Hydraulic Characterization of Ceramic Foam Filters Used in Aluminum Filtration
Abstract
:1. Introduction
2. Theory
- The first region (Darcy law) is the Darcian flow regime at extremely low (<1 mm·s−1) fluid velocities—there is a linear relationship between the friction factor and Rei, and viscous forces are predominant.
- At the upper end of the Darcian flow regime, the transition flow starts and the linear relation between the friction factor and Rei starts to bend, and the viscous forces are not predominant anymore.
- The third region (Turbulent flow) is the Forchheimer or turbulent flow regime, where the form drag forces are dominant. The Fanning friction factor gets close to zero at the upper end of the transition zone, and the curve becomes almost horizontal.
3. Materials and Methods
3.1. Sample Preparation
3.2. Total Porosity
3.3. Physical Morphology
3.4. Pressure Drop Test
- The water reservoir.
- The thermocouple Probe PT100 and data logger GMH3750 from GHM Group, Remscheid, Germany) to measure the water temperature. The thermocouple was factory-calibrated to an expanded uncertainty of ±0.22 °C with a coverage factor of 2. The software (GSOFT 3050, GHM Group, Remscheid, Germany) was used to transfer data from the logger to the PC.
- The vertical multistage centrifugal pump (GRUNDFOS, Bjerringbro, Denmark) with integrated frequency converter, maximum 10 bar pressure and 20.5 m3·h−1.
- The stainless-steel needle valve regulates the flow of water through the system allowing adjustment of the velocity.
- The sample housing.
- The differential pressure transducers DF2R.
- Poly Methyl Methacrylate (PMMA) pipes used to transport the water in the system. The inlet pipe was 1.3 m long to secure a fully developed laminar flow in the low water velocity range. This length was calculated using Equation (10) where D is the pipe diameter (m), LE the entrance length (m), and ReD the Reynolds number of the pipes calculated from the defined flow rate (dimensionless), i.e., 10 mm·s−1,:
- The digital scale model ME204, METTLER TOLEDO, Switzerland, with the readability of 0.1 mg and a maximum capacity of 220 g. The scale was equipped with a LAB-it View software (version 5.0.1), for computer data storage.
- The swingarm that was part of the piping system.
4. Results and Discussion
4.1. Porosity
4.2. Mean Feret Diameter of the Cell and the Window
4.3. Permeability
4.4. Flow Regimes in CFF
5. Conclusions and Future Work
- Comparing the permeability and mean Window Feret diameter of different filters confirmed the need for a systemic method to categorize CFFs.
- Filtration of Al using CFF is performed at the superficial velocity at which the fluid flow in the channels is turbulent.
