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Numerical Simulation of Turbulent Accelerated Round Jets for Aeronautical Applications ... PDF

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Numerical Simulation of Turbulent Accelerated Round Jets for Aeronautical Applications Pedro Miguel Rosa Ferreira Neto Masters thesis on Aerospace Engineering Jury President: Prof. Fernando Jos´e Parracho Lau Supervisor: Prof. Jos´e Carlos Fernandes Pereira Supervisor: Dr. Carlos Bettencourt da Silva Examiner: Prof. Joa˜o Manuel Gon¸calves de Sousa Oliveira November of 2008 Acknowledgments I would like to express my gratitude to my supervisors, Carlos Bettencourt da Silva, for his orientation and knowledge sharing on what was my entrance to the world of turbulence, and Jos´e Carlos Pereira, for his expertise and for the magnificent way he teaches fluid mechanics and computational fluid dynamics. Thank you to everyone at LASEF, for all the tips and tricks, and for the very good working experience. A very special thanks to Joana, for her invaluable help and support throughout my thesis and all the years of graduation. i Abstract Directandlarge-eddysimulations(DNS/LES)ofacceleratingturbulentroundjetsare used to analyze the effects of acceleration over three main subjects: the kinematics of the coherent structures, their topology and entrainment of the jet in the near field (x/D <12). The acceleration is obtained by increasing the nozzle jet velocity with time in a previously established steady jet. Several acceleration rates and Reynolds numbers (Re =500 => 1000, 1000 => 2000, and 10000 => 20000) were simulated. D Unsteady effects during acceleration include an higher shedding frequency of the pri- mary vortex rings which also become smaller during acceleration. Detailedaccelerationmapsareusedtotrackdownthekinematicsofthevortexmotion inthenearfieldofthejet. Thesheddingfrequencyincreaseslinearlywiththeacceler- ationratewhichcausesanumberofnewprimaryandsecondaryvortexmergingevents in thenear field ofthe jet thatare absent fromsteady jets. The Reynoldsnumberhas no influence in these unsteady effects. Thesmallerprimaryvortexringsshedduringaccelerationaremorestable,i.e. present less azimuthal and radial distortion as they travel streamwise. The acceleration decreases the spreading rate of the jet, in agreement with previous experimental works, but contrary to previous beliefs, the entrainment rate, evaluated intheshearlayerinterface,ishigherduringtheaccelerationphaseofthehighReynolds number LES simulation. Keywords: Unsteady; Round jet; Turbulence; Coherent structures; Entrainment ii Resumo Simula¸c˜oes num´ericas directas (DNS) e simula¸c˜oes das grandes escalas (LES) e jac- tos acelerados turbulentos s˜ao utilizadas para estudar os efeitos da acelera¸c˜ao em trˆes assuntos distintos: a cinem´atica das estruturas coerentes, a sua topologia e o arrasta- mento do jacto na zona pr´oxima (x/D <12). Aacelera¸c˜ao´eobtidaaumentandoavelocidadedesa´ıdadojactoaolongodotempo,a partirdeumjactoemregimeestacion´ariopreviamenteestabelecido. Foramsimuladas v´arias taxas de acelerac¸˜ao e v´arios nu´meros de Reynolds (Re = 500 => 1000, 1000 D => 2000, e 10000 => 20000). Os principais efeitos da n˜ao-estacionaridade s˜ao um aumento da frequˆencia de liber- ta¸c˜ao dos v´ortices toroidais que tamb´em s˜ao menores durante a acelerac¸˜ao. Para estudar a cinem´atica dos turbilh˜oes foram criados mapas de acelerac¸˜ao. Estes permitem calcular a frequˆencia de liberta¸c˜ao e fus˜oes entre estruturas coerentes. A acelera¸c˜ao origina fus˜oes prim´arias e secund´arias entre os v´ortices em anel que n˜ao acontecem durante as fases estacion´arias das simula¸c˜oes. O nu´mero de Reynolds n˜ao tem influˆencia nestes acontecimentos. As estruturas coerentes libertadas durante a fase de acelera¸c˜ao s˜ao mais est´aveis, isto ´e, apresentam menos distor¸co˜es radiais e azimutais enquanto viajam para jusante. De acordo com os resultados experimentais existentes, a acelerac¸˜ao diminui a taxa de alargamento do jacto, no entanto, contrariamente a estes, o arrastamento do jacto, medido na interface da camada de corte, aumenta durante a fase de acelera¸c˜ao na simula¸c˜ao de LES a nu´mero de Reynolds elevado. Palavras-chave: N˜ao-estacionaridade;Jactoaxissim´etrico;Turbulˆencia;Estruturas coerentes; Arrastamento iii Sure as I am breathing, sure as I’m sad. I’ll keep this wisdom in my flesh. I leave here believing more than I had. And there’s a reason I’ll be, a reason I’ll be back. Eddie Vedder iv Contents 1 Motivation 1 2 Introduction 2 2.1 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.1.1 Energy cascade . