Unsteady Numerical Simulations of the Flow Related to the Unstable Energy-Discharge Characteristic of a Medium Specific Speed Double Suction Pump
Regions of positive slope in the pressure-discharge characteristics can result in a reduction or even lack of damping of system instabilities. They are therefore one of the major concerns in design and operation of centrifugal pumps as they are limiting the admissible operating range. The considered preliminary hydraulic design of an industrial double suction pump of medium specific speed n = 0.410 (0.205 per impeller side) shows a marked saddle in the energydischarge characteristic associated to a sudden drop of efficiency versus discharge at part load. Unsteady RANS type flow simulations are performed using hexahedral meshes with 2.5 million nodes to model the inlet casing, the shrouded double sided impeller with 2 x 7 blades, the diffuser with 12 blades and the volute. In unsteady solution monitoring, low frequency (below blade passing frequencies) phenomena are noticed. Therefore, simulation times of up to 10 impeller revolutions at each flow rate are requested to achieve statistically steady behavior of the flow judged on global performance numbers and circumferential flow rate distribution. The numerical simulations emphasize a drop in the characteristic, though at a lower flow rate than found on the test rig. It is shown to be associated to a one-sided separation in the diffuser, further leading to an unbalanced flow rate distribution of about 10% of flow rate between both sides of the impeller. There is a region of hysteresis, where both configurations with balanced and unbalanced flow rate distributions can be obtained for the same global flow rate. The asymmetric flow distribution leads to asymmetric velocity profiles at the impeller-diffuser interface which results in a strongly vortical flow in the diffuser channels, where an important amount of energy is dissipated in regions of increased viscous and turbulent shear.
Pump-Turbine Rotor-Stator Interactions in Generating Mode: Pressure Fluctuation in Distributor Channel
Investigation of the rotor-stator interactions of a reduced-scale model 0.19 ν= pump-turbine in generating mode is presented for the maximum discharge operating condition. This operating point is chosen in order to have the most important rotor-stator interactions. The numerical simulation of the unsteady flow is performed with CFX 5.7™ for a computing domain which is extended to the full pump-turbine from the spiral casing to the draft tube. A computing domain embracing the full geometry enables to minimize the errors, streaming focus the boundary conditions, the periodic interface or the pitch ratio of rotor-stator interface. It also allows considering the fully non uniformity of the in coming flow field from the spiral casing. The pressure measurements are performed with piezoresitive miniature pressure sensors located in the distributor channels. The pressure fluctuations for one distributor channel obtained from the numerical simulation present a very good agreement with experimental data. The numerical result analysis shows, how the pressure fluctuations at blade passage frequency (BPF) and its harmonics vary along a distributor channel of the pumpturbine. The maximum pressure amplitude of BPF occurs in the rotor-stator zone, but it decreases very fast backward to the stay vane. However, the pressure amplitude of the first harmonic corresponding to 2 times the blade passage frequency spreads to the spiral casing highlighting the -2 precessing diametrical mode resulting from the modulation of the interacting stationary and rotating flow field.
Refinement of crystal structure parameters using convergent‐beam electron diffraction: the low‐temperature phase of SrTiO3
The method to refine crystal structure parameters (atom positions and Debye–Waller factors) using convergent-beam electron diffraction (CBED), which is applicable to crystal structure analysis of a small specimen area down to a few nm in diameter, is studied. The line profiles of higher-order Laue-zone reflections are recorded using imaging plates. Theoretical intensities are calculated based on the dynamical theory of electron diffraction with the aid of the generalized Bethe approximation to shorten calculation time. The structural parameters are determined by fitting the experimental profiles with the theoretical ones using a nonlinear least-squares method. The present method has been applied to the low-temperature phase of SrTiO3. The structural parameter or the rotation angle of the oxygen octahedron has been determined to be \varphi = 1.12 (4)°, which shows good agreement with that obtained from electron spin resonance experiments.