- The derived empirical model for the calculation of the pressure drop of CFFs correlates well with the experimental pressure drop data.
- Empirical expressions for calculating the pressure drop over CFF should be derived based on experimental measurements carried out at the velocity range of the application.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A
Grade 30 | Grade 50 | |||
---|---|---|---|---|
Porosity | Uncertainty | Porosity | Uncertainty | |
A1 | 8.72 × 10−1 | 3.92 × 10−4 | 8.39 × 10−1 | 8.19 × 10−4 |
A2 | 8.79 × 10−1 | 7.30 × 10−4 | 8.50 × 10−1 | 1.09 × 10−3 |
A3 | 8.98 × 10−1 | 8.09 × 10−4 | 8.68 × 10−1 | 1.22 × 10−3 |
A4 | 8.77 × 10−1 | 1.02 × 10−4 | 8.41 × 10−1 | 1.16 × 10−3 |
A5 | 8.84 × 10−1 | 9.95 × 10−4 | 8.50 × 10−1 | 7.68 × 10−4 |
A6 | 8.69 × 10−1 | 6.36 × 10−4 | 8.49 × 10−1 | 8.47 × 10−4 |
A7 | 8.80 × 10−1 | 8.87 × 10−4 | 8.56 × 10−1 | 2.43 × 10−3 |
A8 | 8.94 × 10−1 | 8.37 × 10−4 | 8.42 × 10−1 | 8.42 × 10−4 |
A9 | 8.74 × 10−1 | 1.32 × 10−4 | 8.33 × 10−1 | 1.05 × 10−3 |
A10 | 8.83 × 10−1 | 7.53 × 10−4 | 8.45 × 10−1 | 9.21 × 10−4 |
A11 | 8.98 × 10−1 | 1.64 × 10−4 | 8.41 × 10−1 | 7.33 × 10−4 |
A12 | 8.95 × 10−1 | 4.98 × 10−4 | 8.43 × 10−1 | 1.19 × 10−3 |
A13 | 8.95 × 10−1 | 1.54 × 10−4 | 8.60 × 10−1 | 1.14 × 10−3 |
A14 | 8.98 × 10−1 | 1.01 × 10−4 | 8.48 × 10−1 | 1.14 × 10−3 |
A15 | 8.75 × 10−1 | 6.79 × 10−4 | 8.47 × 10−1 | 1.37 × 10−3 |
Grade 65 | Grade 80 | |||
---|---|---|---|---|
Porosity | Uncertainty | Porosity | Uncertainty | |
A1 | 8.73 × 10−1 | 9.35 × 10−4 | 8.63 × 10−1 | 1.11 × 10−3 |
A2 | 8.54 × 10−1 | 1.00 × 10−3 | 8.73 × 10−1 | 3.97 × 10−3 |
A3 | 8.47 × 10−1 | 9.33 × 10−4 | 8.55 × 10−1 | 4.79 × 10−3 |
A4 | 8.49 × 10−1 | 7.50 × 10−4 | 8.51 × 10−1 | 1.47 × 10−3 |
A5 | 8.54 × 10−1 | 1.00 × 10−3 | 8.58 × 10−1 | 2.26 × 10−3 |
A6 | 8.43 × 10−1 | 1.12 × 10−3 | - | - |
A7 | 8.42 × 10−1 | 1.41 × 10−3 | 8.63 × 10−1 | 2.72 × 10−3 |
A8 | 8.45 × 10−1 | 1.19 × 10−3 | 8.44 × 10−1 | 3.12 × 10−3 |
A9 | 8.77 × 10−1 | 1.89 × 10−3 | 8.40 × 10−1 | 1.75 × 10−3 |
A10 | 8.58 × 10−1 | 2.01 × 10−3 | 8.57 × 10−1 | 1.38 × 10−3 |
A11 | 8.47 × 10−1 | 9.59 × 10−4 | 8.55 × 10−1 | 2.63 × 10−3 |
A12 | 8.46 × 10−1 | 1.82 × 10−3 | 8.58 × 10−1 | 2.42 × 10−3 |
A13 | 8.76 × 10−1 | 1.67 × 10−3 | 8.59 × 10−1 | 2.02 × 10−3 |
A14 | 8.55 × 10−1 | 1.34 × 10−3 | 8.42 × 10−1 | 1.76 × 10−3 |
A15 | 8.60 × 10−1 | 1.24 × 10−3 | 8.49 × 10−1 | 1.02 × 10−2 |
30 PPI | 50 PPI | 60 PPI | ||||
---|---|---|---|---|---|---|
Porosity | Uncertainty | Porosity | Uncertainty | Porosity | Uncertainty | |
B1 | 8.83 × 10−1 | 2.89 × 10−4 | - | - | - | - |
B2 | 8.72 × 10−1 | 3.16 × 10−4 | - | - | - | - |
B3 | 8.84 × 10−1 | 2.88 × 10−4 | 8.76 × 10−1 | 3.06 × 10−4 | 8.79 × 10−1 | 2.98 × 10−4 |
B4 | - | - | 8.69 × 10−1 | 3.24 × 10−4 | 8.82 × 10−1 | 2.91 × 10−4 |
B5 | 8.82 × 10−1 | 2.91 × 10−4 | 8.67 × 10−1 | 3.28 × 10−4 | 8.70 × 10−1 | 3.20 × 10−4 |
