Study on the Tip Vortex Control Effect and Rule of Pump Jet Thruster by Groove Structure

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(1.Naval Submarine Academy,Qingdao 266042,China;2.College of Naval Architecture and Ocean,Naval University of Engineering,Wuhan 430033,China)

Abstract: In order to study the tip vortex control effect of pump jet thrusters by groove structure, different forms of groove structures on the inner wall of duct were set and numerical calculation method was adopted to analyze the effect of groove parameters on tip vortex control.The results show that duct groove effectively reduces tip intensity,and that tip vortex control effect changes with axial length,circumferential width, radial depth and number of grooves, providing a new technical path and support for tip vortex control of pump jet thrusters and optimal selection of duct grooves.

Key words:duct inner wall;characteristic parameter;tip vortex intensity;groove structure;pump jet thruster

0 Introduction

Currently, pump jet thrusters have been widely used in underwater vehicles such as nuclearpowered submarines and high-speed torpedoes because of the advantages in delaying cavitation,reducing radiation noise[1]and improving propulsion efficiency. Many scholars have conducted extensive researches on the propulsion plant[2]. When a pump jet propeller rotor works at a high speed, a strong tip vortex will be formed behind the trailing edge of the rotor. As the pressure at the vortex core is low,tip vortex cavitation is easy to generate[3],which is one of main causes for the excessive noise of submarines[4]. Tip clearance cavitation is one of the cavitation types which happen first.Therefore,improving rotor tip flow and suppressing tip vortex cavitation is an important approach to reduce the radiation[5].

A pump jet thruster consists of an external fixed annular catheter and an internal rotating rotor with a complex vortex system in the rotor tip,which is similar to the structure of an aero engine.Significant progress has been achieved in the tip vortex control technologies of an aero-engine compressors,among which the technology of‘processor casing’[6-7]is recognized as one of the most mature passive flow field control technologies. The so-called processor casing is to process a certain shape of groove on the inner wall of the duct near the rotor blade tip. When the rotor blade rotates,the fluid in the groove is pumped and sprayed, which can change intensity and shape of tip vortex,thus realize the purpose of controlling tip vortex intensity.

The main purpose of aero-engine compressor‘processor casing’technology is to control tip vortex to enhance the stability of the flow field in rotor, which is different from that of a pump jet thruster. However, the similarity between them is that they both control the adverse effects induced by tip vortex. Moreover, the processor casing technology has been widely used in high-speed compressors as well as in low-speed compressors. The fluid medium in a low speed compressor can be regarded as an incompressible fluid, which is similar to the fluid medium processing method of a pump jet thruster.

Aero-engine compressors have been greatly developed especially in the tip vortex control technology. In order to further study the influence of“processor casing”on the tip vortex control of aero-engine, we analyzed the effect of‘processor casing’with different characteristic parameters on the aero-engine performance.Wu(1997)[8]researched the effect of the first-stage rotor tip coverage ratio on the performance of a multistage axial compressor. Tuo (2009)[9]analyzed the effect of the number of grooves on the transonic compressor performance. Li (2013)[10]verified the stability enhancement effect of a peripheral shallow groove processor casing.

To reduce radiated noise, traditional methods are mainly active control methods, which improve cavitation resistance by optimization design of rotor line-type and duct line-type[11].By referring to the processor casing technology of compressors, we adopted passive control method in this study to add a series of groove structures on the inner wall of the duct, and studied the influence of groove structure and groove characteristic parameters on tip vortex control by changing axial length,circumferential width, radial depth and number of grooves. The results are of theoretical significance and military application value in enhancing the comprehensive performance of pump jet thrusters and in reducing radiated noise of underwater vehicles.

1 Mathematical model

1.1 Research object

In this study, the pump jet thruster of an underwater vehicle was taken as the research object and a decelerating duct and a prestator were employed.To study the influence of groove characteristic parameters on the tip vortex control effect, different types of groove structures were arranged near the tip of the inner wall of the duct,as shown in Fig.1.The square grooves were uniformly distributed along the inner wall of duct. By changing the axial lengthl, circumference widthb, radial depthhof the groove structure as well as the number of grooves, and comparing the tip vortex intensity of the pump jet thruster with different groove structures, the influence rule of groove characteristic parameter on tip vortex control was investigated.

