Reliability of friction factor in turbulent pipe flow - Investigation from mean velocity profile

Following the recent observation that turbulent pipe flow can be relaminarised by a relatively simple modification of the mean velocity profile, we here carry out a quantitative experimental investigation of this phenomenon. Our study confirms that a flat velocity profile leads to a collapse of turbulence and in order to achieve the blunted profile shape, we employ a moving pipe segment that is briefly and rapidly shifted in the streamwise direction. The relaminarisation threshold and the minimum shift length and speeds are determined as a function of Reynolds number. Although turbulence is still active after the acceleration phase, the modulated profile possesses a severely decreased lift-up potential as measured by transient growth. As shown, this results in an exponential decay of fluctuations and the flow relaminarises. While this method can be easily applied at low to moderate flow speeds, the minimum streamwise length over which the acceleration needs to act increases linearly with the Reynolds number.

Download Full-text

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

Journal of Heat Transfer ◽

10.1115/1.3450785 ◽

1978 ◽

Vol 100 (2) ◽

pp. 224-229 ◽

Cited By ~ 2

Author(s):

O. T. Hanna ◽

O. C. Sandall

Keyword(s):

Heat Transfer ◽

Friction Factor ◽

Pipe Flow ◽

Turbulent Pipe Flow ◽

Fluid Viscosity ◽

Temperature Dependent ◽

Temperature Dependent Viscosity ◽

Analytical Approximations ◽

Constant Viscosity ◽

Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

Download Full-text

Discussion: “Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow” (Haaland, S. E., 1983, ASME J. Fluids Eng., 105, pp. 89–90)

Journal of Fluids Engineering ◽

10.1115/1.3240975 ◽

1983 ◽

Vol 105 (2) ◽

pp. 242-243 ◽

Cited By ~ 1

Author(s):

Don J. Wood

Keyword(s):

Friction Factor ◽

Pipe Flow ◽

Turbulent Pipe Flow ◽

Explicit Formulas

Download Full-text