Consider then how the results of the matrix calculation model differ from the results of the earlier conventional calculation model to see that can the new model offer any extra accuracy for the overall performance prediction. Results are shown in figure 64.
Figure 64. Comparison between new and old calculation models.
In the above figure, there are fouling factors that are needed to get the results to match the measurements. Red spots show the fouling factors needed in a certain case so that the fouling factor used in the earlier conventional calculation model can be seen from the x-axis and the fouling factor used in the new matrix calculation model can be seen from the y-axis. If a red spot is above the blue line and both fouling factors are less than one, results from the matrix calculation model have been corrected less and thus the matrix method has been more accu-rate. If both fouling factors are greater than one, the situation is vice versa. If only one of the fouling factors is greater than one, the place of the spot does not tell which of the models were more accurate. However, there are just a few of these kinds of spots. As can be seen from the figure, both models give quite similar results. However, the new matrix model seems to offer a small improvement to the calculation accuracy. That is also the truth since the average absolute difference between fouling factor and value of one was 0,183 in the case of the matrix calculation model and 0,200 in the case of the conventional calculation model.
9 SUMMARY AND CONCLUSIONS
The purpose of this Master’s thesis was to develop a heat transfer calculation model for back-pass tube bank heat exchangers of fluidized bed steam boilers so that intermediate tempera-tures of each tube row inside the heat exchanger can be obtained. This goal was achieved using a so-called matrix method where tube banks of the heat exchangers were divided into many small parts, in this case to tube rows. The development of the calculation model re-quired, among other things, an understanding of different heat transfer mechanisms which are conduction, convection, and thermal radiation. Also, different heat exchanger configura-tions and how matrix equaconfigura-tions differ between all those situaconfigura-tions were covered. In addition, energy balance and pressure loss calculations of the heat exchangers were discussed.
In the calculation model, heat exchangers consisted of tube banks and cavities between them.
The calculation procedure proceeded so that cavities were calculated first in order to solve the radiation that they sent for the tube banks. Then tube banks were solved, and this alter-nation was continued until the solution was found. Pressure losses were calculated conven-tionally for the whole heat exchanger because pressure does not have a big effect on the heat transfer and because this way computational costs can be reduced.
In the validation process of the calculations model, results from experimental measurements were utilized to find fouling factors for the calculations. As a result of that process, correction factors for different fuel-heat exchanger combinations were found. It was noticed that cal-culations must be corrected more in the case of economizers than superheaters probably due to the bigger effect of condensation fouling mechanism which occurs in lower temperatures.
Also, it was found that there where condensation fouling can occur, that is in economizer section, calculations must be corrected more in case of biomass fuels than coal because of the larger amount of condensable inorganic species in the biomass fuels. In the case of su-perheaters, fuel seems to not have an effect on the fouling factor. In the validation process, the total amount of investigated cases was quite low and only heat exchangers of CFB boilers were investigated. Thus, many more cases need to be validated in the future to obtain more reliable validation results, and also separate validation needs to be done for BFB boilers.
Results of the new matrix calculation model were also compared to the results from the earlier conventional calculation model and it was found that the matrix calculation model offers slightly more accurate results. The main reason for that is probably the fact that fluid properties and thus also all heat transfer parameters are calculated more accurately in the new model than in the conventional model where just overall average fluid properties are used. In addition, the new model makes it possible to take into account changes in tube material and tube thickness through the heat exchanger that is not possible in the earlier conventional calculation model where averaged values need to be used for the whole heat exchanger.
In the future, it would be good to compare the results from the calculation model to the more accurate measurements where also some intermediate temperatures from the real heat ex-changers are known in addition to overall inlet and outlet temperatures. This is important because even if the outlet temperature calculated by the model corresponds to the measure-ments, the temperature profile given by the model may still be different from the real tem-perature profile. In addition to experimental measurements, the results from the computa-tional fluid dynamics (CFD) simulations could also provide good reference data for the val-idation process.
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Matrix equations where only outside of the matrix A and outside variables are shown
Outside inlet is known 1 row
Outside outlet is known 1 row
Matrix equations where only inside of the matrix A and inside variables are shown
Parallel flow, not mixed, 1 row per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Parallel flow, not mixed, 2 rows per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Parallel flow, not mixed, 3 rows per pass Inside inlet is known
1 pass
Parallel flow, not mixed, 3 rows per pass Inside outlet is known
1 pass
Parallel flow, mixed, 1 row per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Parallel flow, mixed, 2 rows per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Parallel flow, mixed, 3 rows per pass Inside inlet is known
1 pass
Parallel flow, mixed, 3 rows per pass Inside outlet is known
1 pass
Counter flow, not mixed, 1 row per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Counter flow, not mixed, 2 rows per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Counter flow, not mixed, 3 rows per pass Inside inlet is known
1 pass
Counter flow, not mixed, 3 rows per pass Inside outlet is known
1 pass
Counter flow, mixed, 1 row per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Counter flow, mixed, 2 rows per pass Inside inlet is known
1 pass
Inside outlet is known 1 pass
Counter flow, mixed, 3 rows per pass Inside inlet is known
1 pass
Counter flow, mixed, 3 rows per pass Inside outlet is known
1 pass
Emissivity diagrams for carbon dioxide and sulfur dioxide
Carbon dioxide
Sulfur dioxide