Schematic of the test model with gravity oriented upward (i.e., showing the working surface). The locations of the skin-friction balances, PIV systems, and the injector are shown.
Non-injection velocity data from the current experiment scaled with inner variables. Included are results from (+) X = 1.96 m, (×) X = 5.94 m, and (*) X = 10.68 m. Also included are curves for the viscous sublayer (U + = Y +), traditional log-law region (U + = ln(Y +)/κ + B) and the ultimate profile (U + = 11.7 ln(Y +) – 17.0).
Examples of scaled velocity profiles with varying levels of drag reduction. The injection concentration was 4000 wppm for all the conditions shown. (%DR = 18.2, X = 1.96 m, U ∞ = 19.9 m s−1, q = 2 qs, Re θ = 4.6 × 104; %DR = 35.2, X = 5.94 m, U ∞ = 20.0 m/s, q = 10 qs, Re θ = 1.2 × 105; %DR = 53.5, X = 1.96 m, U ∞ = 19.9 m/s, q = 10 qs, Re θ = 4.5 × 104; %DR = 64.8, X = 5.94 m, U ∞ = 6.7 m/s, q = 10 qs, Re θ = 4.6 × 104.) The maximum drag reduction asymptote or ultimate profile (heavy dotted line) and the law of the wall (solid line) are shown also.
The intercept B plotted versus the percent drag reduction. The Reynolds number based on the momentum thickness (Re θ ) ranged from 9.7 × 102 to 1.5 × 105. Results shown are from the (✩) current study, (○) Koskie and Tiederman, 24 (◊) Fontaine et al., 25 (▵) White et al., 26 (□) Petrie et al., 27 (⊲) Hou et al., 28 and (⊳) Somandepalli et al. 29 The symbol color corresponds to the Reynolds number range as shown in the legend. Dashed lines indicate the Newtonian value (B = 5.0) and the ultimate profile (B = −17). The solid line (B = 5 + (0.2)(%DR)) was a linear fit to data presented in Petrie et al. 27
The von Kármán constant as a function of percent drag reduction from several studies (symbols and colors are the same as in Figure 4 ). The dashed lines correspond to the values corresponding to Newtonian (κ = 0.41) and the ultimate profile (κ = 1 / 11.7 ≈ 0.0855). The solid line is a linear fit to data presented in Koskie and Tiederman. 24
Indicator function (ζ) versus inner-variable-scaled wall-normal distance at a free-stream speed of (upper) 6.7 and (lower) 20.3 m/s. All the data shown were acquired at the first measurement station (X = 1.96 m) except for the condition at %DR = 64.8, which was acquired at X = 5.94 m. The Reynolds numbers for %DR = 42.3, 53.0, 64.8, 18.2, 44.0, and 53.5 conditions are Re θ = 1.7 × 104, 1.8×104, 4.6 × 104, 4.6 × 104, 4.6 × 104, and 4.5 × 104, respectively. At each speed a no-injection condition is provided for comparison with the drag reduced results.
Sources of experimental measurements of the mean velocity distribution in PDR TBL flows. Included are the type of polymer used, maximum level of drag reduction and the range of momentum-thickness based Reynolds number.
Summary of conditions where the velocity distributions were measured. The velocities shown are the average free-stream velocity over the length of the test model. Local free-stream velocities varied due to boundary layer growth on the model and tunnel walls (6.7 m s−1 = 6.62, 6.65, 6.77 m s−1; 20.3 m s−1 = 19.9, 20.0, 20.3 m s−1 for X = 1.96, 5.94, 10.68 m, respectively).
Article metrics loading...
Full text loading...