Dietmar Rempfer, PhD

DFG - Pipe Flow Transition
In this project, essential mechanisms responsible for the creation of turbulence in spatially evolving pipe flows are studied. Special emphasis is on the question of what role is played by algebraic instabilities owing to the non-normality of the operator of linear theory for pipe flow. This way we hope to be able to clarify whether these mechanisms can explain the apparent discrepancies between theory and experiment with respect to, e.g. critical Reynolds numbers. The investigations performed here are based on methods for direct numerical simulation of the complete three-dimensional Navier-Stokes equations for incompressible pipe flow.

DNS of Spatial Transition to Turbulence in a Boundary Layer
To get an improved understanding of wall-generated turbulence, a parallelized direct numerical simulation code has been developed for the spatial transition to turbulence in a boundary layer. The code is based on the three-dimensional Navier-Stokes equations for incompressible flow in vertical-velocity/vertical-vorticity formulation. For the spatial discretization fourth-order compact finite differences have been used, and the boundary conditions for the Laplacian of the vertical velocity are determined using an influence matrix method. For the outflow boundary, a buffer domain method in conjunction with parabolization of the Navier-Stokes equations has been used. The elliptic equations in this formulation are solved using a parallelized multigrid solver. Both the algorithmic and implementation scalability features have resulted in efficient parallelization. The validation of the DNS solver has been done both for linear and weakly nonlinear cases. The spatial process of laminar-turbulent transition has been simulated. The ultimate aim is to relate the characteristic structures and events of the turbulent boundary layer to well-known structures and events of transitional boundary layers such as Lambda-vortices and spikes.

Development of LES Sub-Grid Scale Models based on Low-Dimensional POD Approximation
An alternative way to model sub-grid scale stresses (SGS) in the near-wall region is proposed. The key concept of this approach is that near-wall SGS are computed directly by filtering the instantaneous velocity estimated from the velocity reconstruction of a localized low-dimensional model. A blending function is introduced to blend the near-wall SGS to the core-region SGS calculated from a mixed SGS model. As a preliminary study, a globalized low-dimensional model in a wide channel is considered. The model is constructed by projection of the Navier-Stokes equations onto a three-dimensional vector Proper Orthogonal Decomposition (POD). The results show considerable promise. Further study of a localized low-dimensional model is being conducted.

Boundary Conditions for Low-Dimensional Models of the Turbulent Boundary Layer
The appearance of coherent structures in the turbulent boundary layer suggests that the flow can be modeled with low-dimensional systems of ordinary differential equations. Several groups have developed such models, with good qualitative success. However, the significance of interaction between the wall-dominated structures and the free stream remains a subject of controversy.

We examine this issue through the role of boundary conditions on the upper surface of the models. For a gross but mathematically well-defined model, we approximate the free-stream boundary with a plane-Couette condition. We compare behavior of plane-Couette models to boundary-condition-free ODE models and the boundary layer of a full-channel direct simulation. We examine the role of BC terms as inputs to a more generalized plane-Couette model.

AFOSR - Interaction between Near-Wall Turbulent Flows and Compliant Surfaces
The general aim of this project is to get an improved understanding of the interaction between wall-generated turbulence and compliant surface coatings using analysis and direct numerical simulation in an integrated approach. One of the main goals is to design compliant walls that can reduce turbulent sound production and turbulent drag. Among the ultimate goals of this project are, first, to obtain a fundamental understanding of flow-structure interaction phenomena for the case of the compliant-wall/turbulence interaction, and second, to use this understanding to enhance the flight performance of air vehicles by increasing their lift-to-drag ratio.

NSF - Hierarchical Modeling of Incompressible Turbulent Flows using Divergence-Free Vector Wavelets
Wavelet representations of turbulent flow offer potential advantages over Fourier representations, because coherent structures in turbulent flows are of limited spatial extent, like wavelets, whereas Fourier modes are quite the contrary. One way to model incompressible turbulence using wavelets is to combine incompressibility with a wavelet representation, i.e., to use divergence-free wavelets. Numerically, these functions so far have only been used in a simplified setting.

As our research interests mainly lie in the local dynamics of wall-bounded turbulent flows, we intend to adapt the divergence-free wavelet representation to the case of 3D incompressible flow with corresponding wall boundary conditions. Using this new representation, we propose to develop a three-dimensional, divergence-free wavelet based dynamical model appropriate to the turbulent channel flow. As one of the more interesting applications from a physical point of view, we will use our method to analyze the energy flows that are connected to the dynamical behavior of coherent structures in the wall region of the flow domain.

Dynamics of the Large-Scale Motion inside the Cylinder of Internal Combustion Engines.
The aim of this project is to get an improved understanding of the large-scale flow structures that exist in the cylinders of internal combustion engines, and the dynamical effects produced by these structures. It is clear that the nature of these structures has a strong effect on both the structure and the intensity of the turbulence in the engine cylinder, and it is very well known that the quality of the turbulence in engines is of the utmost importance, influencing important engine parameters such as efficiency, knock tendency, and combustion quality. One of our main goals in this project is to better understand the detailed dynamics of the pertinent processes in order to be able to come up with rational recommendations as to how the geometry of the combustion chamber and valve arrangements should be chosen in order to improve fundamental engine parameters.