## Introduction

My research interests have so far been mainly in two areas: fluid flow metrology and fluid turbulence research. I started my career out interested in instrumentation and measurement of fluid flow. Through studying ways to improve fluid flow metrology, it became apparent to me that at the heart of most metering challenges was turbulence. Turbulence has been formally studied since da Vinci more than 500 years ago and almost always by using statistical methods. More recently, the role of coherent structures such as vortices has been investigated, but without tremendous success. By using the tools recently developed in chaos theory and dynamical systems theory applied to the governing equations of fluid motion, it is believed possible discover the role of these coherent structures and even exploit them to predict and control turbulence. Currently, my research aims to test the validity of a dynamical systems description of turbulence and developing techniques that will help predict and control turbulence.

## Research activities

### Previous work in fluid flow metrology

While working at the National Institute of Standards and Technology (NIST) in the Fluid Metrology group, I worked to maintain primary flow standards and improve calibration techniques. This effort included developing physical models and uncertainty analysis for primary flow standards, designing and performing experiments in the wind tunnel facility, and maintained both liquid and air flow primary standards.

#### Airspeed tractability

In order to measure the efflux of greenhouse gasses and other pollutants emitted from the smokestacks of coal burning power plants, permanently installed flow meters and gas composition instrumentation are used. The in the US, the EPA has calibration procedure that is mandated. This procedure recommends that a specific type of fluid velocity sensor be used (a conically shaped multi-holed pitot tube) but, we discovered that this type of instrument experiences a flow transition in the region just above the boundary layer which causes the readings to be off by as much as 30 %. This flow transition was the result of a flow instability that is strongly dependent on the turbulence intensity. While investigating this flow instability, it became apparent that the current philosophy behind anemometer calibrations is the industry as a whole was wrong. Rather than providing the stable environment to provide the best calibration, the anemometer should be calibrated an unsteady flow environment that is the same as where the instrument will be used. In the past few years, at the national primary standards lab level, the literature has begun to reflect this new calibration philosophy.

#### Dynamic Gravimetric flow meter calibration facility

In the early 2000’s I. Shinder and M. Moldover at NIST developed a new method for calibration liquid flow meters that examined the amount of mass collected in a tank as a function of time measured on a weigh scale. The derivative of the mass reading with respect to time is the mass flow rate to second order despite the impinging momentum jet from the liquid into the collection tank. This method had only been implemented in a large scale flow calibration facility with a stable flow rate. By building a smaller scale calibration facility with flow rate that is more easily varied, we were able to show that this method also allows for calibration of the dynamics of flow meters.

#### Improvements to liquid flow meter calibration

Liquid flow measurements are used in a wide variety of applications from measuring the amount of gas you put into your car to metering the cooling water used in the core of a nuclear reactor. High quality measurements require high fidelity calibration facilities. These calibration labs used a surrogate for JP-8 jet fuel that is less flammable, but a known carcinogen. Working with the Air Force’s Primary Standards Lab, we were able to establish a new surrogate working fluid, aqueous solutions of propylene glycol, in the calibration facility that is non-toxic yet is able to reliably match rheological properties of JP-8 jet fuel.

### Current research in fluid turbulence

I am currently working in the Pattern Formation and Control Lab in the physics department of Georgia Tech where I am working to validate a dynamical systems description of fluid turbulence. Dynamical systems theory says that there exist special dynamically relevant solutions to the Navier-Stokes equation. These solutions are stable along most dimensions in its infinite (or practically extremely high) dimensional state space and unstable only along a few dimensions. Curves in state space that are traced out by a trajectory leaving from these unstable solutions along the unstable directions connect to other solutions. These curves form dynamical connections that effectively act as road a map for where a chaotic trajectory in this state space will go next. In theory, this description works wonderfully and offers amazing insight into the time evolution of turbulence, but how does it work practically in a real turbulent flow?

In order to test this turbulence model, fully time-resolved, high resolution, 3-dimensional actual turbulent velocity fields need to be compared with numerically computed unstable solutions to the Navier-Stokes equations.To do this, I am using a custom fully time-resolved tomographic Particle Image Velocimetry (tomo PIV) set up to gain high resolution velocity fields of counter-rotating Taylor-Couette flow in the small aspect ratio regime. Simulations of the Navier-Stokes equation are computed using spectral methods and solutions are found using a Newton-Krylov algorithm.

## Future work

Once the validity of a dynamical systems description of turbulence is established, I intend to turn my attention controlling turbulence. By using finite amplitude perturbations (tiny kicks to the system) to the flow field at just the right times, you should be able to move the system to a region of state space that would evolve along a dynamical connection for long periods of time. By kicking the system in a way that causes it to evolve along dynamical connections that lead to other regions of state space that you want the system to go to, you can control turbulence with a minimal amount of energy.

One of the first places to test this means of control is in the transitional regime of a fluid in and out of turbulence. For moderately turbulent flows, there are dynamical links between the chaotic turbulent attractor and the stable laminar attractor. By kicking the system closer to one of these special dynamical connections, you should be able to influence the system to relaminarize. This requires first finding the edge states whose unstable submanifolds connect to both the turbulent region of state space and to the laminar attractor, then mapping out these unstable submanifolds. Once the dynamical connections have been found, designing the optimal finite amplitude perturbation will be informed by the structure of flow along these dynamical connections.

A copy of my Ph.D. thesis proposal can be found here.