# Performance Study of External Gear Pump using CFD Analysis

Abstract:

In this article, CFD Analysis of an External Gear pump used in automotive industry is explained in detail. Article covers about the modeling, dynamic meshing, and transient simulation & Performance prediction of an oil pump. The focus will be on the study of pump performance by varying governing parameters like pressure head, mass flow rate, clearances, speed and temperature of fluid. Further pump volumetric efficiency predicted by CFD is compared with theoretical calculation.
Introduction:

An external gear pump is a positive displacement (PD) type of pump, generally used in high viscous flows. PD pumps are sometimes called constant-volume pumps because they maintain a constant flow, even if the system pressure varies the flow remains constant. In Automotive applications, Gear pumps are very commonly used as lubrication pumps for power transmissions. The pump is called External Gear pump because two opposing gears are mating external to each other. The gear pump is a precision machine with extremely tight fit and tolerance and is capable of working against high differential pressures.

Virtual Validation as part of Product Design Cycle:

The challenges in front of the design engineer is to develop an optimized design right at the first time in less time and cost. With the advancement of Simulations the product design time and cost can be reduced. Also, by using Virtual validation, concept finalization and optimized design can be achieved faster. Without simulation product performance and failures cannot be foreseen upfront, which leads to multiple prototyping and testing before achieving the final product. When Simulation is used concurrent to design phase, more insight to the product functioning can be ascertained which helps in achieving optimized design.

Theoretical Pump Displacement Calculation:

In case of external gear pump, the fluid in the suction side is delivered to the discharge side, through the fluid volume between the gear tooth spaces. Volume discharge (VD) by the gear pump in one revolution of rotor can be calculated by the below mentioned formula.

The flow rate can be calculated by multiplying Displacement with the speed of the pump. Theoretical flow rate is the expected flow by the pump with zero gap and slip. Hence the actual flow measured will be always less than theoretically calculated value.
CFD Simulation Methodology:
Fluid Domain preparation strategy:

Gear pump 3D model is cleaned up and simplification of small features like chamfers, fillets, etc. are made in order to generate good quality mesh. Then fluid volumes of Inlet & Outlet ports and Rotor core are extracted. Rotor core fluid volume includes tip clearance & clearance between gears. Appropriate Boundary names are created for assigning Boundary conditions, monitoring solutions during the simulation and post processing.
CFD Model Strategy & Setup details:

Gear pump flow areas are split into 3 domains inlet port, rotor core, and outlet port. Rotor core is meshed with Prism elements to enable solver to use 2.5D dynamic motion of rotor core (refer fig. 04). Initially, Rotor core is meshed with 2D triangular elements and extruded along the normal axis of the specific dynamic zone to generate prism elements. Then the ports (Inlet & Outlet) are meshed with tetrahedral elements and two Non-conformal interfaces will be created between the Ports (Inlet & outlet) and rotor Mesh.

Dynamic Motion is achieved in Fluent using 2.5 D Meshing method. Inputs for dynamic motion, such as rotor speed will be applied using User Defined Function (UDF). Based on the given speed and time steps, number of rotor positions will be calculated. For Each rotor position, mesh will be modified and smoothened to improve quality. Rotor gear faces are considered as rigid body motion.
Transient analysis is carried out in this case to capture the time based variation in the performance parameters (refer fig. 05).
Pump Performance Prediction:

The pump performance is studied by varying the pump’s critical parameters such as Clearances, Speed, Pressure Head and Temperature.
a. Effect of Pump Clearances on Pump Performance

3D CAD model of Gear pump should be as per the product design, with correct clearance (Tip clearance and clearance between Gears). CFD Simulation is carried out on three models with three different clearances, to study the sensitivity of clearance on volumetric flow rate.

As given in the below table, leakage of oil from rotor core to inlet is more with higher clearances as in Model 01. With minimum clearance in Model 03, leakage of oil is less. Modelling minimum clearance is very complex due to challenge in maintaining the good mesh quality with minimum clearances. However, modelling with correct clearances as per Product is important for the better prediction.

Based on this above result, Model 03 has less leakage, so it is chosen for all the subsequent parametric studies.
b. Effect of Pressure Head on Pump Performance

More pressure head at outlet causes the reverse flow (slip) through the clearance. With rise in pressure head at outlet, high slip is observed which causes reduction in volumetric efficiency of the pump. It is observed that volumetric efficiency is reduced from 89% to 82% between Case b4 and b6, due to increase in pressure head from zero to 1.75bar.

c. Effect of Speed on Pump Performance

Pump performance is studied by varying the rotor speed and compared with Theoretical flow rate for respective speeds.

With rise in speed of the pump, the flow rate increases linearly as expected. The above shown performance curve is for constant temperature fluid 135oC having dynamic viscosity 0.0047 Kg/m-sec equivalent to 5.5cSt. Density of the fluid assumed constant 855kg/m3. Rise in volumetric efficiency observed as speed of the pump increases. 20% rise in efficiency observed between case c2, c4 & c6 with respective speed 650rpm 1750rpm and 3000rpm at same pressure head 1.75bar.
d. Effect of Temperature on Pump Performance at Given Pressure Head

Pump is analyzed with low & high pressure head for 0 and 135 oC. It is observed that flow rate at peak pressure is more sensitive to oil temperature variation. So sensitivity study of different temperatures done at Peak pressure head of 1.75 bar.

Mass flow rate increase as temperature of oil decreases, due to increase in density at lower temperatures. This behavior is evident in the following cases d1 to d5 (refer figure 10 & 11).

Challenges faced:

• Maintaining the minimum clearances (40 micron) between the rotating parts. Which is crucial for the accuracy of Prediction.
• Capturing the transient flow phenomenon between the gears with acceptable quality criteria, achieved through re-meshing and smoothing.
• Applying Boundary conditions on the moving mesh
• Optimal Mesh count with less clearance and good quality mesh.

Conclusion:

CFD Analysis of an external Gear pump using Dynamic Meshing approach is studied to predict the performance curve, by varying design parameters such as Speed, Pressure Head, Temperature and Clearances.
From CFD Simulation, it is observed that leakage is more when pump clearances are more and hence pump efficiency is very less. The leakage also increases when pressure head at outlet is high, which is due to more oil slips back to inlet. Volumetric flow rate increases linearly when pump speed is increased from 650 RPM to 3000 RPM. However, at higher speed Cavitation phenomenon may take place. Beyond 3000 RPM, flow rate may not increase linearly with respect to speed. Pump flow rate is also sensitive to change in temperature, which is due to different viscosities for different temperatures. However, in Gear pump, change in flow rate due to temperature variation is expected to be minimal.
So with the help of CFD Simulation, pump performance and efficiency can be studied for the given design and design can be optimized with the help of CFD to meet the product requirements. It will be value addition and Cost reduction to design & develop Gear pump concurrent with CFD simulation.