The method to control the submarine horseshoe vortex by breaking the vortex core*

LIU Zhi-hua (劉志華), XIONG Ying (熊鷹)

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

E-mail: meining1014@sina.com

TU Cheng-xu (涂程旭)

College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China

The method to control the submarine horseshoe vortex by breaking the vortex core*

LIU Zhi-hua (劉志華), XIONG Ying (熊鷹)

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

E-mail: meining1014@sina.com

TU Cheng-xu (涂程旭)

College of Metrology and Measurement Engineering, China Jiliang University, Hangzhou 310018, China

(Received May 12, 2013, Revised March 15, 2014)

The quality of the inflow across the propeller is closely related with the hydrodynamic performance and the noise characteristics of the propeller. For a submarine, with a horseshoe vortex generated at the junction of the main body and the appendages, the submarine wake is dominated by a kind of highly non-uniform flow field, which has an adverse effect on the performance of the submarine propeller. In order to control the horseshoe vortex and improve the quality of the submarine wake, the flow field around a submarine model is simulated by the detached eddies simulation (DES) method, and the vortex configuration is displayed using the second invariant of the velocity derivative tensor. The state and the transition process of the horseshoe vortex are analyzed, then a modified method to break the vortex core by a vortex baffle is proposed. The flow numerical simulation is carried out to study the effect of this method. Numerical simulations show that, with the breakdown of the vortex core, many unstable vortices are shed and the energy of the horseshoe vortex is dissipated quickly, and the uniformity of the submarine wake is improved. The submarine wake test in a wind tunnel has verified the effect of the method to control the horseshoe vortex. The vortex baffle can improve the wake uniformity in cases of high Reynolds numbers as well, and it does not have adverse effects on the maneuverability and the speed ability of the submarine.

horseshoe vortex, submarine wake, flow uniformity, vortex baffle

Introduction

The submarine propeller operates in the wake of a submarine, so the quality of the wake has a direct influence on the hydrodynamic performance and the noise characteristics of the submarine propeller. The submarine horseshoe vortex generated at the junction of the main body and the appendages (such as rudder, sail and stern foil), is mainly responsible for the nonuniformity in the submarine wake[1-3]. In order to improve the uniformity in the submarine wake and the submarine propeller performance, the submarine flow fields were extensively studied, and some useful methods to improve the quality of submarine wake were proposed. Rhee et al.[4]studied the flow around an appended submarine model using the numerical simulation method; the detailed flow structures were analyzed. Zhang et al.[5]simulated the submarine wake with different Reynolds numbers and studied the influence of the Reynolds number on the vortex strength in the wake. Wu et al.[6]carried out an optimization design study of the sail of a submarine in order to improve the wake flow.

In order to reduce the strength of the submarine horseshoe vortex, Paul[7]designed a small lifting surface located in the body-appendage junction area, to induce the tip vortex to disturb and weaken the horseshoe vortex. Adding an arc fillet at the body-appendage junction deems an effective method to improve the flow uniformity at the submarine propeller disc. Li et al.[8]and Zhang et al.[9]carried out pertinent studies with numerical simulations and model experiments.

Liu et al.[10]presented a method to control thesubmarine horseshoe vortex by inducing a counter revolving vortex.

In this paper, a modified method is proposed to control the horseshoe vortex by disturbing the initial vortex state, and its effectiveness is shown by numerical simulations and wind tunnel experiments.

1. Simulation and visualization of submarine horseshoe vortex

1.1 Numerical simulation method

But for the detailed flow structure, some high precision turbulent models and transient simulation methods should be applied in order to obtain valuable and accurate results. In this paper, the detached eddies simulation (DES) method is used to simulate the submarine horseshoe vortex.

The DES model combines the fine tuned RANS method in the thin turbulent boundary layers with the powerful LES in the outer flow regions, to take advantages of the both methods.

In the DES method, a transform function is needed to control the transition between the computation methods. Because the variable,d, which stands for the distance from the computational node to the closest wall, is used in both RANS and LES, so in the DES model,d is replaced with a new length scale,, defined as:=min(d,Cdes.Δ). Here the grid spacing,Δ, is based on the largest grid space inx,y and zdirections in the computational cell. The DES model functions as the RANS model for=dand as the LES model for=Cdes.Δ.

1.2 Configuration of study model

According to the configuration characteristics of a submarine, the study model is designed as shown in Fig.1, which includes a main body and a sail model. The main body is 1 m in length and its maximum diameter is 0.12 m. The sail model is 0.1 m in length and 0.07 m in height, the section of the sail is shown in Fig.2, which has a maximum thickness of 0.025 m. This study model is named the SBM.

The flow field around the study model of the SBM is simulated by the DES method with the transient state, and the computation grid is as shown in Fig.3.

