Development of a Stability Based Transition Transport Modeling Framework

Principal Investigator:
Philip Ströer, Anthony D. Gardner, Kurt Kaufmann

Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen

Local Project ID:

HPC Platform used:
SuperMUC and SuperMUC-NG of LRZ

Date published:


The physical process of a laminar boundary layer becoming turbulent is called “laminar-turbulent transition”. Since the flow physics and in particular the skin friction responsible for the drag is significantly influenced by the state of the flow, that is laminar or turbulent, transition plays an important role in external aerodynamics. For example, for rotorcraft computations it was shown that the skin friction was significantly overpredicted (depending on the geometry and the flow state) applying a fully turbulent simulation compared to a simulation that considered laminar-turbulent transition [1]. An overestimation of skin friction leads to an overestimation of power demand which needs to be avoided. However, on complex industrially relevant configurations, like a helicopter rotor, incorporating transition prediction capabilities into the simulation is not straightforward.

State-of-the-art streamline-based methods require a great implementation effort, massive user input and a detailed expert knowledge. Additionally, computing helicopter rotors is inherently computationally expensive, requiring unsteady computations on a fine grid (Fig. 1), with a long computation time to establish the flow. The addition of boundary layer transition to the computation requires even finer time-steps and additional effort to compute the transition position.

While streamline-based methods are relatively effective, they are not easily parallelizable to a large number of cores. Therefore, in the last decade transition transport models have been developed that aim at simplifying the incorporation and parallelization of the laminar-turbulent transition significantly. These models are only based on information available at each grid point, using transport type partial differential equations.

Results and Methods 

In this project extensive investigations of different approaches to transition modelling on rotors were undertaken, including comparison to experimental data and results of other European CFD codes, see [2]. One finding was that for flows at Reynolds numbers below 500,000 the transition transport models predict unphysically large areas of laminar flow compared to the experimental data, see Fig. 2. To solve this problem a new boundary-layer transition model was developed by Ströer et al. [3,4] to improve the transition prediction for a wide range of parameters crucial to external aerodynamics. The new model was already validated for fixed-wing applications [3,4], and can be used for both compressible and incompressible flows.

A drawback of the model proposed in Refs. [3,4] is the lack of Galilean invariance (GI). For problems where the velocities can be transformed relative to an adjacent wall, the lack of Galilean invariance can be mitigated. However, for complex test cases (like helicopter computations) the formulation of a model should be as universal as possible. Therefore, a new model is under development that is Galilean invariant [5].

The final transition modeling framework [3,4,5] includes a four, a three, and a one equation model. The objective is to provide a flexible framework that can be used to meet rapidly changing industrial requirements. The new models were implemented into the DLR TAU code.

TAU is the compressible finite-volume Navier-Stokes solver of the German Aerospace Center (DLR) used for all computations mentioned. The new model works on either structured or unstructured grids. The simulations performed are RANS computations using an eddy-viscosity type turbulence model for the turbulent flow region.

Fig. 3 shows results for the RTG helicopter rotor. The 2D airfoil was extracted at a constant radial position following Weiss et al. [6]. The figure shows the transition onset position for different collective pitching angles. The agreement of the proposed model with the experimental data is significantly improved compared to the results of the basic transition transport model (γReθ model).

Fig. 4 shows results for the full 3D rotor obtained by the new GI model. The transition positions as well as the surface pressure are well matched over the range of surface positions for which experimental data are available. The new transition model framework utilizes the standard MPI code parallelization of TAU, and the needs very limited expert knowledge and user interaction. The parallel speedup known from other test cases is preserved.

Ongoing Research / Outlook

The results obtained by the new model show promising improvements compared to state-of-the-art models (cf. Ströer et al. [3,4]). The development of this new model is promising, and it will now be applied to currently flying helicopters to prove its industrial relevance. The resources provided by the LRZ on SuperMUC-NG were invaluable in supporting this development.

References and Links

[1] Dietz, M., Dieterich, O., “Towards increased industrial Application of Rotor Aeroelastic CFD”, 35th European Rotorcraft Forum, Hamburg, September 22-25, 2009.

[2] Kaufmann, K., Ströer, P., Richez, F., Lienard, C., Gardarein, P., Krimmelbein, N., Gardner, A. D., "Validation of boundary-layer-transition computations for a rotor with axial inflow", Vertical Flight Society 75th Annual Forum, Philadelphia, May 1316, 2019.

[3] Ströer, Ph., Krimmelbein, N., Krumbein, A., Grabe, C., AIAA Journal, Vol. 85, No. 4, 2020, pp. 1506-1517.

[4] Ströer, Ph., Krimmelbein, N., Krumbein, A., Grabe, C., AIAA SciTech 2020, Orlando, FL, USA, 2020.

[5] Ströer, P.; Krimmelbein, N.; Krumbein, A.; and Grabe, C., "Galilean-Invariant Stability-Based Transition Transport Modeling Framework, " AIAAJ, Vol. 60, No. 7, 2022, pp. 4126-4139 doi: doi/abs/10.2514/1.J061401.

[6] Weiss, A., Gardner, A. D., Schwermer, T., Klein, C., and Raffel, M., AIAA Journal, Vol. 57, No. 1, 2019, pp. 252-266.


Philip Ströer1, Anthony D. Gardner2, Kurt Kaufmann2

1 C2A2S2E – Center for Computer Applications in AeroSpace Science and Engineering, Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen
2 Helicopter Department, Institute of Aerodynamics and Flow Technology, German Aerospace Center (DLR), Göttingen

Scientific Contact

Dr. habil. Anthony Gardner
Institute of Aerodynamics and Flow Technology
German Aerospace Center / Deutsches Zentrum für Luft- und Raumfahrt (DLR)
Bunsenstraße 10, D-37073 Göttingen (Germany)
e-mail: Tony.Gardner [@]

NOTE: This report was first published in the book "High Performance Computing in Science and Engineering – Garching/Munich 2020 (2021)" (ISBN 978-3-9816675-4-7)

Local project ID: pr83su

September 2021