B6 | 8.87 × 10−1 | 2.80 × 10−4 | - | - | - | - |
B7 | 8.89 × 10−1 | 2.75 × 10−4 | 8.71 × 10−1 | 3.19 × 10−4 | 8.74 × 10−1 | 3.12 × 10−4 |
B8 | 8.77 × 10−1 | 3.04 × 10−4 | 8.80 × 10−1 | 2.96 × 10−4 | 8.79 × 10−1 | 2.98 × 10−4 |
B9 | 8.77 × 10−1 | 3.04 × 10−4 | - | - | - | - |
B10 | 8.77 × 10−1 | 3.04 × 10−4 | 8.73 × 10−1 | 1.78 × 10−3 | 8.67 × 10−1 | 3.28 × 10−4 |
B11 | - | - | 8.69 × 10−1 | 3.23 × 10−4 | - | - |
B12 | - | - | - | - | - | - |
B13 | - | - | 8.79 × 10−1 | 3.00 × 10−4 | 8.67 × 10−1 | 3.29 × 10−4 |
B14 | - | - | - | - | 8.73 × 10−1 | 3.14 × 10−4 |
B15 | - | - | 8.70 × 10−1 | 3.22 × 10−4 | 8.70 × 10−1 | 3.22 × 10−4 |
30 PPI | 50 PPI | 60 PPI | ||||
---|---|---|---|---|---|---|
Porosity | Uncertainty | Porosity | Uncertainty | Porosity | Uncertainty | |
C1 | 8.88 × 10−1 | 2.30 × 10−4 | - | - | 8.89 × 10−1 | 2.30 × 10−4 |
C2 | 8.81 × 10−1 | 2.47 × 10−4 | 8.98 × 10−1 | 2.10 × 10−4 | 8.91 × 10−1 | 2.25 × 10−4 |
C3 | 8.82 × 10−1 | 2.43 × 10−4 | 8.93 × 10−1 | 2.22 × 10−4 | - | - |
C4 | 8.86 × 10−1 | 2.37 × 10−4 | - | - | - | - |
C5 | - | - | 8.91 × 10−1 | 2.25 × 10−4 | 8.85 × 10−1 | 2.39 × 10−4 |
C6 | 8.81 × 10−1 | 2.45 × 10−4 | 8.93 × 10−1 | 2.22 × 10−4 | 8.89 × 10−1 | 2.29 × 10−4 |
C7 | 8.85 × 10−1 | 2.38 × 10−4 | - | - | - | - |
C8 | - | - | - | - | - | - |
C9 | 8.87 × 10−1 | 2.34 × 10−4 | 8.92 × 10−1 | 2.24 × 10−4 | 8.87 × 10−1 | 2.33 × 10−4 |
C10 | 8.78 × 10−1 | 2.52 × 10−4 | 8.88 × 10−1 | 2.32 × 10−4 | 8.81 × 10−1 | 2.48 × 10−4 |
C11 | - | - | 8.99 × 10−1 | 2.09 × 10−4 | - | - |
C12 | - | - | 9.03 × 10−1 | 2.00 × 10−4 | - | - |
C13 | - | - | - | - | 8.88 × 10−1 | 2.34 × 10−4 |
C14 | - | - | - | - | 8.84 × 10−1 | 2.39 × 10−4 |
C15 | - | - | 8.86 × 10−1 | 2.36 × 10−4 | 8.78 × 10−1 | 2.54 × 10−4 |
G30 | G50 | |||||
---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
A1 | 97 | 252.3 | 853.3 | 240 | 201.1 | 444 |
A2 | 543 | 257.9 | 685.4 | 183 | 163.1 | 579.7 |
A3 | 485 | 256.1 | 654.5 | 485 | - | 386.2 |
A4 | 209 | 226.6 | 960.4 | 191 | 206.9 | 604 |
A5 | 105 | 270.4 | 768.9 | - | - | - |
A6 | 212 | 284.2 | 948.6 | 219 | 214.9 | 433.3 |
A7 | 117 | 254.4 | 759.8 | 158 | 151.3 | 537.1 |
A8 | 135 | 206.1 | 564.5 | 135 | 130.7 | 471.2 |
A9 | 83 | 268.2 | 626.5 | 766 | 173.9 | 464.5 |
A10 | - | - | - | 136 | 109.7 | 430.8 |
A11 | - | - | - | 146 | 124.4 | 521.7 |
A12 | 108 | 296.8 | 725.6 | 178 | 121.4 | 539.7 |
A13 | - | - | - | 129 | 147.4 | 573.4 |
A14 | 172 | 252.2 | 759.1 | 189 | 184 | 529.1 |
A15 | 446 | 292.3 | 705.8 | 174 | 133.8 | 534.2 |
Grade 65 | Grade 80 | |||||
---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
A1 | 167 | 131.2 | 436.4 | 296 | 92.2 | 323.1 |
A2 | 106 | 108 | 398.8 | 271 | 98.9 | 285.1 |
A3 | 115 | 87.2 | 443.4 | - | - | - |
A4 | 217 | 165.7 | 411.1 | 143 | 78.5 | 283.3 |