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.1.2 Influence of the Reynolds number. . . . . . . . . . . . . . . . . . 5 2.2 The Round Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.1 Laminar round jet . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Turbulent jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Computational Fluid Dynamics . . . . . . . . . . . . . . . . . . . . . . . 8 2.3.1 Direct Numerical Simulations . . . . . . . . . . . . . . . . . . . . 8 3 State Of The Art 12 3.1 Turbulent Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.1 Instability frequencies . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Unsteady Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.3 Vortex Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.1 Helmholtz theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3.2 Vorticity wake . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4 Numerical Method 23 4.1 Governing Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.2 Code Philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2.1 Computational box . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3 Numerical Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3.1 Spatial discretization . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3.2 Temporal advancement . . . . . . . . . . . . . . . . . . . . . . . 26 v 4.3.3 Pressure-velocity coupling . . . . . . . . . . . . . . . . . . . . . . 26 4.3.4 LES sub-grid scale model . . . . . . . . . . . . . . . . . . . . . . 27 4.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4.1 Lateral boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4.2 Inlet condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.4.3 Outlet condition . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5 Linear Acceleration of Turbulent Round Jets 32 5.1 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 5.2 Overview of the Base Simulation . . . . . . . . . . . . . . . . . . . . . . 34 5.3 Kinematics of the Vortex Motion . . . . . . . . . . . . . . . . . . . . . . 39 5.3.1 Acceleration maps . . . . . . . . . . . . . . . . . . . . . . . . . . 39 5.3.2 Influence of the Reynolds number. . . . . . . . . . . . . . . . . . 40 5.3.3 Vortex ring merging events . . . . . . . . . . . . . . . . . . . . . 41 5.3.4 Characteristic frequencies . . . . . . . . . . . . . . . . . . . . . . 44 5.4 Topology of the Vortex Rings . . . . . . . . . . . . . . . . . . . . . . . . 47 5.4.1 Influence of the acceleration rate . . . . . . . . . . . . . . . . . . 51 5.5 Jet Entrainment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.5.1 Jet width - δ . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 0.5 5.5.2 Streamwise mass flow rate . . . . . . . . . . . . . . . . . . . . . . 53 5.5.3 Radial velocity - Shear layer interface . . . . . . . . . . . . . . . 54 5.6 Deccelerated Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 6 Conclusion 59 6.1 Kinematics of Vortex Motion and Topology of the Vortex Rings . . . . . 59 6.1.1 Shear layer mode . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 6.1.2 Preferred mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 6.1.3 Secondary instabilities . . . . . . . . . . . . . . . . . . . . . . . . 62 6.2 Entrainment Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 A Q Criteria Visualization 64 B Article no. 1 72 Bibliography 77 vi List of Figures 2.1 Flow past a cylinder at different Reynolds numbers, from Frisch [19] . . 3 2.2 Energy spectra, from Geurts [20] . . . . . . . . . . . . . . . . . . . . . . 4 2.3 Sketch of a round jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Round jet at different Reynolds numbers, from Kwon & Seo [28] . . . . 8 2.5 Cost of computing since 1945, from Moravec [38] . . . . . . . . . . . . . 9 2.6 Filtering f(x), from Frisch [19] . . . . . . . . . . . . . . . . . . . . . . . 11 3.1 Spreading rate results from Kwon & Seo [28] and Bogey & Baily [2] . . 13 3.2 The Kelvin-Helmholtz instability, from Brederode [14] . . . . . . . . . . 