Date of Award

Spring 1-1-2012

Document Type


Degree Name

Master of Science (MS)

First Advisor

John P. Crimaldi

Second Advisor

Roseanna M. Neupauer

Third Advisor

Harihar Rajaram


We used analytical and numerical techniques to examine reaction rates of two initially distant scalars released into a cylinder wake at a Reynolds number of 97.4. Two scalars, C1 and C2, are released into the flow upstream of the cylinder with an initial lateral separation. As the scalars advect in the flow, the plumes coalesce in the well-developed vortex street where the plumes are stretched and folded by vortex interaction. The scalars diffuse along the elongated interface and mix together, or react.

The finite element analysis software, COMSOL, is used to solve the Navier-Stokes equations for the cylinder wake flow field, and a pair of coupled advection-diffusion-reaction equations are solved for the transport and reaction of two initially distant scalar concentrations. In a series of simulations, we examine the reaction rates for various scalar release geometries, reaction speeds, and scalar diffusivities. For each model, the reaction rate is calculated by lateral integrating the C1C2 product and phase averaging over one shedding period.

A model without the cylinder is created as a baseline case for direct comparisons to the cylinder wake case. With no stirring mechanism in the flow, scalar reaction only occurs by diffusion. Comparing the cylinder wake case with the no-cylinder case shows the effect on reaction due directly to the wake.

The analytical solution is derived for the limiting case of integrated reaction rate and is found to be a function of a single parameter. The analytical solution, numerically integrated solution, and the numerical simulation show good agreement, validating the numerical models.

The cylinder wake cases showed significant increase in reaction rate compared to the no-cylinder cases for all parameters tested, particularly at large separations, in which, the cylinder wake increased the reaction rate an order of magnitude.