15/01/10Sapienza Activity in ISP-1 Program Pagina 1

PROPULSIONE SPAZIALE

Chemical Rocket Propellant PerformanceAnalysis

REAL NOZZLES

Compared to an ideal nozzle, the real nozzle has energy losses and energy that is unavailablefor conversion into kinetic energy of the exhaust gas. The principal losses are:

1. The divergence of the flow in the nozzle exit sections causes a loss. The losses can bereduced for bell-shaped nozzle contours

2. Small chamber or port area cross sections relative to the throat area or low nozzlecontraction ratios A1/At cause pressure losses in the chamber and reduce the thrust andexhaust velocity slightly

3. Lower flow velocity in the boundary layer or wall friction can reduce the effectiveexhaust velocity by 0.5 to 1.5%

4. Solid particles or liquid droplets in the gas can cause losses up to 5%

5. Unsteady combustion and oscillating flow can account for a small loss

6. Chemical reactions in nozzle flow change gas properties and gas temperatures, givingtypically a 0.5% loss

7. There is lower performance during transient pressure operation, for example during start,stop, or pulsing

8. For uncooled nozzle materials, such as fiber reinforced plastics or carbon, the gradualerosion of the throat region increases the throat diameter during operation. In turn thiswill reduce the chamber pressure and thrust and cause a reduction in specific impulse

9. Non-uniform gas composition can reduce performance (due to incomplete mixing,turbulence, or incomplete combustion regions)

Chemical Rocket Propellant Performance Analysis

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REAL NOZZLES

Calculated Losses in the Space Shuttle Booster RSRM Nozzle

Chemical Rocket Propellant Performance Analysis

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ENERGY LOSSESTwo types of energy conversion processes occur in any propulsion system: the generation of

energy (conversion of stored energy into available energy) and, subsequently, the conversion

into kinetic energy, which is the form of energy useful for propulsion

Typical energy losses for a chemical rocket

• The combustion efficiency for chemical rockets is a measure of the source efficiency forcreating energy. Its value is typically high (approximately 94 to 99%)

• A large portion of the energy of the exhaust gases is unavailable for conversion intokinetic energy and leaves the nozzle as residual enthalpy

Chemical Rocket Propellant Performance Analysis

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ENERGY LOSSESTwo types of energy conversion processes occur in any propulsion system: the generation of

energy (conversion of stored energy into available energy) and, subsequently, the conversion

into kinetic energy, which is the form of energy useful for propulsion

Propulsive efficiency at varying velocities

• The propulsive efficiency determines how much of the kinetic energy of the exhaust jet isuseful for propelling the vehicle. The propulsive efficiency is a maximum when theforward vehicle velocity is exactly equal to the exhaust velocity (residual kinetic energy ofthe jet is zero)

Chemical Rocket Propellant Performance Analysis

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CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 2.3 for frozenequilibrium and 2.5 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value(> 3.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

• Much of the carbon isburned to CO2 and almostall of the hydrogen to H2O

Performance of LOX/RP-1 as a function of O/F

Chemical Rocket Propellant Performance Analysis

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CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 2.3 for frozenequilibrium and 2.5 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value(> 3.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

• Much of the carbon isburned to CO2 and almostall of the hydrogen to H2O

O/F

ch

ara

cte

ris

tic

ve

loc

ity

, m

/s

sp

ec

ific

im

pu

lse

, s

Ch

am

be

r te

mp

era

ture

, K

1 2 3 4 5 6 7 8 9 101000

1200

1400

1600

1800

2000

2200

2400

2600

2800

250

275

300

325

350

375

400

425

450

475

500

500

1000

1500

2000

2500

3000

3500

4000

characteristic velocityspecific impulse (vacuum)Chamber temperature

stoichiometriccondition (max. T

f)

max. Ispvac

max. c*

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel RP­1(L)Oxidizer O

2(L)

Performance of LOX/RP-1 as a function of O/F (assuming shifting

equilibrium during the entire expansion)

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 2.3 for frozenequilibrium and 2.5 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value(> 3.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

• Much of the carbon isburned to CO2 and almostall of the hydrogen to H2O

O/F

ch

ara

cte

ris

tic

ve

loc

ity

, m

/s

sp

ec

ific

im

pu

lse

, s

Ch

am

be

r te

mp

era

ture

, K

1 2 3 4 5 6 7 8 9 101000

1200

1400

1600

1800

2000

2200

2400

2600

2800

250

275

300

325

350

375

400

425

450

475

500

500

1000

1500

2000

2500

3000

3500

4000

characteristic velocityspecific impulse (vacuum)Chamber temperature

stoichiometriccondition (max. T

f)

max. Ispvac

max. c*

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel RP­1(L)Oxidizer O

2(L)

Performance of LOX/RP-1 as a function of O/F (shifting equilibrium and

frozen expansion)

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

4 / 8

CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 2.3 for frozenequilibrium and 2.5 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value(> 3.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

• Much of the carbon isburned to CO2 and almostall of the hydrogen to H2O

O/F

ch

ara

cte

ris

tic

ve

loc

ity

, m

/s

sp

ec

ific

im

pu

lse

, s

Ch

am

be

r te

mp

era

ture

, K

1 2 3 4 5 6 7 8 9 101000

1200

1400

1600

1800

2000

2200

2400

2600

2800

250

275

300

325

350

375

400

425

450

475

500

500

1000

1500

2000

2500

3000

3500

4000

characteristic velocityspecific impulse (vacuum)Chamber temperature

stoichiometriccondition (max. T

f)

max. Ispvac

max. c*

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel RP­1(L)Oxidizer O

2(L)

