Mean velocity profile in high Re-number turbulent boundary layer (Comparison with large wind tunnels in the world)

Abstract

High Reynolds number turbulent boundary layer measurement is performed in the RTRI ’s low-noise wind tunnel in Maibara Japan. The momentum thickness Reynolds number Rθ is up to approximately 8×104. Mean velocity statistics are compared with those of large wind tunnel facilities in Melbourne, Sweden, New Hampshire, Netherland, France and UK. The ratio of momentum thickness θ，displacement thickness δ* and Rotta-Clauser thickness Δ against the boundary layer thickness δ99 does not show the similar trend but depends on the facility. Mena velocity profile is approximated by the log-law relations; U+ = 1/κ ∙ ln(y+) + B + Π/κ ∙ W(y/δc) and (U0 − U)/uτ = − 1/κ ∙ ln(y/Δ) + B1 , where W is wake function, U0 is free stream velocity, uτ is friction velocity, and δc is Coles’ boundary layer thickness. Parameters κ，B, B1, and Π distribute in wide range, but they relate with one another and the simple relation between κ and B is presented. Also the relation between κB1 and Π is confirmed. When the effect of virtual origin is corrected, the Reynolds number Rx′ ≡ U0x′/ν , where x′ = x + x0, x is the distance from the leading edge and x0 is virtual origin, indicates the same trend against Rθ independent of facilities. Also, the skin friction coefficients agree with one another as a function of Reynolds number based on displacement thickness.

Keywords

• turbulence
• turbullent boundary layer
• mean velocity profile
• high reynolds number
• universality