propulsion systems design - university of maryland · propulsion systems design • rocket engine...

55
Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design U N I V E R S I T Y O F MARYLAND Propulsion Systems Design Rocket engine basics Survey of the technologies Propellant feed systems Propulsion systems design 1 © 2016 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu

Upload: others

Post on 24-May-2020

9 views

Category:

Documents


2 download

TRANSCRIPT

Page 1: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Propulsion Systems Design• Rocket engine basics • Survey of the technologies • Propellant feed systems • Propulsion systems design

1

© 2016 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu

Page 2: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Liquid Rocket Engine Cutaway

2

Page 3: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Thermal Rocket Exhaust Velocity• Exhaust velocity is !

!

!

where

Ve =2γγ −1

ℜT0M

1− pe

p0

%

& ' '

(

) * *

γ −1γ

+

,

- - -

.

/

0 0 0

M ≡ average molecular weight of exhaust

ℜ ≡ universal gas const .= 8314.3 Joulesmole°K

γ ≡ ratio of specific heats ≈1.2

3

Page 4: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Ideal Thermal Rocket Exhaust Velocity• Ideal exhaust velocity is !

!• This corresponds to an ideally expanded nozzle • All thermal energy converted to kinetic energy

of exhaust • Only a function of temperature and molecular

weight!

Ve =2γγ −1

ℜT0M

4

Page 5: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Thermal Rocket Performance• Thrust is !

• Effective exhaust velocity !!

• Expansion ratio

T = ˙ m Ve + pe − pamb( )Ae

T = ˙ m c ⇒ c = Ve + pe − pamb( ) Ae

˙ m

AtAe

=γ +12

#

$ %

&

' (

1γ −1 pe

p0

#

$ % %

&

' ( (

1γ γ +1

γ −11−

pep0

#

$ % %

&

' ( (

γ −1γ

*

+

, , ,

-

.

/ / /

Isp =cg0

"

# $ $

%

& ' '

5

Page 6: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

A Word About Specific Impulse• Defined as “thrust/propellant used”

– English units: lbs thrust/(lbs prop/sec)=sec – Metric units: N thrust/(kg prop/sec)=m/sec

• Two ways to regard discrepancy - – “lbs” is not mass in English units - should be slugs – Isp = “thrust/weight flow rate of propellant”

• If the real intent of specific impulse is

Isp =T

mand T = mVe then Isp = Ve!!!

6

Page 7: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Nozzle Design

• Pressure ratio p0/pe=100 (1470 psi-->14.7 psi)Ae/At=11.9

• Pressure ratio p0/pe=1000 (1470 psi-->1.47 psi)Ae/At=71.6

• Difference between sea level and ideal vacuum Ve

!!!

• Isp,vacuum=455 sec --> Isp,sl=333 sec

VeVe,ideal

= 1− pep0

#

$ % %

&

' ( (

γ −1γ

7

Page 8: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Solid Rocket Motor

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

8

Page 9: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Solid Propellant Combustion Characteristics

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

9

Page 10: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Solid Grain Configurations

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

10

Page 11: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Short-Grain Solid Configurations

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

11

Page 12: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Gemini Retrograde Engine

12

Page 13: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Advanced Grain Configurations

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

13

Page 14: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Liquid Rocket Engine

14

Page 15: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Liquid Propellant Feed Systems

15

Page 16: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Space Shuttle OMS Engine

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

16

Page 17: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Turbopump Fed Liquid Rocket Engine

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

17

Page 18: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Sample Pump-fed Engine Cycles

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

18

Page 19: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Gas Generator Engine Schematic

19

Page 20: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

SpaceX Merlin 1d Engines

20

Page 21: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Falcon 9 Octoweb Engine Mount

21

Page 22: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Staged-Combustion Engine Schematic

22

Page 23: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

RD-180 Engine(s) (Atlas V)

23

Page 24: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

SSME Powerhead Configuration

24

Page 25: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

SSME Engine Cycle

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

25

Page 26: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Liquid Rocket Engine Cutaway

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

26

Page 27: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

H-1 Engine Injector Plate

27

Page 28: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Injector Concepts

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

28

Page 29: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

TR-201 Engine (LM Descent/Delta)

