Simulation of Turbulent Flow Around a Wing

**Principal Investigator:**

Torsten Auerswald and Jens Bange

**Affiliation:**

Center for Applied Geoscience, University of Tübingen (Germany)

**Local Project ID:**

WAF

**HPC Platform used:**

Hermit and Hornet of HLRS

**Date published:**

*This project aims at the simulation of the influence of a turbulent atmospheric boundary layer flow on a wing. For this purpose the compressible flow solver DLR-TAU is used, which is developed by the German Aerospace Center (DLR). For initialising the simulation with a turbulent wind field a method to generate synthetic turbulence is used. This method uses statistics from measured time series from the atmospheric boundary layer to generate a threedimensional turbulent wind field which can be used as initial field in the flow simulations.*

**Introduction**

The influence of atmospheric turbulence on an aircraft is an important issue in many aspects of aviation. Since two of the most critical maneuvers, take-off and landing, are taking place in the atmospheric boundary layer (ABL), knowledge about the influence of atmospheric turbulence flow on aircraft aerodynamics is important for the safety and design of aircrafts.

As part of the DFG research unit FOR1066, this project aimed at developing a strategy to simulate the turbulent flow around a wing during take-off or landing realistically. Today's computers are not powerful enough to simulate the flight of an aircraft through a complete ABL. Therefore, some simplifications had to be applied. First of all, not the complete aircraft was simulated but only the wing. And secondly, only a small section of the ABL was simulated by using synthetic turbulence which possesses important characteristics of real ABL turbulence. There are many methods to generate synthetic turbulence. They are all using algorithms for computing random velocity fields, which represent statistical properties of real turbulence. These methods are much faster in producing a turbulence field than simulating the development of real turbulence. But they are not carrying all properties of real turbulence and therefore can be seen as an approximation of real turbulent flow.

**Modelling strategy**

For the simulation of the turbulent flow around the wing, the compressible flow solver DLR-TAU was used. DLR-TAU is developed by the German Aerospace Center (DLR) and allows for the usage of multiple grids which can move relative to each other by using the Chimera method (Schwamborn, 2006). Fig. 1 shows the grid containing the body-fitted grid around the wing with a refined area in front of the wing and the Cartesian grid in front of the wing. The Cartesian grid appears as a grey block, because the grid cells are so small that they can not be depicted in this zoom level in the picture. The high resolution of the Cartesian grid is also the reason for the refined area in the unstructured grid in front of the wing. The refinement ensures proper interpolation between the Cartesian grid and the unstructured grid. The Cartesian grid has a grid cell size of 0.7 m and a volume of 200x200x200 m^{3}. The chord length of the wing is 6 m. In the unstructured grid, the refined area has a grid cell size of the same order like the Cartesian grid. The grid cell size in the unstructured grid ranges from 0.00005 m near the wing to 40 m in the outer region of the unstructured grid. Both grids together comprise a total number of grid points of about 30 millions.

The simulation covered a time span of 4 s. Within the first second, the Cartesian grid containing the turbulent field was moved towards the wing by the mean flow. After 0.9 s, the Cartesian grid was stopped and the turbulent flow field left the Cartesian grid. It then took around 3.1 s for the whole turbulent flow field to flow around the wing. The reason for this strategy is, that the Cartesian grid is better suited to maintain the turbulent flow during the simulation, but the unstructured grid represents the shape of the wing better. Therefore a combined strategy makes use of the advantages of both grid types.

The initial condition for the simulation consisted of the initial turbulent field on the Cartesian grid and the stationary flow field around the wing. The angle of attack for the flow simulation was 6°. For generating the turbulent wind field on the Cartesian grid, the turbulence generator from Auerswald et al. (2012) was used to produce a three-dimensional turbulent wind field with statistical properties taken from measurements.

**Results**

The project succeeded in developing a simulation strategy to simulate the turbulent flow around a wing. In a proof of concept, the flow of a turbulent field around the wing at an angle of attack of 6° was demonstrated. Fig. 2 shows snapshots from that simulation. Depicted is the vertical velocity in m/s at 0.887 s and 2.537 s simulated time. It shows how the turbulent field leaves the Cartesian grid and interacts with the wing. The bigger square marks the position of the outer interpolation boundary and the smaller square the inner interpolation boundary for the interpolation between the two grids.

**Technical Details of the Simulation**

The first part of the simulation was performed on the Cray XE6 computer on 4096 cores with 32 processes per node. The time per iteration was around 0.4 s. One result file has a size of around 6 GB. The second part of the simulation was run on the CRAY XC40 on 4104 cores with 24 processes per node. The time per iteration on that machine is around 0.2 s. The simulation was started in mid March 2014 and finished in mid December of the same year. This time span includes some breaks for changing parameters, waiting times in the queue and maintenance time of the machine.

**References:**

**Schwamborn, D., Gerhold, T. and Heinrich, R.**, 2006**:** “The DLR TAU-Code: Recent Applications in Research and Industry.”, ECCOMAS CFD 2006

**Auerswald, T., Bange, J., Knopp, T., Weinman, K. and Radespiel, R**., 2012: “Large-Eddy Simulations of realistic atmospheric turbulence with the DLR- TAU-code initialized by in situ airborne measurements.” Computers & Fluids, 66, 121–129.

**Scientific Contact:**

Prof. Dr. Jens Bange

Center for Applied Geoscience, Environmental Physics

Hölderlinstr. 12, D-72074 Tübingen (Germany)

e-mail: jens.bange [at] uni-tuebingen.de