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Simulation of Unsteady Interaction Forces on a Ducted Propeller with Pre-Swirl Stators

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Simulation of Unsteady Interaction Forces on a Ducted Propeller with Pre-Swirl Stators Third International Symposium on Marine Propulsors smp’13, Launceston, Tasmania, Australia, May 2013 Simulation of Unsteady Interaction Forces on a Ducted Propeller with Pre-swirl Stators Zhi-Qiang Rao, Wei Li, Chen-Jun Yang State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, China ABSTRACT induced by propulsor, the discussion on the frequency The frequency characteristics of unsteady forces arising characteristics is inevitable. from the hydrodynamic interaction between the rotor and The research on this kind of propulsor is relatively less stators for a ducted propeller with pre-swirl stators is than on ordinary propulsors owing to the complicated analyzed theoretically. It is shown that the axial force and flow phenomenon around the propulsor. A potential-based moment fluctuate at frequencies equal to nZRN on panel method for the duct coupled with the lifting surface condition that nZR=kZS, where k and n are both positive method for the rotor and stators were presented by Hughes integers, ZR and ZS are the rotor and stator blade numbers & Kinnas (1991), Wang & Yang (1993), and Wang & Liu respectively, and N is the shaft frequency of the rotor. The (2007). In these papers the steady performance was lateral forces and moments also fluctuate at multiples of predicted. The unsteady thrust and torque were presented the rotor's blade frequency, but on condition that by Wang & Liu (2007), however the frequency and nZR=kZS±1. Therefore, the axial and lateral forces do not amplitude characteristics were not analyzed nor discussed. fluctuate at the same frequency, and in many cases the During the past forty years, computational fluid dynamics lowest fluctuation frequency of the lateral forces are much (CFD) has been developing rapidly and finding more and lower than that of the axial force. To evaluate the more applications in ship hydrodynamic research. The amplitudes of unsteady interaction forces, RANS flow field of an axisymmetrical body with a ducted simulations are carried out for a ducted propeller with pre- propeller working behind it was studied by Wang et al swirl stators. The CFD results of time-averaged thrust and (2003) using RANS simulation. The hydrodynamic torque agree fairly well with those experimentally simulation of a torpedo with the pump-jet propulsor was measured. The unsteady force fluctuations are quite conducted by Ivanell (2001). The numerical results show clearly captured at frequencies theoretically determined, that CFD is an effective tool for predicting the and are mostly negligible at other frequencies. The results hydrodynamic characteristics of the ducted propeller with indicate that, for the configuration being simulated, the stators. lateral forces fluctuate at much lower frequencies and higher amplitudes than the axial force. The experimental research on the steady performance and cavitation of an underwater vehicle with the pump-jet Keywords propulsor were conducted by Suryanarayana et al (2010a, propeller, duct, rotor, stator, bearing force, CFD 2010b). The wind tunnel experiment show that most of the 1 INTRODUCTION swirl rectification could be attained by the post-swirl As a multi-component marine propulsor, the ducted stator (Suryanarayana et al 2010a). The cavitation tunnel propeller with pre-swirl stators is mainly used on experiment show that cavitation inception on the rotor of underwater vehicles. The main components of this kind of the pump-jet takes place on the tip face side at higher propulsor are stators, rotor (propeller) and duct. The advance ratios and the stators will be free from cavatation stators are installed on the upstream of the rotor, which over the operating envelop of the vehicle (Suryanarayana can improve the inflow by homogenizing the wake and et al 2010b). yielding pre-swirling inflow, thereby restraining cavitation In this work the frequency characteristics of unsteady and reducing the vibration force and radiation noise. forces arising from the hydrodynamic interaction between Compared with ducted propeller, the performance the rotor and stators for a ducted propeller with pre-swirl evaluation and design for the ducted propeller with stators stators is analyzed theoretically. All the hydrodynamic are much more difficult and the hydrodynamic forces and forces and moments fluctuate at multiples of the rotor’s moments are unsteady even in uniform inflow due to the blade frequency. However, the axial force and moment do interaction between the rotor and stators. Furthermore, for not fluctuate