Fig.1 Diagram of duct groove

1.2 Control equation and turbulence model

1.2.1 Introduction of SSTk-ωturbulence model

SSTk-ωturbulence model is short for shear stress transportk-ωmodel, which is transformed fromk-ωmodel.Time homogenization is adopted in the mass and momentum processing of fluid[12].Since Reynolds-average method is capable of calculating average motion only,rather than calculating turbulent flow in different scales, RANS method is not suitable for complex turbulent fluctuations. The transmission equation consists of the kinetic energy equation of turbulent fluctuation (kequation)

whereGkis the generating term of turbulent kinetic energy,Gωis the generating term ofω,ΓkandΓωare the effective diffusion coefficients ofkandωrespectively,YkandYωare the diffusion terms ofkandωrespectively,Dωis the cross-diffusion term,SkandSωare the self-defining source terms.

1.2.2 Introduction of DES turbulence model

DES model,also known as mixed LES/RANS model,combines the features of both RANS model and LES model. RANS model is adopted in the boundary layer region while LES model is employed at other regions when DES model is used for calculation. This feature greatly saves computing resources,as the required number of grids should be larger than that of RANS model but smaller than the number of LES model to guarantee calculation precision. The DES model employed is based on SSTk-ωmodel and the kinetic energy dissipation term is modified as follows

whereCDESis a constant,whose value is 0.61,Δmaxis the local mesh maximum distance as follows

The turbulence scale is defined as

1.3 Computational domain setting and mesh generation

The real-scale model was used for calculation. To exclude the influence of computational domain on the result, the computational domain was set based on the lengthLof the underwater vehicle as benchmark, as shown in Fig.2. The distance between midship and the front and side boundary of computational domain was bothL. The distance between the tail part and the back end of computational domain was 2L. The boundary conditions at the front and back of the computational domain were set as velocity inlet and pressure outlet respectively. The boundary around was set as symmetry plane.

The computational domain consists of four parts:external domain,rotor domain,stator duct domain and duct groove domain.O-H grid is mainly used for integral grid division of four domains.To fully capture the tip vortex flow, rotor domain needs to encrypt tip vortex generation position separately. Hsiao[13]pointed out that the number of radial grid nodes of vortex core should be greater than 15 to ensure computational accuracy of tip vortex. To make the grid transition uniform, multiblock gradient encryption was adopted[14]The rotor grid is shown in Fig.3(a).This study mainly studied the influence rule of groove characteristic parameters on tip vortex control effect. To eliminate the effect of grid scale on the calculated value of tip vortex, identical node partition method was used for the grid division of the conduit grooves. Moreover, the number of nodes was changed according to the change of axial length, circumferential width and radial depth of the groove, so as to ensure consistent maximum mesh size of the duct groove,as shown in Fig.3(b).

Fig.2 Diagram of computing domain size and boundary conditions

Fig.3 Computational domain grid division

1.4 Verification of calculating method

1.4.1 Hydrodynamic performance calculation of standard propeller DTRC4119

Firstly, SSTk-ωturbulence model was used in the numerical calculation of the pump jet thruster.Then,after the calculation tended to be stable,the flow field obtained was taken as the initial condition to be introduced in DES model condition for continued calculation.To verify the accuracy of the method, the standard propeller DTRC4119 was taken as the research object. Based on high-quality structured grid,the open water performance of the propeller and the radial distribution of the propeller tip vortex core were calculated respectively.Then,comparison between the calculated value and the experimental value was carried out[15](EXP represents experimental value and CFD represents experimental value),as shown in Figs.4-5.

Fig.4 shows the curve of open water performance distribution of standard paddle DTRC4119 using SSTk-ωturbulence model.It can be seen that the calculated value and the experimental value of propeller efficiencyη0, propulsion coefficientKTand torque 10KQare approximately the same under different advance coefficients, which indicates that the grid division and solving method are effective in obtaining accurate propeller performance parameters.Fig.5 shows the calculated results by DES turbulent flow model under advance coefficientJ=0.833. It can be seen that the calculated value basically coincides with the experimental value. Whenx/R≤0.15, the vortex core position error between the calculated and the tested value is less than 3%; When 0.15＜x/R≤0.6, the distribution rule remains the same although the error increases.

