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### Active Flow Control and Global Stability Analysis of Separated Flow over a NACA 0012 Airfoil

 Title: Name(s): Active Flow Control and Global Stability Analysis of Separated Flow over a NACA 0012 Airfoil. 107 views 36 downloads Munday, Phillip M. (Phillip Michael), authorTaira, Kunihiko, professor directing dissertationHussaini, M. Yousuff, university representativeAlvi, Farrukh S., committee memberCattafesta, Louis N., committee memberLin, Shangchao, committee member Florida State University, degree granting institution College of Engineering, degree granting college Department of Mechanical Engineering , degree granting department text TextDoctoral Thesis monographic 2017 Florida State UniversityFlorida State University Tallahassee, Florida computeronline resource 1 online resource (124 pages) English The objective of this computational study is to examine and quantify the influence of fundamental flow control inputs in suppressing flow separation over a canonical airfoil. Most flow control studies to this date have relied on the development of actuator technology, and described the control input based on specific actuators. Taking advantage of a computational framework, we generalize the inputs to fundamental perturbations without restricting inputs to a particular actuator. Utilizing this viewpoint, generalized control inputs aim to aid in the quantification and support the design of separation control techniques. This study in particular independently introduces wall-normal momentum and angular momentum to the separated flow using swirling jets through model boundary conditions. The response of the flow field and the surface vorticity fluxes to various combinations of actuation inputs are examined in detail. By closely studying different variables, the influence of the wall-normal and angular momentum injections on separated flow is identified. As an example, open-loop control of fully separated, incompressible flow over a NACA 0012 airfoil at α = 6° and $9° with Re = 23,000 is examined with large-eddy simulations. For the shallow angle of attack α = 6°, the small recirculation region is primarily affected by wall-normal momentum injection. For a larger separation region at α = 9°, it is observed that the addition of angular momentum input to wall-normal momentum injection enhances the suppression of flow separation. Reducing the size of the separated flow region significantly impacts the forces, and in particular reduces drag and increases lift on the airfoil. It was found that the influence of flow control on the small recirculation region (α = 6°) can be sufficiently quantified with the traditional coefficient of momentum. At α = 9°, the effects of wall-normal and angular momentum inputs are captured by modifying the standard definition of the coefficient of momentum, which successfully characterizes suppression of separation and lift enhancement. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the non-dimensional swirl number. With the modified coefficient of momentum, this single value is able to categorize controlled flows into separated, transitional, and attached flows. With inadequate control input (separated flow regime), lift decreased compared to the baseline flow. Increasing the modified coefficient of momentum, flow transitions from separated to attached and accordingly results in improved aerodynamic forces. Modifying the spanwise spacing, it is shown that the minimum modified coefficient of momentum input required to begin transitioning the flow is dependent on actuator spacing. The growth (or decay) of perturbations can facilitate or inhibit the influence of flow control inputs. Biglobal stability analysis is considered to further analyze the behavior of control inputs on separated flow over a symmetric airfoil. Assuming a spanwise periodic waveform for the perturbations, the eigenvalues and eigenvectors about a base flow are solved to understand the influence of spanwise variation on the development of the flow. Two algorithms are developed and validated to solve for the eigenvalues of the flow: an algebraic eigenvalue solver (matrix based) and a time-stepping algorithm. The matrix based approach is formulated without ever storing the matrices, creating a computationally memory efficient algorithm. Based on the matrix based solver, eigenvalues and eigenvectors are identified for flow over a NACA 0015 airfoil at Re = 200,$600, and $1,000. All three cases contain similar modes, although the growth rate of the leading eigenvalue is decreased with increasing Reynolds number. Three distinct types of modes are found, wake mode, steady mode, and modes of the continuous branch. While this method is limited in the range of Reynolds numbers, these results are used to validate the time-stepper approach. Increasing the Reynolds number to Re = 23,000 over a NACA 0012 airfoil, the time-stepper method is implemented due to rising computational cost of the matrix-based method. Stability analysis about the time-averaged flow is performed for spanwise wavenumbers of β = 1$, $10π, and$20π, which the latter two wavenumbers are representative of the spanwise spacing between the actuators. The largest spanwise wavelength (β = 1$) contained unstable modes that ranged from low to high frequency, and a particular unstable low-frequency mode corresponding to a frequency observed in the lift forces of the baseline large-eddy simulation. For the larger spanwise wavenumbers, β = 10π ($L_z/c = 0.2$) and$20π ($L_z/c = 0.1$), low-frequency modes were damped and only modes with $f > 5$ were unstable. These results help us gain further insight into the influence of the flow control inputs. Flow control is not implemented in a manner to directly excite specific modes, but does dictate the spanwise wavelengths that can be generated. Comparing the unstable eigenmodes at these two spacings, the larger spanwise spacing ($\beta = 10\pi$) had a greater growth rate for the majority of the unstable modes. The smaller spanwise spacing ($\beta = 20\pi$) has only a single unstable mode with a growth rate an order of magnitude smaller than $\beta = 10\pi$. With the aid of the increased growth rate, perturbations to the flow with a wider spacing become more effective by interacting with natural modes of the flow. Taking advantage of these natural modes allows for decreased input for the wider spanwise spacing. In conclusion, it was shown that the influence of wall-normal and angular momentum inputs on fully separated flow can adequately be described by the modified coefficient of momentum. Through further analysis and the development of a biglobal stability solver, spanwise spacing effects observed in the flow control study can be explained. The findings from this study should aid in the development of more intelligently designed flow control strategies and provide guidance in the selection of flow control actuators. FSU_2017SP_Munday_fsu_0071E_13086 (IID) A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. Spring Semester 2017. April 13, 2017. Computational Fluid Dynamics, Fluid Mechanics, Global Stability Analysis, Separation Control Includes bibliographical references. Kunihiko Taira, Professor Directing Dissertation; M. Yousuff Hussaini, University Representative; Farrukh Alvi, Committee Member; Louis Cattafesta, Committee Member; Shangchao Lin, Committee Member. Mechanical engineeringAerospace engineering http://purl.flvc.org/fsu/fd/FSU_2017SP_Munday_fsu_0071E_13086 This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s). The copyright in theses and dissertations completed at Florida State University is held by the students who author them. FSU

Munday, P. M. (P. M. ). (2017). Active Flow Control and Global Stability Analysis of Separated Flow over a NACA 0012 Airfoil. Retrieved from http://purl.flvc.org/fsu/fd/FSU_2017SP_Munday_fsu_0071E_13086