THE CO-SIMULATION OF THE AXIAL PISTON PUMP FOR SEAWATER REVERSE OSMOSIS DESALINATION

ZHAI Jiang* ZHOU Hua*

* State Key Lab of Fluid Power Transmission and Control Zhejiang University

38 Zheda Road, Hangzhou, 310027 P. R. China (E-mail: jiangzhai@sina.com)

ABSTRACT One of the most important components for Seawater Reverse Osmosis Desalination (SWRO) system is the high pressure pump. The axial piston pump based on water hydraulics technology can be developed as a high pressure pump in small and medium scale SWRO system. To reduce the cost in the development process, a comprehensive simulation for the pump is critical to evaluate its mechanical characteristics and hydraulic performance before the prototype is made. In this paper, mechanics simulation tools such as ADAMS, and ANSYS were used to evaluate the kinematics and dynamics characters, stress and strain of critical components of the pump, and hydraulic simulation tool such as AMESim was used to evaluate the pressure of the cylinder. In conjunction with these simulation tools, the co-simulation of the pump provided an accurate estimation of the kinematics, main parts loading, hydraulic flow and pressure of the pump.

KEY WORDS

Axial Piston Pump, Sea Water Desalination, Simulation

NOMENCLATURE

PF∑uuv

: total force acting on the piston [N] SN

uuuv: reacting force of the slipper acting on the piston [N]

CNuuuv

: reacting force of the cylinder bush acting on the piston [N]

Cfuuv : friction force of the cylinder bush acting on the

piston [N] Pm : mass of the piston [kg]

PPuuv : hydraulic force acting on the piston [N]

rauuv : component of piston acceleration in r direction [m/s2]

zauuv : component of piston acceleration in z direction [m/s2]

0PV : dead volume of a single cylinder chamber [m3] PA : pressurized area of a single piston [m 2]

R : piston pitch radius [m] iθ : circular position of the piston [rad]

α : swash plate angle [rad] ω : angular speed of the cylinder of the pump [rad/s]

,I OA : orifice area of the cylinder chamber connected with portplate [m/s2]

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,I Op : the intake/output pressure at the port plate [Pa]

ρ : density of seawater [kg/m3]

dC : throttling coefficient [-] B : bulk modulus of seawater [Pa]

PLiQ : leakage flow from the clearance of the piston and the cylinder bush [m3/s]

INTRODUCTION

It is well-known that seawater desalination is an important technique for getting fresh water from sea. Compared to other methods, the reverse osmosis process is an energy-saving technology in seawater desalination projects. [1, 2] One of the most important components in Sea Water Reverse Osmosis (SWRO) desalination system is the high pressure pump. Compared with reciprocating pump and centrifugal pump, the axial piston pump based on water hydraulics technology has remarkable virtues such as high efficiency, low noise and small size. So this type pumps can be developed as high pressure pumps for small and medium scale SWRO desalination projects. Commercial products such as DANFOSS APP series [3] now are available in the markets of China. In order to develop domestic axial piston pumps for SWRO and reduce the cost in the development process, a comprehensive simulation for the pump is critical to evaluate its mechanical characteristics and hydraulic performance before the prototype is made. With the development of simulation technology, the so-called Virtual Prototype Technology (VPT) was used to comprehensive simulate the main characters of oil hydraulic piston pumps. [4-7] But for water hydraulic piston pumps, simulation studies were rarely reported in literatures. Because the working fluid and materials of the axial piston pump for SWRO are quite different from that of oil pump, it is meaningful to simulate the pump for SWRO based on VPT technology.

STRUCTURE AND SOLID MODELING

At present, the maximum flow of axial piston pump can not be compared to multi-stage centrifugal pump and even can not be compared to reciprocating pump, so multi-stage centrifugal pumps’ status in large-scale SWRO projects are still irreplaceable. The high-pressure pump which is axial piston structure should depend on its small size, high efficiency, low noise, all water lubrication and other advantages, and compete with multi-stage centrifugal pumps and reciprocating pumps in small and medium scale SWRO desalination projects. So its application is mainly targeted at the SWRO desalination projects of which the water production is about 120 ~ 150 m3/d. The general anti-osmotic pressure

in SWRO system is about 5.5 ~ 8MPa. For these reasons, the main technical parameters of the pump are showed in Table 1.

Table 1 Main technical parameters of the pump

Rated pressure [MPa] 8.0

Maximum pressure [MPa] 10.0

Nominal displacement [mL/r] 80

Rated speed [rev/min] 1500

Figure 1 The structure of the pump The structure of the pump for SWRO is shown in Fig. 1. The pump is base on axial piston principle. When the main shaft drives the cylinder to rotate, the structure can make the plungers for reciprocating movement along the cylinder axis. With the action of port plate, the water flow can be continually sucked from the inlet and discharged at the outlet. Compared with other structure, the pump using port plate as its flow distribution mechanism can have a better self-priming ability, can run at higher speeds. All this can make a result in a smaller size for a larger flow. The pump is lubricated by water directly, so the materials of port plate pairs, slipper pairs, piston pairs and ball joints are surface treated stainless steel and engineering plastic. Due to the restrictions of current development level of water-lubricated bearing, the pump is so called “half-axle” structure and only one engineering plastic bearing is adopted to support the cylinder-pistons group. The plate at the end of the cylinder is floating installed and has certain "flexibility". The floating plate under the action of the spring can contact with the port plate well, thereby this structure can reduce the internal leakage and improve volumetric efficiency. The pump’s shaft seal is different from the oil one which widely used lip seal and it adopted mechanical seal structure, so the housing of the pump

