Hydrodynamic performance of distributed pump-jet propulsion system for underwater vehicle*

Lü Xiao-jun (呂曉軍), ZHOU Qi-dou (周其斗), FANG Bin (方斌)

Department of Ship Engineering, Naval University of Engineering, Wuhan 430033, China, E-mail: lvxj03@126.com

Hydrodynamic performance of distributed pump-jet propulsion system for underwater vehicle*

Lü Xiao-jun (呂曉軍), ZHOU Qi-dou (周其斗), FANG Bin (方斌)

Department of Ship Engineering, Naval University of Engineering, Wuhan 430033, China, E-mail: lvxj03@126.com

(Received January 29, 2013, Revised June 28, 2013)

A type of distributed pump-jet propulsion system (DPJP) is developed with two or four specially designed pump-jet pods located around the axisymmetric underwater vehicle body symmetrically. The flow field is numerically simulated by solving the RANS equations with the finite volume method. The computational method is validated by comparing the calculated hull resistances of the SUBOFF AFF-3 model and the open water performance of a ducted propeller with experimental data. The hydrodynamic performances of the DPJP with different axial or radial positions and numbers of pump-jet pods are obtained to analyze the interactions between the hull and the pump-jet pods. It is shown in the calculated results that the decrease of the distance between the pods and the hull leads to an increase both in the efficiency of the pods and the thrust deduction factor due to the effect of the stern wake. And, a negative thrust deduction factor can be obtained by locating the DPJP at the parallel middle body near the aftbody of the vehicle to improve the hydrodynamic performance of the DPJP. Besides, the increase of the number of pods will cause a remarkable decrease of the total propulsive efficiency of the DPJP with the pods mounted on the stern planes, while a small decline of the total propulsive efficiency of the DPJP is observed with the pods mounted on the parallel middle body.

distributed pump-jet propulsion system (DPJP), hydrodynamic performance, pump-jet pod, self propulsion point, underwater Vehicle

Introduction

The underwater vehicle faces the difficulties associated with low-speed maneuverability, because the effectiveness of the traditional control surface decreases significantly at low speeds. One effective way out is to equip the vehicle with a distributed pump-jet propulsion system (DPJP) consisting of several pump-jet pods, so that the course can be controlled by regulating vectored forces of the pods[1,2].

Such a propulsion system was not well studied, and related studies mainly focused on the hydrodynamic performances and noises of the pump-jet pods attached to the hulls of the surface ships. For example, Bellevre et al.[3]presented numerical and experimental studies that show a good behavior of the pump-jet pod related to the hydrodynamic efficiency, the maneuverability, the loads on pods, the cavitations and the pressure pulses. Saussereau et al.carried out similar studies[4]. In addition, efforts were made to optimize the performance of the pump-jet propulsor[5-11].

In view of the importance of the pod-hull interaction, it is therefore necessary to study the influences of the axial and radial positions and the number of pump-jet pods on the hydrodynamic performances of the DPJP.

As is mentioned above, a type of pump-jet pod is developed, of which a cylindrical housing with a duct provides a flow path for water and a rotor blade row followed by an array of stator vanes. Two different connection types are selected for the installation of the DPJP, one is to support the pod by an airfoil-shaped strut mounted on the parallel middle body of the vehicle, the other is to fix the pod on the tip of the stern plane. Accordingly, the distributed pump-jet propulsion system (DPJP) is built up by locating two or four pods around the vehicle body symmetrically.

Since the RANS method is developed for the computation of the propeller-hull interaction and isvalidated[12,13], the hydrodynamic performances of the distributed pump-jet propulsion system with different axial or radial positions and different numbers of pump-jet pods can be simulated by the CFD methodology. Results can be used to analyze the interaction between the DPJP and the vehicle hull. Then, the self propulsion point (SPP) and the powering performance can be analyzed and compared to validate the feasibility of applying the DPJP to propel the axisymmetric underwater vehicle.

