Decomposition of power number in a stirred tank and real time reconstruction of 3D large-scale flow structures from sparse pressure measurements

We consider the flow inside an unbaffled stirred tank at Re = 600 and decompose the pressure field into components that are constant, linear and quadratic with respect to the temporal coefficients of velocity POD (proper orthogonal decomposition) modes. The pressure components are used to analyse the power number of individual blades and blade combinations. We also employ an identification algorithm to derive a linear dynamic estimator that allows the reconstruction (in real time) of the instantaneous 3D velocity field from sparse pressure measurements at the impeller blades. The first pair of POD modes are reconstructed with reasonable accuracy using the pressure signal from a single sensor. The results improve with 6 or 12 sensors. Application of the estimator to Re=500 and 700 shows that it is robust to changes in operating conditions. The work opens the possibility for real time control of mixing with targeted feeding location and rate.

Automated summary

This study investigates the flow inside an unbaffled stirred tank at Re=600 and decomposes the pressure field into different components based on the temporal coefficients of velocity proper orthogonal decomposition (POD) modes. The pressure components are used to analyze the power number of individual blades and blade combinations, and a linear dynamic estimator is derived to reconstruct the 3D velocity field in real time from sparse pressure measurements. The results show that the estimator is robust to changes in operating conditions and has potential for real time control of mixing with precise feeding control.