It can be concluded based on the above results that the method can accurately calculate the initial flow field and capture tip vortex trajectory,which meets the calculation requirement.

Fig.4 Open water performance of the propeller

Fig.5 Radial location of tip vortex

1.4.2 Study on calculating method of rotor tip vortex

In order to further determine the calculation method of rotor tip vortex,the influences of different turbulence models on tip vortex calculation result were analyzed.Fig.6 shows the calculated results of the original pump jet thruster using different turbulent modes.It can be seen from Fig.6 that DES model can capture tip vortex more fully.

Fig.6 Tip vortex nephograms of different turbulence models(without groove)

When groove structure was formed on the inner wall of duct, the unsteady performance of the rotor was changed, and time step had a great influence on the calculation results. In order to study the effect of time step on the calculated value of the tip vortex, we calculate tip flow in the grooved structure at different time stepT/n,whereTrepresents the period of rotor rotation,nis the time step in a cycle whose value was set to 200,720,and 1 800 respectively,so that the rotor rotational angular step was set to 1.8°,0.5°and 0.2°respectively.As shown in Fig.7,when angular step decreased from 1.8°to 0.5°,the results of tip vortex changed significantly;when angular step continued to decrease to 0.2°, tip vortex intensity value changed less. Hence, the angular step value of 0.5° meets the requirements of tip vortex intensity calculation.

Groove structure has a great influence on the rotor tip flow, which puts forward a higher requirement for the grid around rotor tip. Consequently, the grids around rotor tip were encrypted in varying degrees, with the grid number being 4.79 million, 6.67 million and 8 million, respectively.The tip vortex calculation results are shown in Fig.8. As can be seen from Fig.8, when the number of rotor grids increased from 4.79 million to 6.67 million, the tip vortex calculation results changed greatly.When the number of grids further increased to 8.82 million,the fluctuation of tip vortex calculated results declined. Therefore, the calculation requirement of tip vortex intensity was satisfied when the number of rotor grids was set to about 6.67 million. In this study, DES turbulence model was adopted in the numerical calculation,with angular step length set to 0.5°and the number of rotor grids set to 6.67 million.

Fig.7 Tip vortex intensity distribution curve with different time steps when x=0.02

Fig.8 Tip vortex intensity distribution curve with different number of grid when x=0.02

2 Groove effect and regularity analysis

2.1 Influence of groove axial length on the tip vortex control effect

To study the influence rule of groove axial length on the tip vortex control, three kinds of grooves with identical circumferential width, radial depth and number of grooves but different axial lengths were designed based on the axial length of the rotor blade as the standard.The three groove types include a groove structure which is shorter than blade tip, a groove structure which is flush with blade tip, and a groove structure which is longer than blade tip, with the axial length set to 34.0 mm,39.8 mm and 54.0 mm respectively.Numerical calculation of pump jet thrusters with different groove axial lengths were carried out using the identical method.The influence of groove axial length on rotor tip vortex intensity was analyzed.In this paper,the rotor tip vortex is marked byQequivalence surface[14],whereQis expressed as

whereSis the deformation rate tensor of the fluid,Ωis the rotation angular velocity tensor of the quasi rigid body.

The calculated results of tip vortex intensity of the pump jet thruster with different groove axial lengths are shown in Tab.1. It can be found that the tip vortex intensities of the pump jet thruster with a groove structure are significantly lower than that of the original pump jet thruster. This indicates that groove structure can effectively inhibit the formation of tip vortex and reduce tip vortex intensity. In addition, it can be found from comparison of the inhibition effect of three groove structures on tip vortex intensity that the tip vortex intensity with a flat blade tip groove structure is significantly lower than those of other two grooved structures at different Δx(Δxis the axial distance between tip vortex section and rotor trailing edge), which indicates that when groove axial length is roughly in line with rotor blade tip,tip vortex suppression effect is more significant,which is beneficial to reducing tip vortex intensity.

