Turbulence structure and polymer drag reduction in adverse pressure gradient boundary layers

John Edward Koskie, Purdue University

Abstract

This study examined one zero pressure gradient Newtonian boundary layer and two adverse pressure gradient equilibrium boundary layers in a water channel. The momentum thickness Reynolds numbers, Re$\sb{\theta}$, were in the range 1360 to 4980. The adverse pressure gradient boundary layers were characterized by equilibrium parameters, $\beta$ of 1.8 and 2.4. These boundary layers were modified by injecting a drag reducing polymer solution at 2.6 and 5.1 times the flow rate of the undisturbed flows inside of y$\sp+$ = 5. The sum of the viscous and Reynolds shear stresses was sometimes less than the total shear stress in the drag reduced boundary layer and in these cases the production of Reynolds shear and normal stresses was virtually eliminated. The mean streamwise velocity measurements in the drag reduced boundary layers showed that both parameters, $\kappa$ and B, of the logarithmic velocity profile changed. The slope parameter, $\kappa$, varied directly with the percent drag reduction. The peak in the root-mean-square streamwise velocities remained essentially unchanged in the presence of polymer but its location moved away from the wall. The root-mean-square normal velocities and the Reynolds shear stress were reduced in the inner region of the boundary layer during drag reduction. The adverse pressure gradient boundary layers did not separate during drag reduction even when large amounts of polymer were injected. The influence of the polymer on the turbulent boundary layer structure was greatly reduced, but the effects of polymer were consistent with those in the zero pressure gradient boundary layer. The hypothesis that the extensional motions in the flow must be strong enough to stretch the polymer molecules so that stretched molecules will form an anisotropic viscosity that damps the small scales of the turbulence (Hinch, 1977) was supported by the present data. Walker's (1985) modified mixing length model correctly predicted the wall shear stress coefficient, c$\sb{\rm f}$, in all the drag reduced boundary layers as long as the measured polymer concentration in the linear sublayer was within the range of concentrations for which the model was derived and the non-Newtonian shear stresses in the boundary layer were small. Mixed scaling of the average time between bursts best scaled the present zero and adverse pressure gradient Newtonian boundary layer data. The data were consistent with the hypothesis that the method of tripping the boundary layer affects the average burst period at very low Reynolds numbers.

Degree

Ph.D.

Advisors

Tiederman, Purdue University.

Subject Area

Mechanical engineering|Aerospace materials

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