On-site calibration of a phase fraction meter by an inverse technique

Abstract

The formal calibration procedure of a phase fraction meter is based on registering the outputs resulting from imposed phase fractions at known flow regimes. This can be straightforwardly done in laboratory conditions, but is rarely the case in industrial conditions, and particularly for on-site applications. Thus, there is a clear need for less restrictive calibration methods regarding to the prior knowledge of the complete set of inlet conditions. A new procedure is proposed in this work for the on-site construction of the calibration curve from total flown mass values of the homogeneous dispersed phase. The solution is obtained by minimizing a convenient error functional, assembled with data from redundant tests to handle the intrinsic ill-conditioned nature of the problem. Numerical simulations performed for increasing error levels demonstrate that acceptable calibration curves can be reconstructed, even from total mass measured within a precision of up to 2%. Consequently, the method can readily be applied, especially in on-site calibration problems in which classical procedures fail due to the impossibility of having a strict control of all the input/output parameters

A Comparison of Two Solution Techniques for the Inverse Problem of Simultaneously Estimating the Spatial Variations of Diffusion Coefficients and Source Terms

“…where r* denotes the vector of coordinates and the superscript * denotes dimensional quantities. Equation (1) can be used for the modeling of several physical phenomena, such as heat conduction [1][2][3][4][5][6][7][8], groundwater flow [9][10][11][12][13] and tomography [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. We focus our attention here to a one-dimensional version of equation 1written in dimensionless form as…”