Pagina 1

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FUNDAMENTALS OF SOLID PROPULSION

• PROS
• SIMPLE
• LONG-TERM STORABLE
• DESIGN CAN BE EASILY SCALED UP/DOWN
• CONS
• PERFORMANCE LOWER THAN LIQUID PROPULSION
• NO RE-IGNITION

D. Lentini Dipartimento di Ingegneria Meccanica e
Aerospaziale CVA Summer School, 06/07/2011
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PERFORMANCE INDICES

• EXHAUST EFFECTIVE VELOCITY c OR SPECIFIC IMPULSE
  Isp
• c F / m? (THRUST / MASS FLOW RATE, m/s)
• Isp F / w? F / (g0 m) (THRUST / WEIGHT FLOW
  RATE, s)
• ? Isp c / g0 c / 9,80665 ? 0,1 c (IN SI
  UNITS)
• STRUCTURAL COEFFICIENT ?s
• ?s ms / (mp ms) (ms STRUCTURAL MASS, mp
  PROPELLANT MASS)
• DESIDERATA (IN ORDER TO GET HIGH PAYLOAD MASS)
• HIGH c
• LOW?s
• WHILE KEEP ING COSTS DOWN!

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EFFECTIVE EXHAUST VELOCITY c

• c CF c
• CF THRUST COEFFICIENT
• (DEPENDING ON NOZZLE EXPANSION RATIO ? Ae/A t,
  AND RATIO CHAMBER/AMBIENT
  PRESSURE)
• c CHARACTERISTIC VELOCITY ? (Tc / M)1/2
• (DEPENDING ON COMBUSTION CHAMBER CONDITIONS)
• Ae NOZZLE EXIT AREA
• At NOZZLE THROAT AREA
• Tc COMBUSTION CHAMBER TEMPERATURE
• M MOLAR MASS OF COMBUSTION PRODUCTS

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THRUST COEFFICIENT CF F/(pc At) vs. NOZZLE
EXPANSION RATIO ?, PARAMETER pc/pa

• MAX FOR ? SUCH THAT NOZZLE EXIT PRESSURE
  AMBIENT PRESS.

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c vs. ?s (IN VACUUM)

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FAMILIES OF LAUNCHERS

• PAYLOAD CAPABILITY GROWTH VIA ADDITION OF
  STRAP-ON BOOSTERS
• SCALING OF SOLID BOOSTER RELATIVELY EASY
• PAYLOAD IN GTO
• Ariane 40 2000 kg
• Ariane 42P 2700 kg
• Ariane 42L 3300 kg
• Ariane 44P 3100 kg
• Ariane 44LP 3800 kg
• Ariane 44L 4300 kg

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SOLID ROCKET MOTOR PERFORMANCE

• HIGHEST ACHIEVED SO FAR
• cS/L 2500 m/s (SEA LEVEL)
• cvac 2980 m/s (VACUUM)
• TO BE COMPARED TO
• cvac 4560 m/s (LIQUID CRYOGENIC)
• cvac 3520 m/s (CRYOGENIC OXIDIZER/STORABLE
  FUEL)
• cvac 3200 m/s (LIQUID STORABLE)

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INTERNAL BALLISTICS

• STUDY OF THE BURNING CHARACTERISTICS OF THE
  SOLID PROPELLANT GRAIN
• PROPELLANT REGRESSION RATE r, DEPENDING ON
• GRAIN COMPOSITION
• CHAMBER PRESSURE pc
• INITIAL PROPELLANT TEMPERATURE Tp
• GAS VELOCITY ug ( GRAIN)
• USUALLY 4 lt r lt 12 mm/s

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DE SAINT-ROBERTs LAW

• FOR Tp Tp0, ug?0
• r a pcn
• a, n DEPENDING ON GRAIN COMPOSITION
• n (COMBUSTION INDEX) GENERALLY IN BETWEEN 0,2 AND
  0,8

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EFFECT OF PROPELLANT TEMPERATURE Tp

• r INCREASES 0,1 TO 0,9 PER DEGREE K
• TOTAL IMPULSE I ? F dt NEARLY CONSTANT

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EFFECT OF GAS VELOCITY ug (EROSIVE BURNING)

