#### Degree Type

Dissertation

#### Date of Award

2011

#### Degree Name

Doctor of Philosophy

#### Department

Mechanical Engineering

#### First Advisor

Michael G. Olsen

#### Second Advisor

James C. Hill

#### Abstract

Vortex behavior and characteristics in a confined rectangular jet with a co-flow were examined using vortex swirling strength as a defining characteristic. On the left side of the jet, the positively (counterclockwise) rotating vortices are dominant, while negatively rotating vortices are dominant on the right side of the jet. The characteristics of vortices, such as population density, average size and strength, and deviation velocity were calculated and analyzed in both the cross-stream direction and the streamwise direction. In the near-field of the jet, the population density, average size and strength of the dominant direction vortices show high values on both sides of the center stream with a small number of counter-rotating vortices produced in the small wake regions close to jet outlet. As the flow develops, the wake regions disappear, these count-rotating vortices also disappear, and the population of the dominant direction vortices increase and spread in the jet. The mean size and strength of the vortices decrease monotonically with streamwise coordinate. The signs of vortex deviation velocity indicate the vortices transfer low momentum to high velocity region and high momentum to the low velocity region. The developing trends of these characteristics were also identified by tracing vortices using time-resolved PIV data. Both the mean tracked vortex strength and size decrease with increasing downstream distance overall. At the locations of the left peak of turbulent kinetic energy, the two point spatial cross-correlation of swirling strength with velocity fluctuation and concentration fluctuation were calculated. All the correlation fields contain one positively correlated region and one negatively correlated region although the orientations of the correlation fields varied, due to the flow transitioning from wake, to jet, to channel flow. Finally, linear stochastic estimation was used to calculate conditional structures. The large-scale structures in the velocity field revealed by linear stochastic estimation are spindle-shaped with a titling stream-wise major axis.

Vortex behavior and characteristics in a confined rectangular wake were also examined using swirling strength as a defining characteristic of a vortex. Instantaneous swirling strength field shows that positively (counterclockwise) rotating vortices are dominant on the right side of the wake and negatively (clockwise) rotating vortices are dominant on the left side. The population density, average size and strength of vortex cores all shows high peak values both sides of the wakes, while these peaks decrease quickly and the profiles broaden as the flow progresses downstream. The changing of vortex core maximum strength is seen relatively faster than the change of the core size. The results of mean cross-stream wise deviation velocity of vortex core shows the vortices in the wake spread from the neighborhood of wake to the centers of the free stream, and the mean streamwise deviation velocity indicates that vortices bringing high momentum fluid of the free stream into the the wake. Two point spatial cross-correlations of swirling strength with velocity fluctuations and concentration fluctuations were also calculated. All the cross correlation fields shown here exhibit a ``butterfly'' like shape, with one ``wing'' with positive correlation values and the other ``wing'' with negative values. The axises of correlation fields are oriented in the streamwise direction in R_{ λ u' } contours, and they tile towards the wake center on the both sides of the wake,while the axises in R _{ λ v'} are oriented in the cross-stream direction, and they tile downstream on the both sides of the wake. The R_{ λ phi'} results show some similarity to those of R_{ λ v'}, indicating the vortices play a similar role in mass transfer as in momentum transfer. Linear stochastic estimation was used to interpret the cross correlation result and visualize the underlining large scale coherent structures. The LSE results show a clear vortex street pattern in far fields of the wake, indicating the vortices, developed independently on both sides of the splitter plates, are reorganized and coherent as the flow develops downstream.

Large-eddy simulations (LES) were performed for a confined rectangular liquid jet with a co-flow and compared in detail with particle image velocimetry (PIV) measurements. A finite-volume CFD library, OpenFOAM, was used to discretize and solve the filtered Navier-Stokes equation. The effects of grid resolution, numerical schemes and subgrid models on the LES results were investigated. Grid independence has been shown. The second and fourth order schemes showed the nearly same performance, while the fourth order scheme costs much more computationally. Subgrid model comparison showed that the locally dynamic procedure is necessary for complex flow simulation. Model validation was performed by comparing LES data for the one-point velocity statistics such as the mean and the root-mean-square velocity, shear stress, correlation coefficient, velocity skewness and flatness with the PIV data. In addition, LES data for the two-point spatial correlations of velocity fluctuations that provide structural information were computed and compared with PIV data. Very good agreement was obtained leading to the conclusion that the LES velocity field captures the large-scale structures present in the actual flow.

Experimental data of combined particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF) measurements are used to analyzed the flow between the two scalar interfaces of confined turbulent jet and wake flow. The fluid of center stream of both flow cases contains a fluorescent dye, and normalized PLIF images were used to discriminate the inner and outer boundaries of the center stream. The growth of the boundaries of both flow cases are plotted and analyzed. The mean and fluctuations of the passive scalar, velocity, stain rate, and vorticity are determined relative to the locations of the two boundaries. The results show some unique perspectives of this co-flowing confined rectangular jet flow. The fluctuations of the passive scalar shows high values close to the outer boundary of jet , and the most of the properties of the velocity fields show high values on the left side of inner boundaries of the jet. The results of wake case are very symmetrical about the center of the wake, indicating the presence of the vortex street.

#### Copyright Owner

Bo Kong

#### Copyright Date

2011

#### Language

en

#### Date Available

2012-04-30

#### File Format

application/pdf

#### File Size

187 pages

#### Recommended Citation

Kong, Bo, "Experimental and computational study of turbulent mixing in a confined rectangular jet" (2011). *Graduate Theses and Dissertations*. 11961.

https://lib.dr.iastate.edu/etd/11961