Hybrid Rockets Hybrid Rockets

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1984 sea launch of Starstruck's (James Bennett) Dolphin rocket,. HTPB and LOX .... n~0.75-0.77; m~0.14-0.16 close to turb. b.l. model l p k o n ox hybrid. Dp. aG.
Hybrid Rockets • Combination of liquid and solid rockets – one propellant “solid” (usually fuel) – 2nd propellant liquid or gas (oxid.)

oxid.

fuel

• 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

Hybrids 1 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

AE6450 Rocket Propulsion

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 Hybrids 2 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

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Example – SRM Replacement • Pressurization – similar options to liquid rockets: gas, turbopump (expander, tap-off, …) • Oxidizer prevaporization • Final volume for propellants to finish burning since not mixed initially – combustion efficiency of 9095% considered pretty good from Sutton Hybrids 3 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

AE6450 Rocket Propulsion

Hybrid Rockets • Hybrid performance – intermediate specific impulse, density-specific impulse, complexity – control: restart, throttleable – improved safety vs. solids (no detonation/explosion) solid – specific impulse O/F varies during fuel burn – lower regression rate than solids – higher fraction of unburned solid after burn Hybrids 4 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

liquid oxid.

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Combustion “Rate” •







Major difference from liquid bipropellant and solid technologies is due to Liquid Bipropellant 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, 100μm 10’s μm 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 Solid (Composite) Propellant

Hybrids 5 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

AE6450 Rocket Propulsion

Hybrid Regression Rate • Hybrid combustion rate – limited by conversion of solid fuel to gas – gas needs to Boundary Diffusion “diffuse” toward Layer Flame Oxid oxidizer across (g) boundary layer Heat/Mass – heat from flame needs to “diffuse” downward to Solid Fuel drive vaporization of solid fuel x • Varies downstream – as boundary layer/flame distance changes – fuel mass injection varies along port length • Depends on oxidizer injection rate Hybrids 6 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

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Multiport Fuel Grains Casing

• 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 Hybrids 7 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

Combustion Ports Unburned

Fuel Grain

Slivers

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Example - Unburned Fuel Before burn

After burn

• Remaining unburned fuel – wasted mass – lower effective densityspecific impulse some solid fuel remaining on struts (structural supports) From Figure 7.19 Humble Hybrids 8 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

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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 − const × c p (μ D )0.2 − 2 3 To − Ts 0.8 re ∝ Pr G∞ e ρs cs Ts − Tp

( ρu )burn G∞

“blowing” ratio of mass fluxes

AE6450 Rocket Propulsion

Hybrids 9 Copyright © 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 rhybrid = f (G∞ , μ , Gsolid G∞ , x,...) n – unlike solid propellant, r ∝ po no direct pressure dependence • From analysis of convective heat transfer in turbulent boundary layer over flat plate with blowing, 0.2 0 .8 Eq. 15-2 in Sutton G∞ ⎛ μ ⎞ 0.23 rhybrid = 0.036 ⎜ ⎟ β (from App. 4,5) ρ sf ⎝ x ⎠ Blowing Coefficient

β≡

Hybrids 10 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

Gsolid −1 − 2 3 St Pr G∞

Pr =

ν h ; St = α ρ ∞ u∞ c p

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Regression Rate Dependence ⎛μ⎞ 0.23 rhybrid = 0.036 ⎜ ⎟ β ρ sf ⎝ x ⎠ • 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 T −T – can show (App. 5) β ~ flame surface high β ⇒ hot flame or easily vaporized solid G∞

0.8

0.2

Δhvap , surface

• Ignores – curvature and radiative heat transfer (e.g., metalized solids, which also tend to increase Tflame) AE6450 Rocket Propulsion

Hybrids 11 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

Empirical Local Regression Rate Models • Ignoring blowing and for given system rhybrid = aG∞n x − m e.g., O2-HTPB, empirical results indicate n~0.75-0.77; m~0.14-0.16 close to turb. b.l. model

• Some empirical data suggests rhybrid = aGoxn pok D lp

– observed pressure and port diameter dependence • Ballistic performance scaling of hybrids complex, less understood – harder to design Hybrids 12 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

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Average Burn Rate • Above are regression rates at some local distance along port (x) • Useful to have avg. regression rate m& f ,total = ravg ρ s Ab

• Def’n. ravg

x

1 ≡ ∫ r ( x′)dx′ x0

4A DP = x S

• Examine using r = aG x n ∞

−m

(

)

= a Gox + G f ( x ) x n

−m

S Ax x

G f (x ) = 4 ρ s ∫ 0

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r ( x′ ) dx ′ DP ( x′)

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Average Burn Rate n x ⎡ ⎤ −m r ( x′ ) r ( x ) = a ⎢Gox + 4 ρ s ∫ dx ′⎥ x DP ( x ′ ) ⎦ 0 ⎣ • Can often assume DP≠DP(x) 60s 40s 20s

G∞↑ downstream offset by b.l. growth

0.1s

≡Ir From Figure 7.7 Humble (calculations based on given propellant data) Hybrids 14 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

r (x ) =

dI r dx

n

⎤ −m ⎡ ρs x ′ ′ ( ) r (x ) = a ⎢Gox + 4 r x d x ⎥ x DP ∫0 ⎦ ⎣ AE6450 Rocket Propulsion

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Average Burn Rate (Uniform Port) n

• Continuing,

⎡ 4 ρ s I r ⎤ −m dI r (x ) = r = aGox ⎢1 + ⎥ x dx ⎣ DP Gox ⎦

• Separate variables depending on x and on Ir, then integrate separately DG I r ( x ) = P ox 4ρs

• Note: ravg

1 ⎡⎛ ⎤ 1− m 1− n ⎞ ( ) ρ 4 1 n a x − s ⎢⎜1 + ⎟ − 1⎥ (1 − m )DPGox1−n ⎟⎠ ⎢⎜⎝ ⎥ ⎣ ⎦

x I (x ) 1 = ∫ r ( x′)dx′ = r x x0

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Hybrids 15 Copyright © 2007 by Jerry M. Seitzman. All rights reserved.

Average Burn Rate (Uniform Port) • So average burn rate over distance x is 1 DP Gox ⎡⎢⎛ 4(1 − n )aρ s x1− m ⎞ 1− n ⎤⎥ ⎟ ⎜1 + ravg = −1 (1 − m )DPGox1−n ⎟⎠ 4 ρ s x ⎢⎜⎝ ⎥ ⎣

• Using Taylor expansion ⎛ ravg

often