The inflow boundary, with an upstream distance of one total model length from the bow of the model, is set as in the velocity-inlet boundary condition. The outflow boundary, with a downstream distance of two times of the total model length from the stern of the model, is set as in the undisturbed pressure-outlet boundary condition. The outer boundary, with a distance of one total model length from the central axis of the model, is set as in the undisturbed velocity boundary condition.

In this flow simulation, the Reynolds numbe6r about the total length of the SBM model is 1.55×10. The grids close to the model is small enough to reflect the small size flow structure, and the distance of the first layer grid to the surface of the body is set to ensure the non-dimensional spacing reaching the target of y+≈1, and the total number of the computational grid is 1.6×107.

1.3 Visualization and analysis of the horseshoe vortex

The transient flow around the SBM model is simulated by the DES method, and the transient simulation is initialized by the primary steady results. According to the requirements of the DES method, the step size of the transient simulation is determined by the Courant-Friedrichs-Lewy (CFL) number.CFL= dtU/Δ, wheredtis the time step size and it should be set to satisfyCFL≈1. Here the time step size,dt, is 4.0×10-5s.

The surface pressure distribution at the junction of the sail and the main body of the SBM is shown in Fig.4 with the calculation time of 0.24 s after convergence.

As shown in Fig.4, both of the highest pressure area and the lowest pressure area appear in the junction region, which induces a great pressure gradient. With the great pressure gradient, the perpendicular joint of the main body and the sail model, the flow becomes very complicated, and the horseshoe vortex is induced.

The horseshoe vortex is the main issue considered in the simulation. When the flow field is solved, the velocity derivative tensor at every point in the flow field can be obtained as dij=?ui/?uj, which is a second-order tensor[16]. The shape and the distribution of vortexes could be expressed by the second invariant of the velocity derivative tensor,I2, as

Here,iand j are the indexes standing forx,y andz.I2is a scalar to scale the strength and the influence area of the three dimensional vortex.

The iso-surface of I2at the calculation time of 0.24 s is shown in Fig.5, which displays the initial state of the horseshoe vortex and its development. The horseshoe vortex will cause the non-uniformity of the wake when it goes downstream to the tail of the model. Figure 6 shows the isoline of the axial flow velocity at the section located at0.978L, the excurvature of the isoline is just caused by the horseshoe vortex.

As shown in Fig.4 and Fig.5, the vortex is generated by the great pressure gradient at the fore part of the sail. With the swash of the inflow and the blocking of the sail, the vortex changes its state from a transverse vortex to a longitudinal vortex and goes downstream. The longitudinal vortex goes straight down to the submarine wake and leads to the flow non-uniformity at the submarine propeller disc. If the longitudinal vortex core is ingeniously disturbed, some significant effect to break or control the vortex can be achieved.

A kind of vortex baffle is designed to break the longitudinal vortex core. As shown in Fig.7, this vortex baffle is in a shape of a rectangle and its dimension is set to match the size of the dimension of the vortex core. Here the vortex baffle is 0.012 m in length and 0.007 m in height, and it is located at the area where the the longitudinal vortex comes into being (as shown in Fig.7).

2. Simulation on the effect of the vortex baffle

The vortex state of the SBM with the vortex baffle is displayed based on the simulation. Figure 9 shows the longitudinal vortex core that has been broken at the calculation time of 0.33 s after convergence.

As shown in Fig.9, the vortex baffle causes a havoc on the longitudinal vortex core, the relatively stable vortex state is disturbed greatly, which accelerates the dissipation of the vortex energy. It is shown from the comparison between Fig.5 and Fig.9, the disturbed horseshoe vortex goes downstream with a much smaller vortex core, and the influence of the horseshoe vortex on the uniformity of the SBM model wake flow is expected to decrease.

Figure 10 shows the isoline of the axial flow velocity of the SBM model with the vortex baffle at the section located at 0.978L. Compared with that of the SBM model without the vortex baffle, it is obviously shown that the camber of the isoline caused by the horseshoe vortex is decreased.

The distribution of the velocity at different radial directions is shown in Fig.11. Here U0stands for the undisturbed inflow velocity,uxstands for the axial velocity component,urstands for the radial velocity component,uθstands for the tangential velocity component, and the superscript “?” stands for the statewith the vortex baffle.R is the maximum radius of the main body of the SBM,r is the distance from the calculation point to the axial line of the model,θ is the circumferential angle(as shown in Fig.10).

As shown in Fig.10 through Fig.13, with the effect of the vortex baffle, the amplitude of the velocity variation against the circumferential angle is decreased markedly, it indicates that the vortex baffle can improve the uniformity of the wake of the SBM model.

In order to study the effect of the vortex baffle with high Reynolds numbers, the flow field around the SBM model is further simulated with the Reynolds numbers of 1.24×107by increasing the inflow velocity. In the simulation, the configuration of the vortex baffle is the same as that in the simulation with the Reynolds numbers of 1.55×106, but the total number of the computational grid increases to 48 million. The result of the simulation is shown in Fig.14.