A5 | - | - | - | 94 | 67.3 | 305.3 |
A6 | 169 | 67.8 | 456 | 200 | 147.1 | 427.9 |
A7 | 168 | 120.9 | 416.1 | 101 | 95 | 397.2 |
A8 | 131 | 97 | 412.2 | 68 | 89.6 | 319.8 |
A9 | 195 | 109.3 | 433.3 | 437 | 77.5 | 287.5 |
A10 | - | - | - | - | - | - |
A11 | 129 | 93.5 | 437 | 186 | 86.7 | 363.5 |
A12 | 196 | 97.8 | 425.7 | 230 | 110.4 | 308.7 |
A13 | - | - | - | 231 | 149.1 | 450.3 |
A14 | 119 | 62.6 | 237.4 | 121 | 70.2 | 397.6 |
A15 | 170 | 85.7 | 378.6 | - | - | - |
30 PPI | 50 PPI | 60 PPI | |||||||
---|---|---|---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
B1 | 158 | 129 | 556.4 | 159 | 96.1 | 507.2 | 137 | 56.5 | 284.7 |
B2 | 127 | 190.5 | 733.6 | 78 | 74 | 480 | 140 | 77.8 | 423.2 |
B3 | 111 | 173.6 | 664.4 | 112 | 82.8 | 442.8 | - | - | - |
B4 | 100 | 136.4 | 636.3 | - | 119.1 | 591.2 | 117 | 81.9 | 370.9 |
B5 | 103 | 183 | 763.6 | 118 | 74.2 | 479.1 | 117 | 87 | 413.5 |
B6 | 131 | 149.2 | 609.8 | 116 | 86.9 | 469 | 115 | 59.3 | 331.4 |
B7 | 124 | 201.8 | 738.8 | 111 | 105.9 | 519.2 | 153 | 62.1 | 337.8 |
B8 | 127 | 203.5 | 824.8 | 144 | 102.9 | 563.1 | 124 | 90.3 | 391.5 |
B9 | 122 | 185 | 716.2 | 133 | 107.1 | 565 | 139 | 72.6 | 392.1 |
B10 | 138 | 165 | 728.5 | 151 | 88.6 | 461.3 | 92 | 106.5 | 417 |
B11 | - | - | - | 115 | 107.2 | 580.8 | 182 | 41.6 | 267.2 |
B12 | - | - | - | 115 | 93.2 | 521.2 | - | 71.4 | 388.4 |
B13 | - | - | - | 146 | 100.7 | 482.4 | 174 | 71.6 | 391.4 |
B14 | - | - | - | 174 | 89 | 444.6 | 116 | 57.9 | 337.1 |
B15 | - | - | - | 133 | 86 | 498.7 | 179 | 43.7 | 249.7 |
30 PPI | 50 PPI | 60 PPI | |||||||
---|---|---|---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
C1 | 119 | 250.7 | 991 | 150 | 176.3 | 775.7 | 374 | 82.5 | 450.8 |
C2 | - | - | - | 167 | 176.3 | 657.5 | - | - | - |
C3 | 109 | 229 | 846.2 | 143 | 192.9 | 789.7 | 210 | 75.4 | 384.2 |
C4 | 132 | 218.8 | 779.3 | 174 | 152.7 | 701.8 | 201 | 83.9 | 435.1 |
C5 | 114 | 226.9 | 928.8 | 129 | 166.3 | 716.5 | - | 80.7 | 436.9 |
C6 | 123 | 260.7 | 1026.8 | 216 | 163.5 | 703.7 | 232 | 84.8 | 449.2 |
C7 | 110 | 293.3 | 1044.7 | 160 | 169.3 | 731.3 | 129 | 64.1 | 370 |
C8 | 111 | 253.3 | 926 | 151 | 188.3 | 825.4 | 206 | 60.5 | 410.3 |
C9 | 148 | 240.8 | 1083.2 | 165 | 130.7 | 640.2 | 231 | 79.6 | 365.7 |
C10 | 148 | 218 | 870.5 | 176 | 162.4 | 712.4 | 201 | 60 | 332.7 |
C11 | 157 | 267.2 | 1065.4 | 198 | 158.5 | 696.1 | 174 | 71.2 | 376.8 |
C12 | 115 | 288.3 | 1040.6 | 133 | 169.4 | 895.8 | 192 | 79.1 | 410.8 |
C13 | 131 | 269.4 | 999.9 | 107 | 176.9 | 720.6 | 183 | 63.9 | 359 |
C14 | 142 | 259.8 | 995.9 | 150 | 146.2 | 644.2 | 238 | 59.2 | 334.6 |
C15 | 160 | 210.2 | 845.9 | 127 | 190.8 | 667.3 | 173 | 68.1 | 382.1 |
Grade 30 | Grade 50 | |||||
---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
