Ewing, Mark E.

Isaac, Daron A.

Iverson, Micheal P.

Richards, Galen H.

English

University of Kentucky

1 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited.  Mark E. Ewing, Galen H. Richards, Micheal P. Iverson, and Daron A. Isaac  ATK Aerospace Systems, Promontory, Utah   5th Ablation Workshop February 28 – March 1, 2012, Lexington, Kentucky  Ablation Modeling of a Solid Rocket Nozzle 2 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Overview Castor 30® motor description Ablation model CFD (Fluent ®) modeling for boundary conditions Hero ablation modeling FEM Builder model coupling Modeling results FEM Builder coupling capabilities On-going work    3 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Motor Description 4 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Ablation Model (In-Depth) •  Pyrolysis  •  Mass/Momentum Equation –  Neglected storage (quasi-steady) –  1-D simplification (with neglected storage) •  Energy Equation 0)()( =∂∂+∂∂−∂∂−−⎟⎟⎠⎞⎜⎜⎝⎛∇⋅∇+∂∂−tTˆtPkˆtˆPˆt ggggvcgggcv ρφβρφαφφρµραρρ Γ0))(( =∇⋅∇−∇⋅+∂∂+∂∂+∂∂−+− ThˆththˆthhQ gDgssggcvgss Kvρρφραρρtt cvs∂∂−−=∂∂ αρρρ )( ( ) ii,amiRTEii 1eAdtdαα−=⎟⎟⎠⎞⎜⎜⎝⎛−∑∑=iiiiixxαα∑∑ ∂∂=∂∂iiiixttααrate of solid density change overall pyrolysis rate overall versus component extent-of-reaction  Arrhenius model for component extent-of-reaction  generation advection (permeation) storage 0)( =⎟⎟⎠⎞⎜⎜⎝⎛∇⋅∇+∂∂− Pˆt ggcv Γµραρρgeneration advection (permeation) dxtAAxm bpxxsp ∫ ∂∂−=ʹ′ʹ′ρ1)(gpyrolysis energy advection conduction storage Hero (Heat Transfer and Erosion Analysis Program) 5 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Ablation Model (Surface Model)  convq ʹ′ʹ′  absradq ,ʹ′ʹ′  4wTεσ  wwhu)(ρ  condq ʹ′ʹ′  cchm ʹ′ʹ′  gghm ʹ′ʹ′  Control-surface for elemental balance Control-surface for energy balance •  Unity Lewis number  •  Equal diffusion coefficients •  Unequal diffusion coefficients •  Surface ablation rate 4,])B1([ wincradwggccwrHeecond TqhBhBhHCuρq εσα −ʹ′ʹ′+ʹ′+ʹ′+ʹ′+−=ʹ′ʹ′4,)( wincradwwggccTiiiwiieMeef.e.gwrHeecond TqhBhBhBhKKCuρhHCuρq w εσα −ʹ′ʹ′+⎥⎦⎤⎢⎣⎡ʹ′−ʹ′+ʹ′+⎟⎠⎞⎜⎝⎛−+−=ʹ′ʹ′ ∑∑4,**)( wincradwwggccTiiiwiieMeef.e.gwrHeecond TqhBhBhBhZZCuρhHCuρq w εσα −ʹ′ʹ′+⎥⎦⎤⎢⎣⎡ʹ′−ʹ′+ʹ′+⎟⎠⎞⎜⎝⎛−+−=ʹ′ʹ′ ∑∑cMeecccchemCuBmsρρρʹ′=ʹ′ʹ′=Thermochemistry “B-prime” tables from ACE code Heat transfer coefficients from CFD modeling 6 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. CFD Modeling (Approach) •  2D axi-symmetric, steady state, 2-phase, non-reacting CFD model •  Simulated 0.6, 15, 30, 45, 60, 75, 90, 105, 120, 135 sec burn times  •  Propellant mass flow rate adjusted to match measured chamber pressure •  Gas properties from NASA Lewis chamber properties at appropriate pressures, frozen chamber Cp and molecular weight, temperature dependent thermal conductivity and viscosity •  K-Omega, SST turbulence model, y+ values 30-100 •  34.6 wt% Al2O3 liquid at equilibrium –  24% large agglomerates, sizes from quench bomb data (40-300 microns) –  76% fines •  ATK droplet breakup model with size dependent critical Weber number Propellant Surface Pressure Outlet Igniter Wall Axis Nozzle Wall 7 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. CFD Modeling (Mach #) Mach # Mach # 0.6 sec 0.6 sec 30 sec 60 sec 135 sec 90 sec 8 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Hero Ablation Modeling (Overview) •  81,092 elements (1st order) •  Heat transfer, pyrolysis, pore pressure, thermochemical surface ablation •  0 – 155 sec –   Δt = 0.01 through 1.5 sec –   Δt = 0.05 through 155 sec 9 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Hero Ablation Modeling (Grid Details) 10 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. FEM Builder Model Coupling •  Initial boundary conditions calculated in Fluent and imported into Hero using FEM Builder (~ 0 sec) •  Hero run for 15 sec (boundary conditions modified within Hero based on transient pressure) •  Eroded surface (at 15 sec) imported into Fluent •  Boundary conditions recalculated –  Eroded surface –  Propellant burn-back –  Imported into Hero •  Process repeated in 15 sec interaction intervals through 155 sec 11 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Modeling Results (Temperature Contours at Intermediate Time)  Temperature Contours of Full Nozzle 12 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Modeling Results (Contours of Temperature and Char)  Temperature Contours in Throat Region Extent-of-Reaction (Char) Contours in Throat Region 13 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Modeling Results (Animated) 0 – 155 sec 15 – 30 sec 14 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. FEM Builder Coupled Fluid-Thermal-Structural Interaction Analysis Solutions type/Time domain •  CFD – Quasi steady •  Heat transfer – Transient •  Structural – Quasi steady CFD – Structural Interactions •  Pressure on structure •  Displacement of CFD boundary CFD – Thermal Interactions •  Surface temperature for CFD model •  Heat flux from CFD model •  Ablation from thermal model (modifies CFD boundary) •  Particle impingement (Slag) Thermal – Structural interactions •  Temperature is applied to the structural model •  Pore pressure (causes stress & permeability is strain dependent) •  Deformation of thermal model Thermal models Structural Models CFD models Reference models Model Coupling Capabilities Flow/Structural Coupling Example 15 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. On-going Work •  CFD 2-phase reacting flow •  Conjugate CFD/ablation modeling •  Grain burn-back modeling •  Additional GUI (FEM Builder) support for generation of coupling scripts •  Surface thermochemistry code development •  Slag impingement heating and erosion modeling •  Comprehensive validation against historical data •  Improved material property characterization methods 16 DISTRIBUTION STATEMENT A.  Approved for public release; distribution is unlimited. Acknowledgements and Model Availability Acknowledgements •  This work was funded by the Air Force Research Laboratory, Solid Rocket Motor Branch at Edwards Air Force Base, under program direction of Lester Knox Program availability •  For questions about availability contact:    Thomas Richardson, Program Manager  Thomas.Richardson@atk.com  (435) 863-3410   Charley Bown, Marketing  Charley.Bown@atk.com  (435)863-5274   

Ablation Modeling of a Solid Rocket Nozzle

https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1035&amp;context=ablation

Ablation Modeling of a Solid Rocket Nozzle

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