The application of large eddy simulation (LES) to flows with increasingly complex geometry necessitates the extension of the LES technique to unstructured meshes. A desirable feature for LES on unstructured meshes is that the filtering operation used to remove small scale motions from the flow commutes with the differentiation operator. If this commutation requirement is satisfied, the LES equations have the same form as the unfiltered Navier Stokes equations. Commutation is generally satisfied if the filter has a constant width. However, in inhomogeneous turbulent flows, the minimum size of eddies that need to be resolved varies throughout the flow. Thus, the filter width should also vary accordingly. Given these challenges, the objective of this work was to develop a generaltheory for constructing discrete variable width commutative filters for LES on unstructured meshes.

In this project, a theory for constructing discrete commutative filters for unstructured meshes in two and three dimensions was developed. In addition to commutation, other issues such as control of filter width and filter profile in wavenumber space were also addressed. In particular, we are able to specify a desired filter width at each point in space and obtain a discrete filter which satisfies this requirement regardless of the choice of the computational mesh.

Large Eddy Simulation of a Low Pressure Turbine Blade Passage
S.Nagarajan

Sponsored by: Franklin P. Johnson Fellowship and ASCI

Loss in efficiency of low pressure turbines at cruise conditions is well known but hardly understood. Interplay of various factors including transition of the boundary layer on the blade surface, separation, and reattachment is suspected to be the cause of this efficiency drop. Overall performance of a gas turbine engine is very sensitive to the performance of the low pressure turbine - a 1% improvement in efficiency of the low pressure turbine causes almost a 1% reduction in specific fuel consumption, a significant improvement by any standard. Since an aircraft spends most of its flight time in cruise, improvement of low pressure turbine efficiency at cruise can lead to significant reduction in operating costs.

An accurate simulation of the flow inside a low pressure turbine blade passage at take-off and cruise conditions should give us valuable insight into the physical phenomena that occur andd their effects on the performance of the low pressure turbine. The main objective of this work is to carry out Large Eddy Simulations (LES) of the flow in a single blade passage of a low pressure turbine so as to capture the important physical phenomena and to glean from them the reason(s) for loss of efficiency. Another objective is to create a reliable database that can be used for development and validation of models that can be used in engineering simulations of these flows.

Wall Model for LES
Jeremy Templeton

When an LES is performed on a turbulent flow, a large number of points must be used near a wall to capture the behavior of the boundary layer and its effect on the whole flow. The goal of this project is to develop a model for what happens in the boundary layer so flow statistics can be captured in the outer region without the cost of computing what is actually going on in the boundary. There are several different approaches that people have tried using the log-layer model, boundary layer equations, RANS (Reynolds Averaged Navier Stokes) computations, and even optimal control theory to produce the right "off the wall" boundary conditions for the outer flow. My project will involve analyzing all these techniques and using/modifying which, if any, work so that they can be used in general turbulence computations.