The Computational Fluid Dynamics (CFD) approach is adopted to study the steady and unsteady performances of the podded propulsor by the Fluent software package. While the interactions of the propeller blades with th...The Computational Fluid Dynamics (CFD) approach is adopted to study the steady and unsteady performances of the podded propulsor by the Fluent software package. While the interactions of the propeller blades with the pod and strut are time-dependent by nature, the mixing plane model is employed firstly to predict the steady performance, where the interactions are time-averaged. Numerical experiments are carried out with systematically varied mesh sizes to investigate the dependence of the predicted force values on the mesh sizes. Furthermore, the sliding mesh model is employed to simulate the unsteady interactions between the blades, pod and strut. Based on the numerical results, the characteristics of unsteady hydrodynamic forces are discussed, and the applicability of the mixing plane model is investigated for puller-type podded propulsor.展开更多
This paper introduces a newly developed Unmanned Wave Glide Vehicle (UWGV), which is driven only by extracting energy from gravity waves, and presents a comprehensive study on the propulsion performance of the UWGV...This paper introduces a newly developed Unmanned Wave Glide Vehicle (UWGV), which is driven only by extracting energy from gravity waves, and presents a comprehensive study on the propulsion performance of the UWGV's propulsor-Wave Glide Propulsor (WGP) in a regular wave. By simplifying the WGP as six 2D tandem asynchronous flapping foils (TAFFs), a CFD method based on Navier-Stokes equations was first used to analyze the hydrodynamic performance of TAFFs with different parameters of non-dimensional wave length rn and non-dimensional wave height n. Then, a series of hydrodynamic experiments were performed. The computational results agree well with the experimental results when n〈0.07 and both of them show the thrust force and input power of the WGP are larger at smaller m or larger n. By analyzing the flow field of TAFFs, we can see that a larger m is beneficial to the forming, merging and shredding of the TAFFs' vortices; as TAFFs are arranged in tandem and have the same motions, the leading edge vortex and wake vortex of the TAFFs are meaningful for improving the thrust force of their adjacent ones.展开更多
Based on the model test of podded propulsor in straight forward motion, the paper presents the results of the effects of geometric parameters on the propulsive characteristics of podded propulsors in viscous flow. Thr...Based on the model test of podded propulsor in straight forward motion, the paper presents the results of the effects of geometric parameters on the propulsive characteristics of podded propulsors in viscous flow. Three main geometrical parameters, i.e. pod diameter, strut distance from the propeller plane, and the maximum thickness of strut are studied with systematically varied geometry while the parameters of propeller blades are fixed. The RANS approach is adopted to study the steady perfomaance using the Huent software package. While the interactions of the propeller blades with the pod and strut are time-dependent by nature, the mixing plane model is employed to predict the steady perfomlance. In considera- tion of the complexity, the research does not deal with the effects of the combination of such three main parameters.展开更多
The flapping motion of a flexible propulsor near the ground was simulated using the immersed boundary method. The hydrodynamic benefits of the propulsor near the ground were explored by varying the heaving frequency (...The flapping motion of a flexible propulsor near the ground was simulated using the immersed boundary method. The hydrodynamic benefits of the propulsor near the ground were explored by varying the heaving frequency (St) of the leading edge of the flexible propulsor. Propulsion near the ground had some advantages in generating thrust and propelling faster than propulsion away from the ground. The mode analysis and flapping amplitude along the Lagrangian coordinate were examined to analyze the kinematics as a function of the ground proximity (d) and St. The trailing edge amplitude (\(a_\mathrm{tail}\)) and the net thrust (\(\overline{{F}}_x\)) were influenced by St of the flexible propulsor. The vortical structures in the wake were analyzed for different flapping conditions.展开更多
During ice-breaking navigation, a massive amount of crushed ice blocks with different sizes is accumulated under the hull of an ice-going ship. This ice slides into the flow field in the forward side of the podded pro...During ice-breaking navigation, a massive amount of crushed ice blocks with different sizes is accumulated under the hull of an ice-going ship. This ice slides into the flow field in the forward side of the podded propulsor, affecting the surrounding flow field and aggravating the non-uniformity of the propeller wake. A pulsating load is formed on the propeller, which affects the hydrodynamic performance of the podded propulsor. To study the changes in the propeller hydrodynamic performance during the ice podded propulsor interaction, the overlapping grid technique is used to simulate the unsteady hydrodynamic performance of the podded propulsor at different propeller rotation angles and different ice block sizes. Hence, the hydrodynamic blade behavior during propeller rotation under the interaction between the ice and podded propulsor is discussed. The unsteady propeller loads and surrounding flow fields obtained for ice blocks with different sizes interacting with the podded propulsor are analyzed in detail. The variation in the hydrodynamic performance during the circular motion of a propeller and the influence of ice size variation on the propeller thrust and torque are determined. The calculation results have certain reference significance for experiment-based research, theoretical calculations and numerical simulation concerning ice podded propulsor interaction.展开更多
