Analysis of Magnetic Performance for Magnetized Packed and Unpacked Bed

3.1. Influence of the Bed Parameter on the Magnetic Intensity

The magnetization characteristics of the magnetized packed bed depend on many factors. Bed porosity is one of characteristics that affect the magnetic properties of the bed elements; it is varied with the diameter of the steel ball used as the bed element. Therefore, 6 mm, 8 mm and 12 mm diameter steel balls formed from three bed magnetization properties were investigated. The magnetic intensity measured values corrected after calculating uncertainty and graphs were plotted using this data. The variations of the magnetic field induction in air space in the axial direction are shown. Uncertainties in the measurement of the magnetic intensity ASME PTC 19.1 set by the 2005 uncertainty analysis methods and the measured magnetic intensity values have been corrected according to the equation. u refers to as the concepts ratio of standard deviation to the square root of number of repeated measurements [15]. The magnetic intensities are measured in air space in the axial direction in the magnetized unpacked bed. The variations of the magnetic intensity are shown in the figure 2-3. Homogeneous distribution can be clearly seen in fig. 1 and 2. It was found that the magnetic field intensity values at four different external magnetic field intensity values at different filter lengths were maximum in the 4-6 cm filter zone corresponding to the middle zone of the filter. On the other hand, it is observed that the values of the external magnetic field density are lower because the element is less tangent in the filter input and output regions. For this reason, it was concluded that the measurements to be made at the center of the bed would be more appropriate. On the other

hand, the magnetic properties of the unfilled bed seem to be increased by the magnetic field strength.

Figure 2. The average magnetizing curve of the magnetized unpacked bed

Figure 3. The magnetic field intensity profiles in the axial direction of the magnetized unpacked bed Different the lengths of the bed at different magnetic strength with the magnetic field variation curves for the bed element diameter B (L) as seen figures 5, 7 and 9 is given. Magnetization curves B (H) is given by figures 4, 6 and 8. The bed element of the magnetization curve as a 6 mm diameter of the bed formed from the ball is shown in Figure 4. B (H) curve can be understood from the bed magnetic show that magnetic intensity, as shown in the figure, the magnetic strength increased up to 279 kA/m. The magnetic intensity is higher in the bed length of 2-6 cm as seen from figure 5. The magnetic intensity is no more than 0.631 T. Because the filter bed increases with increasing porosity of the bed element diameter decreases the magnetic intensity. Because touch contact areas are decreased with the number of balls thus formed around the high gradient magnetic field is reduced.

Figure 4. The average magnetizing curve of the magnetized bed (d=6 mm)

Figure 5. The magnetic induction field profiles of the magnetized bed (d=6 mm) The magnetization curve B (H) of the magnetized packed bed formed from 8 mm steel ball is showed in figure 6. The magnetic intensity as shown in the figure, the magnetic strength reaches the magnetic saturation of the bed 225 kA/m, then no significant change.

Figure 6. The average magnetizing curve of the magnetized bed (d=8 mm)

The magnetic intensity as shown in Figure 7, the maximum intensity value in the bed length 7 cm. Magnetic intensity was decreased the bed length more than 7 cm.

Figure 7. The magnetic induction field profiles of the magnetized bed (d=8 mm) The magnetization curve B (H) of the magnetized packed bed formed from 12 mm steel ball is showed in figure 8. The magnetic field intensity as shown in the figure, the magnetic strength reaches the magnetic saturation of the bed 225 kA/m, then no significant change.

Figure 8. The average magnetizing curve of the magnetized bed (d=12 mm) The magnetic intensity as shown in figure 9, in areas near to the bed outlet (9-10 cm) is reduced. The maximum magnetic intensity was reached in 0 .517 T value.

Figure 9. The magnetic induction field profiles of the magnetized bed (d=12 mm) As a result of studies to determine the magnetic characteristics of the bed, with increasing diameter of the bed element reduced the magnetic intensity. As can be seen from the results in packed bed B(H) relationship is approximately linear. Magnetic strength was increased significantly in the magnetic intensity. Bed area with steel balls bed elements for increasing the intensity of magnetic caused by the increase in magnetic force. This takes place in all magnetized granular packed bed and varies from the porosity of the bed. These experiments to enhance the efficiency of the magnetic filtration the bed having lower porosity (ε = 0.4 to 0.6) so that used smaller diameter in steel balls it showed the need to build the bed. The magnetic particles are hold more in this area because of the higher intensity of the magnetic field in the central compartment of the filter. The magnetization saturation of the bed shows over 250 kA/m.

3.2. Analyses of the Results

3.2.1. Taguchi method Taguchi method utilizes a special design of orthogonal arrays to optimization with only a small number of experiments. Orthogonal array (OA) is minimize the number of experiment. An orthogonal array contains factors or their interactions and the levels of various factors for a particular experimental trial. The diameter of the bed elements, the magnetic strength and the bed length as magnetized bed parameters on the magnetic intensity were chosen as key factors on the magnetic performance of the magnetized bed. The minimum trials number is given in the orthogonal array as following 𝑁𝑚𝑖𝑛 = (𝑙 − 1)𝑘 + 1 (1) where, k is number of factors and its value is 3. l is number of levels and its value is 3. Thus, N min is 7 and according to Taguchi design concept L9 orthogonal array has been selected (Badkar et al. 2012). 9 experiments only are make by using L9. Three factors with three levels were considered as shown in Table 1. Taguchi method is to determined the optimum bed parameters by both to improve the process and to reduce the influence of the noise factors [10-14]. Taguchi orthogonal array experimental design was used for optimization of the bed parameters. ANOVA performed to estimate the impact of each parameter. The S/N ratio approach was used for the magnetic intensity. The each level of the parameter is calculated based on larger-the-better corresponds to better quality characteristics for magnetic intensity. Taguchi method are not sensitive to the variation. Affect of control factor on quality characteristic is performed to see which process parameter is statistically significant.