14 3.3 Spatial growth rate −α as a function of the frequency β: axissymmet- i ric mode (continuous) and helical (dashed) modes, from Michalke & Hermann [36] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4 Both preferred mode shapes in a round jet DNS from the present study 15 3.5 Azimuthal instability in a vortex ring, from Van Dyke [17] . . . . . . . . 16 3.6 Draft illustrating lateral jets formation, from Bancher et al [3] . . . . . 17 3.7 Normalized entrainment from Roy & Johari computational results [42] . 20 3.8 Concentration front on experiment by Zhang & Johari [50]. . . . . . . . 21 3.9 Aproximate sketch of the vortex rings in a round jet, from Abani & Reitz [1] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.10 Instantaneous streamlines and vorticity patches (vortex ring frame of reference), from Dabiri & Gharib [12]. . . . . . . . . . . . . . . . . . . . 22 4.1 SketchoftheU componentintheinletprofile,fromUrbin&M´etais forc [45] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.1 Inlet Reynolds number Re evolution for some simulations . . . . . . . 33 D 5.2 Centerline slice with contour of Q>0.01 prior to the acceleration. . . . 35 5.3 Iso-surfaces of positive Q. . . . . . . . . . . . . . . . . . . . . . . . . . . 36 vii 5.4 Centerline slice with contour of Q>0.01 during the acceleration . . . . 36 5.5 Centerline slice with contour of Q>0.01 at the end of acceleration . . . 37 5.6 Centerline slice with contour of Q>0.01 after the acceleration . . . . . 37 5.7 Spectra of v during acceleration with and without the U component. 38 forc 5.8 Acceleration map of the base simulation, α=0.06, Rei =500 . . . . . 39 D 5.9 Acceleration maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 5.10 Acceleration map for α=0.06, Rei =1000 . . . . . . . . . . . . . . . . 41 D 5.11 Acceleration map of the base simulation, α=0.06, Rei =500 . . . . . 42 D 5.12 Height of zone A for each simulation . . . . . . . . . . . . . . . . . . . . 43 5.13 Number of primary (A) and secondary (B) merging events . . . . . . . . 43 5.14 Influence of the Reynolds number in the vortex shedding frequency for α=0.06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 5.15 Influence of the acceleration rate in the shear layer mode frequency . . . 45 5.16 Evolutionofthemeanshearlayermodefrequencywiththeacceleration rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 5.17 Structure of the jet at the last acceleration instant of the base simulation 47 5.18 Structure of the jet at the final steady stage . . . . . . . . . . . . . . . . 48 5.19 3D iso-surfaces of Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 5.20 Temporal evolution of the streamwise profile of E . . . . . . . . . . . . 50 r 5.21 Temporal evolution of the streamwise profile of E . . . . . . . . . . . . 50 θ 5.22 Evolution of the δ profile for α=0.02 . . . . . . . . . . . . . . . . . . 52 0.5 5.23 δ at a given time for several α’s . . . . . . . . . . . . . . . . . . . . . 53 0.5 5.24 Streamwise evolution of Q∗ at different stages of the base simulation . . 54 5.25 Radial velocity profiles at different stages of the base simulation. . . . . 55 5.26 Entrainment profile of the Rei =500 simulation . . . . . . . . . . . . . 56 D 5.27 Entrainment profile of the Rei =1000 simulation . . . . . . . . . . . . 57 D 5.28 Entrainment profile of the Rei =10000 simulation . . . . . . . . . . . . 57 D 5.29 Acceleration map of the deceleration simulation . . . . . . . . . . . . . . 58 6.1 Sketch of the flow during the a) stationary phase, and b) accelerating phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 6.2 Dye concentration on experiment by Zhang & Johari [50] . . . . . . . . 63 viii List of Tables 5.1 Simulations of accelerated jets performed throughout this work . . . . . 34 A.1 3D iso-surfaces of Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 A.2 2D contours of positive Q during the initial phase. . . . . . . . . . . . . 66 A.3 2D contours of positive Q during acceleration . . . . . . . . . . . . . . . 67 A.4 2D contours of positive Q during the final phase . . . . . . . . . . . . . 68 A.5 Acceleration maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 A.6 Acceleration maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 A.7 Acceleration maps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 ix

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Direct and large-eddy simulations (DNS/LES) of accelerating turbulent The acceleration is obtained by increasing the nozzle jet velocity with time in
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