A podded propulsor in viscous flow is numerically simulated in this article. The region of fluid is divided into efficient calculation grids. The pressure and viscous force of blades, pod and strut are obtained as fun...A podded propulsor in viscous flow is numerically simulated in this article. The region of fluid is divided into efficient calculation grids. The pressure and viscous force of blades, pod and strut are obtained as functions of an advance coefficient. The steady result is used as a base in the unsteady simulation to obtain a solution more quickly. The distributions of the thrust and torque fluctuations of the key blade in one revolution are obtained. The c^lculation results from the mixing plane on steady conditions are compared with those obtained from the sliding mesh model on unsteady conditions. The User-Defined Function (UDF) method is used to simulate the influence of ship hull on the non-uniform wake of the propeller.展开更多
The performance ofbluespotted rays was emulated in the design ofa bioinspired underwater propulsor in the present work. First, the movement of a live bluespotted ray was captured for the swimming mode and useful infor...The performance ofbluespotted rays was emulated in the design ofa bioinspired underwater propulsor in the present work. First, the movement of a live bluespotted ray was captured for the swimming mode and useful information to the biomimetic mechanism design. By virtue of the modular and reconfigurable design concept, an undulatory fin propulsion prototype was developed. With a proper experimental set-up, orthogonal experiments were conducted to investigate the effect of various fin design parameters on the propulsion speed, thrust, and power of the fish robot. The controllable fin parameters include frequency, amplitude, wavelength, fin shape, and undulatory mode. The significance of these parameters was also determined by using the variance analysis. The results demonstrate that the designed propulsor, imitating bluespotted rays with large expanded undulatory fins, is able to propel itself by changing various kinematic parameters.展开更多
Previous studies show that the tip clearance loss limits the improvement of pumpjet propulsor (PJP) performance,and the tip clearance flow field is the most complicated part of PJP flow.In this work,the non-cavitation...Previous studies show that the tip clearance loss limits the improvement of pumpjet propulsor (PJP) performance,and the tip clearance flow field is the most complicated part of PJP flow.In this work,the non-cavitation and cavitation hydrodynamic performances of PJP with a tip clearance size of 1 mm are obtained by using the detached-eddy simulation (DES).At constant oncoming velocity,cavitation first occurs on the duct and then disappears with the decrease of the advance ratio.The rotor blade cavitation occurs at the low advance ratio and comprises tip clearance cavitation,tip leakage cavitation,and blade sheet cavitation.In the rotor region,the typical vortices include tip separation vortex,tip leakage vortex,trailing edge shedding vortex,and blade root horseshoe vortex.Combined with the pressure distribution,both the Q and λ2 criteria give reliable results of vortex identification.The cavitation causes an expansion of tip leakage vortex in the circumferential direction and decreases the intensities of tip separation vortex in the whole tip clearance area and tip leakage vortex in the cavitation area,and enhances the strength of tip leakage vortex in the downstream non-cavitation area.展开更多
Rapidity and agility are equally important to unmanned underwater vehicles(UUVs).In this study we developed a UUV equipped with a hybrid propulsor which consists of a screw propeller and four bio-inspired flippers.The...Rapidity and agility are equally important to unmanned underwater vehicles(UUVs).In this study we developed a UUV equipped with a hybrid propulsor which consists of a screw propeller and four bio-inspired flippers.The bionic flippers rely on their flapping motion to generate both thrust and lateral forces,and the screw propeller provides additional thrust for fast cruise.The maneuverability is greatly improved while the capability of sailing fast is maintained.For the typical sailing requests,the flapping motions of the flippers were designed meticulously,and a control algorithm based on central pattern generators(CPGs)was built to produce rhythmic locomotor signals considering the motion periodicity.Simultaneously,a feedback control method was merged to correct the deviation of the course.A compact concentric-shafts transmission mechanism was employed to overcome the inadequacy of the inside space,and the vehicle was built.Finally,the sailing and maneuvering performance were tested.It was demonstrated that,the UUV’s overall sailing performance was enhanced significantly due to the combination of the flapping flippers and the screw propeller.The hybrid-propulsor vehicle is capable of sailing in multiplicate environments.展开更多
