| For a typical well balanced impeller system where the centers of gravity of the impeller and shaft are perfectly aligned with the axis of rotation and this in turn is perfectly aligned with the vessel centerline, the fluid motion produced by the impeller is not, in general, symmetric in the spatial structures including primary circulation loops, trailing vortices behind the impeller blades and turbulence eddies. The flow in such systems is also unsteady due to low-frequency macro-instabilities, blade passing frequency pseudo-turbulence and high-frequency turbulent motions. The asymmetric and unsteady fluid motion exerts an imbalanced and unstable load on the impeller and causes the elastic shaft to deflect instantaneously. The resulting lateral movements of the impeller in turn induce further nonuniform and unstable flows around it. This behavior in stirred vessels is an example of the bidirectional interactions between a flowing fluid and a flexible structure.In stirred vessel operation, the function of the shaft is to transmit power from the drive train to the impeller, when the resulting torque must be borne by the shaft. Meanwhile, an unstable bending moment is also exerted on the shaft due to the impeller lateral vibration caused by the complex Fluid-Structure Interactions (FSI) in stirred vessel. In the mechanical design of mixing equipment, the underestimation of the shaft bending moment may lead to plastic deformation and fatigue failure of shafts and vessels. However, it is difficult to theoretically determine the shaft bending moment because of the complex coupling dynamics of the FSI in stirred tanks. In this thesis, the shaft bending moment, as one of results of the FSI in stirred vessels with Rushton Turbine (RT) and Pitched Blade Turbine (PBT), was measured using a moment sensor equipped with digital telemetry. The basic characteristics of the bending moment and the effect of impeller mass imbalance, liquid level and gas flow on the bending moment were studied.The analyses of amplitude and Power Spectral Density (PSD) of the shaft bending moment measured show that the bending moment amplitude distribution is well described by Weibull distribution, which reflects that the material elastic reaction pulls the shaft back towards the axis of rotation after the shaft bending deformation. In the range of N/fn>1/nb and N/fr<1(N, fn, fr and nb are operational speed, natural frequency, resonant frequency and blade number, respectively), the dimensionless mean shaft bending moment trend over N/fr manifests a "V" shape, which results from two kinds of resonances. When N/fn approaches1/nb, the FSI resonance occurs and the frequencies related to blade passing frequency are evident in the bending moment fluctuation; when N/fr approaches1, the self-excited resonance due to stirring structure mass imbalances occurs and speed frequency is evident in the bending moment fluctuation. The mean shaft bending moment increases monotonously with the impeller mass imbalance. When the ratio of liquid level height to impeller diameter H/D approaches1.5and2for RT, or1.25and1.7for PBT, the mean shaft bending moment gets stable and keeps constant, respectively. The relative mean shaft bending moment trend over gas flow number presents an "S" shape.Nevertheless, it is difficult to experimentally have a further insight into the FSI in stirred tanks because the shaft bending moment, as a compound result in the FSI, cannot reflect fluid or structure interaction individually. The components causing the bending moment, including fluid loads on the impeller (pressure and viscous stress) and structure loads on stirring structure (inertial load and gravity), are always accompanied mutually due to the FSI. In this thesis, the numerical simulation of the FSI in the RT stirred vessel was performed by means of coupling Computational Fluid Dynamics (CFD) based on Finite Volume Method (FVM) with Computational Structure Dynamics (CSD) based on Finite Element Method (FEM). In the simulation, the governed equations of flow around FSI interfaces are described by Arbitrary Lagrangian-Eulerian (ALE) and controls of mesh motion employ a combination of dynamic mesh with sliding mesh method.The results predicted by the simulation are in good agreement with experimental data, in which relative errors of RT power number are less than5%, and the maximum relative errors of the dimensionless mean shaft bending moment and standard deviation are both less than15%. Analyses of amplitudes of the lateral forces on the RT show that dimensionless lateral fluid force almost keeps constant at different speeds, approaching0.04for RT; dimensionless lateral structure force increases slightly with speed, approaching the simplified theoretic analysis. Meanwhile, it was found that the mean phase difference between the lateral fluid and structure forces approaches90°. Analyses of PSD of the lateral forces on the RT show that the frequencies in the fluctuation of the lateral forces mainly include the rather low frequency, the speed frequency and the blade passing frequency. The low frequency is always prominent in the fluctuation of the lateral fluid force, resulting from macro-instability of bulk flow in stirred tanks. The speed frequency always occurs in the fluctuation of the lateral structure force, resulting from the unbalanced rotation of the impeller, and also in the fluctuation of the lateral fluid force when the stirring structure is remarkably unbalanced, being induced by the unbalanced rotation via the FSI in stirred tanks. The blade passing frequency is evident in the fluctuation of the lateral structure force when the stirring structure is well balanced, which is induced by pseudo-turbulence of blade passing frequency via FSI.In this research, an experimental study of the shaft bending moment caused by the FSI was completed and the results can provide quantitative data for the mechanical design of mixing equipments, such as amplitude mean, standard deviation and peak deviation. A computational study of the FSI was performed by means of a coupling CFD with CSD method and the key information of individual fluid or structure interaction is helpful to get a better understanding of the FSI in stirred tanks. |
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