Sequential data assimilation (DA) was performed on three-dimensional flow fields of a circular jet measured by tomography particle image velocimetry (tomo-PIV). The work focused on an in-depth analysis of the flow enhancement and the pressure determination from volumetric flow measurement data. The jet was issued from a circular nozzle with an inner diameter of [Formula: see text] 20 mm. A split-screen configuration including two high-speed cameras was used to capture the particle images from four different views for a tomography reconstruction of the voxels in the tomo-PIV measurement. Planar PIV was also performed to obtain the benchmark two-dimensional velocity fields for validation. The adjoint-based sequential DA scheme was used with the measurement uncertainty implanted using a threshold function to recover the flow fields with high fidelity and fewer measurement errors. The pressure was determined by either the direct mode, with implementation directly in the DA solver, or by the separate mode, which included solving the Poisson equation on the DA-recovered flow fields. Sequential DA recovered high signal-to-noise flow fields that had piecewise-smooth temporal variations due to the intermittent constraints of the observations, while only the temporal sequence of the fields at the observational instances was selected as the DA output. Errors were significantly reduced, and DA improved the divergence condition of the three-dimensional flow fields. DA also enhanced the dynamical features of the vortical structures, and the pressure determined by both modes successfully captured the downstream convection signatures of the vortex rings.
In steam turbine control valves, pressure fluctuations coupled with vortex structures in highly unsteady three-dimensional flows are essential contributors to the aerodynamic forces on the valve components, and are major sources of flow-induced vibrations and acoustic emissions. Advanced turbulence models can capture the detailed flow information of the control valve; however, it is challenging to identify the primary flow structures, due to the massive flow database. In this study, state-of-the-art data-driven analyses, namely, proper orthogonal decomposition (POD) and extended-POD, were used to extract the energetic pressure fluctuations and dominant vortex structures of the control valve. To this end, the typical annular attachment flow inside a steam turbine control valve was investigated by carrying out a detached eddy simulation (DES). Thereafter, the energetic pressure fluctuation modes were determined by conducting POD analysis on the pressure field of the valve. The vortex structures contributing to the energetic pressure fluctuation modes were determined by conducting extended-POD analysis on the pressure–velocity coupling field. Finally, the dominant vortex structures were revealed conducting a direct POD analysis of the velocity field. The results revealed that the flow instabilities inside the control valve were mainly induced by oscillations of the annular wall-attached jet and the derivative flow separations and reattachments. Moreover, the POD analysis of the pressure field revealed that most of the pressure fluctuation intensity comprised the axial, antisymmetric, and asymmetric pressure modes. By conducting extended-POD analysis, the incorporation of the vortex structures with the energetic pressure modes was observed to coincide with the synchronous, alternating, and single-sided oscillation behaviors of the annular attachment flow. However, based on the POD analysis of the unsteady velocity fields, the vortex structures, buried in the dominant modes at St = 0.017, were found to result from the alternating oscillation behaviors of the annular attachment flow.
Due to the practical space limitation, the control valve in industrial utilities is usually immediately followed by a short flow passage, which would introduce considerable complexity into highly unsteady flow behaviors, along with the flow noise and structure vibration. In the present study, the unsteady behaviors of the steam flow inside a control valve with a T-junction discharge, when the valve operates under the choked condition, are numerically simulated. Toward this end, the detached eddy simulation (DES) is used to capture the spatiotemporally varying flow field in the serpentine flow passage. The results show periodic fluctuations of the aerodynamic forces on the valve spindle and periodic fluctuations of the pressure and flow rate at the two discharge outlets. Subsequently, proper orthogonal decomposition (POD) analysis is conducted using the velocity field and pressure field, identifying, respectively, the dominant coherent structures and energetic pressure fluctuation modes. Finally, the extended-POD method is used to delineate the coupling between the pressure fluctuations with the dominant flow structures superimposed in the highly unsteady flow field. The fourth velocity mode at St = 0.1, which corresponds to the alternating oscillations of the annular wall-attached jet, is determined to cause the periodic flow imbalance at the two discharge outlets, whereas signatures of the first three modes are found to be dissipated in the spherical chamber. Such findings could serve as facts for vibration prediction and optimization design. Particularly, the POD and extended-POD techniques were demonstrated to be effective methodologies for analyzing the highly turbulent flows in engineering fluid mechanics.
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