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14 A3-2 Numerical Analyses in the Secondary Combustion Chamber of the Ducted Rocket Engine 184-8588 2-24-16 E-mail: kikumoto@starcadmechtuatacjp Kousuke KIKUMOTO Dept of Mech Systems Eng Tokyo Noko

1 14 A3-2 Numerical Analyses in the Secondary Combustion Chamber of the Ducted Rocket Engine Kousuke KIKUMOTO Dept of Mech Systems Eng Tokyo Noko Univ Koganei Tokyo APAN A ducted rocket engine is one of the air-breathing engines The thrust is obtained by mixing the combustible material that generated in the primary combustion chamber with the air and re-burning them in the secondary combustion chamber To improve the engine performance it is important to grasp the mixing and combustion characteristics in the secondary combustion chamber In the present study the mixing and re-burning are numerically simulated under the thin layer approximations Computations are performed in the cases of 2 and 4 intakes The effects of the inlets on the mixing and the re-burning processes are explained 1 2% 8% 2 Fig1 (1) Fig 1: Ducted Rocket Engine for Missiles (2) 2 q ω (3) 2 ( ) Navier-Stokes H 2 O 2 N 2 H O OH H 2 O Navier-Stokes (4) Q t + E ξ + F η + G ζ = 1 G v R e ζ + S ρ 1 ρ 1 U ρ 7 ρ 7 U Q = 1 ρu ρv E = 1 ρuu + ξ x p ρvu + ξ y p ρw ρwu + ξ z p e U(e + p) ρq ρqu ρω ρωu ρ 1 V ρ 1 W ρ 7 V ρ 7 W F = 1 ρuv + η x p ρvv + η y p G = 1 ρuw + ζ x p ρvw + ζ y p ρwv + η z p ρww + ζ z p V (e + p) W (e + p) ρqv ρqw ρωv ρωw 1 Copyright c 2 by SCFD

2 G v ρdm 1 X 1ζ ẇ 1 ρdm 1 X 7ζ ẇ 7 = 1 µm 1 u ζ + µm 2 ζ x µm 1 v ζ + µm 2 ζ y S = 1 µm 1 w ζ + µm 2 ζ z m 4 (µ l + µ t /P rq )m 1 q ζ S q (µ l + µ t /P rω )m 1 ω ζ S ω ρ = e = ρ i p = ρ i R M i TX i = ρ i ρ ρ i h i p ρ(u2 + v 2 + w 2 ) m 1 = ζ 2 x + ζ 2 y + ζ 2 z m 2 = 1 3 (ζ xu ζ + ζ y v ζ + ζ z w ζ ) m 3 = 1 ( u 2 + v 2 + w 2) 2 ζ m 4 = µm 1 m 3 + µm 2 W + ρdm 1 (h i X iζ )+κm 1 T ζ µ i Chapman-Enskog µ l Wilke (5) X i µ i µ l = X i + 7 j=1 X j φ ij j i { } 1+[(µ i /µ j )(ρ j /ρ i )] (M i /M j ) 1 4 φ ij = 8[1+(Mi /M j )] 1 2 h i = a i T + a 1i 2 T 2 + a 2i 3 T 3 + a 3i 4 T 4 + a 4i 5 T 5 + H i a i a 4i H i ANAF (8) Evans 7 8 (9) ẇ i = M i 8 (β ij α ij )(R fj R bj ) j=1 R fj R bj (ρu 2 A) j :(ρu 2 A) =1:1 Fig2 3 Tab1 Case Number of Air Intakes Angle Between Intakes (deg) (a) 4 9 (b) 2 18 (c) 2 9 µ t Coakley q ω (6) ρq 2 µ t =9f µ R e ω ρq f µ =45 (1 2 ) exp( 18R e µ l ω ) +45 µ κ D L e =1 µ = µ l + µ t κ = C p ( µ l C p = C pi ρ i P rl + µ t P rt ) ρd =( µ l + µ t ) P rl P rt C pi h i 4 5 (7) Fig 2: Computational Cases Tab 1: Initial Conditions in The Chamber Chamber Length : Diameter L : D =5: 1 Reynolds Number R e = Main Fuel Flow Mach Number M =2 Molar Fraction [H 2 ] :[N 2 ] =3:1 Air Injection Location of Holes x/d = 1 Mach Number M j =3 Molar Fraction [O 2 ] j :[N 2 ] j =1:4 C pi = a i + a 1i T + a 2i T 2 + a 3i T 3 + a 4i T 4 2 Copyright c 2 by SCFD

