Session M39: Pipe Flow

New friction factor and mean velocity profile for turbulent pipe flow at extreme Reynolds number

We report on a novel power-law formula for evaluating the friction factor of turbulent incompressible Newtonian fluid flows, f ∼ 1/Re^2/13. The formula is based on a new phenomenology for coherent structures dominating the momentum exchange in mesoregions that are set by the geometric mean of the viscous and outer length scales that have recently been shown to provide the missing link between the flow's viscous and inertial regions.
  The new formula implies a new asymptotic mean velocity profile  of the form u⁺ ∼ A(y⁺-c)^1/12 for the leading order. Comparison with the Princeton superpipe data shows excellent agreement.   

Turbulent coherent structures in an obstructed pipe flow with favorable pressure gradient

A fully-developed turbulent pipe flow at Re_τ = 3400 was perturbed by an axisymmetric obstruction in the center of the pipe, causing favorable pressure gradients and streamline curvature in the flow. The pipe flow was studied with and without the obstruction using particle image velocimetry (PIV). Changes in flow statistics and in the shapes and inclination angles of turbulent coherent structures were observed from the addition of the obstruction. Conditional averaging and proper orthogonal decomposition were used to examine the turbulent structures. This talk will discuss the changes observed in the structures and connect these observations to the existing literature on turbulent coherent structures in favorable pressure gradients. The implications of the results for future reduced-order modeling efforts will be discussed.   

Statistics of a fully developed turbulent pipe flow perturbed by a streamlined axisymmetric body

A fully developed turbulent pipe flow was perturbed by a streamlined axisymmetric body to study the effects of pressure gradient and streamline curvature. Measurements were taken in a water pipe using PIV at Re_τ≈3400 and in the Princeton Superpipe facility using a nanoscale hot-wire probe with Re_τ up to 100000. Behaviors of the mean velocity and the axial turbulence intensity are explored both at the pipe wall and at the insert body, as well as in a streamline coordinate system. Changes in the statistics compared to canonical pipe flows are clearly correlated with various pressure gradients and streamline curvatures. These changes will be reconciled with the observations from turbulent coherent structures in the same flows. We will also discuss the statistics in terms of turbulence production and their implications for turbulence scaling incorporating pressure and curvature parameters.   

Power law scaling of the friction factor in pipe flow

We present a study of the friction factor scaling for pipe and duct flows at moderate Reynolds numbers (5000<Re<150 000) in experiments and highly resolved direct numerical simulations.
While the experimental and numerical data are in excellent agreement, we find that for Re<80 000 they do not follow the Karman-Prandtl friction relation. Instead the friction factor precisely
follows the Blasius power law. This power law scaling can also be derived based on
Kolmogorov's first hypothesis (assuming local isotropy) in line with an earlier study.  A detailed analysis of the numerical data shows that flows in this Reynolds number regime are indeed locally isotropic and that hence the application of the Kolmogorov theory is justified. Finally, we will show that the deviation of the friction factor from the power law scaling (Re>80 000) occurs when large scale motions (so-called ``superstructures'') arise in the flow and their contribution to the friction factor becomes dominant.   

On the Development of an Apparatus to Examine Rotating Pipe Flow at High Rotation Numbers

Previous experiments and simulations have demonstrated that rotation can potentially stabilize, and possibly even relaminarize, turbulent flows.  However, the mechanism behind this suppression is not well understood.  Prior research studies for different classes of flow indicate that hydrodynamic stability theory can utilized to extract important information about the relaminarization process. Rotating pipe flow is a canonical example of this problem, however the stabilization process is particularly sensitive to the rotation rates and Reynolds number.  Experimental studies covering this range are rare and do not cover the higher rotation rates where relaminarization may manifest.  Here we present progress on the development of a turbulent pipe flow apparatus designed to study a large envelope of Reynolds numbers and rotation rates and provide data facilitating and verifying detailed stability analysis of the problem.