FLOW: DNS of high-Reynolds number turbulent pipe flow

Fully developed incompressible turbulent flow through a smooth pipe is a canonical problem in fluid mechanics. Recently, a resurgence in both experimental [1] and numerical [2] research has taken place pointing out a number of open questions. A visualisation of results from [2] can be seen below.

The Linné Flow Centre is also involved in the CICLoPE project, a large-scale experimental effort which aims at gaining a fundamental understanding of the physics of high Reynolds number turbulence [3].

The aim of the present project is to study large-scale turbulence structures and statistics in fully developed high-Reynolds number turbulent pipe flow through direct numerical simulations (DNS). For other canonical flows (channel and boundary layer flow), high accuracy, efficient DNS codes already exist, but for pipe flow this is a tool that is still missing.

Recent experimental studies show that large-scale structures with lengths of 5R up to 20R (with R the radius of the pipe) are found in fully developed turbulent pipe flow. These large-scale structures are very energetic and active, and thus play an important role in the dynamics of turbulent pipe flow. To detect and qualify such structures in numerical simulations, a high Reynolds number and a long domain is required.

Furthermore, we are interested in the small-scale turbulent structures that occur, so we need to resolve the smallest scales in the flow.

Both of these aspects lead to the demand for large-scale numerical simulations. A comparison between the structures of turbulent pipe flow and similar structures in turbulent boundary layer flow will be made to investigate how universal near-wall turbulence is.

As a first step, we will develop and implement new DNS software. This code should have high numerical accuracy, and high efficiency when running on supercomputers with a large number of processors. Certain numerical difficulties occur when using polar coordinates to represent the axisymmetric geometry of the pipe. One of the major problems is a numerical singularity that occurs in the center of the pipe. This requires special numerical techniques to deal with. Furthermore our code must comply with the latest developments in computer design. The use of multicore processors in supercomputers like Lindgren and Ekman requires new (hybrid) algorithms to ensure that the code runs as efficiently as possible.

[1] McKeon et al. (2004), J. Fluid Mech., 501, 135-147
[2] Wu and Moin (2008), J. Fluid Mech., 608, 81-112
[3] Talamelli et al.(2009), Fluid Dyn. Res., 41, 021407