Effect of Drag-Reducing Additives on Boundary-Layer Turbulence

Abstract

A preliminary investigation has been made concerning the effects of polyethylene oxide on the spectral density of turbulent fluctuations in a boundary layer. The Polyox solution was injected into a two-dimensional boundary layer along a flat plate which was towed at 9.5 fps in the Naval Academy's 85-ft tow tank. Measurements of the mean and fluctuating components of the velocity near the wall were made with conical hot film sensors. Polymer injection resulted in an increase in rms level of the fluctuations and in an increase in spectral density below 200 Hz. Above this frequency, the spectral density decreased, the effect being more pronounced at higher frequencies and at higher polymer concentrations. Measurements of the mean and fluctuating components of the wall shear stress were made with flush-mounted hotfilm sensors submerged in the viscous sublayer. Polymer injection resulted in a decrease in mean shear, in rms level, and in spectral density of the fluctuating wall shear stress. The latter effect increased with increasing frequency and all effects increased with higher molecular weight of the additives. All results suggest the polymer shifts the scale of turbulence away from the energy-dissipating small eddies. Nomenclature A = bridge voltage squared at zero flow B = King's formula constant db = decibels (•• -fluctuating voltage CL = fluctuating linearized voltage Ei, = anemometer bridge voltage Eh = time-averaged bridge voltage EL = linearized voltage / = frequency F c (f) = normalized voltage spectral density F,t(f) = normalized velocity spectral density G x (f) = power spectral density of quantity x in a 1-11/ band l7. r (/)A/ = power spectral density of quantity x in a yVoctave band k\ = one-dimensional wave number K = constant m = linearizer exponent n = King's formula exponent Af = temperature difference between sensor and environment TJ. -turbulence intensity n = fluctuating local velocity V = local velocity I? = time-average local velocity r\ : = convection velocity T W = wall shear stress TV = time-averaged wall shear stress r,,/ = fluctuating wall shear stress

Local drag reduction due to injection of polymer solutions into turbulent flow in a pipe. Part I: Dependence on local polymer concentration

“…Our second point is concerned with the fact that injection techniques have generally been employed mainly as a practical expedient, where premixing of the polymer would be either uneconomic or otherwise undesirable. Not surprisingly, most reports in this area deal with external flows over a solid body (e.g., Love, 1965;Johnson and Barchi, 1968;Granville, 1969;Latto and Shen, 1970;Wu, 1971;Kowalski and Brundrett, 1974), but some practical studies have also been made using boundary-layer or wallregion injection in pipe flows (e.g., Goren and Norbury, 1967;Maus andWilhelm, 1970 Walters andWells, 1971;Ramu and Tullis, 1976). While these papers, in the main, tend to deal with practical aspects of optimizing drag reduction, several of their conclusions are of more general interest and we shall return to these at a later stage.…”

Grid-generated turbulence in dilute polymer solutions

“…Similar measurements near the pipe wall showed that the intensity, spectral shape and dissipation were the same as in pure water. Johnson & Barchi (1968) measured the relative effects of the injection of polytheylene oxide into a turbulent boundary layer using a conical hot-film probe. It was found that the intensity level of the turbulence near the wall increased with injection, and the spectrum showed more energy at low wave-numbers and less a t high wave-numbers compared to that in water.…”

A review on drag reduction with special reference to micellar systems

“…But Gadd [271,272] was among the first to suggest that drag reduction occurred not due to reduced turbulence dissipation, but rather due to a decreased production of turbulence. Johnson and Barchi [273] performed the first few experiments to show that there was a decreased production of small eddies in a developing boundary layer containing a polymer. Walsh [234,274] proposed a comprehensive theory of drag reduction that large scale disturbances which produce Reynolds stresses some distance downstream were, previously, small disturbances at the edge of the viscous sublayer some distance upstream.…”