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Modeling and Numerical Simulation of Ignition Transient of Large Solid Rocket Motor S

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Modeling and Numerical Simulation of Ignition Transient of Large Solid Rocket Motor S Università degli Studi di Roma “La Sapienza” Scuola di Ingegneria Aerospaziale Dottorato di Ingegneria Aerospaziale XV Ciclo MODELING AND NUMERICAL SIMULATION OF IGNITION TRANSIENT OF LARGE SOLID ROCKET MOTOR S Dottorando Ferruccio Serraglia Tutore Prof. Marcello Onofri Correlatore Prof. Maurizio Di Giacinto Correlatore Prof. Bernardo Favini Anno Accademico 2002/2003 1 2 Index INTRODUCTION 1. PHENOMENOLOGY OF THE IGNITION TRANSIENT 10 1.1 GENERAL DESCRIPTION 10 1.2 IGNITION AND COMBUSTION OF SOLID PROPELLANTS 14 IGNITION 14 STEADY-STATE BURNING 19 TRANSIENT AND EROSIVE BURNING 21 1.3 MODELING SRM IGNITION TRANSIENT 23 1D MODELS: STATE OF THE ART 23 GENERAL DISCUSSION 29 2 PHYSICAL AND MATHEMATICAL MODEL 32 2.1 GASDYNAMIC MODEL 32 2.2 IGNITER MODEL AND IMPINGEMENT REGION 36 2.3 PROPELLANT SURFACE HEATING, IGNITION AND REGRESSION 41 IGNITION CRITERION 41 CONVECTIVE HEAT TRANSFER: IMPINGEMENT REGION. 41 CONVECTIVE HEAT TRANSFER: STANDARD REGION 44 RADIATIVE HEAT TRANSFER 45 PROPELLANT HEATING EVALUATION 48 BURNING RATE MODEL 51 SURFACE REGRESSION EVALUATION 52 3 NUMERICAL INTEGRATION TECHNIQUE 54 3.1 DISCRETIZED FLUID DYNAMIC MODEL AND SOLUTION 54 GODUNOV’S METHOD 55 APPLICATION OF THE MODIFIED ENO METHOD TO THE IGNITION TRANSIENT ANALYSIS. 57 RIEMANN PROBLEM 61 3.2 THE ESPRIT SIMULATION CODE 63 4 RESULTS 66 4.1 HEAD-END PRESSURE AND IGNITION SEQUENCE 66 SOLID ROCKET MOTOR # 1 ARIANE 4 SOLID BOOSTER (SRM #1) 66 SOLID ROCKET MOTOR # 2 ARIANE 5 SOLID BOOSTER (SRM #2) 68 SOLID ROCKET MOTOR # 3 VEGA, ZEFIRO SOLID ROCKET STAGE (SRM #3) 71 4.2 OVERPRESSURE PEAK AND EROSIVE BURNING 74 4.3 FLOWFIELD FEATURES 80 4.4 INTERSEGMENT SLOTS AND GAS MIXTURE 87 EFFECTS OF THE SLOTS & SUBMERGENCE MODELING 89 EFFECT OF GAS MIXTURE MODELING 90 CONCLUSIONS 93 ACKNOWLEDGMENTS 95 REFERENCES 95 3 4 Nomenclature 2 Ajet Igniter jet final cross section m 2 AP Propellant port area m 2 Ath Nozzle throat cross section m 2 At ig Igniter nozzle throat cross section m cf Friction coefficient m –1 -1 cp Specific heat at constant pressure per unit mass J kg K –1 -1 cv Specific heat at constant volume per unit mass J kg K Djet Impingement jet diameter on grain surface m Dh Hydraulic diameter m Dtig Igniter nozzle throat diameter m e Total internal energy per unit mass J kg-1 f1 , f2,f3 Erosive burning functions FRC Flame radiation coefficient GRC Gas radiation coefficient -1 Hig Igniter gas total enthalpy per unit mass J kg Hj Distance between igniter nozzle and propellant surface m -1 Hf Propellant gas enthalpy per unit mass J kg -1 Hs Slot gas flow total enthalpy J kg -1 -1 -2 hc Heat transfer convective coefficient J kg s m -1 -1 -2 hc imp Heat transfer convective coefficient at impingement region J kg s m -1 hf Propellant gas enthalpy per unit mass J kg -1 -1 -2 hR center Central cell radiative transfer coefficient J kg s m -1 -1 -2 hR right Right-side cell radiative transfer coefficient J kg s m -1 -1 -2 hR left Left-side cell radiative transfer coefficient J kg s m -1 -1 -2 ˆ Equivalent radiative transfer coefficient J kg s m h R KMR Impingement region proportionality constant -1 -1 kpr Propellant thermal conductivity N s K 3 -1 keb Erosive combustion constant m K J Mj Igniter jet mach number -1 m ig Igniter gas mass flow rate kg s -1 s Total mass flow rate from slots kg s -1 s,pr Propellant gas mass flow rate from slots kg s -1 s,ig Igniter gas mass flow rate from slots kg s -1 s,in Inert gas mass flow rate from slots kg s Nnz Number of igniter nozzles Nigz Number of canted igniter nozzles Naxig Number of axial igniter nozzles n Combustion index Pr, Prig Propellant and igniter gas Prandtl numbers Pb , Pw Combustion and wet perimeters m -2 p , p0 Static and total pressure N m -2 pc Combustion chamber equilibrium pressure N m -2 pcig Igniter chamber total pressure N m -2 Pref Reference pressure for burning rate N m -2 qC Convective heat flux w m -2 qr center Gas radiative heat flux from central cell w m -2 qr right Gas radiative heat flux from right-side cell w m -2 qr left Gas radiative heat flux from left-side cell w m -2 qt Total heat transfer flux w m 5 -2 Equivalent radiative heat flux from right-side cell w m qˆ r right -2 Equivalent radiative heat flux from left-side cell w m qˆ r left Rej Igniter jet Reynolds number -1 r, r0ref Burning rate and reference burning rate m s -1 r0 Saint-Robert pressure dependent burning rate m s -1 reb Erosive burning rate m s 2 Sb Grain propellant burning surface m T Static temperature K Tf Flame temperature K TS0, TS Initial and actual propellant surface temperatures K t Time s u Velocity component in the x-direction m s-1 V Igniter control volume m3 -1 vinj Igniter gas velocity m s x Longitudinal coordinate m Xj Coordinate