• IF ug ( GRAIN) gt 150 200 m/s, REGRESSION
  RATE INCREASES

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EQUILIBRIUM COMBUSTION CHAMBER PRESSURE

• MASS FLOW RATE COMBUSTION GASES NOZZLE FLOW
  RATE
• r ?p Ab a pcn ?p Ab
  ? pc At / (RTc)1/2
• ?p (SOLID) PROPELLANT DENSITY
• Ab BURNING AREA
• ? FUNCTION OF SPECIFIC HEATS RATIO ? cp / cv
• R GAS CONSTANT OF COMBUSTION PRODUCTS
• Tc COMBUSTION CHAMBER TEMPERATURE
• AT EQUILIBRIUM pc (a c ?p K)1/(1-n)
• K Ab /At KLEMMUNG
• (FRACTURES IN GRAIN LEAD TO EXPLOSION)

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STABILITY OF EQUILIBRIUM CONDITIONS

• COMBUSTION INDEX n MUST BE lt 1 FOR STABILITY

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THRUST EVOLUTION IN TIME

• DEPENDS ON BURNING SURFACE Ab(t)
• INCREASING Ab ? K ? pc ? F (AND VICEVERSA)

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GRAIN DESIGN

• SIGARETTE, NEUTRAL
• TUBULAR, INTERNAL BURNING, PROGR.
• TUBULAR, EXTERNAL BURNING, REGR.
• STAR, NEUTRAL
• EXTRUDED, CAST, SEGMENTED

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SLIVER

• UNBURNT PROPELLANT MUST BE ACCOUNTED FOR IN THE
  STRUCTURAL MASS ms
• IF EXACT LOCATION OF SLIVER IS KNOWN IN ADVANCE,
  IT CAN BE REPLACED WITH LOW-DENSITY MATERIAL

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THREE-DIMENSIONAL GRAIN DESIGNS

• TO ENSURE DESIRED THRUST PROFILE (e.g., TO LIMIT
  PEAK DYNAMICAL PRESSURE DURING LAUNCHER ASCENT)

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INSULATION AND LINER

• INSULATION TO CONTAIN CASE TEMPERATURE, AND
  ENSUING LOSS OF MECHANICAL STRENGTH
• LINER TO ENSURE THAT PROPELLANT SAFELY ADHERES
  TO INSULATION (AVOID DEBONDING)

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SOLID PROPELLANTS DESIDERATA

• HIGH Tc
• LOW M OF COMBUSTION PRODUCTS
• HIGH ?p
• LOW TEMPERATURE SENSITIVITY
• LIMITED EROSIVE BURNING
• EASY IGNITION
• GOOD MECHANICAL PROPERTIES
• THERMAL DILATATION COEFFICIENT CLOSE TO CASE
  MATERIALS
• LONG-TERM STABILITY
• SAFE HANDLI NG
• OPACITY TO RADIATION
• LOW COST

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SOLID PROPELLANT FAMILIES

• DOUBLE BASE
• e.g., NITROGLYCERIN NITROCELLULOSE
• SMOKELESS (MILITARY APPLICATIONS)
• MAX c ? 2300 m/s
• DANGEROUS!
• COMPOSITE
• POWDERED OXIDIZER BINDER POWDERED METAL
• MAX c ? 2900 m/s (2980 m/s WITH EXTENDIBLE
  NOZZLE)
• ADOPTED IN SPACE APPLICATIONS
• LESS DANGEROUS

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COMPOSITE PROPELLANT FORMULATION (1/2)

• OPTIMAL PERFORMANCE WOULD REQUIRE 80 90
  OXIDIZER, BUT MECHANICAL PROPERTIES UNACCEPTABLE
• OXIDIZER CONTENT LIMITED TO 70 80 MAX
• PROPELLANT DENSITY ?p ? 1800 kg/ m3
• n LOWER THAN IN DOUBLE BASE
• TWO-PHASE FLOW (DUE TO Al2O3) ?
• Tmelting 2350 K, Tboiling 3250 K

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COMPOSITE PROPELLANT FORMULATION (2/2)

