Direct Numerical Simulation (DNS) in compressible flows
The performance of sub-, trans- and supersonic fluid-dynamic devices may be strongly affected by laminar-turbulent transition and unsteady flow phenomena. Due to their complexity, most of these problems are not yet fully understood. Resolving all relevant flow structures in space and time, Direct Numerical Simulations (DNS) provide a detailed insight into the underlying physical processes.
We developed the DNS code NS3D, solving the complete unsteady compressible 3-D Navier-Stokes equations. The method is thoroughly verified and validated by comparing its results with theory and previously conducted investigations. The spatial discretization is based on 6th-order compact finite differences and a spectral ansatz in the periodic spanwise direction. The spectral discretization is implemented for both symmetric and non-symmetric computations. Computing the second derivatives directly increases the resolution of the viscous terms compared to the often used method of applying the first derivative twice. With a non-vanishing second derivative for the least-resolved waves. Moreover, the stability of the numerical scheme is improved.
The hybrid parallelization is based on a shared-memory parallelization in spanwise direction and domain decomposition in streamwise and normal direction using MPI. With modular boundary conditions, the combination of domain decomposition and numerical grid transformation allows the computation of a wide range of problems and geometries.
The numerical method is successfully running on the high-performance computers of the hww GmbH. Within the Teraflop Workbench, its computational performance is further improved by support of NEC and HLRS. The NS3D code is part of a complete simulation framework including initial conditions, linear-stability-theory analysis and postprocessing based on EAS3.
The applications of the compressible DNS code range from subsonic to supersonic flow regimes.
In aeroacoustic simulations the flow field of a mixing layer behind a splitter plate is investigated with respect to sound genneration mechanisms. Within the simulation, no acoustic analogies are used and the emitted sound is computed directly together with the flow field. Since the amplitudes of the acoustic field are smaller by several magnitudes compared to the disturbances in the flow field, boundary conditions must be chosen very carefully.
In supersonic flows, laminar-turbulent transition strongly affects drag and thermal loads. Additionally to vortical Tollmien-Schlichting-type waves, acoustic second-mode instabilities exist in high-speed boundary layers. The NS3D code is currently used for super- and hypersonic boundary-layer flows to investigate the effect of effusion cooling and transition phenomena on an elliptic cone.
1) Vortex structures in shear flow on notched trailing edge (Subsonic flow: Ma=0.8 (above), Ma=0.2 (below))
2) Stationary vortex structures at blowing into a supersonic boundary layer at Ma=6
(Andreas Babucke, Markus Kloker, Ulrich Rist, Institute for Aerodynamics and Gasdynamics, Universität Stuttgart, and Fred Unger, NEC HPC Europe)
I. Loebich