Direct Numerical Simulations of Compressible Turbulent Boundary Layers

Principal Investigator:
Ulrich Rist, Markus Kloker, Christoph Wenzel

Institute of Aerodynamics and Gas Dynamics, University of Stuttgart

Local Project ID:

HPC Platform used:
Hazel Hen and Hawk of HLRS

Date published:


The present project explores laminar-turbulent transition and flow control in boundary layers at various flow speeds from the subsonic to the hypersonic regime.  Supercomputer resources are indispensable for the multiple-scale problem, due to the need of resolving very small unsteady fluctuations in the flow using high-order numerical methods based on spectral and compact finite-difference schemes for the direct numerical simulations (DNS).  The in-house DNS code is continuously adapted and parallelized in cooperation with HLRS.  The physical problems under investigation deal with prediction of laminar-turbulent transition on airfoils for aircraft, prediction of critical roughness heights in laminar boundary layers, turbulent drag reduction, the origins of turbulent superstructures in turbulent flows, the use of roughness patterns for flow control, effusion cooling in laminar and turbulent supersonic boundary-layer flow, DNS of disturbance receptivity on a swept wing at high Reynolds numbers, and plasma actuator design for active control of disturbances in a swept-wing flow.  To ensure a constant and predictable use of the computing time granted, we have collected these individual topics into one HPC-project under the acronym “GCS-Lamt”, for “Gauss Centre for Supercomputing - Laminar-Turbulent Transition”.

The DNS (direct numerical simulations) group at IAG works on flow instabilities, laminar-turbulent transition, flow separation and turbulence in boundary-layer and shear flows from subsonic to hypersonic speeds.  A compressible in-house code using high-order numerical methods has been newly developed starting in 2016 and carefully checked with respect to theory and wind-tunnel experiments.  The computer code has been optimized to run at teraflop rates on the high-performance computers of the High-Performance Computer Center Stuttgart.  Constant progress is reported in the annual transactions of the high-performance computing center published by Springer under the series titles “High Performance Computing in Science and Engineering”, currently edited by W.E. Nagel, D.H. Kröner and M.M. Resch, and “Sustained Simulation Performance”, currently edited by M.M. Resch, W. Bez, E. Focht, H. Kobayashi and Y. Kovalenko.

The benchmark LAMTUR has been repeatedly used for evaluation of new hardware offers.  LAMTUR/GCS-Lamt is also regularly selected for presentation on the yearly “results- and review-workshop” of HLRS.  Several “Golden-Spike Awards” have been granted, the most recent one in October 2018, by the steering committee.

Codes exist for solving the complete Navier-Stokes equations for compressible and incompressible flow, for solving the linearized Navier-Stokes and linear stability theory equations (one-, two-, and three-dimensional).  The latter two lead to large eigenvalue problems that require a large amount of shared memory.  A problem-specific binary data format with appropriate post-processing tools (eas3) is used by all GCS-Lamt users.  Large data sets can be compressed by two orders of magnitude using a newly developed data compression scheme.

Our DNS algorithms are based on high-order finite-difference/spectral discretisation in space in combination with explicit high-order Runge-Kutta integration in time.  An open inflow-outflow domain is used in streamwise direction with buffer domains to prevent undue disturbance reflections.  The spanwise direction uses periodic boundary conditions such that a Fourier spectral ansatz can be used in that direction.  Parallelization is performed in several ways: domain decomposition using MPI, in 2018 extended to the spanwise direction also, i.e. full 3-d domain decomposition can be done now, and micro tasking using OpenMP.  Input-output is some bottleneck at present such that more effort is needed to parallelize this.  Typically, the simulation results are stored as snapshot data, for modal and stability analysis.  The stability analysis of three-dimensional domains constructs a Krylov subspace from snapshots of the linearized Navier-Stokes equations and computes approximate eigenvalues by the Arnoldi method.  This ansatz is new and still under development.  It allows identifying fundamental mechanisms in the flow.

