Experiments in high Reynolds number turbulent pipe flow

Abstract

An experimental facility was constructed to investigate fully-developed turbulent pipe flow over an unprecedented range of Reynolds numbers (approximately 32 x 10 to 35 x 10 based on average velocity and diameter). The maximum Reynolds number investigated exceeds the highest previously measured by an order of magnitude. To attain high Reynolds numbers at reasonable cost, compressed air (up to 220 aim} was used as the working fluid. The results show that the friction factor depends on Reynolds number logarithmically, as proposed by Prandtl, but a set of new constants are found. The friction factor data show von K&rman's constant to be 0.44. If the velocity profile is normalized using inner scaling variables, a log-law with this slope and an additive constant of 6.3 is in excellent agreement with the data. If the velocity profile is normalized using outer scaling variables, a log-law with this slope and an additive constant of 1.5 is in good agreement with the data. It is also shown that the average velocity occurs at a location approximately 1/4 radius from the wall, independent of Reynolds number. vious studies (for example, [1, 2, 3, 4, 5]), it is difficult to find data at very high Reynolds numbers where many industrial systems operate, or across a large range of Reynolds numbers over which subtle Reynolds number effects can become apparent and basic scaling dependencies can be unambiguously established. Previous investigations have shortcomings due to the limited range of Reynolds numbers covered by the data, the uncertainty in the quality of the surface finish, the uncertain accuracy of the measurements, or an insufficient development length. The present experiment was designed to provide accurate measurements over a very large range of Reynolds numbers in a single apparatus. The lowest Reynolds number investigated was approximately 32 x 10, and the highest exceeded 35 x 10, corresponding to an order of magnitude increase over the highest Reynolds number for mean flow measurements [4], and two orders of magnitude increase over the highest Reynolds number for turbulence measurements [3]. This paper presents the mean flow measurements for this range of Reynolds numbers and addresses the scaling of the mean velocity profile and friction factor.