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AE6450 Lecture #10 Solid Rocket Engines: 1

Copyright © 2003 Narayanan Komerath

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Solid rocket motors Unlike liquid rocket engines, the fuel and oxidizer are premixed in solid rocket. The result is a rubbery solid that burns when heated. Solid rockets are simpler and cost less than liquid-fueled rockets have lower Isp than most liquids (~ 285 sec) are more dense -> higher “density impulse” ρI sp . So packaging is easier. Thrust is limited by nozzle size – not by pump capacity. Easy to get very high thrust for boosters. Cannot be throttled or shut down during the flight (unless pre-designed to do so)

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Solid Propellant Ingredients Tables from Humble

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Oxidizers •Ammonium Perchlorate (AP) – contains chlorine – acid rain •Ammonium Nitrate (AN) is more benign. But inherently low burning rate and a phase change near 30 deg. C.

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Applications

-

Missiles (acceleration, storage) Booster, strap ons (high thrust per size) known ∆V Apogee kick motors

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Star-Grained Solid Rocket Motor

http://www.nf.suite.dk/stargrain/

After 1 minute of burn

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General configuration TE-M-364-4 is a 15,000 lb. thrust solid propellant motor developed for use as an upper stage. It is an enlarged version of the TE-M-364, one of a series of solid propellant motors that powered the workhorse USAF Burner I and Burner IIA upper stages to orbit scientific, weather, navigation, and communications satellites. The TE-M-364-4 powered the upper stages of the USAF Atlas boosters used to launch the Global Positioning System (GPS) satellites. It also was used as the second stage motor on USAF Thor vehicles that launched satellites of the Block 5D Defense Meteorological Satellite Program (DMSP) as well as the third stage motor on the Thor Delta launch vehicles. www.wpafb.af.mil/ museum/engines/eng62.htm Copyright © 2003 Narayanan Komerath

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history.nasa.gov/ rogersrep/v1p56.htm

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STS SRB motors SRB motor: propellant mixture ammonium perchlorate (oxidizer, 69.6 percent by weight), aluminum (fuel, 16 percent), iron oxide (a catalyst, 0.4 percent), a polymer (a binder that holds the mixture together, 12.04 percent), and an epoxy curing agent (1.96 percent). The propellant is an 11-point star- shaped perforation in the forward motor segment and a double- truncated- cone perforation in each of the aft segments and aft closure. This configuration provides high thrust at ignition and then reduces the thrust by approximately a third 50 seconds after lift-off to prevent overstressing the vehicle during maximum dynamic pressure. liftoff.msfc.nasa.gov/ Shuttle/About/detsrb.html

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The SRBs are used as matched pairs and each is made up of four solid rocket motor segments. The pairs are matched by loading each of the four motor segments in pairs from the same batches of propellant ingredients to minimize any thrust imbalance. The segmented-casing design assures maximum flexibility in fabrication and ease of transportation and handling. Each segment is shipped to the launch site on a heavy- duty rail car with a specially built cover.

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The forward section of each booster contains avionics, a sequencer, forward separation motors, a nose cone separation system, drogue and main parachutes, a recovery beacon, a recovery light, a parachute camera on selected flights and a range safety system. Each SRB has two integrated electronic assemblies, one forward and one aft. After burnout, the forward assembly initiates the release of the nose cap and frustum and turns on the recovery aids. The aft assembly, mounted in the external tank/SRB attach ring, connects with the forward assembly and the orbiter avionics systems for SRB ignition commands and nozzle thrust vector control. Each integrated electronic assembly has a multiplexer/ demultiplexer, which sends or receives more than one message, signal or unit of information on a single communication channel.

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The nozzle expansion ratio of each booster beginning with the STS-8 mission is 7to-79. The nozzle is gimbaled for thrust vector (direction) control. Each SRB has its own redundant auxiliary power units and hydraulic pumps. The all-axis gimbaling capability is 8 degrees. Each nozzle has a carbon cloth liner that erodes and chars during firing. The nozzle is a convergent- divergent, movable design in which an aft pivot- point flexible bearing is the gimbal mechanism. The cone- shaped aft skirt reacts the aft loads between the SRB and the mobile launcher platform. The four aft separation motors are mounted on the skirt. The aft section contains avionics, a thrust vector control system that consists of two auxiliary power units and hydraulic pumps, hydraulic systems and a nozzle extension jettison system. Eight booster separation motors (four in the nose frustum and four in the aft skirt) of each SRB thrust for 1.02 seconds at SRB separation from the external tank. Each solid rocket separation motor is 31.1 inches long and 12.8 inches in diameter.