Understanding and predicting the behavior of turbulent boundary layers is among the most challenging topics in fluid dynamics.  In practice it has an impact on the design of energy-efficient vehicles such as cars, trains, airplanes and turbo-machines.  At larger speeds, however, and especially when we consider vehicles operating at supersonic speeds, effects due to the compressibility of air also become important, adding an extra layer of complexity.

In addition, for the flow over any practical vehicle, the effects of pressure gradient that cause either a flow acceleration (favorable) or deceleration (adverse) can be severe, and for strong pressure gradients can lead to separation.  This project performs fundamental studies of the effects of compressibility (expressed by the Mach number), pressure gradient, and wall temperature (among others) on high-speed boundary layers where the effects of compressibility are also important.  It makes a valuable and unique contribution to our knowledge of turbulent flows, and establishes the basis for improved predictions and better design of high-speed vehicles.

At the beginning of the present project stood the idea of performing drag-reduction studies with so-called micro-blowing through the wall.  But these simulations needed reliable reference data for various Mach numbers.  These have been obtained by Wenzel et al. (2018) for flat-plate boundary layers with zero streamwise pressure gradients and compared with incompressible flows via the van Driest transformation.  Thus, these results currently represent the most reliable available data of spatially developing, compressible turbulent boundary layers without pressure gradient, whose reliability is based to a large extent on the large computational area used and the associated low dependence on the turbulent inflow boundary conditions.

For similar studies with generic streamwise pressure gradients, an appropriate technique for specifying free-stream boundary conditions leading to an equilibrium turbulent boundary layer had to be devised first.  Another need was finding new scalings for compressible boundary layers with streamwise pressure gradients for evaluation of the present DNS data.  According simulations were performed and published in the two-part publication (Wenzel et al. 2019b and Gibis et al. 2019).  This work includes the first DNS of self-similar, compressible, turbulent boundary layers with pressure gradient (positive and negative) as well as the corresponding analytical investigations of the self-similarity state for compressible flows, a state which has not been described in the literature so far.  By studying this canonical case, the validity of fundamental compressible principles like the van Driest-Transformation and Morkovin's hypothesis for cases with self-similar pressure gradients could be confirmed.  Enabled by the high degree of self-similarity of the calculated data, a direct connection between traditional and more recent incompressible self-similarity theories could be established, which so far contradicted each other in essential points.

Project Team

Dr. Markus Kloker1, apl. Prof. Dr.-Ing. Ulrich Rist1, Dr.-Ing. Christoph Wenzel, M.Sc.1
1Institute of Aerodynamics and Gas Dynamics (IAG), University of Stuttgart


Wenzel, Christoph; Gibis, Tobias; Kloker, Markus; Rist, Ulrich (2019): Self-similar compressible turbulent boundary layers with pressure gradients – Part 1: DNS and assessment of Morkovin’s hypothesis, Journal of Fluid Mechanics 880:239-283, DOI: 10.1017/jfm.2019.670

Gibis, Tobias; Wenzel, Christoph; Kloker, Markus; Rist, Ulrich (2019): Self-similar compressible turbulent boundary layers with pressure gradients – Part 2: Self-similarity analysis of the outer layer, Journal of Fluid Mechanics 880:284-325, DOI: 10.1017/jfm.2019.672.

Christoph Wenzel, Björn Selent, Markus Kloker and Ulrich Rist (2018): DNS of compressible turbulent boundary layers and assessment of data-/scaling-law quality, J. Fluid Mech. 842:428–468. doi:10.1017/jfm.2018.179

Scientific Contacts

Dr. Markus Kloker, apl. Prof. Dr.-Ing. Ulrich Rist, Dr.-Ing. Christoph Wenzel, M.Sc.
Institute of Aerodynamics and Gas Dynamics (IAG)
University of Stuttgart
Pfaffenwaldring 21, D-70550 Stuttgart (Germany)
markus.kloker [@], ulrich.rist [@], wenzel [@]

Local project ID: GCS-Lamt

October 2020

Tags: HLRS Universität Stuttgart CSE Computational Fluid Dynamics Large-Scale Project