1. Physical model

1.1 Underwater vehicle

The underwater vehicle model studied here is the SUBOFF AFF-3 model. It has an axisymmetric hull body as shown in Fig.1 with an overall length of 4.356 m and a maximum radius of 0.254 m, four identical stern planes mounted on the model hull symmetrically.

1.2 Pump-jet pod

The pump-jet pod consists of 9 rotor blades and 7 stator vanes operating within an axisymmetric housing. The duct provides a flow path for water, and a stator to remove the swirl from the flow. Figure 2 shows the geometry of the pump-jet pod. This pump-jet pod is a type of rim driven thruster similar to that described in Ref.[14]. So the duct internal diameter is equal to the rotor blade diameter. The effect of the airgap flow on the thrust and the torque of the rotor blade is ignored here.

In this paper, a fix sized pump-jet pod is adopted during all CFD calculations, and the main parameters of the pod are shown in Table 1. It is important to point out that the duct internal diameter is equal to the rotor blade diameter.

Figure 3 shows two different connection types for the installation of the DPJP, one is to fix the housing by an airfoil-shaped strut mounted on the parallel middle body of the vehicle, the other is to fix the pod on the tip of the stern plane. It is important to point out that the starboard pump-jet pod is in the right hand, while the larboard one in the left hand, so that the fluid field around the vehicle is symmetrical.

2. Computational method

2.1 Numerical method

The three-dimensional incompressible viscous Reynolds averaged Navier Stokes (RANS) equations for steady flows are applied to calculate the flow fields around the pump-jet pods and the underwater vehicle body, and they are expressed as

where uiand ujare the absolute time averaged velocity components,pis the time averaged pressure, Re the Reynolds number,ajthe propeller revolution rate, andthe Reynolds stress term.

To close the RANS equations, thek-ωturbulence model is adopted in this paper, in which the turbulence viscosity is assumed to be linked to the turbulence kinetic energy and the specific dissipation rate as

where μtis the turbulence viscosity,ρthe fluid density,k the turbulence kinetic energy, andωthe specific dissipation rate.

Two transport equations presented below are to be solved. The stress tensor is computed from the eddy-viscosity concept.

where pkis the production rate of turbulence,μthe viscosity coefficient,β′,α,β,σkand σωare the model constants.

The default near wall treatment of thek-ωturbulence model, which allows for a smooth shift from a low-Reynolds number form to a wall function formulation, is adopted to acquire more accurate results. The second order upwind advection scheme is selected to calculate the advection terms in the discrete finite volume equations. The stage model is adopted to model the frame change between the rotor and the stator, and a steady state solution is obtained by performing a circumferential averaging of the fluxes through bands on the interface.

2.2 Domains, grids, and boundary conditions

Figure 4(a) shows the computational domain used for the prediction of the pump-jet pod open water performance, which is a concentric cylinder on the rotor rotating axis, with a radius of 12Rp. The uniform inflow is used to initialize the inlet, which is set at 8Rpbefore the pump-jet pod and a pressure outlet is set at the exit which is mounted at20Rpbehind the pump-jet pod.

The computational domain used for the simulation of the self-propulsion of the vehicle is simplified to be a semi-cylinder as shown in Fig.4(b), with the symmetry of the problem considered. The radius of the semi-cylinder is 1L , where Lis the length of the vehicle. The uniform inflow is used to initialize the inlet, which is set at1Lbefore the vehicle and a pressure outlet is set at the exit, which is mounted at2L behind the vehicle.

In view of the geometrical complexity of the underwater vehicle and the pump-jet pod, the computational domain is split up into simple blocks so that the hexahedral grids can be applied in the whole region. Boundary layers are attached to the surface of the vehicle and the pod so as to define the location of the first node away from the wall. Local grid refinements are made at stern planes and blades by applying size functions.

