Limitations of the CFD Model

Physical modelling, mesh generation, computational solution and post-processing of results harbour a number of uncertainties. The various uncertainties and errors that can exist within a computational simulation are summarised as follows (NASA, 2008; Gülich, 2010):

1. Physical approximation error due to uncertainty in the formulation of the model (physical modelling error) and deliberate simplifications of the model (geometry modelling error). 2. Computer round-off errors develop with the representation of floating point numbers on

the computer and the accuracy at which the numbers are stored. When compared with other errors these are often considered to be negligible.

3. Iterative convergence error exists because the iterative methods used in the simulation must have a stopping point eventually.

4. The discretisation errors are those that occur from the representation of the governing flow equations and other physical models as algebraic expressions in a discrete domain of space and time.

5. Computer programming errors are “bugs” and mistakes made in programming or writing the code.

6. User errors are caused by negligence, lack of knowledge of the complex computational code and of physical phenomena as simplifications are made due to computational cost and lack of resources.

The computational methodology has been systematic, followed established guidelines and recognised methods, and wherever possible further simulations have been carried out to estimate uncertainties. The total computational error calculated using the root-sum-square method is 0.46% (see 4.6 Summary of Computational Modelling Methodology). However, there might be further errors imposed by the choice of turbulence modelling. The pump experiences recirculation and the flow field is complex by nature; these types of flows are difficult to model correctly. The choice of turbulence model needs to be considered carefully and whether a Reynolds-Averaged Navier-Stokes style model is capable of modelling this type of flow at all. The under-performance of the CFD model may be due to the fact that it is not capturing enough detail and as a result the turbulence may be under resolved. Although the chosen turbulence model was compared to other Two-Equation URANS models, it was not

164 compared to a Scale Resolving Simulation model such as Large Eddy Simulation, Scale Adoptive Simulation and Detached Eddy Simulation which would be more accurate but also computationally more expensive.

Discretisation errors caused by the mesh are unpredictable but can be severe. This error can be quantified and reduced considerably by carrying out successive mesh refinement, using different types of meshes and searching for mesh-independent solutions. A recognised method for the analysing mesh independence (Roache, 1994) was performed in 4.5 Mesh Independence Study and the solutions were well within the asymptotic range. However, the mesh is unstructured due to a combination of limitations imposed by the ANSYS® Meshing® software and the complex geometry, and as such any discretisation errors could be carried forward through the mesh independence study. Furthermore, the difference in volume ratio of the elements close to the domain interfaces of the axial clearance bodies were larger than the thickness of the elements in the clearances. The size of the interface elements was reduced to improve the mesh quality in this aspect, but the problem was only partially solved. A good quality mesh can be obtained with fewer elements for a structured mesh in comparison to an unstructured mesh but it requires the use of a more advanced mesh generation software. Attempts were made to create a hexahedral impeller mesh in order to quantify potential errors of the tetrahedral mesh. Before creating a hexahedral mesh, the volume of each of the basic impeller parts (i.e. the fluid between the blades, of which there are 10 bodies) had to be split into five smaller volumes (see Figure 8-18). By splitting the basic impeller element into five volumes, they should be able to be discretised using a swept mesh. To still be able to use the swept mesh method on the clearance volumes the faces need to match those of the impeller volumes, hence why the axial clearance volumes have also been split along the same circular axis as seen in Figure 8-19.

However, the ANSYS® Meshing® tool does not allow the user as much freedom as more advanced mesh generation software. The sweep meshing method restricts the use of inflation layers. The ‘MultiZone’ method (see Figure 8-20) therefore seems to be more suitable, however the addition of inflation layers impacts the quality negatively. Furthermore, an improved boundary layer resolution results in a mesh with a higher ratio of tetrahedral elements to hexahedral elements.

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Figure 8-18: Volume splitting of a basic impeller element.

Figure 8-19: Volume splitting of axial clearance elements.

Figure 8-20: MultiZone mesh of an impeller fluid volume.

The computational model captures the basic trend of torque versus rotational frequency even though quantitative differences are observed, particularly at higher flow rates. This is in part due to the mechanical losses excluded in the computational prediction, but geometrical inaccuracies which were not included in the computational model can also be influential. The simplification of the inner axial clearance ‘disks’ as detailed 4.2.1.2 Axial Clearance Reduction was done to reduce complexity and streamline the geometry generation for the parametric

166 clearance study. A test case showed that only small differences in pressure exist. However, there were no experimental torque values to compare against. A case featuring one of the experimental test pumps with the added inner clearance disks has been simulated to evaluate the effects on the predicted torque. As before, the inner clearance disks are assumed to be uniform in thickness. The results show however that there is hardly any difference in the predicted torque with and without these clearance disks.

The inherent, periodically unsteady, flow-induced impeller oscillations occurring in the regenerative pump; coupled with high rotational speeds lead to undesired effects such as mechanical vibration, noise and impeller deformation. These dynamic conditions occurring during operation are not captured by the computational model and so a Finite Element Analysis was carried out to investigate the deformation of the experimental test impellers. The study is presented in the next chapter and provides further insight into the disparity between the computational and experimental results.