of the SR ducted propeller and the CR one are shown in Fig. 4 and Fig. 5 respectively. Inlet Fig.3 Far field Flow region grid Rotor/stator contact surface Outlet the duct thrust and the rotor thrust. The open water efficiency is defined as the ratio of the propulsion power to the total dissipated power of the contra-ro tating rotor. Fig. 6 shows the thrust coefficient, the torque coef ficient K Q and the open water efficiency η of the SR ducted propeller, the CR1 designed by scheme 1 and the CR2 designed by scheme 2, respectively. The maximum efficiency of SR is, and the correspond ing advance coefficient J is ; the maximum effi ciency of CR1 is 8, and the corresponding J is 1.4; the maximum efficiency of CR2 is 4, and the corresponding J is 9. Considering the results, the efficiency of CR ducted propeller is higher than that of the SR one. Meanwhile, as the pitch-diameter ra tio increases, the efficiency of the former also im proves and the highest efficiency point also offsets to the right. Fig.4 Rotation domain grid of SR propeller 1.4 SR_KT Open water performance 1.2 1.0 SR_KQ SR_ η CR1_KT CR1_KQ CR1_ η CR2_KT CR2_KQ CR2_ η 0.2 Fig.5 Rotation domain grid of CR propeller Fig.6 Open water performance curves The flow fields of the SR and CR ducted propel lers are solved using the available commercially CFD software ANSYS1/CFX [9-10]. In the numerical calculation, the propeller is set to rotate at a constant speed in the fixed position, and the different advance coefficients J are obtained by changing flow velocity at the inlet. With the method of Moving Reference Frame (MRF), the static domain is solved in the glob al stationary coordinate system, the rotation domain is calculated in the relative rotation coordinate sys tem, and the data are transmitted on the rotor/stator contact surface. 3 Simulation results 3.1 Open water performance Since the ducted propeller is a combined propel ler, both thrust and efficiency need to be analyzed in a combined form. Therefore, the thrust coefficient K T is calculated according to the total thrust, including 0.2 1.0 1.2 1.4 1.6 1.8 2.0 In addition, the most significant change from the SR ducted propeller to the CR one is that the thrust coefficient and torque coefficient are greatly im proved, whose increasing extent continues to rise as the pitch-diameter ratio increases. 3.2 Wake analysis Fig. 7 shows the distribution curves of the rear swirl flow component of the SR ducted propeller when the advance coefficients J are, and, respectively, where V θ is the ratio of the swirl flow velocity at the outlet of the rotor in the first stage to the axial velocity of the. It can be seen from the figure that the rear swirl flow com ponent of the increases as the advance coefficient decreases, which is because when the ad vance coefficient is low, the propeller works more, and its swirl flow component is sure to increase based on the momentum theorem. As can be seen from Fig. 8, the efficiency difference between the CR J

31 ducted propeller and the SR one gradually increases with the increase of flow velocity. J= J= J= (a)sr at VA=6 m/s 0.1 0.2 Fig.7 V θ Tangential velocity distribution of SR in wake Open water efficiency SR CR (b)cr at VA=6 m/s Fig.8 0.2 6 8 10 12 14 16 18 VA /(m s -1 ) Open water efficiency of two kinds of ducted propellers at different inflow velocities For the sake of analysis, Fig. 9 shows contours of the tangential velocity V t at the rear of the CR ducted propeller and the SR one when the in flow velocity V A = 6 m/s and 14 m/s. The lower right point is the rotating shaft of the ducted propeller while the upper left one is the position of the duct's inner wall. Fig. 10 shows the distribution of the tan gential velocity before and after the s along the radius direction, which is used to quantita tively describe Fig. 9. It can be seen that due to the disturbance of the rotation of the blades, there is nearly the same size of swirl flow in front of the pro peller disks of both the CR ducted one and the SR one. When the inflow velocity V A = 14 m/s, the swirl flow in wake at the rear of the contra-rotating propel ler is almost reduced to zero. 3.3 Pressure analysis on the blade surface Fig. 11 shows the pressure distribution contours of the blades of CR ducted propeller and the SR one in the case that the inflow velocity has already been set. It can be seen from the figure that under the premise (c)sr at VA=14 m/s (d)cr at VA=14 m/s of the same thrust generated by CR propeller and SR propeller, the pressure difference between pressure surface and the suction surface of the blade of CR ducted propeller is significantly smaller. Fig.9 Contours of tangential wake velocity

