A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow

A new theory for the streamwise turbulent fluctuations in fully developed pipe flow is proposed. The theory extends the similarities between the mean flow and the streamwise turbulence fluctuations, as observed in experimental high Reynolds number data, to also include the theoretical derivation. Connecting the derivation of the fluctuations to that of the mean velocity at finite Reynolds number as introduced by Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115-145) can explain the logarithmic behaviour as well as the coefficient of the logarithm. The slope of the logarithm, for the fluctuations, depends on the increase of the fluctuations with Reynolds number, which is shown to agree very well with the experimental data. A mesolayer, similar to that introduced by Wosnik et al., exists for the fluctuations for $300\gt {y}^{+ } \gt 800$ , which coincides with the mesolayer for the mean velocities. In the mesolayer, the flow is still affected by viscosity, which shows up as a decrease in the fluctuation

A theory for the streamwise turbulent fluctuations in high Reynolds number pipe flow

A new theory for the streamwise turbulent fluctuations in fully developed pipe flow is proposed. The theory extends the similarities between the mean flow and the streamwise turbulence fluctuations, as observed in experimental high Reynolds number data, to also include the theoretical derivation. Connecting the derivation of the fluctuations to that of the mean velocity at finite Reynolds number as introduced by Wosnik, Castillo & George (J. Fluid Mech., vol. 421, 2000, pp. 115-145) can explain the logarithmic behaviour as well as the coefficient of the logarithm. The slope of the logarithm, for the fluctuations, depends on the increase of the fluctuations with Reynolds number, which is shown to agree very well with the experimental data. A mesolayer, similar to that introduced by Wosnik et al., exists for the fluctuations for 300 > y(+) > 800, which coincides with the mesolayer for the mean velocities. In the mesolayer, the flow is still affected by viscosity, which shows up as a decrease in the fluctuations

Examining the inertial subrange with nanoscale cross-wire measurements of turbulent pipe flow at high Reynolds number near the centreline [post-print]

Highly resolved, two-component velocity measurements were made near the centreline of turbulent pipe flow for Reynolds numbers in the range . These unique data were obtained with a nanoscale cross-wire probe and used to examine the inertial subrange scaling of the longitudinal and transverse velocity components. Classical dissipation rate estimates were made using both the integration of one-dimensional dissipation spectra for each velocity component and the third-order moment of the longitudinal structure function. Although the second-order moments and one-dimensional spectra for each component showed behaviour consistent with local isotropy, clear inertial range similarity and behaviour were not exhibited in the third-order structure functions at these Reynolds numbers. When corrected for the effects of radial inhomogeneities at the centreline following the generalized expression of Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87-109), re-derived for the pipe flow domain, the third-order moments of the longitudinal structure function exhibited a clearer plateau per the classical Kolmogorov \u27four-fifths law\u27. Similar corrections described by Danaila et al. (J. Fluid Mech., vol. 430, 2001, pp. 87-109) applied to the analogous equation for the mixed structure functions (i.e. the \u27four-thirds law\u27) also yielded improvement over all ranges of scale, improving with increasing Reynolds number. The rate at which the \u27four-fifths\u27 law and \u27four-thirds\u27 law were approached by the third-order structure functions was found to be more gradual than decaying isotropic turbulence for the same Reynolds numbers

Acceleration is the Key to Drag Reduction in Turbulent Flow

A turbulent pipe flow experiment was conducted where the surface of the pipe was oscillated azimuthally over a wide range of frequencies, amplitudes and Reynolds number. The drag was reduced by as much as 30\%. Past work has suggested that the drag reduction scales with the velocity amplitude of the motion, its period, or the Reynolds number. Here, we find that the key parameter is simply the acceleration, which reduces the complexity of the phenomenon by two orders of magnitude. This insight opens new potential avenues for reducing fuel consumption by large vehicles and for reducing energy costs in large piping systems.Comment: 8 pages, 5 figure

A New Wall Shear Stress Model for Atmospheric Boundary Layer Simulations

A new wall shear stress model to be used as a wall boundary condition for large-eddy simulations of the atmospheric boundary layer is proposed. The new model computes the wall shear stress and the vertical derivatives of the streamwise velocity component by means of a modified, instantaneous, and local law-of-the-wall formulation. By formulating a correction for the modeled shear stress, using experimental findings of a logarithmic region in the streamwise turbulent fluctuations, the need for a filter is eliminated. This allows one to model the wall shear stress locally, and at the same time accurately recover the correct average value. The proposed model has been applied to both unique high Reynolds number experimental data and a suite of large-eddy simulations, and compared to previous models. It is shown that the proposed model performs equally well or better than the previous filtered models. A nonfiltered model, such as the one proposed, is an essential first step in developing a universal wall shear stress model that can be used for flow over heterogeneous surfaces, studies of diurnal cycles, or analyses of flow over complex terrain