of igniter jet stagnation point m Xi Coordinate of the i-th cell center Z Erosive burning rate exponent ig Inclination of igniter jet axis Rad 2 -1 pr Propellant thermal diffusivity m s 1 , 2 Function in the exponent of erosive burning rate formula ii Radial distance from igniter jet stagnation point m Gas viscosity N s m2 -3 Gas density kg m -3 pr Propellant gas density kg m -3 ig Igniter gas density kg m -3 in Inert gas density kg m -3 p Solid propellant density kg m -2 -4 Stefan-Boltzman constant w K 6 INTRODUCTION The material presented in this doctorate thesis represents the synthesis of the research activities carried out by the author, during last years, at the Department of Mechanics and Aeronautics of the University of Rome “La Sapienza”; results and proceedings of these activities have also been presented in several international meetings and conferences 39, 40, 41, 42, 43. The aim of this work is to present the formulation of a detailed physical-mathematical model, and its numerical solution, for the analysis of the ignition transient of large solid rocket motors (SRM); the result obtained is a complex simulation code able to deal with different rocket engines and igniters, capable of numerical results that show a very good agreement with available experimental data. The operating conditions of the solid rocket motors during the ignition transient are often more critical than those occurring in the subsequent operative phases; within a fraction of a second in the combustion chamber extreme events such as pressure jumps of tenths of atmospheres and temperature peaks of thousands of Kelvin degrees can occur. The ignition transient in fact is an operative phase of the engine characterized by a very strong unsteady behavior that often causes net thrust and pressure transients, possible overpressures, possible hang-fires or misfires, transients of pressure loads on the propellant grain, dynamic loads on the launch vehicle and the ground structure etc.. All these phenomena can seriously compromise not only the engine performance but the overall efficiency of the whole system. The capability to predict and evaluate the above phenomena by means of a numerical simulation model can significantly increase the efficiency of the preliminary design process with a reduction of both the motor development and operational costs. Modeling of this phenomenon has for many years been conducted using zero-dimensional, volume- filling or one-dimensional analyses, and only recently two-dimensional analyses. Currently, with the increasing of computational capabilities, three-dimensional fully coupled flow/structural ignition models are being developed. Although this kind of simulations represent a significant improvement for the analysis of the internal ballistics and other major issues in SRM operations, for what strictly concerns ignition transient, unfortunately, the results obtained by such a great effort often appear insufficient, and do not match with the experimental measurements better than simpler schematizations1. Also, numerical factors such as insufficient grid resolution, or inadequate integration schemes has been invoked as a cause of this disagreement, nevertheless inadequacy of physical modeling is still the real limit of direct simulations2. The main problem of the simulation of the ignition transient is, substantially, the lack of universally accepted theoretical models and experimental data about the main physical phenomena that affect this operative phase of the motor; this is mostly due to the peculiar behavior of each propellant and the high unsteadiness and the strong interactions that exist among heat transfer, combustion and fluid-dynamics. In the open literature, a usual approach for the analysis of the SRM's ignition transient is based on a simplified 1-D schematization of the motor chamber geometry and for the solution of the chamber fluid-dynamics (for example, most models completely neglect the presence of the igniter), coupled with few simplified submodels for the simulation of the main physical phenomena involved3. 7 Simple correlations require the identification of many empirical coefficients that have to be introduced in the model in order to obtain a good agreement between the experimental and numerical results in each single motor. These empirical coefficients, that often take the form of complicated functions of both space and time, relies on "a posteriori" calibrations of empirical laws, rather than on a reliable mathematical modeling of the physics, and, as a consequence, the model overtakes the declared physical phenomenology. In fact, whereas these models are well suited to investigate the influence of slight modifications of the already existing motor configuration they have been calibrated for, they show a significant decay of their prediction ability when they are applied to the preliminary design of a new different motor.
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