Direct Numerical Simulation of Turbulent Plane Couette Flow with Wall-normal Transpiration Velocity

**Principal Investigator:**

Martin Oberlack

**Affiliation:**

Technische Universität Darmstadt (Germany)

**Local Project ID:**

pr92la

**HPC Platform used:**

SuperMUC of LRZ

**Date published:**

*Channel flows are important references for studying turbulent phenomena in a simplified setting. The present project investigates Couette flow, i.e. channel flow driven by a moving wall. Although important to many practical applications, Couette flows have been studied considerably less than other canonical flows, for (a) the experimental setup is very complex, and (b) long and wide structures are present which are characteristic to Couette-type flows. This accounts for long and wide computational domains, which make direct numerical simulations of Couette flow expensive. Even by applying permeable boundary conditions, i.e. blowing from the lower and suction from the upper wall, the Couette-type structures could not be destroyed. Instead, new and unexpected structures close to the wall are observed in the spectra.*

C**ouette Flows with transpiration**

This was the main objective of the project. Couette flows with transpiration have never been studied in laboratory and our own are the first simulations describing this kind of flows properly. The number of simulations ran are summarized in the following table.

The first objective of this subproject was completely achieved, as this set of simulations has given us a perfect benchmark to test our theories about the breaking of symmetries in turbulence, and the generation of new scaling laws.

Moreover, we have seen that the large and wide rolls present in Couette flows are not destroyed by transpiration flows, which was totally unexpected.

And, even more, we have found some structures totally unexpected and that were found looking for a bug in a postprocessing code. In a region very close to the wall structures wider and shorter than expected appeared, with a spectral representation that resembles a butterfly.

These structures may be of importance to understand the dynamics of transpiration flow and the momentum exchange between velocities.

All the raw data set is stored at SuperMUC’s tape system and we are finalizing all the postprocessing routines. The use of fat nodes is necessary due to the relative big size of the data.

**Pure Couette flows**

In order to better study our results and the differences between this and canonical Couette flows, we have run the largest simulation of the latest. This simulation was run in 4096 processors of SuperMUC with excellent results. One of the main results is that the rolls present in Couette Flows are still existing, stronger and longer. This is a bit strange as in theory the highest the Reynolds number, the highest the chaotic behavior. We have also found a slightly lower value for the Karman constant than the one obtained in Poiseuille channels. At this very moment, we are testing our theory in this flow and we will publish our results shortly.

**Realization of the project**

The project has been running without any problem worth to be commented. The code was further accelerated and optimized in 2016’s SuperMUC extreme scaling workshop. Quite surpresively, our routine for all-to-all communications worked better than ALLTOALL MPI routines.

Due to the further optimization of the code and the time granted to us for the participation in this workshop, we still have time that we are using for a challenging computation: Poiseuille channel flows at the highest Reynolds possible. Our objective is to obtain a simulation at the largest Reynolds number possible. In this case it is 10000. Our estimations indicate that we are going to need a total of 3.5M CPU-H.

We would like to stress the importance of this simulation, as it would be a reference for the next years as it would be the first one to reach this high Reynolds number, making our simulation comparable to the largest flows characterized in experiments, with the main advantage that we can know every detail of the flow.

**References:**

1. DNS of a turbulent Couette flow at constant wall transpiration up to Re_\tau=1000, J. Fluid Mech. (2018), vol. 835, pp. 421443.

2. Couette flows up to Re_\tau=2000. J. Fluid Mech, in preparation

3. On the persistence of large-scale turbulent structures in turbulent Couette flow with wall- transpiration, 70th Annual Meeting of the APS Division of Fluid Dynamics

4. DNS of a turbulent Couette flow at constant wall transpiration up to Re_t=1000., Tenth International Symposium on Turbulence and Shear Flow Phenomena 2017

5. DNS of a turbulent Couette flow at constant wall transpiration up to Re_t=1000, iTi Conference on Turbulence VII, Bertinoro, Italy, September 7-9, 2016

6. Turbulent plane Couette flow with wall-transpiration. European Turbulence Conference 15 (ETC 15)

7. Plane turbulent Couette flow: DNS, large scale structures and symmetry induced scaling laws. Ninth International Symposium on Turbulence and Shear Flow Phenomena (TSFP-9)

**Project Team**

Dr. Sergio Hoyas, Universitat Politècnica de València (Spain), Stefanie Kraheberger (TU Darmstadt), Prof. Dr.-Ing. Martin Oberlack (TU Darmstadt / Principal Investigator)

**Scientific Contact:**

Prof. Dr.-Ing. Martin Oberlack

Technische Universität Darmstadt

Fluid Dynamics

Otto-Berndt-Str. 2, D-64287 Darmstadt (Germany)

e-mail: oberlack [@] fdy.tu-darmstadt.de

**NOTE:** This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2018":

*LRZ Project ID: pr92la*

*December 2018*