Numerical Approach on Hydrogen Numerical Approach on Hydrogen Detonation: Fundamentals and Detonation: Fundamentals and Applications Applications -Part 2 Part 2- - - 2007.08.02 2007.08.02 Nobuyuki TSUBOI Nobuyuki TSUBOI ISAS/JAXA, Japan ISAS/JAXA, Japan 1 1
Overview Overview 1.Motivations 2. Introduction of Detonation 3.History and Previous Research 4.Initial and Boundary Condition 5.Effects of Grid Resolutions 6.Detonation Structure by Numerical Simulations(2D,3D) 7.Remaining Tasks and Summary 2 2
Motivations Motivations � Hydrogen/air mixture: detonable gas � Detonation: shock induced combustion -Pressure behind detonation increases about 10 times ambient pressure � Closed environment such as a tunnel causes serious accident. 3 3
What is Detonation? What is Detonation? Combustion Premixed Diffusion High-load combustion combustion combustion Unsteady Steady Laminar/Turbulent Laminar/Turbulent non-uniform Uniform combustion combustion combustion combustion Rocket Chamber Quench Ignition Detonation Deflagration Laminar/Turbulent Steady RAM,SCRAM Jet Engine Combustion propagating propagating limit flame velocity Diffusion Flame Forced Self- Burner burning combustion Combustion combustion velocity 4 4 Premix Flame
What is Detonation? What is Detonation? � Detonation wave is combustion wave Detonation wave is combustion wave � induced by shock wave induced by shock wave Combustion Shock Detonation velocity: 80%H2 20% O2 : 3,400m/s 66%H2 33.3%O2 : 2,850m/s 25%H2 75%O2 : 1,750m/s CH4 + O2 : 2,600m/s 5 5
What is Detonation? What is Detonation? � ZND(Zeldovich ZND(Zeldovich- -Neumann Neumann- -Doering Doering) model ) model � p VN Propagating p 2 =p CJ direction p 3 T VN T 2 =T CJ T 3 p 1 ,T 1 Initial state Static gas Rarefaction wave (premixed gas) CJ state Exothermic Shock wave zone Detonation wave Induction zone (ZND model) 6 6
Triple point Incident shock Mach stem 7 7 p Contact surface What is Detonation? What is Detonation? T Transverse Reaction front shock
History and Numerical History and Numerical Simulation Simulation Oran et al., 2D Oran et al., DDT and structure Numerical Simulations Taki, Fujiwara, Tsuboi, Hayashi, William,Bauwens, 2D spinning detonation Oran, 3D 1906 1940 1881 1926 1960-1970 1978 1981 1996 1999 2005 Champbell, Woodhead discover spinning detonation Chapman,Jouguet, Theory Zei’ldvich,Von Numann, Doring が Berthelot,Vielle et al, 1D model (ZND model) discover detonations Oppenheim,Manson,Wargner,Strehlow,Lee, Soloukin,Schott,Shchelkin,Van Tiggelen, et al., Structure in experiments 8 8
Initial and Boundary Conditions Initial and Boundary Conditions 9 9
Initial Conditions Initial Conditions � 1D : one wall is the boundary at a stationary coordinate system and a high pressure and temperature for ignition is initially imposed near the wall. � 2D : -ZND or 1D results are used -Unburned premixed gas behind the detonation front � 3D : -ZND or 1D results are used -Unburned premixed gas behind the detonation front -Optional initial condition is given to get a desired detonation pattern (square tube) 10 10
Boundary Conditions Boundary Conditions (2D,3D) (2D,3D) � Shock wave coordinate system for the constant Shock wave coordinate system for the constant � tube cross section tube cross section � Upstream boundary : A premixed gas flows with Upstream boundary : A premixed gas flows with � CJ velocity CJ velocity � Downstream boundary: Downstream boundary: � -A CJ pressure A CJ pressure- -fixed BC (transverse wave are fixed BC (transverse wave are - reflects, slight overdriven detonation) reflects, slight overdriven detonation) -An expansion BC proposed by An expansion BC proposed by Gamezo Gamezo - (expansion boundary: reflection of transverse (expansion boundary: reflection of transverse wave can be weaken) wave can be weaken) 11 11
Effects of Grid Resolutions Effects of Grid Resolutions 12 12
Effects of Grid Resolutions on Effects of Grid Resolutions on 1D Detonation 1D Detonation • The important index for grid resolutions is the grid number in the half reaction length of fuel. • The half reaction length is calculated by ZND profile. • Its value for stoichiometric H2/Air is about 160 micron and it is dependent on the (detailed) reaction model. • At least 30 points are better. 13 13