The non-uniformity of the wake can be reflected distinctly by the distribution of the axial velocity component at the propeller disc. As shown in Fig.14, the wake uniformity can be improved by the vortex baffle in cases of high Reynolds numbers as well.

Because the propeller operating in the submarine wake has a diameter generally less than 60% of the maximum diameter of the main body, this method to improve the inflow quality across the propeller is practical in real applications.

2、耕地監(jiān)測。監(jiān)測結(jié)果表明，2012年庫區(qū)耕地1251037.52畝，2017年1240650.22畝，五年間耕地面積減少10387.30畝。庫區(qū)新增耕地主要是由于土地整治開發(fā)將部分林地、園地、草地等地類改造成耕地類型，庫區(qū)耕地面積減少的主要因素是建設(shè)占用和水庫淹沒。

In literature[2], the author of this paper proposed a method to weaken the horseshoe vortex by inducingthe attached vortex, which is shown in Fig.15.

Compared Fig.15 with Fig.9, It can be concluded that, the attached vortex controls the horseshoe vortex indirectly, while the modified vortex baffle can directly break the vortex core, so with much better effect on the improvement of the submarine wake.

3. Experiment to verify the effect of vortex baffle

In order to test whether the vortex baffle has the practical effect to control the horseshoe vortex and improve the inflow quality at the propeller disc, the wind tunnel experiment on an SBM model is carried out. In this experiment, the axial velocity at the tail of the SMB model with and without the vortex baffle is measured by a hot wire velocimeter system.

The SBM model is in the configuration described in Section 1.2. The experiment is carried out in the cycle low-speed wind tunnel, the test section of the wind tunnel is 2 m in length and 0.6 m×0.6 m in cross section, and the turbulent intensity is lower than 1% in design. The test error of the velocimeter system is lower than 0.5%.

Figure 16 shows the tested SBM model in the wind tunnel, and the vortex baffle located at the junction area of the main body and the sail model. The dimension and the position of the vortex baffle is set as the same as that in the simulation; the material of the baffle is cuprum and its thickness is 0.0001 m.

The experiments about the SBM with and without the vortex baffle are carried out and the wind velocity is 264.45 m/s to have the Reynolds number of 1.55×10. The tested non-dimensional axial velocity, ux/U0, is plotted in Fig.17, and the comparison results of the model with and without the vortex baffle are also displayed in this figure. As shown from the comparison, the effect of the vortex baffle to improve the uniformity of the submarine wake is confirmed by experiment.

4. The influence of the vortex baffle on the hydrodynamic force acted on the body

When the submarine navigates in the sea, the hydrodynamic force acted on the submarine has a direct relation to its maneuverability and speed ability. In order to investigate the influence of the vortex baffleon the hydrodynamic force acted on the body, three navigation configurations of the SBM model are simulated, and the resistance, the lift force and the transverse force acted on the SBM model with and without the vortex baffle are analyzed, respectively. The configurations are list in Table 2.

The simulation is carried out and the force to be analyzed is monitored in an iteration process. Figure 18 shows the pressure distribution on the surface of the SBM model after the calculation is converged.

Table 3 shows the resistance, the lift force and the transverse force acted on the SBM model with and without the vortex baffle. Here the forces are presented as the hydrodynamic coefficients which are divided by ρV2L/2, andLstands for the total length of the SBM model.

As shown in Table 2, the vortex baffle has very little influence on the hydrodynamic force acted on the SBM model, and the main reason is that the vortex baffle has a much smaller area than that of the model and it is enveloped in the transverse and vertical projections of the model, so the vortex baffle will not cause an adverse effect on the maneuverability and speed ability of the submarine.

5. Conclusion

The submarine horseshoe vortex generated at the sail-body junction is numerically simulated and visualized by the Detached Eddies Simulation method and the second invariant of the velocity derivative tensor. In order to decrease the influence of the horseshoe vortex on the submarine wake, a modified method to break the vortex core is proposed. The numerical simulation on the effect of this method is carried out. It is shown that, the vortex baffle causes a havoc on the longitudinal vortex core, and the vortex energy is dissipated greatly. With the effect of the vortex baffle, the flow uniformity at the submarine propeller disc is greatly improved. The wind tunnel experiment is carried out to test the axial velocity distribution at the propeller disc of the submarine model, and the effect of the method to improve the flow uniformity of the submarine wake is verified by this experiment. This paper means to help the control of the submarine propeller noise and vibration.

Acknowledgement

This work was supported by the Science Study Foundation of Naval University of Engineering (Grant No. HGDQNJJ12004).

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10.1016/S1001-6058(14) 60070-6

* Project supported by the National Natural Science Foundation of China (Grant No. 51209213).

Biography: LIU Zhi-hua (1981-), Male, Ph. D., Lecturer

XIONG Ying,

E-mail: xiongying0920@163.com