Numerical simulation of turbulent flow in the suction chamber of a gearpump using deforming mesh and mesh replacement

Abstract

The flow in the suction chamber of an external gearpump is numerically analysed. The evolution of the boundaries of the domain is very complex, and an arbitrary Lagrangian–Eulerian (ALE) formulation is used with mesh deformation and local remeshing. Nevertheless, a mesh replacement strategy is also adopted in order to avoid skewed meshes and allow for simulation of solid contact between gears. This process approximates a more realistic flow behaviour when the working pressure is larger than 10 bar, which is an important in fluid power systems where the pressure is usually greater than 100 bar.

Aside from the laminar model, which fails as a result of the vortex configuration in the suction chamber, Standard $k–\epsilon$, RNG $k–\epsilon$, Realizable $k–\epsilon$ and Reynolds Stress Models (RSM) are tested. The numerical flow is compared with experimental data obtained with Time Resolved Particle Image Velocimetry. Although all of the models failed in some respect, the RSM and RNG $k–\epsilon$ were the best choice provided its behaviour close to the gearing zone and general shape of the vortex distribution.

Introduction

External gearpumps are commonly used for high pressure pumping of oil in fluid power transmissions. The simplicity of design and low cost makes gearpumps especially appropriate for small systems. Nevertheless, the reduction in size and higher rotational velocity of the pump usually means an increase in vibration and noise and a reduction of pumping efficiency. It is worthwhile, therefore, to analyse the fluid flow inside the pump, to optimise design parameters that could reduce the impact of the size reduction. The present work is aimed at establishing a numerical procedure for an accurate computer simulation of the flow inside a gearpump.

The fundamental working principle of an external gearpump is the volumetric displacement of a space that opens and is consequently filled by fluid; transport of this fluid to another zone in the machine; and reduction of this space, which increases the pressure of the fluid and forces it through the outlet pipe. The increase and reduction of the space is facilitated by means of two gearwheels that mesh at the centre of the pump. The gearwheels teeth are steeling towards the suction chamber, where the space between teeth is filled and the system is enclosed by the pump case.

For the computation of flow, an Arbitrary Lagrangian–Eulerian [1] approach is used. In the usual Eulerian method, the mesh is steady and the Eulerian Navier–Stokes equations have to be solved, including the convective term. With a pure Lagrangian method, the mesh moves with the fluid particles and the convective term vanish, but the mesh motion can be difficult to compute. In an ALE approach, an intermediate solution is adopted and the mesh is not steady, but instead moves independently with the fluid particles.

Vande Voorde et al. [2] used an ALE approach with a two external gear compressor, forming a structured mesh at each timestep by solving a Laplace equation for a potential function with suitable boundary conditions. Strasser [3] performs a simulation with an external gearpump very similar to the one used in the present simulation, but for mixing purposes. He deforms and remeshes the grid at each timestep. This requires more computational effort, but the mesh does not need to be structured. Houzeaux and Codina [4] adopted quite a different method by taking advantage of the periodicity of the gear motion and constructed 10 meshes for each gearing period. The simulation was performed by interpolating the solutions for each timestep to the next mesh.

Of these three approaches, the first has the disadvantage of requiring a structured mesh. The second is inconvenient because the mesh is distorted unless the timestep is very small. The third method, although it enables the use of high quality meshes, requires the timestep to be quite large (a tenth of the gearing period) unless a large number of meshes are constructed.

Moreover, of these approaches, only the third correctly deals with the problem of the contact point between gears. The first two consider that if the gap between gears is sufficiently small, the leakage is negligible. This may be acceptable if the pressure difference between inlet and outlet is not high. However, this issue cannot be avoided when the pressure difference is important. In the simulation by Houzeaux and Codina [4], the contact is already integrated into the mesh since there is no actual gear movement relative to each other.

In the present work, the mesh is deformed and locally remeshed, like in the simulation by Strasser [3], however, the mesh is replaced after a predefined number of timesteps in order to avoid large distortions. Ten different meshes are used in each gearing period, similar to the simulation by Houzeaux and Codina [4]. This allows for (i) a substantial mesh quality, (ii) a controllable timestep and (iii) contact between gears, as explained in Section 2.1.

This work is mainly concerned with the turbulent flow in the suction chamber of a gearpump. It is suggested that the inlet chamber has a major influence on the performance of the pump and, therefore, it is worthy to investigate the flow characteristics and how the geometry of the pump can be modified in order to increase its efficiency. It has been experimentally shown [5] that, although the velocity in the chamber is not high enough to have a turbulent Reynolds number in the sense of pipe flow, the stirring produced by the gears, which result in sudden variations in volume and pressure, produces an injection of energy that cannot be dissipated by molecular viscosity and, therefore, turbulence arises. Laminar; $k–\varepsilon$, and its variants RNG and Reliable; and Reynolds Stress Models (RSM) are tested. The laminar model has been used to demonstrate the turbulent characteristics of the flow. $k–\varepsilon$ models (Standard, RNG and Reliable) [6] have been the most used turbulent models in Engineering for decades. Although the RSM consumes an appreciable amount of computational resources, the quality of the simulation has been confirmed, primarily for anisotropic turbulence [7].

In this two-dimensional simulation, the fluid is typically mineral oil, the characteristics of which are shown in Table 1. The geometry and operating conditions of the pump are presented in Table 2 (also see Fig. 2). The meshing and turbulence models used are described, in Section 2. The results are presented and discussed in Section 3 and, finally, conclusions are described in Section 4.