Towards the Simulation of the Flow Phenomena at a Helicopter Rotor Using a High-order Method

**Principal Investigator:**

Manuel Keßler

**Affiliation:**

Institute of Aerodynamics and Gas Dynamics, University of Stuttgart

**Local Project ID:**

DGDES

**HPC Platform used:**

Hazel Hen and Hawk of HLRS

**Date published:**

In times when available computing power has become an easily accessible and still steadily growing resource, the demand for precise predictions of phenomena in nature and engineering has increased immensely. This also holds for the field of Computational Fluid Dynamics (CFD). From an engineering point of view, simulations of flow problems for technical applications should be as realistic as possible. However, this usually increases the complexity of the simulated flow problems, often requiring specific toolchains that must be applied efficiently on high-performance computing (HPC) systems.

At the Institute of Aerodynamics and Gas Dynamics (IAG) of the University of Stuttgart, the helicopter and aeroacoustics group simulates the complex aerodynamics and aeromechanics of rotorcraft and provides reliable results for a range of relevant engineering problems. A fundamental component of the toolchain utilized is the CFD solver based on a classical Finite Volume (FV) method. However, FV solvers usually need to work on smooth and highly resolved structured meshes in order to produce reliable and accurate results. Furthermore, the spatial order of accuracy of the FV method typically stagnates at second order.

Thus, the development of a new fluid flow solver technology was motivated and a very promising candidate was discovered in the Discontinuous Galerkin (DG) method. The DG method is able to compute flow solutions of arbitrary high order in space using unstructured grids, which are less time-consuming to generate compared to structured grids. Furthermore, DG provides excellent parallelization characteristics. However, the DG method is quite costly per degree of freedom and thus can pay off the large computational effort only if high accuracy is required for the problem at hand.

The Stuttgart University Numerical Wind Tunnel (SUNWinT) is such a DG based CFD solver, which has been further developed within the DGDES project and has the goal of providing an alternative tool for the simulation of the flow phenomena at helicopter rotors. In the meantime, the development has led to a point where first preliminary simulations of a rotor in hover could be performed. For this to accomplish, different technologies like the usage of high-order grids for an accurate body surface representation or an Arbitrary Lagrangian Eulerian method to consider grid movements have been implemented successfully.

Additionally, a Chimera method, well known from FV methods, is employed. The Chimera method is an overset grid technology allowing a numerical setup to consist of an arbitrary number of individual component grids. Each grid is integrated into a complete simulation setup and is furthermore able to perform relative movements to other grid components. The advantage of this method clearly lies in the simplification of the grid generation process for complex configurations, e.g. helicopter rotors or even complete helicopter configurations. The downside of the Chimera method is the additional computational effort to provide an accurate exchange of flow data between the grid components. However, the ability to perform relative movements, especially when helicopter rotors are the main target of the application, outweighs the drawbacks.

Figure 1 shows an exemplary result of a first preliminary simulation of a rotor in hover. The wake of the two bladed rotor is visualized by isosurfaces of the Q criterion – an indicator for the detection of vorties. To indicate the dimension of the Chimera grid used, the figure also shows some slices of the blade grid at different blade sections for the blade on the left side. Since the simulations are still in a trial state, the spatial accuracy order was only three and a few assumptions had to be made in order to simplify physics. Nevertheless, the application of the Chimera method already provides a quite sharp resolution of the tip vortices, which contract and convect downwards as known from FV simulations.

Although the first results already indicate a promising trend, many further simulations are necessary to gain experience with the simulation of rotorcraft using a higher order method. Besides the flow simulation of a rotor in hover, a rotor in forward flight is the next level of complexity. In forward flight each blade performs an individual movement during the rotation of the blade consisting of a pitch, flap and lag motion. These simulations are the challenge of current research.

Beyond these experimental test cases, in which the general applicability of the code should be examined, future work will concern the implementation of methods to increase the level of modeling reality within the simulations. To this end, computational features such as turbulence modeling, shock capturing and fluid-structure coupling will be integrated or improved and generalized compared to the current preliminary realization in a next step.

A lot of work still has to be invested until Discontinuous Galerkin methods are competitive to current state of the art solvers. However, the results achieved indicate a promising trend towards the applicability of the DG method on complex flow problems. 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.

**Scientific Contact**

PD Dr. rer. nat. Manuel Keßler

Institut für Aerodynamik und Gasdynamik

Universität Stuttgart

Pfaffenwaldring 21, D-70550 Stuttgart (Germany)

e-mail: kessler [@] iag.uni-stuttgart.de

Website: Helicopter and Aero Acoustics Group, IAG, University of Stuttgart

*Local project ID: DGDES*

*July 2020*