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3-D transonic flow dynamics with nonequilibrium condensation [Elektronische Ressource] / Kevin A. Goodheart

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266 Pages
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Published 01 January 2004
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3-D Transonic Flow Dynamics with
Nonequilibrium Condensation
by
Kevin A. Goodheart
Munich 2004Title Picture: Top: Snapshot of unsymmetric oscillation mode in the 3-D axisymmetric
nozzle, [T =295 K, p = 1 bar, φ =95%, f ≈ 1350 Hz ].01 01 0
Bottom: Mach contour on the top surface of the F-16 Fighting Falcon
◦ 12 −3wing, [T = 295 K, p = 1 bar, M = 0.9, α = 0 , N = 10 m ,∞ ∞ ∞ het,0
−8 6R = 1x10 m, φ = 90%, MAC = 2.72 m, Re = 54.8 10 ].p ∞ ∞,MAC¨ ¨Technische Universitat Munchen
¨Lehrstuhl fur Fluidmechanik
3-D Transonic Flow Dynamics with
Nonequilibrium Condensation
Kevin A. Goodheart
Vollst¨andiger Abdruck der von der Fakult¨at fu¨r Maschinenwesen der Technischen Univer-
sitat Munchen zur Erlangung des akademischen Grades eines¨ ¨
Doktor-Ingenieurs
genehmigten Dissertation.
Vorsitzender: Univ.-Prof. Dr.-Ing. Dr.-Ing. habil. Rudolf Schilling
Prufer der Dissertation:¨
1. Univ. Prof. Dr.-Ing. habil. Gu¨nter H. Schnerr
2. Univ.-Prof. Dr.-Ing. Dr.-Ing. habil. Rainer Friedrich
DieDissertationwurdeam22.10.2003beiderTechnischenUniversitatMuncheneingereicht¨ ¨
und durch die Fakult¨at fu¨r Maschinenwesen am 26.01.2004 angenommen.Preface
The work in this thesis could not have been done without the understanding and patience
of my wife. I thank her for making it through these times.
I must make a special thank you to Dr. Inz. Slawomir Dykas who took the time to teach
me CFD in regards to compressible flow.
The final thesis was prepared at TU Munich but two years of the work was spent at the
University of Karlsruhe (TH) in the Fachgebiet Str¨omungsmaschinen and my appreciation
and regards go out to the group there.
ThefinalyearoftheworkwasperformedatTUMunichintheLehrstuhlfu¨rFluidmechanik
under the directionof Prof. Dr.-Ing. habil. R. Schilling itis his group and ideas that made
my stay here comfortable and fun, I will miss the Kaffeerunden and Sommerfest.
and to
Prof. Dr.-Ing. habil. G.H. Schnerr thank you for giving me the freedom to explore CFD,
we made it through.
Muggensturm, in February 2004 Kevin A. GoodheartContents
Symbols V
1. Introduction 1
1.1. Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Literature Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3. Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2. Physical Modeling 17
2.1. Thermodynamic Principals For Moist Air . . . . . . . . . . . . . . . . . . 17
2.2. Fluid Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1. Conservation Equations . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2. Reynolds Averaged Navier-Stokes Equations . . . . . . . . . . . . . 21
2.3. Turbulence Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.1. Wilcox k−ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2. Menter SST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3.3. EASM(k−ω) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4. Condensation Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.4.1. Moist Air Homogeneous Condensation . . . . . . . . . . . . . . . . 29
2.4.2. Moist Air Heterogeneous Condensation . . . . . . . . . . . . . . . 31
2.4.3. Nitrogen Homogeneous Condensation . . . . . . . . . . . . . . . . . 32
2.5. Frozen Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6. Condensation Auxiliary Relations for Moist Air . . . . . . . . . . . . . . . 34
2.7. Condensation Auxiliary Relations for Nitrogen . . . . . . . . . . . . . . . . 37
3. Numerical Methods 39
3.1. Equation Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2. Finite Volume Method 3-D . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.1. Fractional-Step-Method . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2. Time Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.2.1. Steady-State Solution 1st Order . . . . . . . . . . . . . . 45
3.2.2.2. Unsteady Solution 2nd or 4th Order Runge-Kutta . . . . 47
3.2.3. Calculation of the Fluxes - Integration in Space . . . . . . . . . . . 48
3.2.3.1. Convective Fluxes AUSMD . . . . . . . . . . . . . . . . 50
III Contents
3.2.3.2. Viscous Fluxes . . . . . . . . . . . . . . . . . . . . . . . . 53
3.2.3.3. Source Terms . . . . . . . . . . . . . . . . . . . . . . . . 56
3.2.4. Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . . 56
3.2.4.1. Initial Conditions . . . . . . . . . . . . . . . . . . . . . . 56
3.2.4.2. Boundary Conditions . . . . . . . . . . . . . . . . . . . . 59
3.2.5. Coupling the System of Equations . . . . . . . . . . . . . . . . . . 66
3.3. Implementation and Program Structure . . . . . . . . . . . . . . . . . . . 67
4. Validation 69
4.1. Steady flow with Condensation . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.1. S1 Nozzle - Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.1.1.1. Geometry and Grids . . . . . . . . . . . . . . . . . . . . . 69
4.1.1.2. Adiabatic . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.1.1.3. φ = 37.2% . . . . . . . . . . . . . . . . . . . . . . . . . . 720
4.1.1.4. φ = 71.3% . . . . . . . . . . . . . . . . . . . . . . . . . . 730
4.1.2. A1 Nozzle - Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1.2.1. Geometry and Grid. . . . . . . . . . . . . . . . . . . . . . 74
4.1.2.2. Adiabatic . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4.1.2.3. φ = 35.6% . . . . . . . . . . . . . . . . . . . . . . . . . . 750
4.1.2.4. Unsteady . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.2. Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2.1. CAST-10 Airfoil - Turbulent . . . . . . . . . . . . . . . . . . . . . . 81
4.2.2. BAII–Nozzle - Euler . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.2.3. S1–Nozzle - Euler . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3. Turbulence Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.1. Sajben Transonic Diffusor . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.1.1. Geometry and Grid. . . . . . . . . . . . . . . . . . . . . . 94
4.3.1.2. Weak Shock pre-shock M ≈ 1.21 . . . . . . . . . . . . . 94
4.3.1.3. Strong Shock pre-shock M ≈ 1.35 . . . . . . . . . . . . 96
4.3.2. RAE 2822 Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.3.2.1. Geometry and Grid. . . . . . . . . . . . . . . . . . . . . . 99
4.3.2.2. Case 6 pre-shock M ≈ 1.23 . . . . . . . . . . . . . . . . . 100
4.3.2.3. Case 10 pre-shock M ≈ 1.30 . . . . . . . . . . . . . . . . 102
4.3.3. 3-D Skewed Bump . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.3.3.1. Geometry and Grid. . . . . . . . . . . . . . . . . . . . . . 104
4.3.3.2. Test Case Results. . . . . . . . . . . . . . . . . . . . . . . 105
4.4. Turbulence and Condensation . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.4.1. S1 Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.5. Validation of Hertz-Knudsen Model . . . . . . . . . . . . . . . . . . . . . . 113
4.6. Validation Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118