Non-Darcian air flow in wood
Creators: name: Lu, Jianxiong
Publisher: name: University of British Columbia
Year: 2009

description: The purpose of this thesis research was to better understand the nature of gas flow in wood, and especially the phenomenon of non-Darcian air flow. Specifically, the objectives were to evaluate the non-Darcian air flow due to (1) specimen length; (2) nonlinear flow; and, (3) slip flow in wood, through a systematic investigation of the air flow phenomena in two softwoods and two hardwoods. Throughout the thesis, over the experimental range, the hypothesis that Darcy's law is not of universal application to gas flow in wood was shown to be true. Firstly, non-Darcian behaviour due to specimen length seemed common in the studied species. In the experimental range of specimen lengths, there was an existence of a certain length above which the permeability values were nearly identical for the various lengths of the tested species. These specimen lengths were found to be 140, 100, 60 and 40 mm for red oak heartwood, red alder heartwood, ponderosa pine sapwood, and Douglas-fir sapwood, respectively. When the specimen length was below a critical value for the different species described above, permeability increased drastically with decreasing specimen length. The higher the air permeability of a species, the greater was the critical specimen length. When the specimen length is above a critical value for the different species described above, the pressure drop caused by end effects due to the shape and condition of the specimen entrance is negligible. Secondly, except for red oak heartwood, there was no evidence of non-Darcian flow due to nonlinear flow in the studied species throughout the entire measured range of flow rates. For red oak heartwood, when the lower flow rates are used (Q≤ 19.57 cm³/s), the test results for the detection of nonlinear air flow were exactly the same as the specimen groups of red alder heartwood, ponderosa pine sapwood and Douglas-fir sapwood. That is, both permeability measurement and pressure-flow rate-relationship methods for the detection of nonlinear flow, indicated the existence of linear flow components only within the specimen. However, when the flow rates used were above 19.57 cm³/s, the test results showed that, the superficial specific permeability at the mean pressure of 0.5xl0⁵ Pa decreased with the increase of the flow rates, and the expression equation of pressure drop and flow rate at a given mean pressure of 0.5x10⁵ Pa involved both a linear and quadratic dependence of the pressure drop on the flow rate, thus demonstrating the presence of the nonlinear flow components in the specimen. The calculated value of Reynolds' number in the range of 0.263 to 1.05 further suggested that, the nonlinear flow found in the red oak heartwood at higher flow rates in this study was probably nonlinear laminar flow due to the kinetic-energy losses occurred in the curved openings. Finally, the test results indicated that the non-Darcian air flow due to slip flow existed in all the studied specimen groups. The true permeability of red oak heartwood, red alder heartwood, ponderosa pine sapwood and Douglas-fir sapwood was 20.91, 7.05, 0.51 and 0.068 μm³/μm, respectively. The average ratios of the superficial specific permeability at 0.5xl0⁵ Pa mean pressure to the true permeability were found to be: red oak heartwood: 1.047; red alder heartwood: 1.204; ponderosa pine sapwood: 1.292; and, Douglas-fir sapwood: 1.53. The slip flow constant b was highest (0.265xl0⁵Pa) for Douglas-fir sapwood, higher (0.146xl0⁵Pa) for ponderosa pine sapwood, lower (0.102xl0⁵Pa) for red alder heartwood, and lowest (0.023xl0⁵Pa) for red oak heartwood. The radius (r) and the number (n) of average effective openings were found to be: red oak heartwood: 17.432 μm and 0.066xl0⁶ per cm²; red alder heartwood: 3.955 pm and 7.5xl0⁶ per cm²; ponderosa pine sapwood: 2.972 μm and 3.3xl0⁶ per cm²; and, Douglas-fir sapwood: 1.552 μm and 3.6xl0⁶ per cm².