Vector Diagrams at x/d = 3 and Fuel Trajectory Lines from The Chamber Front H H 2 O ( ) R AH2 O= Ψ da A Ψ = ( 2ρH2 M H2 /A

3 3 Fig3 (b) Fig 3: Mach Line Contours in The Case (b) Fig4 3/5 ( ) (2) ( ) 3 (a) (b) 8 (c) 4 (c) 2 1 (b) (c) 2 (b) 2 4 I II 2 III IV 2 I II Tab2 (b) (c) I II III IV Fig5 (c) Fig6 Fig7 H 2 H 2 O H 2 H 2 O (c) Fig6 (x/d =4) H 2 Fig 4: Velocity Vector Diagrams at x/d = 3 and Fuel Trajectory Lines from The Chamber Front H H 2 O ( ) R AH2 O= Ψ da A Ψ = ( 2ρH2 M H2 /A 2ρ H2O M H2O + ρ H M H + ρ OH M OH + 2ρ H 2O M H2O Fig8 (x/d =1) (x/d=4) 9 H H 2 O (c) (a) (b) ) 3 Copyright c 2 by SCFD

Tab 2: The number of Regions Regions Case I II III IV (RD) (RS) (LD) (LS) Mixing-(a) 8 Combustion-(a) 8 Mixing-(b) 4 4 Combustion-(b) 4 4 Mixing-(c) 2 2 Combustion-(c) 2 2 R : L : D : S : Fuel Rich

4 Tab 2: The number of Regions Regions Case I II III IV (RD) (RS) (LD) (LS) Mixing-(a) 8 Combustion-(a) 8 Mixing-(b) 4 4 Combustion-(b) 4 4 Mixing-(c) 2 2 Combustion-(c) 2 2 R : L : D : S : Fuel Rich Region Fuel Lean Region Directly Generated Region Secondary Induced Region 1 2 (c) 3 4 9% H 2 CO 1 Vol 39 No Kikumoto K and Higashino F Numerical Analyses in The Secondary Combustion Chamber of The Ducted Rocket Proceedings of 8th Annual Conference of The CFD Society of Canada 2 pp Takakura Y Ogawa S and Ishiguro T Turbulence Models for 3-D Transonc Viscous Flows AIAA Paper No Shinn Yee H and Uenishi K Extension of a Semi-Implicit Shock-Capturing Algorithm for 3-D Fully Coupled Chemically Reacting Flows in Generalized Coordinates AIAA Paper No Reid R Prausnitz and Poling B The Properties of Gasses and Liquid 4th Edition McGraw-Hill Book Company Coakley T Turbulence Modeling Methods for the Compressible Navier-Stokes Equations AIAA Paper No Gordon S and McBride B Computer Program for Calculation of Complex Chemical Equilibrium Compositions Rocket Performance Incident and Reflected Shocks and Chapman-ouguet Detonations NASA SP 273 Nondimensionalized Temperature 15 3 Fig 5: Temperature Contours 8 Chase M r Davies C Downey r Frurip D McDonald R and Synerud A ANAF Thermochemical Tables Third Edition ournal of Physical and Chemical Reference Data Vol 14 Supplement No Evans and Schexnayder C Influence of Chemical Kinetics and Unmixedness of Burning in Supersonic Hydrogen Flames AIAA ournal Vol 18 No pp Copyright c 2 by SCFD

5 Nondimensionalized H 2 Density 25 5 Fig 6: H 2 Density Contours Fig 8: Burnup Fraction Nondimensionalized H 2 O Density 1 2 Fig 7: H 2 O Density Contours 5 Copyright c 2 by SCFD

: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs

: u i = (2) x i Smagorinsky τ ij τ [3] ij u i u j u i u j = 2ν SGS S ij, (3) ν SGS = (C s ) 2 S (4) x i a u i ρ p P T u ν τ ij S c ν SGS S csgs 15 C11-4 Numerical analysis of flame propagation in a combustor of an aircraft gas turbine, 4-6-1 E-mail: tominaga@icebeer.iis.u-tokyo.ac.jp, 2-11-16 E-mail: ntani@iis.u-tokyo.ac.jp, 4-6-1 E-mail: itoh@icebeer.iis.u-tokyo.ac.jp,