A formation criterion for synthetic jets is proposed and validated. A synthetic jet actuator is a zero-net mass-flux device that imparts momentum to its surroundings. Jet formation is defined as the appearance of a time-averaged outward velocity along the jet axis and corresponds to the generation and subsequent convection or escape of a vortex ring. It is shown that over a wide range of operating conditions synthetic jet formation is governed by the jet Strouhal number Sr (or Reynolds number Re and Stokes number S). Both numerical simulations and experiments are performed to supplement available two-dimensional and axisymmetric synthetic jet formation data in the literature. The data support the jet formation criterion 1/Sr = Re/S 2 > K, where the constant K is approximately 1 and 0.16 for two-dimensional and axisymmetric synthetic jets, respectively. In addition, the dependence of the constant K on the normalized radius of curvature of a rounded orifice or slot is addressed. The criterion is expected to serve as a useful design guide for synthetic jet formation in flow control, heat transfer, and acoustic liner applications, in which a stronger jet is synonymous with increased momentum transfer, vorticity generation, and acoustic nonlinearities.

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This paper proposes and validates a jet formation criterion for synthetic jet actuators. The synthetic jet is a zero net mass flux device, adding additional momentum but no mass to its surroundings. Jet formation is defined as a mean outward velocity along the jet axis and corresponds to the clear formation of shed vortices. It is shown that the synthetic jet formation is governed by the Strouhal number (or Reynolds number and Stokes number). Numerical simulations and experiments are performed to supplement available two-dimensional and axisymmetric jet formation data in the literature. The data support the jet formation criterion , where the constant 2 Re/ S K > K is approximately 2 and 0.16 for two dimensional and axisymmetric synthetic jets, respectively. This criterion is valid for relatively thick orifice plates with thickness-to-width ratios greater than approximately 2. This result is expected to be useful for the design of flow-control actuators and engine nacelle acoustic liners.

I am grateful to several individuals for their support in my dissertation work. The greater part of this work was made possible by the instruction of my teachers, and the love and support of my family and friends. It is with my heartfelt gratitude that I acknowledge each of them. Firstly, I would like to express sincere thanks and appreciation to my advisor, Dr. Wei Shyy, for his excellent guidance, support, trust, and patience throughout my doctoral studies. I am very grateful for his remarkable wisdom, thought-provoking ideas, and critical questions during the course of my research work. I thank him for encouraging, motivating, and always prodding me to perform beyond my own limits. Secondly, I would like to express sincere gratitude towards my co-advisor, Dr. Nagaraj Arakere, for his firm support and caring attitude during some difficult times in my graduate studies. I also would like to express my appreciation to the members of my dissertation committee Dr. Louis Cattafesta, Dr. James Klausner, and Dr. Don Slinn, for their valuable comments and expertise to better my work. I deeply thank Dr. Siddharth Thakur (ST) for providing me substantial assistance with the STREAM code and for his cordial suggestions on research work and career planning. My thanks go to all the members of our lab, with whom I have had the privilege to work. Due to the presence of all these wonderful people, work is more enjoyable. In particular, it was a delightful experience to collaborate with Jiongyang Wu, Tushar Goel, and Baoning Zhang on various research topics. v I would like to express my deepest gratitude towards my family members. My parents have always provided me unconditional love. They have always given top priority to my education, which made it possible for me to pursue graduate studies in the United States. I would like to thank my grandparents for their selfless affection and loving attitude during my early years. My wife's parents and her sister's family have been extremely supportive throughout my graduate education. I greatly appreciate their trust in my abilities. Last but never least, I am thankful beyond words to my wife, Neeti Pathare. Together, we have walked through this memorable, cherishable, and joyful journey of graduate education. Her honest and unfaltering love has been my most precious possession all these times. I thank her for standing besides me every time and every where. To Neeti and my parents, I dedicate this thesis! vi