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can withstand greater pressure. The pump parts (including housing) are made of high quality stainless steel and engineering plastics, have excellent resistance to seawater corrosion and long service life. The geometrical characters of the main parts of the pump are complicated and many parts are manufactured with different materials. In order to acquire the accurate data

of the geometrical and inertial characters of the pump, the solid model of the pump was created by Pro/Engineer. After solid modeling in Pro/Engineer, the centers of gravity, masses, moments of inertia of the main moving parts can be automatic generated. Table 2 presents the main inertia information of the moving parts of the pump for simulation.

Table 2 Inertia information of the pump ’s main moving parts

Moment of inertia

Main parts Mass [kg] Ixx

[kg·m3] Iyy

[kg·m3]

Izz [kg·m3]

Ixy [kg·m3]

Izx [kg·m3]

Iyz [kg·m3]

Main shaft 1.218 1.751×10-4 3.069×10-3 3.065×10-3 0 3.661×10-5 0 Cylinder group 6.341 1.573×10-2 1.332×10-2 1.332×10-2 4.989×10-7 1.897×10-6 -7.457×10-6 Single piston 0.136 7.843×10-5 7.843×10-5 1.133×10-5 0 0 0 Single slipper 0.036 2.587×10-6 2.587×10-6 3.437×10-6 0 0 0 `Floating plate 0.851 8.511×10-4 8.516×10-4 1.673×10-3 0 0 6.121×10-8

MECHANCIAL MODEL

In order to seamlessly export the solid model files of the pump of Pro/Engineer to ADAMS, an ADAMS module named as Mech/Pro in Pro/Engineer environment was used to do this. In the environment of Mech/Pro and Pro/Engineer, the rigid bodies of moving parts of the pump were created and other all fixed parts such as

swash plate, port plate, housing with the cylinder slide bearing were created as a ground. Different types of joints were used between the moving and fixed parts, such as cylindrical joints, fixed joints, planar joints and spherical joints. After this, the model can be transport from Pro/Engineer to ADAMS. Figure 2 presents the models of the pump in Pro/Engineer and in ADAMS respectively. Table 3 illustrates the joints between the moving and fixed parts.

Figure 2 The solid model of the pump in Pro/Engineer and in ADAMS

Table 2 Joints between moving and fixed parts

Parts of the pump Ground Main shaft Cylinder group Single piston Single slipper Valve plate Ground - Cylindrical Cylindrical - - Planar

Main shaft Cylindrical - Fixed - - - Cylinder group Cylindrical Fixed - Cylindrical - Cylindrical Single piston - - Cylindrical - Spherical - Single slipper - - - Spherical - - Floating plate Planar - Cylindrical - - -

Pro/Engineer

ADAMS

Mech/Pro

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For the body of one piston, shown in Figure 3, the instantaneous force on the piston is given by:

( )P S C P C P z rF N N P f m a aΣ = + + + = +uuv uuuv uuuv uuv uuv uuv uuv

(1)

From Eq.(1) and Figure 3, we can know that the force acting on the piston is due to the geometry structure of

the pump, the rotation velocity and the hydraulic pressure in the cylinder. The forces on other parts, such as slippers, cylinder, valve plate, and main shaft, have the similar mechanical characters. For these reasons, the accurate profile of cylinder pressure is necessary for the mechanical model.

Figure 3 Diagram of the piston with instantaneous force

HYDRAULIC MODEL

Figure 3 also showed the sectioned view of the one piston within the cylinder block as it operates within the pump. From the kinematics and geometrical character of the pump, the volume of a single cylinder chamber Vci is given by

0 (1 cos ) tanPi P P iV V A R θ α= + + (2) If i represent the sequence number of the piston from the up dead point and the pump has N pistons, we can get

2( 1)i t iNπ

θ ω= + − (3)

Because of the low viscosity of the seawater, a high Reynolds number tends to characterize the seawater flow in and out of the cylinder chamber. This flow Qi may be modeled using an orifice pressure-flow equation, and this result is given by

, , ,2 sgn( )Pi d I O Pi I O Pi I OQ C A p p p pρ

= − − (4)

Figure 4 presents two kidney ports connected to the suction and delivery volumes and two silencing grooves

that allow the cylinder to pass smoothly from inlet to delivery. The areas of the variable orifices Ai and Ao depend on the position of the cylinder block with respect to the port plate. The pressure of the cylinder chamber varies with time to account for the periodicity change from the output pressure to the intake pressure. The intake pressure can set to be as the value of the inlet pressure of the pump, and the output pressure can be controlled by an orifice. Considering the continuity equation and ignoring the leakage of the cylinder, the dynamic pressure of each cylinder chamber is determined for the cylinder volume, so one can obtain

d dd d

Pi PiPi PLi

i

p VB Q Qt V t

= − −

(5)

and

Pi pP p A=uv (6)

