Sensitivity analysis on a CFD model for prediction of a gear pump leakages

In the field of modern fluid mechanical problems, the evolution of numerical simulation codes and the availability of high-computational-power platforms allowed the spread of Computational Fluid Dynamics (CFD) techniques with the aim of predicting complex fluid-flow phenomena. CFD is frequently used on applications where the object needs a detailed analytic study in spite of the lack of parameters. A typical example is represented by the clearances inside a volumetric pump during his functioning. This uncertainty affects other potential sources of CFD errors like the numerical ones, caused by the discretization of the equations, the modelling ones, due to the description of fluid phenomena and, at lower lever, the user or software errors. A complex model, that contains many important uncertainties, is presented in this work, which main purpose is a sensitivity analysis on key operating parameters of a gear pump studied with both numerical and experimental techniques. In particular, the study is focused on the calibration of the fixed displacement machine clearances. Gear pumps represent the majority of the fixed displacement machines used for flow generation in fluid power systems. The internal conformation of this system contains many undetermined variables, due to both the manufacturing techniques and the breaking-in pressure, that strongly affect the pump performance. The 3D CFD model of this type of products is particularly difficult to develop [1], because of the deforming volumes in-between the gears, the structural deformation of the case during the functioning and the moving operating point. These transient modifications of the initial geometry of the pump highly influence the outer mass flow and it must be estimated through mathematical methods. A classical methodology was used for the purpose by starting from the 3D geometry of the pump. Subsequently, the fluid domain was extracted, the mesh was created and the moving boundary conditions were set. The deformation of the fluid domain was managed by the skewness level of the mesh and deformed with a smoothing and remeshing approach by using a dynamic mesh. The model was solved with a commercial code, and then post processed. The comparison between experimental and numerical results, united with the widely investigated Richardson Extrapolation (RE) method for the discretization error estimation [2], led to an accurate sensitivity analysis of the clearances. The future aim of this work is to obtain, thanks to the sensitivity analysis, the pump volumetric efficiency as a function of the leakages between the machine gears and case, which highly affect the numerical results. A future purpose is to provide the characteristic curves of the gear pump depending on the breaking-in pressure. The results obtained is a sensitivity analysis that is able to compare the gap between the gears, at different mesh level of accuracy, with the experimental data in order to evaluate the influence of the analyzed parameters on the numerical results. [1] S. Mancò, N. Nervegna, "Simulation on an external gear pump and experimental verification" In Proceedings of the JHPS International Symposium on Fluid Power, 139-152, (Tokio, Japan,1989). [2] Celik, I. B., Ghia, U., Roache, P.J. Freitas, C. J., Coleman, Raad, P. E., "Procedure for Estimation and Reporting of Uncertainty Due to Discretization in CFD Applications," ASME J. Fluids Eng., 130(7), (2008).