A1 | 110 | 392.5 | 948.2 | 155 | 459.1 | 972.7 |
A2 | 348 | 1237.7 | 1836.5 | 149 | 771.3 | 1186.3 |
A3 | 561 | 755.7 | 1070.7 | 1203 | 336.2 | 565.3 |
A4 | 94 | 290.6 | 740.1 | 143 | 797.5 | 1370.7 |
A5 | 134 | 579.2 | 1179.4 | 109 | 722.6 | 1272 |
A6 | 162 | 345.3 | 1083 | 164 | 469.5 | 879.1 |
A7 | 143 | 630.6 | 1178.3 | 427 | 635.9 | 957.6 |
A8 | 180 | 411.2 | 827.5 | 178 | 754.7 | 932.8 |
A9 | 90 | 802.4 | 1661.8 | 948 | 686.9 | 993.4 |
A10 | - | - | - | 69 | 599.3 | 1376.1 |
A11 | - | - | - | 125 | 732.4 | 1571.5 |
A12 | 107 | 1624 | 1871.9 | 160 | 537.8 | 1129.6 |
A13 | - | - | - | 156 | 649.7 | 1006.9 |
A14 | 148 | 360.5 | 983.1 | 225 | 537.5 | 796.9 |
A15 | 421 | 1195.5 | 1676.2 | 97 | 277.4 | 706.4 |
Grade 65 | Grade 80 | |||||
---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
A1 | 240 | 412.4 | 729.2 | - | - | - |
A2 | 137 | 488.8 | 868.2 | 402 | 603.6 | 770 |
A3 | 62 | 620.6 | 1154.6 | - | - | - |
A4 | 219 | 612.2 | 1133.6 | 239 | 354.3 | 525.3 |
A5 | - | - | - | 181 | 435.1 | 713.6 |
A6 | 222 | 476.6 | 943.2 | 406 | 595.5 | 814.7 |
A7 | 140 | 444 | 990.9 | 205 | 474.4 | 759.9 |
A8 | 220 | 568.7 | 833.8 | 194 | 383.5 | 600.2 |
A9 | 232 | 452.7 | 720.3 | 682 | 401.3 | 596.2 |
A10 | - | - | - | - | - | - |
A11 | 158 | 443.7 | 914.9 | 552 | 527.4 | 342.3 |
A12 | 198 | 687.4 | 1020.8 | 329 | 282.9 | 594.9 |
A13 | - | - | - | 226 | 343 | 767.9 |
A14 | 186 | 548.9 | 812.4 | 195 | 310.5 | 739.3 |
A15 | 509 | 552.7 | 513.3 | - | - | - |
30 PPI | 50 PPI | 60 PPI | |||||||
---|---|---|---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
B1 | 196 | 980.1 | 1259.5 | 189 | 734.2 | 1252.2 | 257 | 807.9 | 1244.2 |
B2 | 146 | 678.2 | 1491.6 | 135 | 440.2 | 1046 | 281 | 444.7 | 878.8 |
B3 | 253 | 1157.4 | 1397.6 | 313 | 893.8 | 1208.9 | - | - | - |
B4 | 277 | 1054.5 | 1520.6 | 205 | 505.7 | 1066.2 | 265 | 528.7 | 942.2 |
B5 | 83 | 491.1 | 1280.1 | 216 | 468.5 | 1003.4 | 336 | 537.9 | 946.3 |
B6 | 264 | 881 | 1105.2 | 167 | 744.9 | 1208.2 | 244 | 505.2 | 919 |
B7 | 218 | 545.5 | 1140.6 | 151 | 462.5 | 1202.8 | 258 | 566.7 | 835.4 |
B8 | 166 | 844.5 | 1382.5 | 409 | 567.9 | 919.3 | 252 | 629.2 | 1016.6 |
B9 | 88 | 709.3 | 1484.6 | 146 | 595.7 | 1216.7 | 175 | 575.9 | 1139.6 |
B10 | 182 | 613.4 | 1173.1 | 237 | 507.6 | 918.2 | 235 | 824.8 | 911.1 |
B11 | - | - | - | 444 | 1162.7 | 1435.3 | 275 | 548.8 | 846.7 |
B12 | - | - | - | 206 | 484.3 | 1012.3 | 247 | 414.1 | 631.7 |
B13 | - | - | - | 141 | 684.9 | 1229.8 | 356 | 583 | 721.8 |
B14 | - | - | - | 178 | 709.4 | 1156.8 | 392 | 346.5 | 559.7 |
B15 | - | - | - | 205 | 669.8 | 1135.4 | 365 | 576.9 | 742 |
30 PPI | 50 PPI | 60 PPI | |||||||
---|---|---|---|---|---|---|---|---|---|
Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | Counts | St. Dev. (µm) | Mean (µm) | |