32 CLC number: U661.3 Pressure/Pa 300 000 180 000 60 000-60 000 CR_before the CR_after the SR_before the SR_after the -0.2-0.1 0.1 0.2 V θ (a)upstream velocity at VA=6 m/s CR_before the CR_after the SR_before the SR_after the edge are more gentle. Besides, reduction of blade load and improvement of the pressure distribution will result in superior cavitation performance. In ad dition, under the same thrust, the probability for the pressure difference of the CR propeller blades be be lower than the cavitating critical pressure, namely, the possibility of the formation of cavitation, signifi cantly decreases. 1 0-1 -180 000-300 000 Fig.11 (b)sr Pressure contours on blade surface CR_front_R CR_back_R SR_R -0.2-0.1 0.1 0.2 Cp -2 V θ Fig.10 (b)upstream velocity at VA=14 m/s Upstream and downstream tangential velocity distribution of propeller along radical direction -3-4 Fig. 12 shows the distribution of pressure along the chord length at R and R of CR propeller's front and back blades as well as the single blade, where the ordinate Cp is the pressure coefficient and the abscissa x/c is the dimensionless chord length. As can be seen from the figure, the pressure distribu tion of the twin propellers is more uniform, while pressure gradients near the leading edge and trailing Pressure/Pa 300 000 Cp 1 0-1 -2-3 0.2 1.0 x/c (a)at R CR_front_R CR_back_R SR_R 180 000-4 60 000-60 000-180 000-300 000 (a)cr 0.2 1.0 4 Conclusions A SR ducted propeller and two CR ducted propel lers with different pitch-diameter ratios are designed Fig.12 x/c (b)at R Distribution of pressure along the chord length

33 in this paper on the basis of the cascade theory, and the designs of two CR ducted propellers are respec tively carried out using the equal tangential induced velocity at the outlet and equal work ratio schemes. To ensure that thrusts of the three propellers are the same at the same speed, the design rotate speed of the CR ducted propeller is decreased, that is, pitch-diameter ratio of the contra-rotating rotor is improved. With the same advance speed and thrust, namely, different rotate speed conditions, the follow ing conclusions can be drawn by analyzing the hydro dynamic performance of three ducted propellers: 1) Through reducing the speed of the contra-rotat ing propeller, the efficiencies of the CR ducted pro pellers in schemes 1 and 2 are 8% and 4% higher than that of the SR ducted propeller. 2) The advance coefficient corresponding to the highest efficiency point of the CR ducted propeller is higher than that of the SR one, and its thrust coeffi cient, torque coefficient and performance ability are improved remarkably. 3) The recovery effect of the swirl kinetic energy in the wake of the CR ducted propeller is obvious, and the swirl flow in the wake can even be eliminat ed at the designed speed. 4) On the premise of the same thrust, blade load of the contra-rotating propeller is lower. References [1] WEIR R J. Ducted propeller design and analysis[r]. Albuquerque,NM:Sandia National Labs,1987. [2] WANG Zhanzhi,XIONG Ying,QI Wanjiang. Numeri cal prediction of contra-rotating propellers' open water performance[j]. Journal of Huazhong University of Sci ence and Technology (Natural Science Edition), 2012,40(11):77-80,88(in Chinese). [3] BRIZZOLARA S,TINCANI E P A,GRASSI D. De sign of contra-rotating propellers for high-speed stern thrusters[j]. Ships and Offshore Structures,2007,2 (2):169-182. [4] YANG C J,TAMASHIMA M,WANG G Q,et al. Pre diction of the steady performance of contra-rotating propellers by lifting surface theory[j]. Transactions of the West-Japan Society of Naval Architects,1991, 82:17-31. [5] GRASSI D,BRIZZOLARA S,VIVIANI M,et al. De sign and analysis of counter-rotating propellers-com parison of numerical and experimental results[j]. Jour nal of Hydrodynamics:Series B, 2010, 22(5): 570-576. [6] SHU Shizhen,ZHU Li,KE Xuanling,et al. Principle of turbomachinery[m]. Beijing:Tsinghua University Press,1991(in Chinese). [7] ZHOU Junwei,WANG Dazheng. Analysis of tip leak age vortex of different blade in ducted propeller[j]. Journal of Harbin Institute of Technology,2014,46 (7):14-19(in Chinese). [8] ZHOU Junwei,NI Haoliang. Preliminary hydrodynam ic design and analysis of contra-rotating ducted propel ler[j]. Ship Science and Technology,2014,36(12): 16-22(in Chinese). [9] YU L,GREVE M,DRUCKENBROD M,et al. Numer ical analysis of ducted propeller performance under open water test condition[j]. Journal of Marine Sci ence and Technology,2013,18(3):381-394. [10] CAO Q M,HONG F W,TANG D H,et al. Predic tion of loading distribution and hydrodynamic mea surements for propeller blades in a rim driven thruster [J]. Journal of Hydrodynamics:Series B,2012,24 (1):50-57. 大螺距对转导管螺旋桨的水动力分析 梅蕾, 周军伟, 倪豪良 哈尔滨工业大学 ( 威海 ) 船舶与海洋工程学院, 山东威海 264209 摘要 : 基于叶栅理论设计了 1 台单转子导管螺旋桨和 2 台不同螺距的对转导管螺旋桨, 并采用商用 CFD 软件对流场进行了数值模拟 对转导管螺旋桨的上游转子螺距比分别为 1.451 和 2.108, 下游转子螺距比按消除尾流旋流的原则进行设计 结果表明 : 随着螺距比的增大, 对转导管螺旋桨的推力系数与扭矩系数显著提高, 效率略有提高, 其最高效率点向右偏移 与单转子导管螺旋桨的对比发现, 对转导管螺旋桨能够在更大的螺距比下保持较高的推进效率 关键词 : 螺旋桨 ; 对转导管螺旋桨 ; 大螺距比 ; 推进效率