In order to determine the influences of the element number on the computational error of the hull resistance, a group of grids is generated, which consists of three different grids. Figure 5 shows the meshes on the surfaces of stern planes. The sizes of Grid 1 (the coarsest) through 3 (the finest) are 0.9×106, 2.3×106and 6.1×106, and the grid refinement ratio is2. All three grids have the same mesh size at the boundary layer, and the value ofy+is about 100 on average.

Figure 6 shows the meshes on the surfaces of the pump-jet pod and the vehicle body. The quality criteria necessary for thek-ωturbulence is measuredby the y+value model, which mounts up 125 on average for the pump-jet pod and about 100 for the underwater vehicle. The total number of elements is about 2.2×106for the prediction of the pump-jet pod open water performance, and 6.0×106for the simulation of the self-propulsion of the vehicle.

3. CFD results

3.1 Validation of calculation method

Since the calculation of the open water performance of the duct propeller was already validated in Ref.[15], only the validation of the calculation of the hull resistance is presented here.

The calculation of the vehicle hull resistance at speed of 5.92 knots is carried out with the three different grids. The comparison of calculated results and experimental data is shown in Table 2. It can be concluded that the increase of element number can decrease the computational error. Besides, for coarser grids with an average y+value lower than 100, the computational error of the hull resistance can also be controlled within 3% by applying the second order accuracy discretization scheme.

3.2 Hull resistance of the vehicle

Before the propulsive performances analysis, a calculation without pump-jet pods is performed to determine the hull resistances over the speed range of 1 m/s-5 m/s. Results are shown in Fig.7.

3.3 Open water performance of the pump-jet pod

For reference and comparison, the open water performance of the pump-jet pod is calculated. Results of the total thrust coefficient KT, the duct thrust coefficient KTN, the blade thrust coefficient KTP, the torque coefficient KQand the open water efficiency η0are presented in Fig.8 for different advance coefficientsJ at speed of 4 m/s.

3.4 Effect of propulsion system on the hull resistance

In order to study the interaction between the hull and the propulsion system, four different axial positions of the DPJP with two pump-jet pods are selected and shown in Fig.9. The two pump-jet pods are mounted on the tips of the horizontal stern plane in Case 1, while two identical struts connecting the pump-jet pods are mounted on the hull at angles of 90oand 270oin Cases 2 to 4 (0oat the top dead center).

In order to study the propulsion characteristics, calcul atio ns of th e hydrody namic performa nce o f the DPJParecarriedoutoverthespeedrangeof1m/s-5 m/s. The rotor blades operate at the self propulsion point with zero net longitudinal force in a steady motion with all control surfaces at zero angle and with no drift or pitch angle.

The calculated thrust deduction factorst, the wake fractionswand the total propulsive efficiencies of the DPJPηare shown in Fig.10. It can be seen from the figure that the thrust deduction factors in Case 1 are larger than that in other three cases, which does not result in a decrease of the total propulsive efficiencies, mainly due to the larger wake fractions.

Especially, the thrust deduction factor in Case 2 is negative, which means that the hull resistance of the vehicle with the DPJP is smaller than that of the vehicle without pods. It is important to note that the resistance of the struts includes the hull resistance.

This phenomenon can be explained by a comparison of the pressure coefficientCp along the right meridian line of the hull as shown in Fig.11, in which the curve peaks are caused by the presence of the struts and the stern planes. The pump-jet pods in Case 2 reduce the fow velocities at the aftbody of the vehicle and the frictional resistance and increase the pressure in the aftbody, thus the inviscid resistance is reduced. A negative thrust deduction factor as such may improve the hydrodynamic performance of the DPJP and will be discussed later.

3.5 Effect of stern wake on the propulsive performance

To study the effect of the stern wake on the propulsive performance, a dimensionless parameterk is defined as followswhere dis the perpendicular distance between the rotor axis and the vehicle axis,Rmaxthe maximum radius of the vehicle body.

The axial position of the DPJP adopted here is the same as in Case 1, andkvaries from 0.9 to 1.3 as shown in Fig.12.

