Pressure Peak Compensation
The pressure peaks of up to 20 MPa could damage the pump and produce a lot of noise. To get a more robust pump, these pressure peaks need to be compensated. The peaks occur when the cylinder chamber is disconnected from the intake and outtake channels and the fluid is compressed. To shorten the period of disconnection from the channels and to give the fluid more room, an additional compensation chamber with an elastic wall was introduced. The cylinder chamber connects to the compensation chamber when it is disconnected from the pump’s main channels.
In the phase of compression, the compensation chamber is connected to the fluid volume in the cylinder; the surplus fluid can flow into the compensation chamber, which results in a reduction of the pressure peaks. When the pistons move back, increasing the volume of the cylinder chamber, the compensation chamber again connects to the cylinder and the fluid can flow back. As the different cylinder chambers (in most cases seven, nine, or 11 cylinder chambers are used) compress in an alternating cycle, one compensation chamber can be used for all cylinders.
First experimental tests showed that the introduction of the compensation chamber reduced the pressure peak value by 50% without decreasing the efficiency of the pump. The main objective of the interdisciplinary numerical simulation is to find the optimal layout of the compensation chamber. Differences in shape, elasticity, and volume, and their effect on the pressure peak values, are to be investigated. Computational fluid dynamics (CFD) models of the pump and FEA models of the elastic compensation chamber are developed.
Coupled CFD and FEA Simulation
A CFD model of the PWK pump, including the compensation chamber, was developed. For most simulations, a symmetric half-model of a pump with two cylinder chambers and the compensation chamber was used to keep the model relatively small and simple. A full model of a pump with seven cylinder chambers was also developed. The CAD geometry that was used to generate the models is depicted in Figure 2. Fluent (version 12.1) was used for the CFD simulations. The movement of the pistons and the commutating bushing (connecting the cylinder chamber with the intake and outtake channels, as well as the compensation chamber) was modeled with user-defined functions.
The wall of the compensation chamber is subject to pressure exerted by the hydraulic oil. To catch the deformation of the elastic wall, an Abaqus/Explicit (version 6.11) model — only consisting of the wall of the compensation chamber — was created. Abaqus/Explicit simulates the deformation of the elastic wall using the fluid pressure calculated with Fluent as a boundary condition. Fluent receives the deformation of the wall and updates the fluid domain mesh. This is a classic example of fluidstructure interaction. To pass the quantities between Abaqus/Explicit and Fluent, Fraunhofer SCAI’s code-coupling tool MpCCI was used.
This description of the simulation models will only refer to the symmetric half-model with two cylinder chambers. The mesh in Fluent consists of hexahedral elements. The increasing and decreasing of the cylinder chamber volume is realized by the dynamic layering method. The motion of the pistons and the bridge connecting the cylinder chamber to intake and outtake channels, and the compensation chamber, are implemented with user-defined functions.
The hydraulic oil is assumed to be slightly compressible — the density is defined with a user-defined function. The transient problem is solved using the Spalart-Allmaras turbulence model and a coupled solver for pressure and velocity. Two cycles of the pump (depending on the configuration) take 0.08 s. A time step of 1e-05 s or 5e-05 s is used. The high pressure in the outtake channel is 10 MPa and the low pressure is set to 0.2 MPa.
The geometry of the Abaqus/Explicit model can be seen in Figure 3. It consists of linear quadrilateral shell elements of type S4. Boundary conditions are employed to keep the top and bottom fixed. The left and right sides of the chamber wall are also fixed with the help of boundary conditions. The wall of the compensation chamber is slightly larger than the chamber itself, which can be seen in Figure 4. The overlapping parts on the left and right are kept in a fixed position due to pump design. The thickness of the elastic wall is 1.5 mm.