Heat and Flow Properties of Thread-Complexity:Part 2 : Flow Property of Parallel-Thread-Complexity
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Concerning the flow-property of porous-materials, there have been researches of Darcy (1856) in laminar-flow, and of M. Muskat (1949) in turbulent-flow, but those of J.C.Ward (1964) in laminar-turbulentflow seem to be well agreed with experiments. Bit, the definition of the constant of the porous materials, C, has not been well-explained.<BR>Thus, a general expression of laminir-turbilent flow for the parallel -thread complexity is investigated and the property of "C" is studied in this report.<BR>THEORY : The turbulent flow in the porous materials is expressed as follows : <BR>ΔP/ΔL=a·v=+b·v<SUP>2</SUP>… (1) <BR>whereυ : velocity.<BR>Here, J.C. Ward (1964) got the expression (2) <BR>by means of the Demensional Analysis.<BR>ΔP/ΔL=C<SUB>1</SUB>·μ·v/k+C<SUB>2</SUB>·ρ/√k·v<SUP>2</SUP>… (2) <BR>Whereμ : viscosity<BR>ρ : density<BR>k : permeability<BR>On the other hand, Darcy's law (3) can be applied to the laminar flow in the porous materials : <BR>ΔP/ΔL=μ·v/k… (3) <BR>From the expressions (2) and (3), we get the expression (4) when C<SUB>1</SUB>=1 and C<SUB>2</SUB>=C.<BR>ΔP/ΔL=μ/k·v+C·ρ·v<SUP>2</SUP>/√k=a·μ·v+β·rho;·v<SUP>2</SUP>… (4) <BR>where a=1/k, β=c/√k.<BR>Although the combination of viscous effect and inertia effect has not been justified from the stand point of pure theory, this has been supported experimentally by G. S. Beavers (1969). Following J. C. Ward, if we define the Reynolds number of porous materials as R=√k·ρ·υ/μ, and the coefficient of nondimensional Fanning friction of porous materials as F=ΔP·√k/ (ΔL·rho;·υ<SUP>2</SUP>), the expression (4) will be reduced to<BR>F=1/R+C… (5) <BR>where C (=β·√k) is the "Constant of porous materials". This is expressed as F=1/R in Darcy's law.<BR>CONSIDERATION ON EXPERIMENTAL DATA : <BR>The linearity ofΔP/ΔL·μ·υ) -rho;·υ/μ is verified from its chart, and the values "k" and"C" are calculated through the expression (4) since the y value at x=0 is d=1/k, and the slope is β=c/√k.<BR>EXPERIMENTS : The brass-thread with diameters, 1.2, 2, 3, 4, 5 (mm), length, 150 (mm), 2ψ-100 (mm), 3φ-200 (mm) is used as the experimental thread, the experiment is done in the range of 25<R<SUB>e</SUB><16 500and 0.7<R<110.<BR>RESULTS : (1) The experimental expression for the paralllel-thread-complexity isΔP/ΔL==C<SUB>e</SUB>·R<SUB>e</SUB>+7·C<SUB>e</SUB>·R<SUB>e</SUB><SUP>2</SUP> (kg/m<SUP>3</SUP>) <BR>where C<SUP>e</SUP>=48.5·μ<SUP>2</SUP>·m/ (ε<SUP>1.66</SUP>·rho;·d<SUP>3</SUP>) (kg/m<SUP>3</SUP>) η=0.00862·m·ε<SUP>0.83</SUP>, d=≥10<SUP>-3</SUP> (m) ε<0.25ε<SUP>1.66</SUP>·d<SUP>2</SUP>≥10<SUP>-7</SUP> (m<SUP>2</SUP>) m=d/d0≤0.167 (ε : Air permeability, d<SUB>0</SUB> : diameter of the test tube) <BR> (2) Generally speaking, "C" is constant depending on the structure of the porous material.
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