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Solid rocket Explosion: Large fragments created

www.wstf.nasa.gov/.../ Explosion/HEBFTesting.htm Copyright © 2003 Narayanan Komerath

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Inertial Upper Stage

W. Paul Dunn

www.aero.org/.../crosslink/ winter2003/08.html Copyright © 2003 Narayanan Komerath

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Stinger Man-Portable S-A Missile

www.combatindex.com/.../ detail/mis/stinger.html

Stinger Unofficial names/slang: n/a Function: To provide close-in, surface-to-air weapons for the defense of forward combat areas, vital areas and installations against low altitude air attacks. Date deployed: 1987 Contractor: General Dynamics /Raytheon Unit cost: $38,000 Length: 5' - 0" Wingspan: 3.5" Diameter: 0' - 0" (0.00m) Speed: Supersonic Weight at launch: 34.5 lbs (launcher w/ missile) Guidance: Fire-and-forget passive infrared seeker Range: approx. 1 - 8 km Engine: Dual thrust solid fuel rocket motor Warhead: High explosive

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Pintle-controlled Solid Rocket Motor: CFDRC www.cfdrc.com/ research/pintle.html 6-inch diameter heavy wall system capable of producing a range of thrust of approximately 150 to 750 pounds thrust. The motor uses ten pounds of cartridge-loaded propellant, which for these tests was a 1.1 class, min-smoke formulation that is a current production Army SRM propellant. The motor was fired in both a fixed mode and a closed-loop active control mode based on motor pressure.

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SOLID ROCKET MOTOR DISPOSAL

combines cryowashout of the propellant from the motor casing with a simple supercritical water oxidation reactor for environmentally safe disposal of the effluent.

page: www.ga.com/atg/ aps/solid1.html 17 Copyright © 2003 Narayanan Komerath

Solid Propellants Double Base – molecules of fuel/oxidizer are mixed (e.g., gun powder dissolved in nitroglycerine) – oxygen in both (less common, more explosive) Composite – Heterogeneous mixture of fuel, oxidizer and binder, plus some other additives – more common.

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Fuels ← Powdered Aluminium

STS

Powdered Mg

Binders HTPB ←

PBAN ← RSRM

most popular now

The binder holds the entire formulation in a structurally sound propellant grain, under temperature and pressure variations, plus accelerations and vibration loads of flight. Binders should have low density and energy of combustion, plus structural integrity using minimal binder volume. “Solids Loading” = percentage the total propellant mass taken up by fuel + oxidizer. Usually > 90% Binders are usually long-chain polymers – keep the propellant powders and crystals in a continuous matrix through polymerizing and cross-linking. Copyright © 2003 Narayanan Komerath

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Other Ingredients Fixers (bonding agents): improve bond between oxidizer and binder Curatives: increase rate of polymerization. Plasticizer: improve physical properties at low temperatures Darkening agents: reduce thermal radiation losses through translucent propellant HMX: increases burning rate. Can cause detonations too.

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Propellant Burning Rate

r = aPc or

n

Regression Law – St. Robert’s Law

ln ( r ) = n ln ( aPc )

regression rate proportional to pressure to some n

A “plateau” type burning rate law is more common, where n becomes close to zero over a range of pressure. Note: n has to be < 1 for stability  m  r ,m

n <1

n >1

Pc Copyright © 2003 Narayanan Komerath

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Grain cross sections to control burning •End grain: neutral •Internal Burning Tube: progressive •Internal-External Burning Tube: neutral •Rod and Tube: neutral •Internal Burning Star: neutral •Dog Bone: neutral •Slots and Tube: neutral •Slotted Tube: neutral •Wagon Wheel: neutral •Multiple Perforations: neutral •Neutral thrust history generally gives the smallest inert mass since the maximum and average pressures on the structure are nearly the same with this. Else use regressive thrust profiles. Copyright © 2003 Narayanan Komerath

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Simple Solid Rocket Analysis In a solid rocket motor, the “chamber” pressure is related to the geometry and burn rate. Therefore we must know something about the geometry to find Pc (time) and thus thrust and Isp vs. time. Lweb pc

r

Then from conservation of mass: .

