Page 1
1
AE6450 Rocket PropulsionHybrids 1Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Hybrid Rockets• Combination of liquid and solid rockets
–one propellant “solid” (usually fuel)–2nd propellant liquid or gas (oxid.)
• Early history–1930’s combustion tests of
• coal and N2O(g) at I.G. Farben, Germany• coal and GOX by Calif. Rocket Soc.• tar-wood-saltpeter and LOX by Hermann Oberth
(von Braun’s teacher), Germany–1933 flight test GIRD-09 (15 s flight, 1.5 km)
• Gasoline-gum rosin (gel) on metal frame and pressurized LOX, Sergei Korolev and Tikhonravov
oxid.
fuel
AE6450 Rocket PropulsionHybrids 2Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Hybrid Rockets• 1950’s-70’s
– mostly polymer fuels and numerous oxidizers• GE:1951-1956 (Moore) polyethylene and 90% H2O2• Volvo: 1965-1971, Flygmotor (SR-1 80 km sounding rocket)
– testing of inverse hybrids (liquid fuel, sol. ox.), Johns Hopkins
• 1980’s-2000’s (US)– 1983 Firebolt target drone entered USAF service (UTC hybrid)– 1984 sea launch of Starstruck’s (James Bennett) Dolphin rocket,
HTPB and LOX, 175kN thrust, follow-on tests at AMROC: up to 324 kN (H-500)
– 1999-2002 NASA-DARPA initiated program (ground test NASA Stennis), 70” D, 45 ft L, 250klbf (1.1 MN) thrust, T/W=2, 27 s burn
– 2004 small hybrid (HTPB-N2O; 88kN)used to launch Space Ship one
Page 2
2
AE6450 Rocket PropulsionHybrids 3Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Example – SRM Replacement• Pressurization
– similar options to liquid rockets: gas, turbopump (expan-der, tap-off, …)
• Oxidizer pre-vaporization
• Final volume for propellants to finish burning since not mixed initially– combustion
efficiency of 90-95% considered pretty good
from Sutton
AE6450 Rocket PropulsionHybrids 4Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Hybrid Rockets• Hybrid performance
– intermediate specific impulse, density-specific impulse, complexity
– control: restart, throttleable– improved safety vs. solids (no
detonation/explosion)– specific impulse O/F varies during
burn– lower regression rate than solids– higher fraction of unburned solid
after burn
liquid oxid.
solidfuel
Page 3
3
AE6450 Rocket PropulsionHybrids 5Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Combustion “Rate”• Major difference from liquid bipropellant
and solid technologies is due to combustion process
• Processes limiting burn rate are:– mass injection rate– mixing (often requires conversion
to gas)– chemistry (generally fast)
• Liquid bipropellants, pressurization system controls mass injection, combustion primarily limited by mixing rate
• Solid propellants, well mixed (at least within 10-100 μm), combustion limited by mass injection, depends on heat transfer from flame to surface
100μm10’s μm
Liquid Bipropellant
Solid (Composite) Propellant
AE6450 Rocket PropulsionHybrids 6Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Hybrid Regression Rate• Hybrid combustion rate
– limited by conversion of solid fuel to gas– gas needs to
“diffuse” toward oxidizer across boundary layer
– heat from flame needsto “diffuse” downward to drive vaporization of solid fuel
• Varies downstream– as boundary layer/flame distance changes– fuel mass injection varies along port length
• Depends on oxidizer injection rate
Boundary Layer
Solid Fuel
Oxid(g)
Diffusion Flame
Heat/Mass
x
Page 4
4
AE6450 Rocket PropulsionHybrids 7Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Multiport Fuel Grains
• Hybrids generally have lower regression rate than solid propellants – higher burn area
required to achieve high thrust
– use multiple ports– also reduces distance
to oxidizer stream• More complex casting
required• Unburned “slivers”
– left over or broken off
Casing
FuelGrain
Combustion Ports Unburned
Slivers
AE6450 Rocket PropulsionHybrids 8Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Example - Unburned Fuel
• Remaining unburned fuel– wasted mass– lower effective
density-specific impulse
From Figure 7.19 Humble
some solid fuel remaining on struts (structural supports)
Before burn After burn
Page 5
5
AE6450 Rocket PropulsionHybrids 9Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Hybrid Regression Rate