C1 | 125 | 1174.6 | 1778.9 | 164 | 991.1 | 1953.7 | 449 | 606.2 | 923.8 |
C2 | - | - | - | 274 | 657 | 1167.2 | - | - | - |
C3 | 136 | 1198.9 | 1955.1 | 153 | 1294.8 | 1908 | 236 | 567.4 | 1018.4 |
C4 | 150 | 1428 | 2017.6 | 192 | 879.8 | 1499.9 | 298 | 509.9 | 960 |
C5 | 82 | 1738.4 | 2530.5 | 173 | 876.9 | 1545 | 342 | 415.7 | 711.6 |
C6 | 75 | 1251.1 | 2342.7 | 155 | 1003.1 | 1770.7 | 429 | 660.5 | 1012.6 |
C7 | 101 | 1158.4 | 2292.3 | 269 | 515.5 | 1066.1 | 233 | 561 | 906.4 |
C8 | 99 | 1066.9 | 2030.5 | 264 | 646.3 | 1098.3 | 295 | 563.4 | 933.9 |
C9 | 109 | 1348.2 | 2211.3 | 354 | 582.2 | 1072.4 | 323 | 536.1 | 885.6 |
C10 | 123 | 942.1 | 1866.3 | 263 | 821.4 | 1278.3 | 307 | 465.5 | 835 |
C11 | 118 | 928.1 | 2011.2 | 195 | 755.3 | 1386.8 | 290 | 454.5 | 820.9 |
C12 | 102 | 1054.4 | 2147.1 | 282 | 744.3 | 1229.6 | 308 | 650.1 | |
C13 | 92 | 1518.3 | 2582.7 | 129 | 815.3 | 1453.6 | 407 | 480.7 | 846.7 |
C14 | 112 | 709.8 | 1872 | 133 | 750.4 | 1396.7 | 301 | 460.1 | 838.1 |
C15 | 110 | 1355.4 | 2239.4 | 111 | 842.4 | 1614.1 | 244 | 577.8 | 1012.3 |
Grade 30 | Grade 50 | |||
---|---|---|---|---|
Permeability (m2) | St. Dev. (m2) | Permeability (m2) | St. Dev. (m2) | |
1 | 8.80 × 10−8 | 6.70 × 10−10 | 1.00 × 10−8 | 8.60 × 10−11 |
2 | 4.40 × 10−8 | 6.40 × 10−9 | 2.30 × 10−8 | 3.60 × 10−10 |
3 | 2.80 × 10−8 | 3.30 × 10−9 | 2.40 × 10−8 | 3.80 × 10−10 |
4 | 4.90 × 10−8 | 1.10 × 10−8 | 4.50 × 10−8 | 1.20 × 10−9 |
5 | 4.10 × 10−8 | 5.00 × 10−10 | 2.50 × 10−8 | 1.20 × 10−9 |
6 | 7.20 × 10−8 | 7.60 × 10−10 | - | - |
7 | 7.40 × 10−8 | 5.10 × 10−9 | 2.50 × 10−8 | 8.60 × 10−10 |
8 | 3.90 × 10−8 | 1.10 × 10−9 | 1.30 × 10−8 | 5.50 × 10−10 |
9 | * 2.5 × 10−7 | 1.10 × 10−8 | 1.60 × 10−8 | 8.90 × 10−11 |
10 | 6.90 × 10−8 | 2.80 × 10−9 | 1.90 × 10−8 | 1.40 × 10−9 |
11 | 3.80 × 10−8 | 3.60 × 10−10 | 7.60 × 10−8 | 3.90 × 10−10 |
12 | 7.30 × 10−8 | 1.10 × 10−9 | 1.30 × 10−8 | 4.30 × 10−10 |
13 | 1.10 × 10−7 | 2.60 × 10−9 | 2.40 × 10−8 | 1.80 × 10−10 |
14 | 5.60 × 10−8 | 3.20 × 10−10 | 1.70 × 10−8 | 1.40 × 10−9 |
15 | 9.80 × 10−8 | 3.60 × 10−9 | 2.00 × 10−8 | 1.20 × 10−9 |
Grade 65 | Grade 80 | |||
---|---|---|---|---|
Permeability (m2) | St. Dev. (m2) | Permeability (m2) | St. Dev. (m2) | |
1 | - | - | 1.50 × 10−8 | 1.40 × 10−9 |
2 | 9.90 × 10−9 | 9.60 × 10−11 | 8.90 × 10−9 | 3.60 × 10−11 |
3 | 8.30 × 10−9 | 5.60 × 10−10 | 3.30 × 10−9 | 2.50 × 10−11 |
4 | 1.60 × 10−8 | 7.70 × 10−10 | 1.10 × 10−8 | 5.70 × 10−10 |
5 | 2.10 × 10−8 | 7.70 × 10−10 | 1.20 × 10−8 | 7.40 × 10−11 |
6 | - | - | - | - |
7 | 1.10 × 10−8 | 1.10 × 10−10 | 6.80 × 10−9 | 2.50 × 10−11 |
8 | 8.50 × 10−9 | 5.60 × 10−10 | 5.30 × 10−9 | 2.60 × 10−11 |
9 | 2.40 × 10−8 | 3.20 × 10−10 | 5.40 × 10−9 | 1.70 × 10−11 |
10 | 7.50 × 10−9 | 4.80 × 10−10 | 4.90 × 10−9 | 2.70 × 10−10 |
11 | - | - | 2.40 × 10−9 | 4.20 × 10−10 |