.

.

m burn = mvolume + m exit

Ab

.

m exit

(Simple end-burner design)

…..(1)

(mass released from surface per unit time = mass added to growing chamber volume + mass exhausted) . ∂ Ab ( t ) ρ p r = ( ρcVc ) + m exit ∂t

ρp

….(2)

density of solid

ρc

density of gas in bore

mp

propellant mass flow rate

.

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T

Recall Isp =

.

=

CF Pc At

g0 mp

or

.

mP =

Pc ∆t C

*

.

g 0 mp .

= mexit

CF C * = g0

….(3)

So A ( t ) ρ r = V ∂ρc + ρ ∂V + Pc At b p c c ∂t ∂t C* where

r = aPc n

(St. Robert’s Law)

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…..(4)

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Let us first assume: 1) ∂ρc = 0 ∂t 2) ρ ∂V c ∂t

is small (note that ρc

3) Ab ( t )

is constant (end burner type design)

n 4) r = aPc

(n < 1)

in equilibrium

(and “a”, n,

is a gas density)

ρ p ,C * do not change over time)

then .. A Pc b = Pc = At rC * ρP aPc n C * ρ p

(

)

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Ab = At

(

aPc n

)

Pc  1m   1MPa  C* ρp    100cm  1* 106 Pa 

………(5) (This is a steady-state approximation)

(steady-state lumped-parameter) where Pc → MPa cm

s MPan C* → m s Kg ρP → 3 m a→

Pay particular attention to units in (5) if we are going to use Humble’s table of “a” in Table 6.9. We can use equation (5) to estimate the size of an end-burner for a desired Pc and performance. Copyright © 2003 Narayanan Komerath

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Example Pc = 4Mpa ← target C * = 1500m / s Cfv = 1.85

f ≈ 1.2

(note

for solids)

ρP = 1800Kg / m3 r = .40 [Pc ]

.3

in cm/s (Pc =MPa)

If the desired TVac = 500,000N and Find At , Ab , and lweb T = Cf At Pc

tb = 100 sec

500000N = 1.85 At 4 * 106 Pa At =.0676m2

{

lweb = rtb = .40 [ 4MPa ]

.3

} (100 sec )

lweb = 60.629cm = .6063m Copyright © 2003 Narayanan Komerath

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from (5)

Ab = At

{

.4 [ 4MPa ]

Ab = 244.35 At

.3

}

So

4MPa

(1500m / s ) (1800Kg / m3 ) 

1m   1MPa     100cm   1* 106 Pa 

(

Ab = 244.35 .0676m 2

Ab = 16.51m 2 and Db =

Ab

π

)

*2

Db = 2.293m Lweb = .132 Db

If this geometry is unacceptable, we can change Pc and resize. For example, a higher Pc will make a longer, more slender solid rocket.

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Time varying Burn Area For a more general cross section (tube, stov, Wagon, Wheel, etc) we would expect the cross-sectional area or the total exposed burn area to change with time. Given the initial geometry r = aPc n =

dx dt

and 1   1− n

 A   1m   1MPa Pc =  b  aC * ρ p    6 100 A cm   1* 10 Pa   t 

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Time varying Burn Area In the units we have been using for each, where typically assume a,C * , ρ , and n are constant. p

But Let

Ab , At ,

and Pc can change with time

Ab = Ab ( x )

and

At

be fixed

Then n  1− n

dx  1m    Ab ( x )  *  1m   1MPa = a   aC ρ p     dt  100cm    At   100cm   1* 106 Pa  

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n  1− n

 1m    Ab ( x )  *  1m   1MPa ∫ ( dx ) = x − xi = ∫ a  100cm   At  aC ρ p  100cm   1* 106 Pa    x 0 x

t

dt

i

(at x=xf, t=tb) for most complex shapes, we will need to integrate the R.H.S. numerically, and Ab ( x ) may be a complex calculation over multiple regions. For a simple shape Ab ( x ) = 2π xL x

where L= bore length

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So

x

∫

dx

n xi 1− n x

n 1− n t

 * a  2π aC ρ pL  =   100  At 1* 108   

(

)

∫ dt

0

Integrating this (left to HW) gives X(t) - regression amount as a function of time and therefore

A (t )

Pc(t)

Thrust (t) = Pc ( t ) AtCf And the total burn time, t b , can be calculated for when x = xmax

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