Effects of Grid Resolutions on Effects of Grid Resolutions on 1D Detonation Velocity 1D Detonation Velocity •Detonation velocity oscillates near CJ velocity for fine grid. •Weakly “stable” overdriven detonation for coarse grid due to numerical dissipation. Stoichiometric H2/Air, 1atm, 300K 3500 3000 Detonation velocity, m/s 2500 2000 dx=2.5mm dx=5 μ m 1500 dx=7.5 μ m dx=10 μ m dx=20 μ m 1000 0 0.02 0.04 0.06 0.08 14 14 Time, msec
Effects of Grid Resolutions on Effects of Grid Resolutions on 1D Instantaneous Pressure 1D Instantaneous Pressure •Detonation oscillates near CJ velocity for fine grid because combustion front separate or catch up with the shock periodically. •Weakly “stable” overdriven detonation for coarse grid due to numerical dissipation N1000 N22000 N4000 N25000 N7000 N28000 6 10 6 6 10 6 N10000 N31000 N13000 N34000 N16000 N37000 N1000 N19000 N40000 N4000 5 10 6 5 10 6 N7000 N10000 N13000 N16000 4 10 6 4 10 6 N19000 Pressure, Pa Pressure, Pa 3 10 6 3 10 6 2 10 6 2 10 6 1 10 6 1 10 6 0 0 5 10 -2 1 10 -1 1.5 10 -1 5 10 -2 1 10 -1 1.5 10 -1 2 10 -1 0 0 x,m X,m 15 15 dx=5micron dx=10micron
Effects of Grid Resolutions on Effects of Grid Resolutions on 2D Detonation 2D Detonation •Cell structure becomes clearly unstable and large for finer grid (a)2.5 micron 2mm (b)5 micron (c)7.5 micron (d)10 micron 30 atm 70 atm 16 16
Detonation Structure by Numerical Numerical Detonation Structure by Simulations: Simulations: 2D Detonation Structure 2D Detonation Structure 17 17
2D Detonation Structure 2D Detonation Structure Maximum pressure history Combustion front Mach stem Reflected shock Transverse shock Contact surface Triple point Incident Shock Density(white), specific energy release Pressure 1 60 atm 1e5 J/m 3 0 18 18
2D Detonation Structure 2D Detonation Structure � Keystone structure was observed Keystone structure was observed � experimentally by Pintgen Pintgen et al. et al. experimentally by Mach stem Reflected shock Transverse shock Keystone Triple point Incident Shock OH mass fraction Pressure 1 60 atm 0 0.03 19 19
2D Detonation Structure 2D Detonation Structure � The schematic figure of the basic two The schematic figure of the basic two- -dimensional dimensional � detonation proposed by Lefebvre et al. detonation proposed by Lefebvre et al. Mach stem Combustion front Transverse Reflected detonation shock Slip line Transverse shock Incident shock (a)Single Mach (b)Double Mach (c)Complex Mach reflection reflection reflection 20 20
Detonation Structure by Numerical Numerical Detonation Structure by Simulations: Simulations: 3D Detonation Structure 3D Detonation Structure (Square Tube) (Square Tube) 21 21
Simulation Conditions (Half Cell) Simulation Conditions (Half Cell) Computational grids Δ x=5; Δ y, Δ z=10 [ μ m] Grid points :601x101x101(uniform grid) Total : 6 millions Numerical conditions ・ Gas composition: ・ Gas composition: Stoichiometric Stoichiometric H2/Air H2/Air ・ Pressure ・ Pressure : 0.1 [MPa] : 0.1 [MPa] ・ Temperature ・ Temperature : 298.15 [K] : 298.15 [K] ・ Initial condition ・ Initial condition : 1- -D simulation results D simulation results : 1 ・ Iteration : 57,000 ・ Iteration : 57,000 ・ CPU time: about 140 hours (on SX ・ CPU time: about 140 hours (on SX- -6 (1node,8 CPU)) 6 (1node,8 CPU)) 22 22
Initial Conditions (Half Cell) Initial Conditions (Half Cell) Propagation Unburned gas pocket Detonation front (Rectangular mode in phase) 1mm Flow(CJ velocity) 1mm 3mm 1D simulation results are pasted Diagonal mode Rectangular mode partially out of phase 23 23
Maximum Pressure History (Half Cell) Maximum Pressure History (Half Cell) 2D Rectangular mode in phase Slapping Wave Diagonal mode Rectangular mode partially out of phase (Spin mode) 20 60 atm 24 24
Instantaneous Pressure Contours (Half Cell) Instantaneous Pressure Contours (Half Cell) Triple lines Triple lines Mach Mach Incident shock stem stem Incident shock 1 60 atm 1 60 atm (a)Rectangular mode in phase (b)Diagonal mode Mach stem Triple lines Mach Incident shock stem 1 60 atm (c)Rectangular mode partially out of phase(spin mode) 25 25
Instantaneous H2 Massfraction Massfraction Contours (Half Cell) Contours (Half Cell) Instantaneous H2 27.92msec. 26.32msec. Unreacted gas pocket Unreacted gas pocket (b)Diagonal mode (a)Rectangular mode in phase 25.09msec. (c)Rectangular mode partially out of phase(spin mode) 0.0 0.029 26 26
Recommend
More recommend