The present work is devoted to developing an efficient method for the analysis and design of hybrid contra-rotating shaft pod(HCRSP)propulsors.The geometry of contra-rotating propulsor(CRP)was then analyzed,and a stea...The present work is devoted to developing an efficient method for the analysis and design of hybrid contra-rotating shaft pod(HCRSP)propulsors.The geometry of contra-rotating propulsor(CRP)was then analyzed,and a steady integral panel method that treats the forward and aft propellers as a whole part is presented.During the study,the control equation of the steady integral panel method for CRP is derived in detail.From the experience of developing an integral panel method for CRP,the characteristics of panel singularity strength in HCRSP propulsor was analyzed.Based on this analysis,an integral panel method for HCRSP propulsor is developed and the wake model discussed.Then,the method is applied in the performance analysis of HCRSP propulsor.Comparison between experimental data and numerical results shows that the steady integral panel method has good accuracy in terms of open water performance.Regarding the latter,the error source in the steady integral panel method is discussed.展开更多
This paper presents an effective method for computing the internal and external viscous flow field around the ducted propulsor behind an axisymmetric they by using a new Navier-Stokes equations solver with primitive v...This paper presents an effective method for computing the internal and external viscous flow field around the ducted propulsor behind an axisymmetric they by using a new Navier-Stokes equations solver with primitive variable continuity equation formulation. In the present numerical method, the calculation equation for pressure with well-defined coefficient,which form is similar to the artificial compressibility method, is developed. A semi-staggered grid system is adopted. Not only the advantage of staggered grid system can be retained but the boundary conditions on the inner and outer surface of the duct can be also carried out easily. By using a special grid system and the programming technique for implementing the jump boundary condition on the duct surfaces, the internal and external viscous flow field around the ducted propulsor behind the axisymmetric they may be calculated integrally in an unified numbered grid system. Some configurations are calculated and compared with experimental date and numerical results of other methods. Illustrative calculations are also presented for a stern of axisymmetric body with the backstep fitted a duct to illustrate the capability of the present method. Beside that, the effect of axial distribution of they force is considered and discussed in order to extend the application range of the present method.展开更多
The requirement of low radiated noise is increasing for underwater propulsors as the noise significantly affecting the comfort and quietness of ships,submarines,and vessels.To broaden the view of noise characteristics...The requirement of low radiated noise is increasing for underwater propulsors as the noise significantly affecting the comfort and quietness of ships,submarines,and vessels.To broaden the view of noise characteristics of pump-jet propulsors(PJPs),this paper considers the radiated noise of a pre-swirl stator PJP with the effects of the advance coefficient and rotor rotational speed.Radiated noise is obtained by the“hybrid method”approach,which combines a hydrodynamic solver with a hydroacoustic solver.The turbulence flow is obtained through improved delayed detached eddy simulation(IDDES),which show good agreement with the experiment,including the performance and flow field.The solver precision,permeable surface size,and sampling frequency notably affect the noise calculation.The spectra of thrust fluctuation and radiated noise are characterized by the tonal phenomenon around the blade passing frequency and its harmonics.The spectrum of radiated noise and overall sound pressure level(OSPL)are considerably affected by both the advance coefficient and the rotor rotational speed.Overall,the numerical results and analysis given in this paper should be partly helpful in deepening the understanding of the radiated noise characteristics of PJPs.展开更多
基金supported by the"Knowledge-based Ship Design Hyper-Integrated Platform(KSHIP)"a key project of the Ministry of Education and the Ministry of Finance of China
文摘The Computational Fluid Dynamics (CFD) approach is adopted to study the steady and unsteady performances of the podded propulsor by the Fluent software package. While the interactions of the propeller blades with the pod and strut are time-dependent by nature, the mixing plane model is employed firstly to predict the steady performance, where the interactions are time-averaged. Numerical experiments are carried out with systematically varied mesh sizes to investigate the dependence of the predicted force values on the mesh sizes. Furthermore, the sliding mesh model is employed to simulate the unsteady interactions between the blades, pod and strut. Based on the numerical results, the characteristics of unsteady hydrodynamic forces are discussed, and the applicability of the mixing plane model is investigated for puller-type podded propulsor.