• Hybrid burning rate limited by heat transfer back to solid fuel– similar issue seen in erosive burning of
solid propellants– recall Lenoir-Robillard model (1957) based
on heat transfer boundary layer
“blowing” ratio of mass fluxes
( ) ( )∞
×−
∞−
−−
∝ Gu
const
ps
so
ss
pe
burn
eGTTTTPrD
cc
rρ
ρμ 8.032
2.0
AE6450 Rocket PropulsionHybrids 10Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Analytic Hybrid Regression Rate• So we expect solid fuel regression rate in
hybrid to be function of
– unlike solid propellant,no direct pressure dependence
• From analysis of convective heat transfer in turbulent boundary layer over flat plate with blowing,
( ),...,,, xGGGfr solidhybrid ∞∞= μnopr ∝
23.02.08.0
036.0 βμρ
⎟⎠⎞
⎜⎝⎛= ∞
xGr
sfhybrid
Eq. 15-2 in Sutton (from App. 4,5)
321 −−
∞
≡ PrStG
Gsolidβpcu
hStPr∞∞
==ρα
ν ;BlowingCoefficient
Page 6
6
AE6450 Rocket PropulsionHybrids 11Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Regression Rate Dependence
• Increases with local free stream mass flux (G∞=oxid.+fuel+products)– G∞typically increases downstream
• 1/x dependence– due to boundary layer growth
• Increases with relative importance of injection from solid– can show (App. 5)
• Ignores– curvature and radiative heat transfer (e.g.,
metalized solids, which also tend to increase Tflame)
23.02.08.0
036.0 βμρ
⎟⎠⎞
⎜⎝⎛= ∞
xGr
sfhybrid
surfacevap
surfaceflame
hTT
,
~Δ
−β high β ⇒ hot flame or
easily vaporized solid
AE6450 Rocket PropulsionHybrids 12Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Empirical Local Regression Rate Models• Ignoring blowing and for given system
• Some empirical data suggests
– observed pressure and port diameter dependence
• Ballistic performance scaling of hybrids complex, less understood – harder to design
mnhybrid xaGr −
∞= e.g., O2-HTPB, empirical results indicate n~0.75-0.77; m~0.14-0.16
close to turb. b.l. model
lp
ko
noxhybrid DpaGr =
Page 7
7
AE6450 Rocket PropulsionHybrids 13Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Average Burn Rate
• Above are regression rates at some local distance along port (x)
• Useful to have avg. regression rate
• Def’n.
• Examine using
bsavgtotalf Arm ρ=,&
( )∫ ′′≡x
avg xdxrx
r0
1
mn xaGr −∞= ( ) ( )
( )∫ ′′′
=x
Psf xd
xDxrxG
0
4ρ
SAD x
P4
= Ax
S
( )( ) mnfox xxGGa −+=
AE6450 Rocket PropulsionHybrids 14Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Average Burn Rate
• Can often assume DP≠DP(x)
( ) ( )( )
m
nx
Psox xxd
xDxrGaxr −
⎥⎦
⎤⎢⎣
⎡′
′′
+= ∫0
4ρ
From Figure 7.7 Humble(calculations based on given propellant data)
( ) ( ) m
nx
P
sox xxdxr
DGaxr −
⎥⎦
⎤⎢⎣
⎡′′+= ∫
0
4 ρ≡Ir
( )dxdIxr r=
G∞↑ downstream offset by b.l. growth
0.1s
20s40s60s
Page 8
8
AE6450 Rocket PropulsionHybrids 15Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Average Burn Rate (Uniform Port)
• Continuing,
• Separate variables depending on x and on Ir, then integrate separately
• Note:
( ) mn
oxP
rsox
r xGDIaG
dxdIxr −
⎥⎦
⎤⎢⎣
⎡+==
ρ41
( ) ( )( ) ⎥
⎥
⎦
⎤
⎢⎢
⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛−−
+=−
−
−
11141
4
11
1
1 n
noxP
ms
s
oxPr GDm
xanGDxI ρρ
( )∫ ′′=x
avg xdxrx
r0
1 ( )xxIr=
AE6450 Rocket PropulsionHybrids 16Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Average Burn Rate (Uniform Port)• So average burn rate over distance x is
• Using Taylor expansion
– get S(t), Ax(t) from regression rate
( )( ) ⎥
⎥
⎦
⎤
⎢⎢
⎣
⎡−⎟⎟
⎠
⎞⎜⎜⎝
⎛−−
+=−
−
−
11141
4
11
1
1 n
noxP
ms
s
oxPavg GDm
xanx
GDr ρρ
often <<1
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛⎟⎠⎞
⎜⎝⎛−+⎟
⎠⎞
⎜⎝⎛−
≅ −
−
−n
oxP
ms
mnoxavg GD
xm
anxG
mar 1
1
12
11
ρ
( )ερ +′⎟⎟⎠
⎞⎜⎜⎝
⎛′+′≅ −
−
−− 1~21 1
1mn
oxnoxP
m
smn
oxavg xGaGD
xanxGaruseful for prelim. design process ( ) ( ) ( ) ( ) mn
oxsbsavgf LtGtSaALrtm −′= 1~ ρρ&
Page 9
9
AE6450 Rocket PropulsionHybrids 17Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Example Regression Law Data
Table 7.5 Humble
AE6450 Rocket PropulsionHybrids 18Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Example Regression Law Data
Table 7.6 Humble
Aluminized Propellants
Page 10
10
AE6450 Rocket PropulsionHybrids 19Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Motor Ballistics• As with solid motors, use mass
conservation to determine motor conditions
exitm&
Vo
( ) exitoxbsfboo
o
o mmrArAdt
dpRTV
&& −+=+ ρρ
liquid oxid.
