Discontinuous Galerkin Methods for Detached Eddy Simulation
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart (Germany)
Local Project ID:
HPC Platform used:
Hornet and Hazel Hen of HLRS
The helicopter and aeroacoustics group at IAG has been simulating the complex aerodynamics and aeromechanics of rotorcraft since the early 90s. Starting from inviscid flow simulations on isolated rotors, technology improved steadily over the years, including structural dynamics coupling, turbulence modelling, trim and acoustics up to the full helicopter configurations possible today, including tail rotor and fuselage as well as consideration of the engine flow.
The grand challenge here is the combination of highly sophisticated numerical algorithms for different physical phenomena (various flow features, bi-directional coupling to structure dynamics, acoustics) applied to engineering relevant, very complex, realistic geometry configurations. Depending on the flight state, some ten revolutions of the rotor are required until the solution is fully converged to free flight conditions. This is a consequence of the fluid-structure coupling at the rotor blades – and the fuselage, recently – and the corresponding changes in attitude and steering controls to establish stationary flight without residual forces and moments.
The helicopter and aeroacoustics group at IAG of the University of Stuttgart usually simulates the complex aerodynamics and aeromechanics of rotorcraft, delivering reliable results for relevant engineering problems. However, the conceivable development of computational hardware technology, with increasing discrepancy between floating point performance and memory bandwidth available, as well as thousands (and millions in the near future) of cores led to the development of new fluid flow solver technology. The hardware trend is reflected in the usage of highly sophisticated numerical algorithms of high accuracy, needing many operations on (relatively) few data points. Furthermore, unstructured grids allow more freedom in the strategic placement of grid refinements in specific regions of interest. Discontinuous Galerkin methods allow arbitrary high order discretisations on such unstructured grids, having excellent parallelisation characteristics as an added benefit. However, they are quite costly and thus pay off the large computational effort only if high accuracy is required for the problem at hand.
A specific application of interest, where such accuracy is required to represent the flow physics appropriately, is the dynamic stall of a fast pitching airfoil. In this case the airfoil can deliver more lift at large angles of attack in this instationary upstroke than in a static setting, but beyond the angle of maximum lift it declines quickly, yielding very high pitching moments, until the flow re-attaches again in the downstroke and lift collapses to the stationary value. To capture such complex flow phenomena, advanced turbulence modelling like DES (Detached Eddy Simulation) is needed.
Beyond such generic test cases the final goal of application is the simulation of rotorcraft as with our current tool chain. To this end, computational features like overlapping Chimera grids, fluid-structure coupling and mesh movements are to be implemented. The physical surfaces of wings, rotor blades and other aerodynamic components is usually smooth. In order to maintain the high accuracy of the method, the (comparably coarse) meshes then have to be curved within the cells, as otherwise the discretisation would compute the flow around a polygon with corners and edges, which does not represent the real physics.
Although results are quite satisfactory already, a lot of work still has to be invested until Discontinuous Galerkin solves can compete to current state of the art solvers. The researchers at the IAG of the University of Stuttgart are confident, though, to have a next-generation solver available in the medium-term future when the current tool chain might lose significance.
Institut für Aerodynamik und Gasdynamik, Universität Stuttgart
Pfaffenwaldring 21, D-70550 Stuttgart/Germany
e-mail: kessler [@] iag.uni-stuttgart.de