• OXIDIZERS
• AMMONIUM PERCHLORATE NH4ClO4 (AP)
• HIGHEST PERFORMANCE
• TOXIC COMBUSTION PRODUCTS (HCl)
• AMMONIUM NITRATE NH4NO3 (AN)
• SLIGHTLY LOWER PERFORMANCE
• RELATIVELY BENIGN COMBUSTION PRODUCTS
• BINDERS
• ASPHALT
• HTPB (HYDROXIL TERMINATED POLYBUTADIENE)
• PBAN (POLYBUTADIENE ACRYLIC ACID ACRYLONITRILE)
• METALS
• BERYLLIUM (VERY HIGH c, BUT EXTREMELY TOXIC)
• ALUMINUM (NO MORE THAN 20 ON MECHANICAL GROUNDS)

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COMPOSITE PROPELLANTS TWO-PHASE FLOW

• CONICAL NOZZLES (HEAVIER, HIGHER LOSSES w.r.t.
  BELL NOZZLES)
• CONICAL
• BELL
• DAMPING EFFECT ON COMBUSTION PRESSURE
  OSCILLATION (COMBUSTION INSTABILITY)
• DUE TO VISCOUS COUPLING BETWEEN THE TWO PHASES
• VISCOELASTIC BEHAVIOUR OF GRAIN , AND
  INCREASING CHAMBER SIZE, ALSO CONTRIBUTE TO
  SMOOTH OSCILLATIONS

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METAL POWDER SIZE

• SMALL PARTICLES BURN FASTER
• AVERAGE PARTICLE SIZE MUST BE TAILORED SO AS TO
  SUPPRESS COMBUSTION PRESSURE OSCILLATIONS
• HOWEVER, PARTICLE SIZE IS DISTRIBUTED OVER A RANGE

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HEAT TRANSFER

• NO COOLANT AVAILABLE
• SHORT BURNING TIME
• ABLATIVE THERMAL PROTECTIONS IN MOST SENSITIVE
  SECTIONS

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EXERCISE ROD AND TUBE GRAIN (IN VACUUM)

• F 1000 kN, tb 60 s, ? 20, Tc 3000 K, pc
  5 MPa, ? 1,25,
• M25 kg/kmol, ug100 m/s, ?p 1800 kg/m3, a 10-7
  m/(s Pan), n 0,7
• DETERMINE CF, c, c, m?(mass flow rate), mp
  (propellant mass), At, Ae, r, b (web thickness),
  K, Ab, D1, D2, D3, L (grain length), L/D3

10/02/2011
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ROD AND TUBE GRAIN (1/4)

• CF F / (pc At) ?2 ?/(?-1)? 1 - (pe/pc)
  (?-1) /? 1/2 ? (pe/pc - pa/pc)
• ? ? 1/2 2/(? 1)(?1)/2(?-1)
• pe/pc OBTAINED BY (ITERATIVELY) INVERTING
• ? Ae/At ? / 2? /(? -1) ? (pe/pc) 2/? 1-
  (pe/pc) (?-1) /?1/2
• c pc At / m? (R0 Tc/M) 1/2 / ? R0 univ.
  gas const. 8314 J/(kg K)
• c CF c
• m? F / c

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ROD AND TUBE GRAIN (2/4)

• mp m? tb (EXCL.
  SLIVER)
• At F / (CF pc), Ae ? At
  
• r a pcn (UNITS!)
• b 1,01 r tb (1
  TO ACCOUNT FOR SLIVER)
• K OBTAINED BY INVERTING
• pc (a c ?p K)1/(1-n)
• Ab K At

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ROD AND TUBE GRAIN (3/4)

• ASSUME D0 b
• D1 D0 2 b, D3 D2 2 b
• D2 DETERMINED BY ENFORCING VALUE OF ug
• Ap ? (D22 - D12 ) / 4 (PORT AREA)
• m? ?c ug Ap, WITH ?c pc / (R Tc),
  R R0 / M
• L Ab / ? (D1 D2 )
• mp ?p Aweb L, WITH Aweb ? (D32 D22 D12
  D02) / 4

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ROD AND TUBE GRAIN (4/4)

• pe/pc 0,00507, CF 1,820, c 1540 m/s, c
  2804 m/s,
• m? 357 kg/s, mp 21627 kg, At 0,1099 m2,
  Ae 2,198 m2,
• r 4,89 mm/s, b 0, 2963 m, K 368, Ab
  40,522 m2,
• D0b, D1 0,889 m, D2 1,303 m, D3 1,896 m,
• L 5,884 m, L/D3 3,103

10/02/2011