基金financially supported by the National Natural Science Foundation of China(Grant No.51479039)China Postdoctoral Science Foundation(Grant No.2013M540271)
文摘This paper introduces a newly developed Unmanned Wave Glide Vehicle (UWGV), which is driven only by extracting energy from gravity waves, and presents a comprehensive study on the propulsion performance of the UWGV's propulsor-Wave Glide Propulsor (WGP) in a regular wave. By simplifying the WGP as six 2D tandem asynchronous flapping foils (TAFFs), a CFD method based on Navier-Stokes equations was first used to analyze the hydrodynamic performance of TAFFs with different parameters of non-dimensional wave length rn and non-dimensional wave height n. Then, a series of hydrodynamic experiments were performed. The computational results agree well with the experimental results when n〈0.07 and both of them show the thrust force and input power of the WGP are larger at smaller m or larger n. By analyzing the flow field of TAFFs, we can see that a larger m is beneficial to the forming, merging and shredding of the TAFFs' vortices; as TAFFs are arranged in tandem and have the same motions, the leading edge vortex and wake vortex of the TAFFs are meaningful for improving the thrust force of their adjacent ones.
基金supported by the Fundamental Research Funds for the Central Universities (Grant No.HEUCFT1001)the"Knowledge-based Ship Design Hyper-Integrated Plat form(KSHIP)",a Key Project of the Ministry of Education and the Ministry of Finance of China
文摘Based on the model test of podded propulsor in straight forward motion, the paper presents the results of the effects of geometric parameters on the propulsive characteristics of podded propulsors in viscous flow. Three main geometrical parameters, i.e. pod diameter, strut distance from the propeller plane, and the maximum thickness of strut are studied with systematically varied geometry while the parameters of propeller blades are fixed. The RANS approach is adopted to study the steady perfomaance using the Huent software package. While the interactions of the propeller blades with the pod and strut are time-dependent by nature, the mixing plane model is employed to predict the steady perfomlance. In considera- tion of the complexity, the research does not deal with the effects of the combination of such three main parameters.
基金supported by the Creative Research Initiatives (Grant 2016-004749) program of the National Research Foundation of Korea (MSIP)
文摘The flapping motion of a flexible propulsor near the ground was simulated using the immersed boundary method. The hydrodynamic benefits of the propulsor near the ground were explored by varying the heaving frequency (St) of the leading edge of the flexible propulsor. Propulsion near the ground had some advantages in generating thrust and propelling faster than propulsion away from the ground. The mode analysis and flapping amplitude along the Lagrangian coordinate were examined to analyze the kinematics as a function of the ground proximity (d) and St. The trailing edge amplitude (\(a_\mathrm{tail}\)) and the net thrust (\(\overline{{F}}_x\)) were influenced by St of the flexible propulsor. The vortical structures in the wake were analyzed for different flapping conditions.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51679052,51639004 and51809055)the Defense Industrial Technology Development Program(Grant No.JCKY2016604B001)the Natural Science Foundation of Heilongjiang Province of China(Grant No.E2018026)
文摘During ice-breaking navigation, a massive amount of crushed ice blocks with different sizes is accumulated under the hull of an ice-going ship. This ice slides into the flow field in the forward side of the podded propulsor, affecting the surrounding flow field and aggravating the non-uniformity of the propeller wake. A pulsating load is formed on the propeller, which affects the hydrodynamic performance of the podded propulsor. To study the changes in the propeller hydrodynamic performance during the ice podded propulsor interaction, the overlapping grid technique is used to simulate the unsteady hydrodynamic performance of the podded propulsor at different propeller rotation angles and different ice block sizes. Hence, the hydrodynamic blade behavior during propeller rotation under the interaction between the ice and podded propulsor is discussed. The unsteady propeller loads and surrounding flow fields obtained for ice blocks with different sizes interacting with the podded propulsor are analyzed in detail. The variation in the hydrodynamic performance during the circular motion of a propeller and the influence of ice size variation on the propeller thrust and torque are determined. The calculation results have certain reference significance for experiment-based research, theoretical calculations and numerical simulation concerning ice podded propulsor interaction.