According the principle represented by Eq. (2) - Eq. (5), the AMESim model which simulate the dynamic pressure of the cylinder chamber can be constructed. Figure 5 presented the schematic of the model in AMESim environment.

x

y y

z o o

ω

fs

Ns P az fZ

Nc

Nc

az

Cylinder

Slipper

θi

R

Piston

Floating plalte

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Figure 4 Diagram of the piston with instantaneous force

Figure 5 The hydraulic model of the pump in AMESim

From Figure 5, we can see that the pressure at the pump’s outlet is due to the variable orifice. The rotation velocity of the cylinder is due to the output of the pump’s mechanical model in ADAMS, and the hydraulic force acting on the piston will be calculated and transfer to ADAMS. These data exchanging process is implemented by the interface module in AMESim.

FEM MODEL In order to analyze the stress and deformation of the main parts such as pistons and main shaft, the rigid bodies of these parts have to be made to be flexible. This work can be implemented by the interface between ADAMS and ANSYS. The models of the parts in Pro/Engineer can seamlessly transfer to ANSYS without geometrical error. After the elements type, materials ’ properties, tagged point, rigid region and meshing method were set in ANSYS environment, the FEM models of the main parts such as the piston and main shaft would be generated and could be exported as MNF files. In ADAMS environment the rigid bodies of the pistons and main shaft were replaced by these FEM models, and the models of pistons, main shaft were flexible. By this method, the mechanical model of the pump in ADAMS was created as a mixture model with rigid and flexible bodies. Figure 6 presented the FEM model of the pistons and main shaft in ANSYS. Figure 7 presented the rigid model and the rigid-flexible mixture model in ADAMS respectively.

Interface module between ADAMS and AMESim

Delivery port

Silencing groove

Suction port

Cylinder slot

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Figure 6 FEM models of the piston and main shaft in ANSYS

Figure 7 Models of main parts of the pump in ADAMS

CO-SIMULATION RESULTS The co-simulation model of the pump was run in ADAMS environment with the communication between AMESim. Many simulation results can be acquired.

Figure 8 Angular velocities of the cylinder and the motor

Figure 8 presented the curves of angular velocities of the cylinder and the motor. The motor is a idealized driver which can keep a constant angular velocity at 1500rpm. We can see that the angular velocity of the cylinder have an overshoot at the initial time and will be stable after 0.005s. The reason for this phenomenon is that the main shaft model is flexible and its stiffness is finite.

Figure 9 Velocity and acceleration of one piston in z direction

Rigid model Rigid-flexible mixture model

ANSYS

Rigid region

Flexible region Flexible region

Rigid region

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Figure 9 showed the velocity and acceleration of the center gravity on one piston in z direction. The piston and main shaft models are flexible, so the kinematic characters are obviously different. The acceleration curve has many high-frequency ripple and the velocity curve is not a strict sinusoid.

Figure 10 Hydraulic and inertia force in z direction acting on one piston

Figure 10 presented hydraulic and inertia force components in z direction acting on one piston. The red curve represented the sum of hydraulic force and inertia force, and the blue represented the hydraulic force. The inertia force can be omitted when it compared with the hydraulic force.

Figure 11 Driving torque on the main shaft Figure 11 presented driving torque on the main shaft. The initial torque is about 2 order magnitude of the stable driving torque, the reason is that the driving motor is idealized and the main shaft is flexible. Figure 12 presented the flow rate and pressure at on the outlet of the pump, these curves have similar trend.

Figure 12 Pressure and flow rate at the outlet

Figure 12 Von Mise stress of the flexile body

Figure 12 presented the Von Mise stress of the flexile body at 0.0003s and 0.0422s. From the simulation results, the maximum Von Mise stress of the piston was occurred at 0.0002s and the value is 587.121 MPa. The maximum Von Mise stress of the main shaft was occurred at t=0.003s and the value is 429.401 MPa. But when the rotation velocity of the pump is stable, the value of

t=0.0003s

t=0.0422s

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maximum stress is sharply decreased. The maximum Von Mise stress of the piston was 209.318 MPa and the danger point was on its neck. The maximum Von Mise stress of the main shaft was only 82.322 MPa.

CONCLUSION This article illustrated the co-simulation process of an axial piston pump for SWRO. With the mechanical and hydraulic simulation tools such as ADAMS, ANSYS and AMESim, the kinematics and dynamics characters of the pump, stress and strain of critical components, the hydraulic characters such as the flow rate and pressure can were acquired. The results would benefit the improvement and optimal design of the pump.

ACKNOWLEDGEMENT

The authors would like to thank the Ministry of Science and Technology of PRC for the National "Eleventh Five-Year" Technology Support Program (No. 2006BAF01B03-02), the Ministry of Education of PRC for the Program for New Century Excellent Talents in University (No. NCET-06-0529). Both these research projects provide the funding for this work.

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