Tab.1 Tip vortex intensity of pump jet thruster with different groove structure axial lengths

Fig.9 Rotor tip vortex distribution nephogram at different locations

To further analyze the influence rule of the axial length of groove structure on tip vortex control, the tip vortex distribution nephogram of the pump jet thruster with different groove structures at different sections was plotted as shown in Fig.9. The tip vortex intensity of the grooved pump jet thruster is significantly lower than that of the original one at all Δx.By comparing the tip vortex intensity distributions of different groove structures at the position ofx=0.02, it can be seen that tip vortex intensity of rotor is significantly lower than that of the other two types of grooved pump jet thrusters whenl=39.8 mm. This indicates that the groove structure can effectively inhibit tip vortex formation and reduce tip vortex intensity, and the inhibition effect is the most significant when the groove axial length is flush with rotor blade tip.

2.2 Influence of groove circumferential width on tip vortex control effect

Groove structure is located near the rotor blade tip. Rotor rotation will drive the fluid reversal due to the small clearance between the tip of the rotor and the inner wall of the duct. When the inverted fluid flows between the rotor blade tip and the inner wall of duct, partial fluid will enter the groove. The greater the groove circumferential width is, the more the fluid will flow into the groove at one time,and the greater the influence of the groove structure on the fluid flow will be.In order to study the influence of the groove circumferential width on the tip vortex control, three types of groove structures with groove circumferential widths ofb=4 mm,b=8 mm andb=12 mm were designed on the premise of ensuring identical groove number, groove radial depth and axial length.Numerical calculation of pump jet thrusters with different groove circumferential widths was carried out using the same method and the influence of the circumferential width on rotor tip vortex intensity was also analyzed.

According to the data in Tab.2, it can be found that the tip vortex intensity of pump jet thrusters with different groove circumferential widths are significantly lower than that of the original pump jet thruster.This indicates the groove structure can effectively inhibit the formation of tip vortex.Moreover,since the tip vortex intensity at positionx=0.02 is the maximum,the tip vortex intensity at this position is taken as standard when analyzing the control effect of groove circumferential width on the tip vortex.From the comparison of the tip vortex intensity at the position ofx=0.02,the tip vortex intensities of three grooved pump jet thrusters withb=4 mm,b=8 mm andb=12 mm arelower than those of the original pump jet thrust by 20.54%,19.60% and 20.68% respectively. The tip vortex control effect of the three types of groove structures is similar to each other, which makes tip vortex intensity decrease by about 20%.

Tab.2 Tip vortex intensity of pump jet thrusters with different groove structure circumferential widths

As shown in Fig.10, although the tip vortex intensity of the groove structure with circumferential widthb=8 mm is larger than those of the other two groove structures,the increase amplitude is not significant. Moreover, the tip vortex intensities at positionx=0.02 withb=4 mm andb=12 mm are similar to each other, which further indicates that the groove circumferential width has little influence on tip vortex control effect.

Fig.10 Tip vortex distribution curve when Δx=0.02

2.3 Influence of groove radial depth on tip vortex control effect

To study the effect of groove radial depth on the tip vortex control, four types of groove structures with different radial depths(h=4 mm,h=8 mm,h=12 mm andh=16 mm respectively)but identical axial length and circumferential width were designed. The numerical calculation of the pump jet thruster with different groove radial depths was conducted by the same method and the influence of the groove radial depth on the vortex strength of the rotor tip was analyzed.

Tab.3 shows the calculated results of tip vortex intensity of the pump jet thruster with different groove radial depths. It can be found from Tab.3 that the rotor tip vortex intensity of the pump jet propeller with groove structure is significantly lower than that of the original pump jet thruster at all Δx,indicating that the groove structure can effectively inhibit the formation of tip vortex and reduce tip vortex intensity. The rotor tip vortex control effect changes with the groove radial depth changing. When the groove radial depth ish=12 mm, the tip vortex thruster at the position ofx=0.02 is 620 460,which is 34.75%lower than that of the original pump jet thruster.The tip vortex control effect ath=12 mm is the most significant.

Fig.11 shows the tip vortex intensity distribution curve at the position ofx=0.02 for pump jet thrusters with different groove structures.It can be seen from the figure that the tip vortex decreased gradually with the increase of groove radial depth.When the groove radial depthhincreased to 12 mm, the tip vortex intensity was the smallest. As the rotor radial depth further increased, the rotor tip vortex intensity started to increase instead. This indicates that with the increase of the groove radial depth, the tip vortex control effect became increasingly significant at first and then gradually tended to be stable. The tip vortex control effect was the most significant when the groove radial depthhwas controlled around 12 mm.

