Lecture 9 Hybrid Rocket Propulsion Liquefying Fuels

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1 Lecture 9 Hybrid Rocket Propulsion Liquefying Fuels Prepared by Arif Department of Aeronautics and Astronautics May 09, 2012

2 Entrainment Mass Transfer Mechanism ρ e u e Liquid Layer Fuel Grain Reacting Droplets Diffusion Flame Roll Waves A new transfer mechanism: Certain fuels form a liquid layer If the conditions are right, mechanical entrainment of liquid droplets occur Enhanced mass transfer due to the new mechanism Effective use of energy since vaporization is not required for entrained mass Liquid Layer Hybrid Combustion Theory (Stanford ) Regression Rate = Entrainment + Vaporization 2

3 Liquid Layer Hybrid Combustion Theory Outline Steps of the Theory Development Estimate film thickness Stability of the liquid film Scaling for the entrainment mass transfer Modify Diffusion Limited Model for the existence of entrainment. 3

4 Film Thickness Model-Pentane a r& t h = 4

5 Film Stability Model G = ρ e u e g x δ λ Wave form Mean Velocity Profile Liquid y h v l u( y) Solid Ýr 5

6 Orr-Sommerfeld Equation Stream function u = ϕ y v = ϕ x Form of Solution - (Surface disturbance) iα x ct ϕ ( x, y,t) = φ( y)e ( ) η = εe ( iα ( x ct ) ) Stability equation (Nondimensional) ( ) φ IV 2α 2 φ + α 4 φ b ( φ α 2 φ )= iα Re y c ( φ α 2 φ) 6

7 Perturbation Solution Follow Craik (b=0, JFM 1966) Consider power series solution (N=6) ( ) = A n n=0 φ y N Rapid convergence for y n α 2 << 1 Re < O(1) b < O( 1) Solution for eigenvalue problem Tα 2 + G P g η + 3i τ g η 2α = 1 c ( ) c ( ) ( ) b + 6α 2 iα Re 7

8 Exact Solution Solution for Orr-Sommerfeld equation φ φ φ 1 ( y) = e αy φ 2 where ( y) = e αy ( y) 1 y [ ( )] ( B 2) z y y e ( yˆ ) 3 = sinh α ˆ Aiz( yˆ ) + 2 α y o [ B 4]y dˆ ( y) 1 y [ ( )] ( B 2) z y y e ( yˆ ) 4 = sinh α ˆ Biz( yˆ ) + 2 α y o ( ) 1 3 B = ib α Re [ B 4]y dˆ 8

9 Film Stability-Pentane Film Re= U l hρ l µ l 9

10 Entrainment Mass Transfer Scaling for entrainment mass transfer m& ent P σ α d π h µ β γ l Gater & L Ecuyer (1970)- RP1, methanol α = 1.5 β = 2 Operational Parameters: (Pressure, Oxidizer Flux) Material Properties: (Viscosity, Surface Tension) 10

11 Liquid Layer Hybrid Combustion Theory Modification on the classical Hybrid Combustion Theory Reduced heating requirement for the entrained mass. Reduced Blocking Effect due to two phase flow. Increased heat transfer due to the increased surface roughness. 11

12 Liquid Layer Hybrid Combustion Theory r& v Mass balance r & = r& v + r& ent Energy balance µ g & & C r c ρf CHo [ ( )] ( ) R + R r& r& r& H = F 1+ Q Q B G + z he hv v ent r Entrainment regression rate r& ent = aent G r& 12 2α β

13 Theory-Pentane Predictions 13

14 Theory Effect of Melt Layer Properties Propellant Melt Layer Viscosity Melt Layer Surface Tension Pentane C 5 H 12 Acetone C 3 H 6 O 2,2,5 tmh HFI Isopropanol C 3 H 8 O Entrainment Parameter, a ent Observed Regression Rate 1 ~1 ~

15 Homologous Series of n-alkanes (C n H 2n+2 ) Normal Alkanes: Fully saturated, straight-chain hydrocarbons Examples: Methane (CH 4 ): C Ethane (C 2 H 6 ): C-C. Pentane (C 5 H 12 ): C-C-C-C-C. Wax (C 32 H 66 ): C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C-C A number of of practical fuels (pure form or or mixtures): Methane, Kerosene (n~10), Paraffin Waxes (n=16-45), PE waxes (n=45-90), HDPE Polymer (n (n in in thousands) 15

16 Melt Layer Temperatures for C n H 2n+2 Series 16

17 Entrainment for C n H 2n+2 Series Methane (Tested) Pentane (Tested) Paraffin Waxes PE Waxes HDPE Polymer (Tested) C: Mw: (g/mol) , ,000 Cryogenic Non-cryogenic Gas Liquid Solid Polymer Entrainment Entraiment Boundary Mw 17

18 Theory Prediction and Motor Test Data for C n H 2n+2 Regression rate rate increase over over the the classical value value is is as as high high as as Paraffin waxes waxes burn burn times times faster faster than than the the HDPE HDPE polymer Theory Theory prediction is is fairly fairly accurate 18

19 Stanford Motor Tests Formulated paraffin-based fuel SP-1: Melting temperature: 70 C Structural and optical additives Stanford lab-scale tests confirmed the prediction Low oxidizer mass flux (< 15 g/cm 2 -sec) Low chamber pressure (~150 psi) Small physical scale (i.e OD) 19

20 NASA Ames Hybrid Combustion Facility (HCF) Oxidizer: Gaseous oxygen up to 16 kg/sec 10 OD steel test section. 20 Cartridge loaded 7.5 OD grains up to 45 in length. 41 motor tests since September 2001.

21 Test Motor Configuration 21

22 Regression Rate Law for Paraffin-Base Fuel, SP-1a r & = Gox Three fold improvement is is confirmed 22

23 Effect of Chamber Pressure on the Regression Rate No No Pressure Effect 23

24 Effect of Fuel Grain Length on the Regression Rate No No Length Effect 24

25 Motor Test Experience Small Scale(i.e lbf): >1000 tests Scale-up (i.e lbf): >125 tests Oxidizers: GOX, LOX, N2O 25

Homework # cm. 11 cm cm. 100 cm. MAE Propulsion Systems, II

Homework # cm. 11 cm cm. 100 cm. MAE Propulsion Systems, II Homework #3.1 Nitrous Oxide HTPB Hybrid Rocket design Desired Thrust of 8 knt Operate near optimal mixture ratio (based on C*) Nozzle A/A * =16.4, exit diameter = 19.17 cm, Nozzle Exit Divergence angle