基金Supported by National Natural Science Foundation of China (41176074, 51209048,51379043,51409063) High tech ship research project of Ministry of industry and technology (G014613002) The support plan for youth backbone teachers of Harbin Engineering University (HEUCFQ1408)
基金Foundation item: Supported by the National Natural Science Foundation of China (Grant Nos. 41176074, 51379043 and 51409063)Acknowledgement This project was supported by the National Natural Science Foundation of China (Grant Nos. 41176074,51379043 and 51409063) and was conducted in response to the great support received from a basic research project entitled "Multihull Ship Technology Key Laboratory of Fundamental Science for National Defence", which was conducted at Harbin Engineering University. The authors would like to extend their sincere gratitude to their colleagues in the towing tank laboratory.
文摘试验性的测试被进行评估 L 类型 podded propulsor 的水动力学性能在直向前,用一台开水的测量仪器的运动和离开设计条件为 podded propulsors 由作者发展了,拖引坦克的一个轮船模型,并且在水粒子图象 velocimetry (PIV ) 下面测量系统。在条件的三种类型下面, L 类型 podded propulsor 的主要参数被测量,包括推进器戳和转矩,以及整个豆荚单位的戳,方面力量,和时刻。另外,在推进器和神气之间的节上的流动领域被分析。试验性的结果证明动态 azimuthing 率和方向和转弯的方向在推进器和整个豆荚单位上影响力量。因为推进器旋转的效果,力量不均匀地在左、正确的 azimuthing 方向之间被散布。这研究的调查结果为关于 L 类型 podded propulsors 的进一步的研究提供一个基础。
基金Project supported by the "Knowledge-based Ship Design Hyper-Integrated Platform (KSHIP)"a key project of the Ministry of Education and the Ministry of Finance of China
文摘A podded propulsor in viscous flow is numerically simulated in this article. The region of fluid is divided into efficient calculation grids. The pressure and viscous force of blades, pod and strut are obtained as functions of an advance coefficient. The steady result is used as a base in the unsteady simulation to obtain a solution more quickly. The distributions of the thrust and torque fluctuations of the key blade in one revolution are obtained. The c^lculation results from the mixing plane on steady conditions are compared with those obtained from the sliding mesh model on unsteady conditions. The User-Defined Function (UDF) method is used to simulate the influence of ship hull on the non-uniform wake of the propeller.
文摘The performance ofbluespotted rays was emulated in the design ofa bioinspired underwater propulsor in the present work. First, the movement of a live bluespotted ray was captured for the swimming mode and useful information to the biomimetic mechanism design. By virtue of the modular and reconfigurable design concept, an undulatory fin propulsion prototype was developed. With a proper experimental set-up, orthogonal experiments were conducted to investigate the effect of various fin design parameters on the propulsion speed, thrust, and power of the fish robot. The controllable fin parameters include frequency, amplitude, wavelength, fin shape, and undulatory mode. The significance of these parameters was also determined by using the variance analysis. The results demonstrate that the designed propulsor, imitating bluespotted rays with large expanded undulatory fins, is able to propel itself by changing various kinematic parameters.
基金the National Natural Science Foundation of China(Nos.51709229 and 51879220)the Natural Science Basic Research Plan in Shaanxi Province(No.2018JQ5092)the Fundamental Research Funds for the Central Universities of China(No.3102019HHZY030019)。
文摘Previous studies show that the tip clearance loss limits the improvement of pumpjet propulsor (PJP) performance,and the tip clearance flow field is the most complicated part of PJP flow.In this work,the non-cavitation and cavitation hydrodynamic performances of PJP with a tip clearance size of 1 mm are obtained by using the detached-eddy simulation (DES).At constant oncoming velocity,cavitation first occurs on the duct and then disappears with the decrease of the advance ratio.The rotor blade cavitation occurs at the low advance ratio and comprises tip clearance cavitation,tip leakage cavitation,and blade sheet cavitation.In the rotor region,the typical vortices include tip separation vortex,tip leakage vortex,trailing edge shedding vortex,and blade root horseshoe vortex.Combined with the pressure distribution,both the Q and λ2 criteria give reliable results of vortex identification.The cavitation causes an expansion of tip leakage vortex in the circumferential direction and decreases the intensities of tip separation vortex in the whole tip clearance area and tip leakage vortex in the cavitation area,and enhances the strength of tip leakage vortex in the downstream non-cavitation area.
