# Project HRPIPE, Direct Numerical Simulation of Pipe Flow at High Reynolds Numbers

Turbulence is a flow regimen which is dominated by a wide range of length and time scales. The largest scale of motion depends on the geometry of the problem and the smallest scale of motion on the material properties of the liquid. In the atmosphere the largest scales of motion can be a few hundred kilometers big while the smallest scale of motion are a few millimeters. In an engineering application the largest scales of motion are much smaller than in the atmosphere but still there is a very big difference between the smallest and largest scale of motion. The Reynolds number of the flow gives an indication for the range of scales. If one wants to resolve all scales of motion in a turbulent flow, the numerical grid has to be sufficiently fine to resolve the smallest scales of motion but it has also to span the entire flow geometry to capture the large scale effects. This poses enormous constraints on the numerical resolution needed for these computations.

**Turbulent Pipe Flow**

In this specific project, which was made possible through the Partnership for Advanced Computing in Europe (PRACE) on HLRS supercomputer Hermit, researchers from the Delft University of Technology put their primary focus on pipe flow. From an engineering point of view turbulent pipe flow is a one of the most important flow geometries because of its wide range of technical applications. Although many engineering problems involving pipe flows can be solved by simple engineering correlations or by turbulence modes, there is considerable fundamental interest in turbulent pipe flow. One of the open questions is the scaling of turbulent statistics in pipe flows. For instance, in the past it has been argued that the peak of the axial root mean square (rms) value of the turbulent fluctuations is nearly constant and thus independent of the Reynolds number. Furthermore there is some experimental indication that at higher Reynolds numbers long meandering structures will be generated. Until now the origin of these structures is unknown. Better knowledge of turbulence in pipe flows will help scientists and engineers to develop (control) techniques to decrease turbulent skin friction and to optimize turbulent heat and mass transfer.

**Project Results **

In the project three well resolved direct numerical simulations of turbulent pipe flow have been performed. Reynolds numbers, based on the bulk velocity, range from 25,000 to 76,000, using up to 7.6 billion grid points on 24,000 nodes. The simulation model uses high order numerical methods. For the parallelization, the researchers use the open source package 2DECOMP&FFT on top of MPI that is very well suited for computational fluid dynamics problems. The lowest simulated Reynolds number is used to compare with existing literature data, both experimental and numerical. Results show an excellent agreement between the scientists’ work and the literature data. The higher Reynolds numbers are used to study turbulent physics and the scaling of the flow with the Reynolds numbers. First results of the data analysis show some interesting findings. For instance the indicator functions for the mean velocity profiles show that there is no constant value for the von Karman “constant” (not a new result) and (a new result) that the indicator functions more or less resemble the function for boundary layer flow and not for channel flow. This implies that the wake region has a much larger influence on the near wall behavior of turbulence than commonly accepted. Secondly, it is shown that the peak values of the turbulence intensity are a weak function of the Reynolds number and thus not constant as is often assumed. Furthermore, all velocity statistics show a weak dependency on the Reynolds number. The strange scaling behavior sometimes observed in experiments has thus probably not a physical nature but is probably related to calibration of diagnostic equipment.

The very long structures that have been observed in previous simulations with shorter computational domains have also been observed but with a much lower energy content. Most likely, the structures observed previously were an artifact of a too small computational domain. In the near future the scientists intend to use the very detailed information which is now available to study the mechanism behind turbulent drag reduction.

**Highlights**

Source: © Delft University of Technology, The Netherlands

Source: © Delft University of Technology, The Netherlands

Source: © Delft University of Technology, The Netherlands

Source: © Delft University of Technology, The Netherlands

Bendiks Jan Boersma, Mathieu Pourquie & Rene Pecnik

Energy Technology, Delft University of Technology

Mekelweg 2

NL-2628 CD Delft/The Netherlands

e-mail: B.J.Boersma@tudelft.nl