lyu, Xipeng
(2022)
An improved SPH method and its application in the turbulence multiphase flow in the bearing chamber of aeroengine.
PhD thesis, University of Nottingham.
Abstract
This thesis is devoted to the propose a novel particle stabilization scheme, improve the existing Smoothed Particle Hydrodynamics (SPH) and apply it to the multiphase turbulent flow in the bearing chamber of an aeroengine.
In SPH, the motion of particles is based on symmetric interparticle forces, such that the conservation of momentum is guaranteed. Interparticle forces, however, can not prevent particle clustering. Clustering may occur for several reasons. A fundamental issue is the socalled tensile instability, which is caused by the properties of the kernel gradient. Clustering may also be caused by discontinuities in the pressure (e.g. due to surface tension) and the pressure gradient (e.g. due to gravity), which may lead to instabilities around the interface between two fluids (Kruisbrink et al., 2018 [1]). Wall penetration is also a form of particle clustering.
Standard SPH is known to suffer from particle clustering, which affects the stability of simulations in particular in cases with large deformations and high fluid velocities. One of the grand challenges defined by the SPHERIC Steering Committee is the clustering of particles. Kruisbrink et al. (2018) developed a particle collision model to reduce particle clustering. This model is quite effective and performs the best for socalled inelastic collisions. However, by changing the approach velocities of colliding particles, the model is energy dissipating to some extent.
As further work, it is investigated in this thesis whether the original particle collision model may be further developed into a shift model, such that there is no dissipation of global kinetic energy. This has resulted in the particle collision shift model, where the positions of colliding particles are changed, but not their velocities. Thus, kinetic energy is conserved. It is demonstrated that potential energy is also conserved in a constant force field, like gravitation. With these features the particle collision shift model is nondissipative in the simulation of many real cases.
To allow for the modelling of the multiphase flow in a bearing chamber, characterized by an incompressible (oil) phase and a compressible (air) phase, a compressible flow solver is needed. For this purpose, weakly compressible SPH is used. Moreover, at the higher rotational shaft speeds in a bearing chamber, the air flow is turbulent. Turbulence modelling is relatively underdeveloped in SPH. Some available SPH turbulence models and models from the CFD literature are explored, in particular SPH versions of the mixing length and SpalartAlmaras turbulence models, as made available in the WCSPH code Hydra of the University of Nottingham.
The particle collision shift model in WCSPH is used in combination with socalled SPH, a method from the SPH literature to reduce highfrequent fluctuations in the density and pressure. In this thesis a simplified version of SPH is used, to decrease the computational cost.
The abovementioned SPH modelling approach is used to validate the two turbulence models in WCSPH against the commercial CFD code Ansys Fluent. As benchmark case the TaylorCouette flow between two concentric rotating cylinders is chosen, as a simplified bearing chamber without sump and vent pipes. A number of twodimensional configurations is studied, at different rotational speeds and radius ratios of the cylinders, under single phase and multiphase, laminar and turbulent flow conditions.
The agreement of the single phase, laminar and turbulent SPH results with those of Fluent is good in terms of velocity and pressure profiles, and reasonably well in terms of turbulent viscosity. The turbulent viscosity obtained with the SpalartAlmaras turbulence model matches better with Fluent than that of the mixing length turbulence model, but the model is computationally much more expensive.
The agreement of the multiphase, turbulent SPH results with Fluent is reasonable, in terms of velocity and pressure profiles, although the latter show more pressure fluctuations. The turbulent viscosity is underpredicted by both SPH turbulence models, compared to that of Fluent, whilst the difference between the two SPH turbulence models is small.
Finally, two and three dimensional SPH simulations are performed of a simplified bearing chamber with one suction pipe. Multiphase turbulent flow conditions are modelled with air around a rotating inner shaft and a liquid film along the outer chamber wall. Surface tension is taken into account, as modelled by the continuum surface force model of Brackbill, in Fluent as well as SPH. The results of the 2D bearing chamber show similar trends as those of the corresponding TaylorCouette flow. The results of the 3D bearing chamber show quite some dissipation of energy, due to a turbulent viscosity, which is much higher than that of Fluent, and affects the velocity distribution.
In summary:
An energyconserving shift (collision shift) model to prevent the particle clustering is derived and through the comparative study with the Fickian shift model, the superiority of the collision displacement model in terms of accuracy, stability, computational efficiency and dissipation characteristics is obtained.
A hybrid method which combines the socalled δSPH and the collision shift model is proposed. The potential of this hybrid method in application with multiphase flow is demonstrated in five benchmark case studies.
Progress has been made in the turbulence modelling with SPH in applications that are moving towards that of a bearing chamber in aeroengines. In particular the results of the twodimensional simulations are promising, as they show a reasonable agreement with those of Fluent, whilst further investigation is needed in the application of the SPH models to three dimensional cases, towards the real bearing chamber.
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