基金supported by the National Natural Science Foundation of China(11272310,11625211,and 11621202).
文摘Rapidity and agility are equally important to unmanned underwater vehicles(UUVs).In this study we developed a UUV equipped with a hybrid propulsor which consists of a screw propeller and four bio-inspired flippers.The bionic flippers rely on their flapping motion to generate both thrust and lateral forces,and the screw propeller provides additional thrust for fast cruise.The maneuverability is greatly improved while the capability of sailing fast is maintained.For the typical sailing requests,the flapping motions of the flippers were designed meticulously,and a control algorithm based on central pattern generators(CPGs)was built to produce rhythmic locomotor signals considering the motion periodicity.Simultaneously,a feedback control method was merged to correct the deviation of the course.A compact concentric-shafts transmission mechanism was employed to overcome the inadequacy of the inside space,and the vehicle was built.Finally,the sailing and maneuvering performance were tested.It was demonstrated that,the UUV’s overall sailing performance was enhanced significantly due to the combination of the flapping flippers and the screw propeller.The hybrid-propulsor vehicle is capable of sailing in multiplicate environments.
基金The present work is supported by the National Natural Science Foundation of China(Grant no.51479207).
文摘The present work is devoted to developing an efficient method for the analysis and design of hybrid contra-rotating shaft pod(HCRSP)propulsors.The geometry of contra-rotating propulsor(CRP)was then analyzed,and a steady integral panel method that treats the forward and aft propellers as a whole part is presented.During the study,the control equation of the steady integral panel method for CRP is derived in detail.From the experience of developing an integral panel method for CRP,the characteristics of panel singularity strength in HCRSP propulsor was analyzed.Based on this analysis,an integral panel method for HCRSP propulsor is developed and the wake model discussed.Then,the method is applied in the performance analysis of HCRSP propulsor.Comparison between experimental data and numerical results shows that the steady integral panel method has good accuracy in terms of open water performance.Regarding the latter,the error source in the steady integral panel method is discussed.
文摘This paper presents an effective method for computing the internal and external viscous flow field around the ducted propulsor behind an axisymmetric they by using a new Navier-Stokes equations solver with primitive variable continuity equation formulation. In the present numerical method, the calculation equation for pressure with well-defined coefficient,which form is similar to the artificial compressibility method, is developed. A semi-staggered grid system is adopted. Not only the advantage of staggered grid system can be retained but the boundary conditions on the inner and outer surface of the duct can be also carried out easily. By using a special grid system and the programming technique for implementing the jump boundary condition on the duct surfaces, the internal and external viscous flow field around the ducted propulsor behind the axisymmetric they may be calculated integrally in an unified numbered grid system. Some configurations are calculated and compared with experimental date and numerical results of other methods. Illustrative calculations are also presented for a stern of axisymmetric body with the backstep fitted a duct to illustrate the capability of the present method. Beside that, the effect of axial distribution of they force is considered and discussed in order to extend the application range of the present method.
基金The National Natural Science Foundation of China(Grant No.51979226).
文摘The requirement of low radiated noise is increasing for underwater propulsors as the noise significantly affecting the comfort and quietness of ships,submarines,and vessels.To broaden the view of noise characteristics of pump-jet propulsors(PJPs),this paper considers the radiated noise of a pre-swirl stator PJP with the effects of the advance coefficient and rotor rotational speed.Radiated noise is obtained by the“hybrid method”approach,which combines a hydrodynamic solver with a hydroacoustic solver.The turbulence flow is obtained through improved delayed detached eddy simulation(IDDES),which show good agreement with the experiment,including the performance and flow field.The solver precision,permeable surface size,and sampling frequency notably affect the noise calculation.The spectra of thrust fluctuation and radiated noise are characterized by the tonal phenomenon around the blade passing frequency and its harmonics.The spectrum of radiated noise and overall sound pressure level(OSPL)are considerably affected by both the advance coefficient and the rotor rotational speed.Overall,the numerical results and analysis given in this paper should be partly helpful in deepening the understanding of the radiated noise characteristics of PJPs.