2.4 Influence of the number of grooves on the tip vortex control effect

The effect of the number of grooves on the tip vortex control was investigated by changing theb/Bratio (i.e. changing the number of groove) while maintaining remaining groove circumferential width,radial depth and axial length unchanged.Numerical calculation of the pump jet thruster with different number of grooves was carried out by the same method. The control effect of the groove structure on the rotor tip vortex as well as the influence rule of number of grooves on tip vortex intensity control were analyzed.

Fig.11 Tip vortex distribution curve when Δx=0.02

Tab.4 shows the calculated results of tip vortex intensity of the pump jet thruster with different number of grooves.According to the data in the table,the tip vortex intensities of pump jet thrusters with a groove structure are significantly lower than that of the original pump jet thruster. When the number of grooves is 80 and 120, the tip vortex intensity at the position ofx=0.02 is 704 990 and 754 260 respectively. Compared with the original pump jet thruster, the tip vortex intensity is reduced by 25.86%and 20.68%respectively,showing a significant tip vortex suppression effect.This indicates that the groove structure can effectively inhibit the formation of tip vortex and reduce tip vortex intensity.

Tab.4 Tip vortex intensity of pump jet thruster with different number of groove

For the convenience of analyzing the control effect of a groove structure on rotor tip vortex, tip vortex nephogram with the number of grooves of 0, 80 and 120 was plotted, as shown in Fig.12. It can be found that the tip vortex intensity with the groove structure is significantly smaller than that of the original pump jet thruster,which further indicates that the groove structure can effectively inhibit tip vortex formation.

Fig.12 Rotor tip vortex distribution nephogram with different number of groove

Fig.13 shows the tip vortex intensity distribution curve at the position ofx=0.02 with different number of grooves. According to the curve distribution rule, it can be found that the tip vortex intensity decreased gradually with the increase of number of grooves firstly, and then turned to increase when the number of grooves exceeded 80.This indicates that the tip vortex control effect was the most significant when the number of grooves was controlled around 80.

Fig.13 Tip vortex intensity distribution curve when Δx=0.02

2.5 Effect of grooves on hydrodynamic performance parameters of pump jet thruster

In order to study the influence of duct groove on the hydrodynamic performance parameters of the pump jet thruster, numerical calculation were carried out for the thruster with groove structure and the original one. The calculated values of hydrodynamic performance parameters of the two types of thrusters are shown in Tab.5.

According to Tab.5,it can be found that after the installation of the groove structure,the rotor’s propulsion efficiencyη1, torqueKQand thrust coefficientKT1are almost consistent with those without groove, indicating that there is little effect of the groove structure on the hydrodynamic performance of the rotor.For the whole thruster,the thrust coefficientKT2and propulsion efficiencyη2are 0.398 7 and 0.726 7 respectively before installation of the groove structure, after which, the calculated values of the thrust coefficient and propulsion efficiency are 0.388 4 and 0.710 1, which are reduced by 2.6% and 2.3% respectively, indicating that the groove structure has little effect on the propulsion efficiency and other hydrodynamic performance parameters of the pump jet thruster.

Tab.5 Performance parameters of pump jet thruster at J=1.15(with&without groove)

3 Conclusions

In this paper,a series of grooves were added in the inner wall of a pump jet thruster duct.Different types of groove structures were designed by changing the groove axial length, radial depth,circumferential width and number of grooves. Based on STAR-CCM+ software, the effect of groove characteristic parameters on tip vortex control was analyzed,and the following conclusions are drawn:

(1) The tip vortex intensity of a pump jet thruster with groove structure is significantly lower than that of the original pump jet thruster,indicating that the groove structure can effectively inhibit tip vortex formation and reduce tip vortex intensity.

(2) Different groove characteristic parameters have a different influence on tip vortex control.The tip vortex control effect is more significant when the groove axial length is roughly flush with the blade tip. As the groove radial depth increases, the tip vortex intensity first decreases and then tends to be stable.The distribution curve of tip vortex intensities with different number of grooves atx=0.02 follows a parabolic pattern.When the number of groove is controlled at 80,the calculated result of tip vortex intensity is the smallest and the control effect of tip vortex is the most significant.However, the tip vortex intensities change insignificantly with the circumferential width of the groove, which shows that the groove circumferential width has little influence on the tip vortex control effect.