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CFD Modeling of an Internal Rotary Pump
Posted Wed November 14, 2001 @06:18PM
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Application The internal rotary pump is a positive displacement type device that is commonly used to pump the oil in an automobile engine. For a simple positive displacement device, it exhibits relatively low pulsation compared to other gear type pumps. Internal rotary pumps feature an inner gear (idler) mounted eccentrically within a larger gear (rotor). Pumping action is generated when the gear teeth unmesh, causing the gear-gear cavity to expand (inflow), and mesh, causing the gear-gear cavity to contract (outflow).


A generic internal rotary pump. (courtesy pumpschool.com)

Internal rotary pumps are used for practically all capacities and pressures. Internal rotary pumps can be operated at varying speeds and in reverse which provides a large amount of flexibility. The mechanical efficiency of internal rotary pumps when handling liquids with good lubricating value is good. Overall efficiency increases with flow rate and discharge pressure to a maximum of around 75%.


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The pump studied is an example of a special class of internal rotary pump which utilizes cycloidal gear profiles [pdf file]. This means that the gear profile is generated by rolling, without slippage, a circle around a larger fixed circle. Usually the outer gear, or trochoid, is generated in this fashion and the inner gear is the conjugate shape to the outer gear. This leads to the term generated-rotor or gerotor pump.

In this example, there are nine lobes on the outer gear and eight lobes on the inner gear. The outer gear maximum diameter is approximately 45 mm and the inner gear maximum diameter is approximately 41 mm. The rotor thickness is 10 mm and the outer gear is revolved at 1000 RPM. The working fluid is oil and the flow is turbulent.

The gerotor pump was analyzed using the moving mesh capability in CFX-TASCflow. When the moving mesh feature is used additional terms are included in the governing equations to account for the movement of the grid. These terms account for the velocity of each grid node, since the position of the grid nodes change with time. The grid topology and number of nodes remain constant whereas the nodal position and velocity change each timestep.

A CFX-TASCtool macro was written to create the initial structured mesh in the rotor using gear profiles that were imported from a file. The rotor mesh is updated on-the-fly in the CFX-TASCflow flow solver by a user-accessible subroutine. This subroutine adjusts the rotor node positions at the start of each time step. Minimum grid skew is about 20 degrees, while maximum aspect ratio is about 24:1.


The deforming computational mesh in the gerotor pump.

A minimum clearance of 0.5 mm was used between the inner and outer gears, however the actual clearance is approximately an order of magnitude smaller. Later simulations will attempt to determine the limits of the allowable clearance. Limiting factors will likely be grid aspect ratio and geometric precision. High aspect ratios may require using the flow solver in double precision.

CFX-HEXA was used to create the simple intake and outlet port grids. A non-matching grid interface was used to connect the intake and outlet port grid to the rotor grid. The grid interface is updated by CFX-TASCflow at the start of each time step after the rotor grid has been moved to its new position. A specified total pressure inlet and static pressure outlet were used to define the flow boundary conditions. The inlet to outlet pressure ratio was specified as 10 psi.


Flow streak lines in the ports and rotor colored by speed.
Lower speed is blue, and higher speed is red.

In theory, a trochoidal-type pump should be optimally designed, however, losses produced by gear meshing and the influence of the intake and output ports reduce the efficiency of the pump. CFD can be used to analyze these losses and make design modifications which can improve performance. In the plot above, flow streaklines are seen in the intake port, rotor, and output port. It can be easily seen that the flow in the intake and output ports near the rotor is not streamlined and, therefore, not optimal.


Static pressure in the ports and rotor.
Lower pressure is blue, and higher pressure is red.

In the plot of static pressure above, it is evident that there is a large pressure gradient across the tooth interface as it progresses from the intake to outlet port. The pressure gradient drives the flow in the reverse direction resulting in leakage, thereby reducing the efficiency of the pump.

CFD analysis of this gerotor pump has shown the detailed flow characteristics in the intake and output ports and in the rotor. Such observations are difficult, expensive, and time-consuming to achieve with testing. CFD analysis is shown to be an effective tool for optimizing the design of this class of hydraulic machine.

Rob Broberg specializes in CFD turbomachinery applications at ANSYS CFX in Waterloo, Ontario, Canada. He can be reached at ansysinfo@ansys.com.

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