The lower and upper limits of the magnetic strength which was applied in filtration matrices in our experiments were selected as ranging from 175 to 280 kA/m. The lower limit was adopted in consideration with the fact that particles are weakly captured with lower magnetic strength. The upper limit of the magnetic strength is greater than 250 kA/m due to magnetic saturation of the bed. Preliminary experiments revealed that the magnetic intensity were too low for the bed lengths shorter than 2 cm and filter pores were saturated with the captured particles when the length was above 6 cm. The lower limit for the diameter of the bed element was taken as smallest available 6 mm, because the filter clogs due to a pressure drop when this diameter is smaller than 3 mm. The upper limit was chosen as 12 mm although the magnetic intensity might decrease at this level. In this study, the diameter of the bed elements, the magnetic strength and the bed length were considered in three levels to determine the optimum process parameters. Taguchi method was applied by using the Design-Expert 6.1 (DX6). The diameter of the bed elements were selected as 6:8:12; the magnetic field strength was selected as 175:225:280 kA/m and the bed length was 2:4:6 cm in three levels. The used parameters and levels are presented in Table 1. Table 1. Variable Factor Levels Factors Diameter of the bed elements, d (mm) Magnetic field strength, H (kA/m) Bed length, L (cm)

The level numbers of 1, 2 and 3 are the lowest, mid and highest levels, respectively. L 9 orthogonal array that have to be considered for performance of experiments in 9 runs. L9 consist of three parameters in three levels mean. L9 is given in Table 2. Table 2. The Layout of L9 Diameter of the bed elements d (mm) 1 1 1 2 2 2 3 3 3

The performance of the process is distinguished both design and noise factors. The S/N ratio is the performance measurement. The aim is to make products that are strong with respect to noise factors (N). N are the uncontrollable factors such as external factors, manufacturing imperfections and product deterioration. S is signal as design parameters. S/N ratio are the improvement of the quality. The S/N ratio can be classified to lower-the-better, larger-the-better and the nominal. The larger S/N means to the quality will become better. The related S/N ratio is defined by equation 2. The S/N ratio is selected as “larger the better” quality characteristics in order to maximize the magnetic intensity. Larger the better characteristic is given by:

where y, is the data obtained from experiments and n is the number of repetition [10-14,1617]. The magnetic intensity measurements were repeated for three times. The each measurement results were given arithmetic means. The corresponded S/N ratio to a parameter in each level was ordered in each column to calculate the mean of S/N ratio. The magnetic intensity (B) and calculated S/N ratio of each experiment are presented in table 3 and 4. The maximum and minimum S/N ratios gives on these tables. The highest value of S/N ratio for a parameter was considered as optimum level of the parameter. Table 3. L9 Orthogonal array of Taguchi and their S/N ratio value. Response Magnetic Intensity B (T)

Average B (T) S/Ni 0.335 0.437 0.561 0.431 0.489 0.613 0.339 0.432 0.390

Table 4. the best design set is decided by choosing the level with the highest value for each factor. The optimum process parameter levels were d2. H3. and L3. The most effective factor on the magnetic intensity is the highest difference value. It was found with the difference value of 2.935 for the magnetic strength. The least effective factor is the lowest difference value 0.688 for the bed length of bed. Table 4. The response table of S/N ratios Level 1 Level 2 Level 3 Difference

3.2.2. Analysis of variance ANOVA is a computational technique which is is performed to make out which process each parameters in terms of percent contribution on the overall response. ANOVA is required for estimating the variance of error for the effects and confidence interval of the prediction error. The ANOVA table contains the degree of freedom, sum of square, mean square, f value and contribution that is shown by table 5. The parameters with higher contribution are ranked higher in terms of importance in the experiment and also have significant effects in controlling the overall response. The same ANOVA table 5 also shows the R 2. The coefficient of determination R2 (0≤R2≤1) indicates the goodness of fit for the model if R2 are nearly equal to 1. R2 with larger 1083

values is more desirable. The model has a high F value, low probability values (Prob > F). The probability values show the significance of each term. Since this has the highest F value and percentage of contribution. ANOVA can be predicted the optimum bed parameters. It was found to be the most significant parameter for the magnetic intensity. ANOVA is applied to find out the significant factors for the chosen criterion. The result are given in Table 5. It is the most important factor with a contribution ratio of 51.9% on the magnetic strength followed by the diameter of the bed elements at 32.1 %.On comparing the percentage of contribution and ANOVA results for the magnetic strength and the diameter of the bed elements has greater influence than the bed length. The magnetic strength and the diameter of the bed elements have greater influence. Time has little effect on the bed length. Table 5. ANOVA results for the Taguchi method for magnetic intensity Sum of square 8.18 13.2 0.805 25.5