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Correction for dynamic bias error in transmission measurements of void fraction
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Image of FIG. 1.
FIG. 1.

Flow modes of vertical two-phase flow. From left; bubbly flow, slug flow, churn flow, and annular flow.

Image of FIG. 2.
FIG. 2.

A cross section of the test case under study, illustrating the simulated geometry investigated with 13 beam lines marked in red in the figure. As the evaluated void fractions are presented below, these lines of sight are denoted 1–13 from the top downwards.

Image of FIG. 3.
FIG. 3.

The modeled temporal void distribution is a square pulse, ranging from a void fraction of 0–1, i.e., with an average of 0.5 and a variance of 0.25. The period is 50 ms.

Image of FIG. 4.
FIG. 4.

Schematic overview of the case study. Note that in a real measurement situation only steps (3) and (4) would be performed, the other steps are included here only for validation of the correction method.

Image of FIG. 5.
FIG. 5.

An example of the simulated distribution of N τ compared with the Poisson distribution (λ = 3.3). Bars represent 1σ uncertainty. It should be noted that although the distributions look very much alike, the Poisson distribution is slightly narrower, with a higher peak and lower tails. The sample variance of the simulated data is 2.6% larger than the variance of the Poisson distribution. This indicates an additional source of variance in the simulated data, i.e., the dynamic void fraction.

Image of FIG. 6.
FIG. 6.

The distribution of the estimated variance of the void fraction in 1000 simulated measurements on line of sight # 7. The true (simulated) variance is 0.25.

Image of FIG. 7.
FIG. 7.

The results of the void fraction estimates in line of sight #7. The true value of the void fraction is 0.5, i.e., there still remains a bias error after the correction procedure. However, the suggested correction method leads to a significant improvement in the void estimate.

Image of FIG. 8.
FIG. 8.

The estimated void fraction in the cylindrical two-phase flow system illustrated in Fig. 2 before and after applying the suggested dynamic bias correction on simulated data. The uncorrected void fraction estimates are presented with the solid curve, the corrected estimates using the suggested method are presented with the dashed curve and the true simulated void fraction is presented with the dotted curve. The bars in the figure represent the 1σ random errors of the void fraction estimates, based on the standard deviations of the void fraction estimates in the 1000 independent simulations.

Image of FIG. 9.
FIG. 9.

The bias errors of all the modeled temporal void distributions before and after correction. Note the different scales on the axes.

Image of FIG. 10.
FIG. 10.

The bias errors with and without performing the proposed correction as a function of the variance of the void fraction. Bars represent 1σ uncertainty.


Generic image for table
Table I.

Results of 1000 simulated void fraction measurements in 13 lines of sight through the simulated object. Errors are absolute errors expressed in void percent units.

Generic image for table
Table II.

The modeled temporal void functions and the result of the simulations of the bias error with and without the suggested correction procedure.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Correction for dynamic bias error in transmission measurements of void fraction