SINGLE CORRELATION OF EDDY DIFFUSIVITY AND MIXING LENGTH IN CORE REGION OF POROUS PIPE FLOW WITH INJECTION AND SUCTION

Abstract

The velocity profile and pressure gradient of turbulent flow in a porous pipe were measured at inlet Reynolds numbers of (1.01, 2.09, 3.08)×10⁴ and ratios of injection/suction velocity to inlet average velocity of (-7.8 to 3.9)×10^-3. From the similarity of velocity profile, the maximum velocity, the radial position having average velocity and the axial momentum flux have been examined, and the eddy diffusivity and the mixing length have been obtained. Variation of the friction factor was smaller than predicted by the film theory.
The eddy diffusivity and the mixing length in the core region have been correlated into the same form asin the case without injection/suction by introducing defect parameters as
E(r/R)=(ε_M/ν)(u⁺_max-1/√C_f/2)(r/R)(τ_w/τ)/R⁺
L(r/R)=(l/R)(u⁺_max-1/√C_f/2)√(r/R)(τ_w/τ)
and
E(r/R)=L(r/R)√r/R
The pressure gradient and the local values of velocity, eddy diffusivity and mixing length can be estimated from the correlations obtained.