AAE SOLID ROCKET PROPULSION (SRP) SYSTEMS

Transcription

1 7. SOLID ROCKET PROPULSION (SRP) SYSTEMS Ch7 1

2 7.1 INTRODUCTION 7.1 INTRODUCTION Ch7 2

3 APPLICATIONS FOR SRM APPLICATIONS FOR SRM Strap-On Boosters for Space Launch Vehicles, Upper Stage Propulsion System for Orbital Transfer Vehicles (OTV), Spin and Despin Systems for Spacecraft, Strategic and Tactical Missile Propulsion Systems, Jet-Assisted-Takeoff (JATO) units on early aircraft, Gas Generators for starting liquid engines and pressurizing tanks, Attitude Control Propulsion Systems. Ch7 3

4 HARDWARE & SUBSYSTEMS HARDWARE & SUBSYSTEMS Ch7 4

5 EXAMPLES Ch7 5

6 7.2 PERFORMANCE PREDICTION 7.2 PERFORMANCE PREDICTION Ch7 6

7 PROPELLANT BURN RATE PROPELLANT BURN RATE St. Robert s Law r b = a p c n [m s] The propellant burn rate is the rate at which the exposed propellant surface is consumed. (It is measured as distance normal to surface consumed in a given time.) Solid Rocket Motor Definitions: Restrictors or Inhibitors Web Distance W (Propellant Web) is defined as the linear amount of propellant consumes as measured normal to the local burn surface. W = r b (t)dt Burn Rate Coefficient: Burn Rate Exponent: Typical Values: Important: a n Determined experimentally! in/s Burn rates are determined in sub-scale firing. Firing motors with different throat sizes, burn rate is obtained as a function of different chamber pressures. Burn rate is an empirical representation and doesn t address complex thermochemical and combustion processes. t b! 0 Ch7 7

8 PROPELLANT BURN RATE PROPELLANT BURN RATE The performance of a SRM depends on: Propellant burn rate, Exposed propellant grain surface area, Nozzle throat and exit area, Amount of energy in propellant. Propellant Burn Rate: Burn Rate Coefficient: Burn Rate Exponent: a n r b = a p c n Determined experimentally! Mass generated due to propellant burn (Mass entering chamber):!m in =! propellant r b A burn Depending on the burning progression, we distinguish between: Progressive Burning: burn surface increases with time, Neutral Burning: burn surface remains relatively constant with time, Regressive Burning: burn surface decreases with time. Ch7 8

9 Mass Exiting Nozzle: GOVERNING EQUATIONS GOVERNING EQUATIONS!m out = p chamber A throat c * Conservation of Mass: dm chamber dt =!m in!!m out = " propellant r b A burn! p chamber A throat c * Rate of change of mass (in chamber) is equal to difference between the mass entering chamber and mass leaving through throat. Perfect Gas Law: m chamber = p chamber V chamber M!T chamber Differentiation dm chamber dt = m chamber p chamber dp chamber dt + m chamber V chamber dv chamber dt dv chamber dt = r b A burn m chamber p chamber dp chamber dt =! propellant r b A burn " p chamber A throat c * " m chamber r b A burn V chamber m chamber p chamber dp chamber dt! 0 = r b A burn (! propellant "! chamber )" p A chamber throat c * =! propellant,! propellant!! chamber Ch7 9

10 Equilibrium Operation: SRM CHAMBER PRESSURE SRM CHAMBER PRESSURE!m in =!m out a p chamber n! propellant A burn = p chamber A throat c * SRM Chamber Pressure: " p chamber = a! A c * % propellant burn $ ' # $ A throat &' 1 1(n Equilibrium Condition: n < 1 (typical values: 0.2 < n <0.6) Explosive: n > 1 Ch7 10

11 BURN RATE VS. TEMPERATURE BURN RATE VS. TEMPERATURE Temperature has a significant impact on operation of a SRM: Temperature affects chemical reaction rates, Burn rate depends on the initial ambient temperature of propellant grain, Temperature Sensitivity of Burn Rate: Expresses percent change of burn rate per degree change in propellant temperature at a particular chamber pressure. #! p = "ln r b % $ "T & ( ' p 0 =const. = 1 # r % $ "r b "T & ( ' p Typical Values: per K Temperature Sensitivity of Pressure Expresses percent change of chamber pressure per degree change in propellant temperature at particular value of geometric function K=A b /A t. #! K = "ln p & $ % "T ' ( K =const. = 1 # "p & p 0 $ % "T ' ( K Typical Values: % per C Ch7 11

12 BURN RATE VS. TEMPERATURE BURN RATE VS. TEMPERATURE Relation between Temperature Sensitivities! K = 1 1" n # p π K and σ p are strong functions of nature of propellant burn rate, composition, combustion mechanism of propellant. Equation valid when the variables are constant over the chamber pressure and temperature range. Chamber Pressure as a Function of Grain Temperature!p = p 0 " K!T Propellant Burning Rate Approximation vs. Temperature r b = a p n e! p "T Ch7 12

13 AREA RELATIONSHIP AREA RELATIONSHIP Conservation of Mass A b r b! b = d dt " (! 0 V 0 ) + A t p 0 # 2 & RT 0 $ % " +1' ( " +1 " )1 Rate of Gas Generation Change of Propellant Mass Nozzle Flow ( ) A b = K = p " # 2 " +1 %" '1 0 $ & = p 1'n " # 0 $ 2 " +1 A t r b! b RT a! 0 b RT 0 " +1 ( ) % & " +1 " '1 Approximation p 0!! # " A b A t $ & % 1 1'n = K 1 1'n Area Ratio Chamber Pressure K = A b 1!n = p A 0 t 1 ( a " b c *) 1!n ( ) 1!n p 0 = K a " b c * Ch7 13

14 INTERNAL BALLISTIC PROPERTIES INTERNAL BALLISTIC PROPERTIES Internal Ballistic Properties govern burn rate and mass discharge rate of motors. Internal Ballistic Analysis predicts the time history of chamber pressure in the motor. Burn Rate Area Ratio Temperature Sensitivity of Burn Rate Temperature Sensitivity of Pressure r b K σ p π K Internal Ballistic Properties govern and control the subsequent performance parameters of SRMs. Thrust, Ideal Exhaust Velocity, Specific Impulse, Flame Temperature, Temperature Limits, Duration, etc. Ch7 14

15 Characteristic Velocity PERFORMANCE PARAMETERS PERFORMANCE PARAMETERS c* =! c* c * theoretical c* Efficiency:! c* = 1 t b g p c A t m p " dt 0.96 <! c * < 1.0 c* 0 th Averaged delivered vacuum Specific Impulse: I sp,vacuum = 1 m p t b! 0 ( F + p a A e )dt Overall Efficiency! 0 = I sp,vacuum " $ Small Motors : 80% <! 0 < 87% # I sp,vac/th Large Motors : 88% <! 0 < 96% %$ Thrust F =! 0 I sp,vac/th!m Ch7 15

16 SRM THRUST PROFILE SRM THRUST PROFILE Ch7 16

17 7.3 SRM GRAIN PROPERTIES 7.3 SRM GRAIN PROPERTIES Ch7 17

18 GRAIN CORSS-SECTION GEOMETRY GRAIN CORSS-SECTION GEOMETRY Pressure and Thrust Response are strong functions of Grain Cross-Sectional Geometries. By altering the grain design, we can achieve progressive or neutral burning. Ch7 18