29

Page 30: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Solid Rocket Nozzle (Heat-Sink)

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

30

Page 31: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Ablative Nozzle Schematic

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

31

Page 32: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Active Chamber Cooling Schematic

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

32

Page 33: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Boundary Layer Cooling Approaches

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

33

Page 34: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Hybrid Rocket Schematic

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

34

Page 35: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Hybrid Rocket Combustion

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

35

Page 36: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Thrust Vector Control Approaches

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

36

Page 37: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Gemini Entry Reaction Control System

37

Page 38: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Apollo Reaction Control System Thrusters

38

Page 39: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

RCS Quad

39

Page 40: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Apollo CSM RCS Assembly

40

Page 41: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Lunar Module Reaction Control System

41

Page 42: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

LM RCS Quad

42

Page 43: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Viking Aeroshell RCS Thruster

43

Page 44: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Viking RCS Thruster Schematic

44

Page 45: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Space Shuttle Primary RCS Engine

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

45

Page 46: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Monopropellant Engine Design

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

46

Page 47: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Cold-gas Propellant Performance

From G. P. Sutton, Rocket Propulsion Elements (5th ed.) John Wiley and Sons, 1986

47

Page 48: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Total Impulse• Total impulse It is the total thrust-time product for

the propulsion system, with units <N-sec> !

!

!

!

• To assess cold-gas systems, we can examine total impulse per unit volume of propellant storage

48

It = Tt = mvet

t =⇢V

m

It = ⇢V ve

ItV

= ⇢ve

Page 49: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Performance of Cold-Gas Systems

49

Page 50: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Self-Pressurizing Propellants (CO2)

50

Page 51: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Self-Pressurizing Propellants (N2O)

51

Density!1300 kg/m3

Density!625 kg/m3

Page 52: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

N2O Performance Augmentation

52

• Nominal cold-gas exhaust velocity ~600 m/sec • N2O dissociates in the presence of a heated catalyst

engine temperature ~1300°Cexhaust velocity ~1800 m/sec

• NOFB (Nitrous Oxide Fuel Blend) - store premixed N2O/hydrocarbon mixtureexhaust velocity >3000 m/sec

2N2O �! 2N2 +O2

Page 53: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Pressurization System Analysis

Pg0, Vg

PL, VL

Pgf, Vg

PL, VL

Adiabatic Expansion of Pressurizing Gas

Initial Final

pg,0Vgγ = pg, fVg

γ + plVlγ

Known quantities:

Pg,0=Initial gas pressure

Pg,f=Final gas pressure

PL=Operating pressure of propellant tank(s)

VL=Volume of propellant tank(s)

Solve for gas volume Vg

!53

Page 54: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Boost Module Propellant Tanks• Gross mass 23,000 kg

– Inert mass 2300 kg – Propellant mass 20,700 kg – Mixture ratio N2O4/A50 = 1.8 (by mass)

• N2O4 tank – Mass = 13,310 kg – Density = 1450 kg/m3

– Volume = 9.177 m3 --> rsphere=1.299 m • Aerozine 50 tank

– Mass = 7390 kg – Density = 900 kg/m3

– Volume = 8.214 m3 --> rsphere=1.252 m54

Page 55: Propulsion Systems Design - University Of Maryland · Propulsion Systems Design • Rocket engine basics • Survey of the technologies • Propellant feed systems ... From G. P

Rocket Propulsion ENAE 791 - Launch and Entry Vehicle Design

U N I V E R S I T Y O FMARYLAND

Boost Module Main Propulsion• Total propellant volume VL = 17.39 m3

• Assume engine pressure p0 = 250 psi • Tank pressure pL = 1.25*p0 = 312 psi • Final GHe pressure pg,f = 75 psi + pL = 388 psi • Initial GHe pressure pg,0 = 4500 psi • Conversion factor 1 psi = 6892 Pa • Ratio of specific heats for He = 1.67 !

• Vg = 3.713 m3 • Ideal gas: T=300°K --> ρ=49.7 kg/m3 (4500 psi = 31.04 MPa) MHe=185.1 kg

4500 psi( )Vg1.67 = 388 psi( )Vg

1.67 + 312 psi( ) 17.39 m 3( )1.67

ρHe =pg,0M ℜT0

55