12 | 9.10 × 10−9 | 1.20 × 10−10 | 5.70 × 10−9 | 2.60 × 10−10 |
13 | 9.00 × 10−9 | 2.20 × 10−10 | 9.30 × 10−9 | 8.20 × 10−10 |
14 | 9.90 × 10−9 | 1.90 × 10−10 | 4.90 × 10−9 | 4.30 × 10−11 |
15 | 1.10 × 10−8 | 1.20 × 10−10 | 1.10 × 10−8 | 6.60 × 10−10 |
30 PPI | 50 PPI | 60 PPI | ||||
---|---|---|---|---|---|---|
Permeability (m2) | St. Dev. (m2) | Permeability (m2) | St. Dev. (m2) | Permeability (m2) | St. Dev. (m2) | |
1 | 4.1 × 10−8 | 1.1 × 10−9 | - | - | - | - |
2 | 3.5 × 10−8 | 8.2 × 10−10 | - | - | - | - |
3 | 1.7 × 10−7 | 2.9 × 10−9 | 1.0 × 10−8 | 8.7 × 10−11 | 1.1001 × 10−8 | 2 × 10−10 |
4 | - | - | 1.8 × 10−8 | 1.4 × 10−10 | 9.4303 × 10−9 | 1 × 10−10 |
5 | 9.1 × 10−8 | 8.9 × 10−10 | 2.2 × 10−8 | 2.2 × 10−10 | 5.8 × 10−9 | 8 × 10−11 |
6 | 4.5 × 10−8 | 3.7 × 10−10 | - | - | - | - |
7 | 1.1 × 10−7 | 9.7 × 10−10 | 1.6 × 10−8 | 2.4 × 10−10 | 1.09 × 10−8 | 1 × 10−10 |
8 | 5.9 × 10−8 | 8.3 × 10−10 | 1.3 × 10−8 | 1.3 × 10−10 | 9.5434 × 10−9 | 9 × 10−11 |
9 | 1.1 × 10−7 | 1.5 × 10−9 | - | - | - | - |
10 | 2.1 × 10−8 | 2.2 × 10−10 | 1.5 × 10−8 | 1.3 × 10−10 | 8.45 × 10−9 | 6 × 10−11 |
11 | - | - | 1.6 × 10−8 | 1.8 × 10−10 | - | - |
12 | - | - | - | - | - | - |
13 | - | - | * 5.5 × 10−8 | 3.1 × 10−10 | 6.16 × 10−9 | 4 × 10−11 |
14 | - | - | - | - | 6.06 × 10−9 | 2 × 10−11 |
15 | - | - | 1.3 × 10−8 | 1.0 × 10−10 | 6.66 × 10−9 | 4 × 10−11 |
30 PPI | 50 PPI | 60 PPI | ||||
---|---|---|---|---|---|---|
Permeability (m2) | St. Dev. (m2) | Permeability (m2) | St. Dev. (m2) | Permeability (m2) | St. Dev. (m2) | |
1 | 1.8 × 10−7 | 2.9 × 10−9 | - | - | 9.1 × 10−9 | 1.9 × 10−10 |
2 | 6.6 × 10−8 | 2.5 × 10−9 | 7.0 × 10−8 | 7.1 × 10−10 | 1.2 × 10−8 | 1.8 × 10−10 |
3 | 1.5 × 10−7 | 1.6 × 10−9 | 2.7 × 10−8 | 2.1 × 10−10 | - | - |
4 | 9.2 × 10−8 | 1.4 × 10−9 | - | - | - | - |
5 | - | - | * 9.8 × 10−8 | 2.2 × 10−9 | 1.2 × 10−8 | 1.7 × 10−10 |
6 | 8.8 × 10−8 | 8.6 × 10−10 | 3.8 × 10−8 | 5.4 × 10−10 | 9.2 × 10−9 | 1.1 × 10−10 |
7 | 2.2 × 10−7 | 2.4 × 10−9 | - | - | - | - |
8 | - | - | - | - | - | - |
9 | 7.0 × 10−8 | 1.1 × 10−9 | 3.8 × 10−8 | 5.5 × 10−10 | 1.1 × 10−8 | 1.1 × 10−10 |
10 | 9.9 × 10−8 | 6.5 × 10−10 | 4.3 × 10−8 | 7.4 × 10−10 | 1.2 × 10−8 | 4.1 × 10−10 |
11 | - | - | 3.9 × 10−8 | 3.3 × 10−10 | - | - |
12 | - | - | 4.8 × 10−8 | 1.4 × 10−9 | - | - |
13 | - | - | - | - | 1.7 × 10−8 | 4.5 × 10−10 |
14 | - | - | - | - | 1.0 × 10−8 | 6.8 × 10−11 |
15 | - | - | 3.2 × 10−8 | 5.0 × 10−10 | 1.2 × 10−8 | 8.7 × 10−11 |
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CFF Supplier | Dimensions (Length × Width × Height) (mm) | Grade | PPI |
---|---|---|---|
A | 584.2 × 584.2 × 51 | 30, 50, 65 and 80 | - |
B | 584.2 × 584.2 × 51 | - | 30, 50, and 60 |
C | 508 × 508 × 50 | - | 30, 50, and 60 |
