RANS modelling of an auto-igniting turbulent methane jet ... ?· an auto-igniting turbulent methane…

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  • Universita di Pisa

    SCUOLA DI INGEGNERIA

    Corso di Laurea Magistrale in Ingegneria Energetica

    Tesi di laurea magistrale

    RANS modelling ofan auto-igniting turbulent methane jet flame

    using unsteady flamelet/progress variable approachwith presumed PDF

    Relatori:

    Asst. Prof. Chiara GallettiAsst. Prof. Ricardo Novella (UPV,Valencia)Dott. Ing. Bertrand Naud (CIEMAT,Madrid)

    Candidato:

    Domenico Collazzo

    Anno Accademico 20142015

  • Contents

    1 Introduction 1

    2 Turbulent combustion modelling 32.1 Motivations and interests for numerical

    modelling in combustion science . . . . . . . . . . . . . . . . . . . . . 32.2 The complexity of turbulent combustion:

    a matter of dierent time and length scales . . . . . . . . . . . . . . . 52.3 CFD frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.3.1 Direct Numerical Simulation (DNS) . . . . . . . . . . . . . . . 82.3.2 Large Eddy Simulations (LES) . . . . . . . . . . . . . . . . . 82.3.3 Reynolds-Averaged and Favre-Averaged Navier-Stokes equa-

    tions Simulation (RANS/FANS) . . . . . . . . . . . . . . . . . 92.4 Combustion modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 12

    2.4.1 Treatment of chemical reactions . . . . . . . . . . . . . . . . . 132.4.2 Modes of combustion and modelling strategies . . . . . . . . . 172.4.3 RANS modelling strategies for turbulent non-premixed com-

    bustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    3 Unsteady Flamelet/Progress Variable approach 333.1 Backgrounds of UFPV model . . . . . . . . . . . . . . . . . . . . . . 34

    3.1.1 Dierences between steady and unsteady amelet modelling . 343.1.2 Flamelet model with progress variable . . . . . . . . . . . . . 35

    3.2 Laminar amelets resolution . . . . . . . . . . . . . . . . . . . . . . . 373.2.1 Characteristics of steady and unsteady amelet resolution . . 40

    3.3 Presumed PDF closure . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.1 Further assumptions and steps for PDF presuming . . . . . . 42

    3.4 Properties tabulation and RANS code coupling . . . . . . . . . . . . 453.4.1 Tabulation of averaged properties . . . . . . . . . . . . . . . . 453.4.2 Implementation in openFOAM . . . . . . . . . . . . . . . . . 47

    4 Methane jet ame in vitiated co-ow 494.1 Experiments at UC Berkeley . . . . . . . . . . . . . . . . . . . . . . . 494.2 Further experiments at University of Sydney . . . . . . . . . . . . . . 53

    5 RANS simulations 555.1 Domain denition and meshing . . . . . . . . . . . . . . . . . . . . . 555.2 Boundary and initial conditions . . . . . . . . . . . . . . . . . . . . . 575.3 Properties tabulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 595.4 Non-reactive simulations . . . . . . . . . . . . . . . . . . . . . . . . . 60

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  • CONTENTS

    5.4.1 k turbulence model setup . . . . . . . . . . . . . . . . . . 605.4.2 Eect of turbulent Schmidt number . . . . . . . . . . . . . . . 62

    5.5 Reactive simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.5.1 Flame structure and impact of st-PDF . . . . . . . . . . . . . 625.5.2 Sensitivity analysis on co-ow velocity . . . . . . . . . . . . . 71

    6 Conclusions 72

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  • List of Figures

    2.1 Length and time scales in turbulent combustion as reported by Echekki[1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

    2.2 Ranges of numerical approaches based on time and length scales im-plemented [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

    2.3 Temporal evolution of a reacting mixture in the mass fraction space(YA, YB) starting from dierent initial compositions I [3]. . . . . . . 16

    2.4 The one-dimensional manifold for the predicted number of moles of Hatoms per unit mass as a function of the predicted number of moles ofCO2 per unit mass. These data were derived from a reduced schemefor the combustion of CO + H2, at 1300 K. The nal equilibriumis denoted by . The heavy line represents the solutions derived byQSSA or PEA applied to a conventional reduced mechanism. Thebroken line is the slow manifold [4][5]. . . . . . . . . . . . . . . . . . . 16

    2.5 Dierent modes of laminar combustion . . . . . . . . . . . . . . . . . 182.6 Characteristic length scales in turbulent diusion ames [6]. . . . . . 212.7 Flames regimes in a turbulent non-premixed combustion [3] . . . . . . 232.8 Length Lf of a jet ame as a function of the jet Reynolds number [3] 232.9 Shapes of the function PDF for dierent value of Z and [7]. . . . 252.10 Presumed PDF method for fast chemistry coupled with a RANS

    framework [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.11 Diusion ame structure for nite rate chemistry [8]. . . . . . . . . . 262.12 Presumed PDF-amelet model for nite rate chemistry coupled with