oxm&
fm&
( ) ( )oxfexitoo mmmVdtd
&&& +−+= ρ0
( )( )
to
o
oxbosfo
o
o
ARTp
mrAdt
dpRTV
121
12 −
+
⎟⎟⎠
⎞⎜⎜⎝
⎛+
−
+−=
γγ
γγ
ρρ &
AE6450 Rocket PropulsionHybrids 20Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Motor Ballistics• Using our model for the avg.
regression rate – and assuming quasi-steady
operation with a high density fuel
– possible time-dependent variables (nozzle erosion significant issue in oxidizer rich cases)
exitm&
Vo
oxm&
fm&
( )
⎥⎦
⎤⎢⎣
⎡+′⎟
⎠⎞
⎜⎝⎛ +
= −−
+
oxnoxn
x
bmsf
t
oo mm
ASLa
ART
p &&112
1
21 ργγ γ
γ
mnoxavg LGar −′≅
( )oxptooo mDAMWTpp &,,,,, γ= ( )pxp DfAS =,
Sp
Ax
Page 11
11
AE6450 Rocket PropulsionHybrids 21Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
“Unsteady” Behavior
• Already know Dp changes with time– suggest po and therefore thrust may
change with time• From previous analysis, also know
– O/F ratio can also change with time
( ) ( ) ( ) ( ) ( )( )
n
x
oxmnoxf tA
tmtSLtGtStm ⎥⎦
⎤⎢⎣
⎡=∝ − &
& 1
( )[ ]( ) ( )[ ] n
ox
nx
f
ox tmtStA
mm −∝ 1&&
&
( )oxptooo mDAMWTpp &,,,,, γ=
AE6450 Rocket PropulsionHybrids 22Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
O/F Ratio• Change in O/F with time
– e.g., circular port
– for fixed oxid. flow rate
– estimate amount from volum. loading effic.≡ Volume Grain/Volume Chamber, typically ~0.6
121/ −−∝ nP
nox DmFO &
O/F ↑ if n>0.5
( )[ ]( ) ( )[ ] n
ox
nx
f
ox tmtStA
mm −∝ 1&&
&
( )( )
12
,
,
−
⎟⎟⎠
⎞⎜⎜⎝
⎛=
n
initialP
finalP
initial
final
DD
FOFO
( )[ ]( ) chambergraingrainchamber
chamber
initialP
chamber
initialP
finalP
VVLVVLV
DD
DD
−− 11~~~ 5.0
5.0
,,
,
6.1~6.01
1~,
,
−initialP
finalP
DD ( )
( ) 3.1~initial
final
FOFO
for HTPB/LOX n~0.75
reduced “burn” rate even as Ab increase, because lower heat xfer
Page 12
12
AE6450 Rocket PropulsionHybrids 23Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
O/F Ratio Importance• Besides reduction in fuel mass flux through rocket,
does change in O/F ratio have any other effects
Tad
Flam
e Te
mp.
(K)
O/FFigure B.29 Humble
AE6450 Rocket PropulsionHybrids 24Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
O/F Ratio Importance• Besides reduction in fuel mass flux through rocket,
does change in O/F ratio have any other effects
Figure B.30 Humble⇒ po, c* and thus τ,Isp unsteadiness
MW
MW
Pro
duct
s
O/F( )MWTpp ooo ,= ( )MWTcc o ,** =
Page 13
13
AE6450 Rocket PropulsionHybrids 25Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
O/F Ratio
• Again for circular port– n=0.5 removes dependence on port size
• freestream mass flux dependence of burn rate (Ax
0.5~D) cancels ~Ab (P×L~D) dependence– but also likely results in lower regression
rate
121/ −−∝ nP
nox DmFO &
mnoxavg xGar −′~
AE6450 Rocket PropulsionHybrids 26Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Oxidizer Control
• Can use oxidizer flow rate to control O/F
• If O/F increasing then can offset by reducing oxidizer flow rate– but that means lower total mass flow rate
through rocket• will tend to lower thrust, partly made up by
increase in specific impulse, exit velocity• If trying to throttle engine, same concerns
( )[ ]( ) ( )[ ] n
ox
nx
f
ox tmtStA
mm −∝ 1&&
&
Page 14
14
AE6450 Rocket PropulsionHybrids 27Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Throttling via Oxidizer Flowrate
• weak dependence of O/F on Gox for n→1(Gf linearly proportional to Gox in that case)
• when throttling down, usually O/F↓ (richer), can add oxid. downstream of fuel to maintain constant O/F
Figure 7.10 Humble
oxid.
fuel
n=0.50.60.70.80.91.0
AE6450 Rocket PropulsionHybrids 28Copyright © 2007 by Jerry M. Seitzman. All rights reserved.
Hybrid Design
• Preliminary design approach similar to previous cases• Assume given thrust and burn duration requirements, possibly
maximum motor diameter or length constraints1. choose propellants: oxidizer and fuel
⇒ based on performance and handling/storage2. try to find optimum Isp, c* (cτ for nozzle)
⇒ optimum O/F ⇒ feed system (pressure) requirements (oxidizer)
3. size system⇒ total propellant mass, oxid. storage, port/grain design (fuel)
4. estimate initial conditions and performance variation over burn time⇒ ballistics (+ nozzle erosion)
5. Iterate from 2 if necessary