Study of the Reduction of Turbulent Drag by Photon Correlation Spectroscopy
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STUDY OF THE REDUCTION OF TURBULENT DRAG BY PHOTON CORRELATION SPECTROSCOPY P. [1] [2] [3]
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TONG', W. I. GOLDBURG', and J. S. HUANG Department of Physics, Oklahoma State University, Stillwater, OK 74078 Department of Physics, University of Pittsburgh, Pittsburgh, PA 15260 Exxon Research and Engineering Company, Annandale, NJ 08801
ABSTRACT Turbulent drag reduction in a dilute polymer solution has been studied using the technique of photon-correlation homodyne spectroscopy to measure velocity differences in a concentric cylinder cell, in which the inner cylinder rotates. A large anisotropic suppression of turbulent velocity differences is found in the bulk region of the turbulent fluid. The suppression effect occurs at various length scales up to - 1 mm, which is far beyond the Kolmogorov dissipation length Ed (- 0.04 mm). The large-scale velocity fluctuations are suppressed, but their statistical properties remain unchanged. The small-scale fluctuations, on the other hand, are damped out much more strongly, resulting in a different functional form for the velocity density function. The latter observation is consistent with the notion that the polymer-turbulence interaction causes a truncation of the turbulent energy cascade at small scales. I. INTRODUCTION It has been known that trace amount of flexible polymers in solution can significantly reduce the drag of turbulent flow below that for the solvent alone. The phenomenon, which has stimulated much research in past decades, has important applications, such as increasing pipeline. capacities and speeding ships. However, the exact mechanism for the drag reduction effect is not well understood, and only tentative explanations exist. It is believed that turbulent flow strongly stretches polymer chains in the solution, and the reaction of the stretched polymer chains to the flow gives rise to the drag reduction. One hypothesis for the drag reduction assumes that the stretched polymer chains affect the turbulent energy cascade at small scales via the enhancement of the elongational viscosity 1 - 3 or via some elastic modulus of the stretched chains. 4 Another hypothesis assumes that polymer molecules cause stabilization of viscous boundary 5 6 layers, and hence reduce the production of turbulence. , Two important questions concerning the phenomenon of turbulent drag reduction are: 1) whether the influence of polymer additives is restricted to regions near the wall or if it also extends to the turbulent core region; 2) at what length scales polymer additives affect the turbulent flow. Is the turbulence damped at small scales comparable to the turbulent dissipation length or at both the small and large scales? To answer these questions one has to study spatial structures of the turbulence in polymer solutions at different positions and at various length scales. In this paper we report an experimental study of turbulent drag reduction using the technique of photon-correlation homodyne spectroscopy (HS),' from which the probability density function P(V, R) of the relati
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