CFF Supplier | True Particle Density (kg·m−3) | Std. Dev. (kg·m−3) | Average True Particle Density (kg·m−3) | |
---|---|---|---|---|
A | Grade 30 | 3413.6 | 9 | 3426.3 |
Grade 50 | 3431.5 | 3.8 | ||
Grade 65 | 3434.4 | 6.2 | ||
Grade 80 | 3425.8 | 4 | ||
B | 30 PPI | 3427.8 | 7.8 | 3427.9 |
50 PPI | 3417.3 | 8.3 | ||
60 PPI | 3438.8 | 4.4 | ||
C | 30 PPI | 3398.3 | 8.1 | 3388.8 |
50 PPI | 3391.7 | 7.3 | ||
60 PPI | 3376.5 | 3 |
Supplier A | Supplier B | Supplier C | |||||||
---|---|---|---|---|---|---|---|---|---|
G * 30 | G 50 | G 65 | G 80 | 30 PPI | 50 PPI | 60 PPI | 30 PPI | 50 PPI | 60 PPI |
0.88 | 0.85 | 0.86 | 0.85 | 0.88 | 0.87 | 0.87 | 0.88 | 0.89 | 0.89 |
* Grade |
Supplier and Grade/PPI Number | Counts (Number of Samples) | Cell | Window | ||
---|---|---|---|---|---|
Mean Feret Diameter (µm) | Pooled Std. Dev. (µm) | Mean Feret Diameter (µm) | Pooled Std. Dev. (µm) | ||
A Grade 30 | 12 | 1254.7 | 893.1 | 751.0 | 262.9 |
A Grade 50 | 14 | 1047.8 | 577.8 | 503.5 | 388.6 |
A Grade 65 | 12 | 886.3 | 531.4 | 407.2 | 109.3 |
A Grade 80 | 12 | 655.9 | 460.2 | 345.8 | 102.2 |
B 30 PPI | 10 | 1323.5 | 872.0 | 697.2 | 172.8 |
B 50 PPI | 15 | 1134.1 | 722.6 | 501.0 | 93.7 |
B 60 PPI | 14 | 881.1 | 568.3 | 354.4 | 69.7 |
C 30 PPI | 14 | 2134.1 | 1219.1 | 960.3 | 249.1 |
C 50 PPI | 15 | 1429.3 | 793.5 | 725.2 | 167.7 |
C 60 PPI | 13 | 900.4 | 535.3 | 389.3 | 73.4 |
Equality of the Sample Variances (F-Test) | Significance of the Means (t-Test, Equal Variances) | |||
---|---|---|---|---|
Mean Permeability (m2) | A30 = 6.29 × 10−8 | B30 = 7.5 × 10−8 | A30 = 6.29 × 10−8 | B30 = 7.5 × 10−8 |
Observation Number | A30 = 14 | B30 = 9 | A30 = 14 | B30 = 9 |
Degrees of Freedom (df) | A30 = 13 | B30 = 8 | 21 | |
F or T-critical (One tail) | 0.36 | 1.72 | ||
Test Statistic | 0.28 | 0.82 | ||
Null (H0) | S *A302 = SB302 | |||
Reject Null | No | No | ||
* “S” is the sample standard deviation. ** “” is the sample mean. |
Supplier B | Supplier C | ||||||
---|---|---|---|---|---|---|---|
PPI 30 | PPI 50 | PPI 60 | PPI 30 | PPI 50 | PPI 60 | ||
Supplier A | Grade 30 | ||||||
Grade 50 | |||||||
Grade 65 | |||||||
Grade 80 |
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Hassanabadi, M.; Berto, T.; Akhtar, S.; Aune, R.E. Hydraulic Characterization of Ceramic Foam Filters Used in Aluminum Filtration. Materials 2023, 16, 2805. https://doi.org/10.3390/ma16072805
Hassanabadi M, Berto T, Akhtar S, Aune RE. Hydraulic Characterization of Ceramic Foam Filters Used in Aluminum Filtration. Materials. 2023; 16(7):2805. https://doi.org/10.3390/ma16072805
Chicago/Turabian StyleHassanabadi, Massoud, Thomas Berto, Shahid Akhtar, and Ragnhild E. Aune. 2023. "Hydraulic Characterization of Ceramic Foam Filters Used in Aluminum Filtration" Materials 16, no. 7: 2805. https://doi.org/10.3390/ma16072805