Retrieving of the initial moisture field in porous material based on temperature measurements during drying

Figures & data

Figure 1. The experimental stand for the paper vacuum drying experiment: (a) cross-section of the vacuum chamber, (b) position of thermocouples inside the chamber and paper roll.

Figure 2. Values of the sensitivity coefficients for all sought parameters at point no. 1 inside the paper roll.

Table 1. Results of the parameter regularization approach for different values of the regularization parameter (see Equation (19)).

Regularization parameter	0.0	1.0	10.0	100.0	1000.0
Cmt	0.27994	0.30547	0.30087	0.30032	0.30000
X0,1	0.03657	0.03626	0.03620	0.03614	0.03589
X0,2	0.05539	0.05481	0.05537	0.05676	0.05809
X0,3	0.04636	0.04569	0.04544	0.04417	0.04309
X0,4	0.02760	0.02746	0.02763	0.02885	0.02971
X0,5	0.04872	0.04778	0.04730	0.04510	0.04298
X0,6	0.04659	0.04646	0.04690	0.04807	0.04921
X0,7	0.03410	0.03389	0.03354	0.03287	0.03204
X0,8	0.05156	0.05116	0.05147	0.05225	0.05305
X0,9	0.04050	0.03985	0.04006	0.04003	0.04004
Water mass	0.021342	0.021113	0.021182	0.021172	0.021198

Table 2. Results of the initial distribution regularization (or water mass regularization) approach for different values of the regularization parameter (see Equation (26)).

Regularization parameter	0.0	1.0	10.0	100.0	1000.0
Cmt	0.27994	0.05140	0.09330	0.07719	0.05639
X0,1	0.03657	0.05346	0.04443	0.04580	0.05008
X0,2	0.05539	0.11372	0.07251	0.07542	0.08327
X0,3	0.04636	0.08622	0.06140	0.06407	0.07194
X0,4	0.02760	0.03661	0.03260	0.03340	0.03560
X0,5	0.04872	0.10209	0.06617	0.06887	0.07562
X0,6	0.04659	0.06392	0.05438	0.05575	0.05940
X0,7	0.03410	0.04945	0.04086	0.04197	0.04521
X0,8	0.05156	0.08884	0.06531	0.06770	0.07432
X0,9	0.04050	0.06665	0.05264	0.05492	0.06157
Water mass	0.021342	0.035950	0.027164	0.028148	0.031264

Figure 3. The water content distribution in the paper obtained from inverse procedure for: (a) parameter regularization approach, (b) water mass regularization approach.

Figure 4. Time history of temperature values at point no. 9.

Figure 5. Time history of temperature values at point no. 1.

Figure 6. Time history of temperature values at point no. 8.

Figure 7. Time history of temperature values at point no. 1.

Figure 8. The L-curve for the parameter regularization approach.

Figure 9. The L-curve for the mass regularization approach.

Table 3. Values of both terms of the objective function (18) and the value of the function itself for parameter regularization approach for different values of the regularization parameter.

λ			Δ
0.0	22.74	0.07202	22.74
1.0	24.25	10.18	34.43
10.0	20.99	2.053	41.53
100.0	24.64	2.656	290.2
1000.0	39.68	5.075	5114.8

Table 4. Values of both terms of the objective function (20) and the value of the function itself for water mass regularization approach for different values of the regularization parameter.

λ			Δ
0.0	22.74	0.4025·10^−1	22.74
1.0	22.99	0.2988·10^−2	23.00
10.0	22.83	0.7606·10^−7	22.83
100.0	22.99	0.1019·10^−7	22.99
1000.0	39.68	0.1891·10^−10	39.68