The propulsive performance of the pump-jet pod is calculated for 1.3＜J＜1.75at the speed of 4 m/s. As shown in Fig.13, the average axial velocityV′in front of the rotor blade decreases slightly when the pod moves towards the stern hull. The increasing trend of the total thrust and the duct thrust coefficients with the decrease of parameter kis shown in Figs.14 and 15, respectively. And, the efficiencies of the pump-jet podη′at different advanced coefficients are presented in Fig.16. It should be noted that the increase of the total thrust is mainly due to the duct thrust. In addition, the decrease of parameterk will cause an increase of the thrust deduction factor.

The maximum efficiency at k=0.9 is about 5 percents higher than that of the open water efficiency, because the stern wake enhances the hydrodynamic performance of the DPJP.

3.6 Influence of the number of pods on the propulsive performance

One of the parameters influencing the propulsive performance of the DPJP is the number of the pumpjet pods, which is selected to be 2 or 4 here so as to maintain the symmetry of the flow field.

On the basis of the calculated results, two different installation positions, marked as Schemes A and B respectively, are selected for studying the influence of the number of pods on the hydrodynamic performance of the DPJP. Figure 17(a) presents the installation position of Scheme A, corresponding to the axial position in Case 1 withkequal to 0.9, and Fig.17(b) shows the installation position of Scheme B, representing the axial position in Case 2. The pods are located at the angles of45o,135o,225oand 315ofor the DPJP with four pump-jet pods.

Calculations of the hydrodynamic performance of the DPJP with two and four pump-jet pods are con-ducted at the self propulsion point over the speed range of 1 m/s-5 m/s. Comparisons of the thrust deduction factors and the total propulsive efficiencies of the DPJP are presented in Fig.18, which shows the influence of the number of pump-jet pods.

It is indicated that the increase of the number of pump-jet pods increases the thrust deduction factor in Scheme A, and decreases the thrust deduction factor in Scheme B. On the other hand, the total propulsive efficiencies of the DPJP in both cases decrease if the number of pump-jet pods increases. However, the decreased amplitude of the total propulsive efficiency of the DPJP in Scheme B is much lower than that in Scheme A. This is mainly due to the different change trends of the thrust deduction factors in two schemes.

4. Conclusions and future work

A type of DPJP is developed with two or four specially designed pump-jet pods located around the axisymmetric underwater vehicle body symmetrically. Two different connection types are selected for the installation of the DPJP, one is to support the pod by an airfoil-shaped strut mounted on the parallel middle body of the vehicle, and the other is to fix the pod on the tip of the stern plane.

The hydrodynamic performances of the DPJP with diverse axial or radial positions and different numbers of pump-jet pods are calculated to analyze the interactions between the hull and the pump-jet pods. The conclusions are as follows:

(1) The decrease of the distance between the pod and the hull increases both the efficiency of the pod and the thrust deduction factor due to the effect of the stern wake. This can be applied to improve the hydrodynamic performance of the DPJP on the only occasion that the number of the pump-jet pods is small.

(2) A negative thrust deduction factor can be obtained by locating the DPJP at the parallel middle body near the aftbody of the vehicle, which enhances the hydrodynamic performance of the DPJP when more pump-jet pods are installed.

(3) The increase of the number of pods will cause a remarkable decrease of the total propulsive efficiency of the DPJP with the pods mounted on the stern planes, while a small decline of the total propulsive efficiency of the DPJP is observed with the pods mounted on the parallel middle body.

Overally, the results have validated the feasibility of applying the DPJP to propel an axisymmetric underwater vehicle. However, issues and questions listed below are still open:

(1) To achieve better performance of the DPJP, the optimization design of the pump-jet pod has to be carried out with the consideration of the real inflow conditions and the cavitation performance.

(2) The benefits of the DPJP on the low-speed maneuverability require further investigation.

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10.1016/S1001-6058(14)60059-7

* Biography: Lü Xiao-jun (1985-), Male, Ph. D.

ZHOU Qi-dou,

E-mail: Qidou_Zhou@126.com