Performance of LOX/RP-1 as a function of O/F (shifting equilibrium,

frozen expansion, and Bray’s throat freezing point)

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 3.8 for frozenequilibrium and 4.6 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value (8.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

O/F

ch

ara

cte

ris

tic

ve

loc

ity

, m

/s

sp

ec

ific

im

pu

lse

, s

Ch

am

be

r te

mp

era

ture

, K

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 161000

1200

1400

1600

1800

2000

2200

2400

2600

2800

250

275

300

325

350

375

400

425

450

475

500

500

1000

1500

2000

2500

3000

3500

4000characteristic velocityspecific impulse (vacuum)Chamber temperature

stoichiometriccondition (max. T

f)

max. Ispvac

max. c*

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Performance of LOX/LH2 as a function of O/F (assuming shifting

equilibrium during the entire expansion)

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 3.8 for frozenequilibrium and 4.6 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value (8.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

O/F

ch

ara

cte

ris

tic

ve

loc

ity

, m

/s

sp

ec

ific

im

pu

lse

, s

Ch

am

be

r te

mp

era

ture

, K

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 161000

1200

1400

1600

1800

2000

2200

2400

2600

2800

250

275

300

325

350

375

400

425

450

475

500

500

1000

1500

2000

2500

3000

3500

4000characteristic velocityspecific impulse (vacuum)Chamber temperature

stoichiometriccondition (max. T

f)

max. Ispvac

max. c*

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Performance of LOX/LH2 as a function of O/F (shifting equilibrium and

frozen expansion)

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

5 / 8

CHEMICAL ROCKET PROPELLANT PERFORMANCE ANALYSIS

• For maximum specificimpulse, the optimum O/Fis ≈ 3.8 for frozenequilibrium and 4.6 forshifting equilibrium

• The maximum values of c∗

are at slightly different O/F

• The optimum O/F is notthe one for highesttemperature, which isusually close to thestoichiometric value (8.0)

• The temperature and themolecular weight at thenozzle exit increase forshifting equilibrium due torecombination reactions

O/F

ch

ara

cte

ris

tic

ve

loc

ity

, m

/s

sp

ec

ific

im

pu

lse

, s

Ch

am

be

r te

mp

era

ture

, K

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 161000

1200

1400

1600

1800

2000

2200

2400

2600

2800

250

275

300

325

350

375

400

425

450

475

500

500

1000

1500

2000

2500

3000

3500

4000characteristic velocityspecific impulse (vacuum)Chamber temperature

stoichiometriccondition (max. T

f)

max. Ispvac

max. c*

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Performance of LOX/LH2 as a function of O/F (shifting equilibrium,

frozen expansion, and Bray’s throat freezing point)

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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FROZEN VS SHIFTING EQUILIBRIUM GAS COMPOSITION

Combustion chamber Nozzle exit

• Dissociation of molecules requires considerable energy and causes a decrease in thecombustion temperature, which in turn can reduce the specific impulse

• Atoms or radicals such as O or H and OH are formed. As the gases are cooled in theexpansion, the dissociated species recombine (shifting equilibrium) and release heat intothe flowing gases. Only a small percentage of dissociated species persists at the nozzle exit

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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FROZEN VS SHIFTING EQUILIBRIUM GAS COMPOSITION

O/F

Co

mp

os

itio

n, m

as

s f

rac

tio

n

2 3 4 5 6 7 8 9 10 11 12 13 14 15 160.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0 H2

O2

H2O

H

O

OH

solid lines = chamber compositiondash­dotted lines = exit composition

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Mass fraction

O/F

Co

mp

os

itio

n, m

ole

fra

cti

on

2 3 4 5 6 7 8 9 10 11 12 13 14 15 160.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

H2

O2

H2O

H

O

OH

solid lines = chamber compositiondash­dotted lines = exit composition

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Mole fraction

• Dissociation of molecules requires considerable energy and causes a decrease in thecombustion temperature, which in turn can reduce the specific impulse

• Atoms or radicals such as O or H and OH are formed. As the gases are cooled in theexpansion, the dissociated species recombine (shifting equilibrium) and release heat intothe flowing gases. Only a small percentage of dissociated species persists at the nozzle exit

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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FROZEN VS SHIFTING EQUILIBRIUM GAS COMPOSITION

O/F

Mo

lec

ula

r m

as

s, k

g/k

mo

le

Ex

it t

em

pe

ratu

re, K

2 3 4 5 6 7 8 9 10 11 12 13 14 15 163

6

9

12

15

18

21

24

250

500

750

1000

1250

1500

1750

2000

2250

2500Molecular mass (chamber)

Molecular mass (exit)

Exit temperature

stoichiometriccondition (max. T

f)

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Shifting equilibrium

O/F

Mo

lec

ula

r m

as

s, k

g/k

mo

le

Ex

it t

em

pe

ratu

re, K

2 3 4 5 6 7 8 9 10 11 12 13 14 15 163

6

9

12

15

18

21

24

250

500

750

1000

1250

1500

1750

2000

2250

2500Molecular mass (chamber)

Molecular mass (exit)

Exit temperature

stoichiometriccondition (max. T

f)

nozzle expansion ratio 40Pressure 1000 psi (69 bar)Fuel H

2(L)

Oxidizer O2(L)

Frozen

• Dissociation of molecules requires considerable energy and causes a decrease in thecombustion temperature, which in turn can reduce the specific impulse

• Atoms or radicals such as O or H and OH are formed. As the gases are cooled in theexpansion, the dissociated species recombine (shifting equilibrium) and release heat intothe flowing gases. Only a small percentage of dissociated species persists at the nozzle exit

Chemical Rocket Propellant Performance Analysis

PROPULSIONE SPAZIALEDaniele Bianchi

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