    RANS code [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.13 Mechanical energy transfer through turbulence structures . . . . . . . 30

    3.1 Schematic diagram of the steady versus the unsteady amelet regimes.The black line is Equation 3.4. The dashed line illustrates the morerapid decrease of st with residence time in a turbulent jet ame [7]. . 35

    3.2 Typical representation of steady amelet solutions in terms of tem-perature and dissipation rate [9]. . . . . . . . . . . . . . . . . . . . . 36

    3.3 Opposed jet conguration [6] . . . . . . . . . . . . . . . . . . . . . . . 383.4 Set of steady amelet solutions for the methane lifted ame conditions

    [10]. Red curves: steady burning branch. Blue curves: unstablebranch. Black curves: extinction limit. . . . . . . . . . . . . . . . . . 40

    3.5 Time evolution (t = 0.3 ms) of unsteady amelets at (a) a = 25s1,(b) a = 100s1, (c) a = 250s1, (d) a = 1000s1 . . . . . . . . . . . . 41

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  • LIST OF FIGURES

    3.6 Representation of the sample space of possible values (st, yc) of stand Yc|st for given values of Z and S.(represented in logarithmicscale on the right hand side). The bottom grey line represents theinert solution Yc,MIN . The top black line represents the steady statesolution Y maxc |st(st) and together with the dashed black line onthe right hand side it represents the limit maxst (yc) [11]. . . . . . . . . 43

    3.7 Logic scheme of the coupling between pre-integrated tables and RANSsolver for every iteration, adapted from [6] and [12]. . . . . . . . . . . 46

    4.1 Picture and a schematic representation of the Jet in Vitiated Co-owburner designed at UC Berkeley . . . . . . . . . . . . . . . . . . . . . 50

    4.2 Scheme indicating the elements of the burner [13] . . . . . . . . . . . 514.3 Radial proles of Favre averaged mean temperature and mixture frac-

    tion for all the axial position measured at UC Berkeley by Cabra . . . 524.4 Sensitivity of CH4/air ame lift-o height to co-ow velocity and jet

    velocity . The shaded circle represents the base-case lift-o heightestablished by the unaided eye [10]. The thick line in the second plotshows the prediction from Kalghatgi's correlation for lift-o . . . . . . 53

    4.5 Radial proles of mean and standard deviation of axial velocity forthe reacting (left) and non-reacting (right) cases. [14, 15] . . . . . . . 54

    5.1 Representation of the lifted methane ame in vitiated co-ow and thedomain selected for simulations (adapted from [6]). . . . . . . . . . . 56

    5.2 Pseudo-2D geometry and mesh used in foam-EXTEND . . . . . . . . 565.3 Normalized axial velocity compared with experimental data by Wu

    et al. [16]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585.4 User dened proles for BCs of U , k and . . . . . . . . . . . . . . . . 585.5 Mixture fraction (left) and excess mean velocity Uo = Ucenterline

    Ucoflow (right) along the axis compared with exp. data respectivelyfrom Cabra et al. [10] (reactive case but until 35d can be comparedwith inert results as well) and Gordon [17] (non-reactive case). Redline represents results with C1=1.6 while green line C2=1.8. Dashedred line corresponds to C1=1.6 and Sct=0.7. . . . . . . . . . . . . . . 60

    5.6 Radial plots of mixture fraction (left) and normalized mean velocityUnorm = [UUcoflow]/[UcenterlineUcoflow] (right) compared with exp.data respectively from Cabra et al. [10] (reactive case but until 35dcan be compared with inert results as well) and Gordon [17] (non-reactive case). Red line represents results with C1=1.6 while greenline C2=1.8. Dashed red line corresponds to C1=1.6 and Sct=0.7. . 61

    5.7 Contour plots for the 3 cases simulated: (a) =

    2, (b) = 1, (c) = 0. Stoichiometric mixture fraction iso-surface (Zst = 0.177) isunderlined in black while iso-surface for YOH = 2 104 is underlinedin white. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

    5.8 Mean and RMS axial plots for mixture fraction and temperatureagainst experimental data . . . . . . . . . . . . . . . . . . . . . . . . 64

    5.9 Mean and RMS radial plots for temperature against mixture fraction.Dots: experimental data. Red line: =

    2. Blue line: = 1. Black

    line: = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

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  • LIST OF FIGURES

    5.10 Mean and RMS radial plots for mixture fraction (a) and temperature(b). Dots: experimental data. Red line: =

    2. Blue line: = 1.

    Black line: = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.11 Mean and RMS radial plots for CH4 (a) and O2 (b). Dots: exper-

    imental data. Red line: =

    2. Blue line: = 1. Black line: = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

    5.12 Mean and RMS radial plots H2 (a) and OH (b). Dots: experimentaldata. Red line: =