The goal of this project is to develop a better understanding of how transverse oscillations alter turbulent pipe flow. Since almost all flows are subject to some level of oscillations or vibrations, usually in the a direction perpendicular to flow, it is important to understand the effects of oscillations. Furthermore, knowing what levels of oscillation will significantly change the flow would be helpful in the design of new devices. This project will also extends the methodology used to model the oscillations so that the effects can be determined using numerical simulations.

Some previous research was conducted on flow through an oscillating pipe. Benhamou eta. al., experimentally studied pipes oscillating at low frequencies with large amplitudes. By visualizing when the flow became turbulent, Benhamou showed the oscillations caused the transition from laminar to turbulence to occur at a lower Reynolds number. Due to experimental limitations, no information about how the oscillations effect fully turbulent flows is available. This project will use numerical methods to examine the effect of oscillations in fully turbulent flows.

This research project is being conducted using a finite difference code known as NGA. Using NGA, a variety of simulations are being conducted for various oscillation frequencies and amplitudes in an effort to characterize how each parameter changes the flow. The flows are being compared visually as shown by the example movie below and by plots of turbulent statistics.

The cost of fuel injection is driven by both the need to pump the fuel to the injection pressure and to add parts for the injector head. A potential solution is to use integrated circuit technology to produce a cost effective MEMS fuel pump/atomizer. An approach is to explore an integrated pump and injector. Micropumps have been designed to deliver small fluid volumes in a variety of systems ranging from chemical and biological assay systems, to propulsion systems for space exploration. By integrating a micropump with the injection nozzles, a very compact and potentially economic device can be constructed.

Another approach to small-scale fuel injection is to capitalize upon the benefits of electrohydrodynamics (EHD) and enhance fuel atomization. The application of a strong electric within the domain of interest has been demonstrated by many researchers. An example is shown in Figure \ref{fig:Unipolar}. There are many possible benefits to EHD aided atomization for combustion, such as smaller droplets, wider spray cone, and the ability to control or "tune" the spray for improved performance. For these reasons a numerical investigation of electrohydrodynamic atomization is proposed, with the following expected results:

• Development of a technique for modeling the three-dimensional nature of electrohydrodynamic atomization in dielectric liquids such as hydrocarbon fuels, requiring the coupling of multiphase methods for liquid atomization with the dynamics of applied electric fields.
• Predictions of the dominant breakup mechanisms and capillary phenomena for electrohydrodynamic atomization over a range of relevant geometric and physical parameters.
• An improved understanding of interactions among geometry, fluid and electrical properties, and EHD to enable optimization of fuel injection designs.

Homogeneous Compressible Turbulent Mixing for Variable Density Flows

Almost all fluid systems of practical relevance are characterized by interacting fluid species of differing molecular masses. In such systems, called variable density flows, compressible turbulent mixing plays an important role. Of particular interest are the rates at which each fluid mixes, since heavier fluids carry stronger inertial effects. Homogeneous compressible turbulent mixing between two fluids of differing characteristic densities is studied to investigate the asymmetric mixing property. The flow is initialized as random blobs of the two pure fluids. A velocity field is applied to the initial conditions consistently with the governing equations such that turbulent mixing occurs. Periodicity is imposed in all physical dimensions of the computational domain to simulate an infinite physical domain. Direct numerical simulations, where all scales of motion are fully resolved, will be run for this problem to investigate the variable density, compressibility, and mass diffusivity effects of the mixing processes.

Rayleigh-Taylor Instability

Rayleigh-Taylor instability is an fundamental varaible density flow. The instability is observed in a wide variety of systems incluiding supernovae, the Earth's atmosphere, and inertial confinement fusion processes. It is a buoyantly driven instability and occurs when a heavy fluid lies on top of a lighter fluid within a gravitational field. More generally, when a less dense fluid pushes on a more dense fluid, Rayleigh-Taylor instability inevitably develops. The heavy fluid falls into the light fluid as "spikes" as the fluid system begins to grow a mixing layer. The homogeneous compressible turbulent mixing problem will shed light on the dynamics of this mixing layer. The structures that develop within the mixing layer can be orders of magnitude smaller than the characteristic scales of the instability. Therefore, direct numerical simulations, which resolves all present scales instead of applying turbulence models, requires efficient numerical methods to handle the wide range of scales. A wavelet-based adaptive grid method is used to study the growth of Rayleigh-Taylor instability. The fully compressible case is simulated in order to investigate how compressiblity and variable density effects modify the growth of the instability.

Adaptive Wavelet Collocation Method

In order to resolve all scales present in the problems of interest, simulations are performed using the Adaptive Wavelet Collocation Method, which utilizes wavelets to perform grid adaptation. Wavelets are localized functions that are used as a set of basis functions for wavelet decomposition. By separating those basis wavelet functions which are significant in representing the solution from those that are unimportant, computations can be performed on a highly compressed number of points. This allows for an optimal use of computational resources.

The ocean bathymetry is a spatially varying, intricate, and complex surface. Using current techniques for representation of this bottom boundary results in a surface that is either too crude (stair step representation) or too expensive (body-fitted meshes). The volume penalization approach combined with an adaptive grid, can make the implementation of complex geometry boundaries accurate and feasible for even a simulation run on a standard desktop computer.

Volume penalization works by penalizing the equations in such a way that the boundary conditions are automatically satisfied. This is done by solving the regular governing equations in the fluid region, which is determined by some mask function. The rest of the computational domain is marked as the solid region and in this region the penalized form of the equations is solved. This technique has been tested for no slip boundary conditions for numerous cases including both compressible and incompressible flows.

In order to avoid resolving the boundary layer associated with no-slip conditions, the volume penalization was extended to slip conditions. The extension of the method is based on the realization that if the solution in the penalized region adjusts to the solution of the slip equation on a time scale considerably shorter than convective time scale, then the slip boundary conditions at the solid boundary will be automatically satisfied. A number of different volume penalization methods were developed and evaluated with results from the best one shown below.

Demonstration of slip boundary conditions with and without Brinkman penalization for Κ = 10.

Wind turbines are the predominate technology for non-hydro renewable energy. As turbines extract energy from wind, a wake or disturbed, turbulent region of wind is created downstream of the turbine. Wind turbines located in the wake of another turbine do not produce as much power as the upstream turbine. Current modeling efforts fail to accurately predict power losses in downstream turbines by not completely capturing wake effects. Further research to understand and model wake effects is necessary to reduce wake power losses and improve overall wind farm power production. A model is created that simulates the neutrally stratified atmospheric boundary layer (ABL). The neutral ABL simulation is validated against three criteria from experimental data. The model is run in both Large Eddy Simulation (LES) and Reynolds Averaged Navier- Stokes (RANS) to compare the two methods. Wind turbines at various downstream positions are modeled within the neutral ABL simulation using an actuator disc. Results from this model include the power deficit ratio of a turbine located in a wake. Power deficit ratios for LES and RANS simulations are within 2-4% and 15-43% of experimental data, respectively. With the results from these simulations, wind farm developers can create a lower-order model to include hundreds of turbines necessary to model an entire wind farm and improve efficiency.

The above image shows intermediate results for generalized fluid shape optimization and the corresponding Level-Set function. This study employed a Level-Set-based geometric boundary representation that avoids the disadvantages of the commonly used material interpolation approach.

Finite element simulation of the flow around a cylinder for a Reynolds number Re = 100.