Cornelia Grabe

Correlation-based Transition Transport Modeling for Three-dimensional Aerodynamic Configurations

The correlation-based γ-Reθt transition transport model was implemented in a hybrid Reynolds-averaged Navier–Stokes solver and validated on various test cases. The γ-Reθt model predicts two-dimensional transition phenomena such as transition due to Tollmien–Schlichting instabilities and separation-induced transition. The present work includes results for the application of the γ-Reθt to two three-dimensional test cases, which are the 6∶1 inclined prolate spheroid and the ONERA M6 wing. Depending on the flow conditions, the computational results are in good agreement with the experimental data. Once the given flow conditions lead to three-dimensional transition phenomena, the transition prediction with the γ-Reθt model is not reliable, because the model is based on the characteristics of two-dimensional boundary layers and three-dimensional transition mechanisms are not taken into account. To close this gap, the γ-Reθt model was extended by an approach that accounts for transition due to crossflow instabil...

Transition Transport Modeling for the Prediction of Crossflow Transition

Two fully local model variants of a correlation-based transition transport model that predicts transition due to crossflow instability as well as two-dimensional transition mechanisms are introduced. While the application of one model variant is restricted to wing-like geometries where the flow fulfills certain requirements, the second model variant is applicable to arbitrarily shaped geometries. The derivation and complete formulation of the two model variants is described in detail. An extensive validation study is presented using experimental data from infinite swept wing flows and three-dimensional configurations with different geometries. The capability of both model variants to predict transition due to crossflow instability is demonstrated and discussed.

Extension of the γ-Reθt Model for Prediction of Crossflow Transition

The extension of the local correlation-based γ-Reθt transition transport model for the prediction of transition due to crossflow instabilities for three-dimensional aerodynamic configurations was already introduced by the authors. Based on this work, the extended model was partly modified and further developed. The details of the latest version of the extended model are given in the present work. The local computation of relevant model quantities within a finite-volume based numerical flow solver is presented. Based on results from computations for an infinite swept wing the characteristics, the application range and the mesh sensitivity of the extended model are shown. Results of the application of the extended model to three-dimensional test cases are given and improved transition prediction capabilities for these cases are demonstrated. Finally, results, open questions and limitations of the model approach are discussed.

Development and Application of Transition Prediction Techniques in an Unstructured CFD Code

For some time computational fluid dynamics (CFD) based numerical simulations are an essential component in the industrial design process of aircraft. For many aircraft configurations it is possible to obtain highly accurate and reliable results using current CFD methods if the simulations are carried out for design point applications. The ever increasing capabilities of high-performance computing (HPC) systems have led to the vision of the ‘digital aircraft’ which can be flown in the computer while it is carrying out unsteady maneuvers. The keyword ‘flying the equations’ is a strongly condensed wording of the idea to execute a highly coupled simulation that, at the same time, incorporates the effects of flight mechanics, the structural deformation of the aircraft and the flow physics, the latter via high-fidelity CFD simulations in a time-accurate manner. First steps towards a highly multi-disciplinary simulation system being the prerequisite for such a coupled simulation are currently done in current research and development projects, such as the DLR project Digital-X [1], in order to support aircraft design and analysis based on a much higher number of numerical simulation results than today. In so doing, the future development and testing of completely new configurations based on highly accurate simulation data within the full flight envelope of an aircraft shall be made possible. At present, it seems that the successful execution of industrial-like Reynolds-averaged Navier-Stokes (RANS) computations of large full-aircraft configurations of highest geometrical complexity, the incorporation of more and more geometrical details and, as a result, the corresponding grid densities and point numbers can be achieved some day from a technical point of view if only the computational resources in terms of memory and processor cores of HPC clusters are large enough. Grid generation techniques and tools are either available today or under development so that appropriate computational grids can be generated exploiting, for example, sliding meshes, overlapping (chimera) grids, or the incorporation of large hexahedral portions within an non-hexahedral remainder of a purely unstructured grid composed of arbitrary cell types. Even the high demands made by the large-scale unsteady effects of maneuvers or the low-frequency unsteadiness that can exist at the borders of the flight envelope can be satisfied, partially by the ongoing development and improvement of numerical algorithms for time-accurate computations or by hybrid parallelization strategies combining classical domain decomposition with multi-threaded processing of the data on each domain [2]. Thus, accurate time-dependent flow solutions for very large aircraft configurations seem to be within reach. The predominant majority of simulations for design point applications is done for steady flows and based on standard RANS turbulence models. Although a number of Reynolds stress models (RSM) [3-7], that are considered to represent the highest level of RANS modeling for practical use, are available, in most CFD simulations one-equation or two-equation eddy viscosity models (EVM) are used in fully-turbulent computations. A major obstacle that hinders RANS-based CFD to yield the desired accuracy of results at the borders of the flight envelope for most cases is the physical models. Many of the crucial physical phenomena in transport aircraft flows in these flight regimes are characterized by strong non-linearities as, for example, flow separation and reattachment, shock/boundary-layer interaction, free vortices, wakes, and free shear layers. For some of them the correct boundary-layer representation in the numerical flow solution is of highest importance. In order to catch these phenomena correctly two modeling areas are of highest importance: turbulence models and laminar-turbulent transition models [8], and the interaction between the two. While for turbulence models one can be skeptical if their predictive capabilities can be improved and, at the same time, a reasonable trade-off between computational effort and accuracy of results can be achieved for situations at the borders of the flight envelope the situation is different for laminar-turbulent transition models.

Coupling of a Reynolds Stress Model with the γ−Reθt Transition Model

A γ−Reθt transition transport model has been coupled with the SSG/LRR-ω differential Reynolds stress model to form a new transition and turbulence model containing nine transport equations. The aim...

Streamline-Based Transition Prediction Techniques in an Unstructured Computational Fluid Dynamics Code

An unstructured flow solver has been equipped with transition prediction techniques based on different streamline-based approaches, applying the eN method for the estimation of the points of transition onset. The integration paths for the N-factor integration can be approximated using lines parallel to the direction of the oncoming flow for some configurations. If arbitrary three-dimensional geometries are to be computed, the local flow direction can be taken into account. The calculation of the laminar boundary-layer data can either be carried out applying a suitable laminar boundary-layer method or by direct determination from the field solution of the unstructured computational fluid dynamics code. The development and characteristics of the two streamline-based transition prediction techniques, their elements, and properties are described. The focus is put on the latest achievements in the development activities of the two approaches and on their application to various configurations, most of them of i...