at the same frequencies as the lateral forces the sake of reducing fluctuating force, vibration and noise and moments. RANS simulations are carried out for a ducted propeller with pre-swirl stators. The CFD results 149 of time-averaged thrust and torque agree fairly well with The total horizontal force of the rotor can be written as those experimentally measured. The unsteady force FyR, fluctuations are quite clearly captured at frequencies ZR 1 (3) theoretically determined, and are mostly negligible at Brk sin kZS i rk sin i B tk cos kZS i tk cos i ik01 other frequencies. The radial component in (3) is 2 THEORETICAL ANALYSIS OF FREQUENCIES ZR 1 OF UNSTEADY FORCES Frisin i As shown in Figure 1, a fixed coordinate system o-xyz is i0 ZR 1 defined with x-, y- and z-axis corresponding to axial, Brk sin kZS i rk sin i (4) horizontal and vertical directions respectively. A polar ik01 1 ZR 1 coordinate system (r, θ) is defined in o-yz plane and θ=0 Brk coskZS 1 i rk cos kZS 1 i rk when r coincides with z-axis. The coordinate system 2 ki10 o-x1y1z1 rotating synchronously with the rotor coincides And with the fixed coordinate system at initial time. Suppose ZR 1 coskZ 1 the stator and rotor blade numbers are ZS and ZR S i rk i0 (5) respectively, where subscript S and R represent the stators ZR 1 21kZS i and rotor respectively. In o-xyz coordinate system Fx, Fy, coskZS 1 rk i0 ZR Fz, Ft, and Fr represent axial, horizontal, vertical, tangential, and radial forces respectively; Mx, My, and Mz Use the following formula, represent torque, horizontal bending moment, and vertical 1 sin (Ry 1) bending moment respectively. R 1 cos(x ry ) cos( x Ry ) 2 (6) 1 r0 2 sin y 2 (5) can be expressed as ZR 1 coskZS 1 i rk i0 (ZR 1)( kZS 1) sin(kZS 1) coskZS 1 rk (7) Z (kZ S 1) R sin ZR 0 (kZ 1 nZ ) SR ZR cos( nZR rk ) ( kZS 1 nZR ) Therefore the radial component in (3) becomes ZR1 ZR Frisin i Brk cos nZR rk , (kZS 1 nZR ) (8) ik012 Figure 1 Definition of coordinate systems, forces, and moments Similarly the tangential component in (3) can be written as ZR1 ZR 2.1 Frequencies of Fy and Fz of the Rotor Fticos i Btk cos nZR tk , (kZS 1 nZR ) (9) ik012 Since the periodical angle of rotor is 2π/ZS, the tangential and radial forces of the ith blade are expressed by the The total horizontal force is trigonometric series as follow, ZR Fy, R Br,, t k sin nZR rk (10) 2 k1 Fti Btk cos kZS i tk k1 in which (1) F Bsin kZ ri rk S i rk k1 BBcos arctan rk tk rk tk th where Btk and Brk are the k -order amplitude of tangential Btksin rk tk and radial forces respectively; and θi=θ+2πi/ZR is the th angular position of the i blade's reference line, in which θ 22 th BBB cos B sin is the reference line angle of the 0 blade. r,, t k rk tk rk tk tk rk tk Then the horizontal force of the ith blade can be expressed The vertical force can be expressed in the same form as as follow, the horizontal force. FFFyi risin i ti cos i 2.2 Frequencies of Fy and Fz of the Stators and Duct Brk sin kZS i rk sin i (2) k1 In the o-x1y1z1 coordinate system, the rotor is stationary but the stator is rotating in the direction opposite to that of Btk cos kZS i tk cos i k1 150 the rotor. Then each stator blade has a periodical angle of The frequencies of interaction forces were derived by 2π/ZR, and the tangential and radial force can be written as Strasberg & Breslin (1975) for contra-rotating propellers (CRPs). The alternating frequency of thrust is F Bcos kZ t1, i t1, k R i t1, k k 1 fkm kYM mZN (18) (11) F Bsin kZ r1, i r1, k R i r1, k where Y and Z are the forward and aft propeller blade k1 numbers respectively; M and N are the rotating speed of where subscript 1 denotes variables in the rotating the forward and aft propellers respectively. When viewing th coordinate system. The reference line angle of the i the ducted propeller with stators in a coordinate system stator blade θi equals to -θ+2πi/ZS, where θ is the which rotates in the same direction as and at a half speed th reference line angle of the 0 stator blade, which is equal (N/2) of the rotor's rotation, the stators (and duct) rotate in th to that of the 0 rotor blade. opposite direction against the rotor. Then (17) and (18) The horizontal and vertical forces can be obtained by yield the same results. projecting tangential and radial forces to the y- and z-axis 2.4 Frequencies of Mx, My and Mz respectively, The moment is the result of multiplying force and force FFFcos sin y1,, i t 1 i i r1, i i arm. Assuming that the change of force arm with the (12) FFFcos sin rotor's angular position is negligible, the frequencies of z1,, i r 1 i i t1, i i Mx, My, and Mz and the conditions for them to occur The horizontal force on one stator blade in the fixed would be the same as those of Fx, Fy, and Fz.
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