AAE 439

Ch7 –1

7. SOLID ROCKET PROPULSION (SRP)SYSTEMS

7. SOLID ROCKET PROPULSION (SRP)SYSTEMS

AAE 439

Ch7 –2

7.1 INTRODUCTION7.1 INTRODUCTION

AAE 439

Ch7 –3

APPLICATIONS FOR SRMAPPLICATIONS 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.

AAE 439

Ch7 –4

HARDWARE & SUBSYSTEMSHARDWARE & SUBSYSTEMS

AAE 439

Ch7 –5

EXAMPLESEXAMPLES

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Ch7 –6

7.2 PERFORMANCE PREDICTION7.2 PERFORMANCE PREDICTION

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Ch7 –7

PROPELLANT BURN RATEPROPELLANT BURN RATE

St. Robert’s Law

The propellant burn rate is the rate at which the exposed propellant surface isconsumed. (It is measured as distance normal to surface consumed in a given time.)

Solid Rocket Motor Definitions:

Burn Rate Coefficient: a

Burn Rate Exponent: n

Typical Values: 0.05–2 in/s

Important: 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 thermochemicaland combustion processes.

rb= a p

c

n[m s]

Determined experimentally!

Restrictors or Inhibitors

Web Distance W (Propellant Web) is defined as the linear amountof propellant consumes as measured normal to the local burn surface.

W = rb(t)dt

0

tb

!

AAE 439

Ch7 –8

PROPELLANT BURN RATEPROPELLANT 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: a

Burn Rate Exponent: n

Mass generated due to propellant burn (Mass entering chamber):

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.

rb= a p

c

n

Determined experimentally!

!m

in= !

propellantrb

Aburn

AAE 439

Ch7 –9

GOVERNING EQUATIONSGOVERNING EQUATIONS

Mass Exiting Nozzle:

Conservation of Mass:

Rate of change of mass (in chamber) is equal to difference between the massentering chamber and mass leaving through throat.

Perfect Gas Law:

!m

out=

pchamber

Athroat

c *

dmchamber

dt= !m

in! !m

out= "

propellantrb

Aburn

!p

chamberA

throat

c *

mchamber

=p

chamberV

chamberM

!Tchamber

dmchamber

dt=

mchamber

pchamber

dpchamber

dt+

mchamber

Vchamber

dVchamber

dt

mchamber

pchamber

dpchamber

dt= !

propellantrb

Aburn

"p

chamberA

throat

c *"

mchamber

rb

Aburn

Vchamber

dVchamber

dt= r

bA

burn

mchamber

pchamber

dpchamber

dt= r

bA

burn!

propellant" !

chamber( )"p

chamberA

throat

c *

= !

propellant, !

propellant! !

chamber ! 0

Differentiation

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Ch7 –10

SRM CHAMBER PRESSURESRM CHAMBER PRESSURE

Equilibrium Operation:

SRM Chamber Pressure:

Equilibrium Condition: n < 1 (typical values: 0.2 < n <0.6)

Explosive: n > 1

!m

in= !m

out

pchamber

=a!

propellantA

burnc *

Athroat

"

#$$

%

&''

1

1(n

a p

chamber

n!

propellantA

burn=

pchamber

Athroat

c *

AAE 439

Ch7 –11

BURN RATE VS. TEMPERATUREBURN 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.

Typical Values: 0.001–0.009 per °K

Temperature Sensitivity of PressureExpresses percent change of chamber pressure per degree change in propellant

temperature at particular value of geometric function K=Ab/At.

Typical Values: 0.067–0.278% per °C

!p=

" ln rb

"T

#

$%&

'(p

0=const.

=1

r

"rb

"T

#

$%&

'(p

!K=

" ln p

"T

#$%

&'(

K=const.

=1

p0

"p

"T

#$%

&'(

K

AAE 439

Ch7 –12

BURN RATE VS. TEMPERATUREBURN RATE VS. TEMPERATURE

Relation between Temperature Sensitivities

πK and σp 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 andtemperature range.

Chamber Pressureas a Function of Grain Temperature

Propellant Burning RateApproximation vs. Temperature

!p = p

0

"K!T

!

K=

1

1" n#

p

rb= a p

ne!

p"T

AAE 439

Ch7 –13

AREA RELATIONSHIPAREA RELATIONSHIP

Conservation of Mass

Approximation

Area Ratio

Chamber Pressure

Ab

rb!

b=

d

dt!

0V

0( ) + A

tp

0

"

RT0

2

" +1

#$%

&'(

" +1

" )1

Ab

At

= K =p

0

rb!

b

" 2 " +1( )#$ %&

" +1

" '1

RT0

=p

0

1'n

a !b

" 2 " +1( )#$ %&

" +1

" '1

RT0

Rate ofGas Generation

Change ofPropellant Mass

Nozzle Flow

p0!

Ab

At

!

"#$

%&

1

1'n

= K

1

1'n

K =A

b

At

= p0

1!na "

bc *( )

1!n

p

0= K

1

1!n a "b

c *( )

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Ch7 –14

INTERNAL BALLISTIC PROPERTIESINTERNAL BALLISTIC PROPERTIES

Internal Ballistic Properties govern burn rate and mass discharge rate ofmotors. Internal Ballistic Analysis predicts the time history of chamberpressure in the motor.Burn Rate rb

Area Ratio K

Temperature Sensitivity of Burn Rate σp

Temperature Sensitivity of Pressure πK

Internal Ballistic Properties govern and control the subsequent performanceparameters of SRMs.Thrust,

Ideal Exhaust Velocity,

Specific Impulse,

Flame Temperature,

Temperature Limits,

Duration, etc.

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Ch7 –15

PERFORMANCE PARAMETERSPERFORMANCE PARAMETERS

Characteristic Velocity

c* Efficiency:

Averaged delivered vacuum Specific Impulse:

Overall Efficiency

Thrust

c* = !

c*c

theoretical

*

!c*=

1

mp

g pc

At

cth

*dt

0

tb

" 0.96 < !c*<1.0

Isp,vacuum

=1

mp

F + pa

Ae( )dt

0

tb

!

!0=

Isp,vacuum

Isp,vac/th

Small Motors : 80% < !0< 87%

Large Motors : 88% < !0< 96%

"#$

%$

F = !

0I

sp,vac/th!m

AAE 439

Ch7 –16

SRM THRUST PROFILESRM THRUST PROFILE

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Ch7 –17

7.3 SRM GRAIN PROPERTIES7.3 SRM GRAIN PROPERTIES

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Ch7 –18

GRAIN CORSS-SECTION GEOMETRYGRAIN CORSS-SECTION GEOMETRY

Pressure and Thrust Response are strong functions of Grain Cross-SectionalGeometries. By altering the grain design, we can achieve progressive orneutral burning.