AS5020W: Propulsion II

Dr. Nagabhushana Rao Vadlamani

nrv@iitm.ac.in
 Course Content
Rocket Propulsion – Non-airbreathing propulsion

Rocket equation, Multi-staging

Performance of rockets (Thrust, specific impulse, characteristic velocity, Thrust

coefficient, etc)

Classification of chemical Rockets:

Liquid propellant (+ turbomachinery), Solid propellant, Hybrid rockets
Components of solid & liquid propellant rockets: Nozzles, Feed systems,
Injectors, Combustion chambers, Pumps, cooling strategies, etc.

Non-Chemical Rockets – Electrical, Nuclear, etc.

Thrust Chambers
(C* & CF)
 Chemical Rockets
Chemical Rockets - Propellant Energy achieved by Fuel + Oxidizer combination
Liquid propellant Rocket Solid propellant Rocket

Hybrid propellant
Rocket
Liquid (One propellant
fuel component is in Propellant grain
liquid & other in solid (premixed combination
Liquid of fuel & oxidiser)
phase)
Oxidiser
pumps
c.c
Engine

nozzle nozzle

Liquid fuel & liquid oxidiser pumped into Burning progresses from propellant surface
combustion chamber Burning rate = f(T, P, burning surface)
Exhaust gases expanded in Nozzle Propellant burns until the grain is consumed
(Combustion Start – stop – restart possible)
 Performance Characteristics
THRUST CHAMBER Assume working fluid to be perfect gas,
1 constant pressure combustion,
Propellant IN expansion in nozzle to be isentropic
C.C
QR = Heating value of propellant (kJ/kg)
2
In combustion chamber (C.C)
* (choked
Nozzle throat)
In Nozzle (Assuming adiabatic expansion)
e
Propellant OUT

For Higher ue
1) We want higher T02  fuel with Higher QR
2) Lower Molecular weight of propellant
3) Lower γ (ue is more sensitive to Molecular
weight than γ)
 Performance Characteristics
THRUST CHAMBER Propellant Mass flow rate:

1 Let A* be the throat area & assume flow to be choked at throat

Propellant IN
C.C
2

* (choked
Nozzle throat)

e
Propellant OUT

C* is the CHARACTERISTIC VELOCITY

(C* is a function of Combustion chamber & Propellant
Independent of nozzle characteristics)
Used to compare relative performance of different chemical
rocket propulsion system designs & Propellants
 Performance Characteristics
THRUST CHAMBER Thrust

Propellant IN 1
C.C
2

* (choked
Nozzle throat)

e
Propellant OUT

CF
CF is the THRUST COEFFICIENT
Function of Nozzle geometry (Ae/A*)
Lower Pe/P02 (Higher chamber pressures) & Lower γ
 Higher CF  Higher thrust
 Performance Characteristics
THRUST CHAMBER
Propellant IN 1

C.C Hence,
2
C* is the ability of the propellant to generate high pressure
Nozzle
* (choked (Talks only about propellant characteristics & Combustion chamber)
throat)
Isp = CFC*/ge is a composite index which describes expanding propellant
e
Propellant OUT i.e. Amplification of thrust due to gases expanding in supersonic nozzle

Note that these expressions of C* and CF

characterize performance of combustion
chamber and nozzle of a IDEAL rocket

Ratios w.r.t real rockets can be specified as:

ηc*= C*real/C*ideal ηF= CF,real/CF,ideal
Typical values ~ 0.92-0.99

Cf is also a convenient parameter to correct sea-level results for flight altitude conditions
 Nozzle design
– CF & Altitude variation
 Nozzle Design
Thrust coefficient, CF is a function of Nozzle geometry:

In this equation, area expansion ratio Ae/A* and pe/p02 can be

further related using mass continuity
P02 Pe Pa
⇒
A*
Ae
 Nozzle Design
Thrust coefficient, CF is a function of Nozzle geometry:

P02
Pe Pa
or Pc
A*
Chamber Ae
pressure For a given A*/Ae find Pe/P02
Use this Pe/P02 to find CF for different values of Pa/P02

γ =1.2
CF vs Throat area ratio Ae/A*
Pa = Pe From Rocket propulsion elements
(Bilbraz & Sutton)

Maximum CF achieved when Pa = Pe

This plot is useful to estimate CF & nozzle
performance variation with altitude
(even when Pa ≠ Pe)
 Nozzle Design
To summarize:
P02
Pe Pa Once Area ratio (Ae/A*) is fixed, Pe is fixed
or Pc
A* Pe = Pa is optimal expansion which maximizes thrust
Chamber Ae
pressure
But Pa (Ambient pressure) is changing with altitude

If Pe > Pa – Under expansion If Pe < Pa – Over expansion

(Thrust is lost) – Expansion (& (Thrust is lost due to shocks)
compression ) waves occur If Pe << Pa – Normal shock &
flow separation occurs in nozzle

Underexpanded & slightly overexpanded flow from Hill & Peterson

Unsymmetric flow separation in nozzle due to shocks – Major issue

Side thrust can develop and change the rocket’s trajectory !
 Nozzle Design
Note that Nozzle design so far is based on 1D flow &
P02 isentropic assumptions - Area ratio is the only parameter
Pe Pa
or Pc
A* But Actual nozzle has 3D features
Chamber Ae Actual thrust also depends on divergence
pressure
angle α of the CD nozzle

Consider CONICAL Nozzle Ideal thrust if exit

flow is entirely axial

For flow leaving at an angle(Assume average angle α/2)

α
r*
re
L

Divergence loss coefficient, λ quantifies the thrust lost due to divergence angle of the nozzle:
To minimize loss, smaller α is preferable, α ~ 15ο
But smaller α implies longer nozzles!
 Nozzle Design
To minimize divergence loss, Shaped Nozzles can be used
P02 (also called Bell / contour nozzles)
Pe Pa
or Pc Divergence angle α decreases from almost 40ο
A* from throat to 8ο at exit
Chamber Ae
pressure

Designed using Method of characteristics

Can be approximated as parabola

α
r*
re Bell vs cone nozzle
L From Rocket propulsion elements (Bilbraz & Sutton)
Considering boundary layer effects, it is beneficial to truncate the bell nozzle
(as the nozzle wall is nearly parallel to axis at exhaust end)

Length of shaped nozzle, Lshaped nozzle ~ 0.75-0.8 Lconical

 Nozzle Design
Performance of conical & shaped (Bell) nozzles is sensitive to altitude (back pressure variation)
Eg: Performance of a nozzle designed for sea-level (high Pa) drops at higher altitude (low Pa)
under-expanded (Pe>Pa) Typically nozzles are designed for intermediate pressures between
sea-level and high-altitude pressures
Hence, these operate over-expanded at sea-level
over-expanded (Pe<Pa)
and under-expanded at high altitudes
 Thrust is lost in this process

Alternate design strategies to minimize thrust loss:

TWO-STEP NOZZLES

Extendible Droppable Insert Dual Bell

(eject insert at high altitudes) (bump between 2 short bell nozzles)
 Nozzle Design
Performance of conical & shaped (Bell) nozzles is sensitive to altitude (back pressure variation)
Eg: Performance of a nozzle designed for sea-level (high Pa) drops at higher altitude (low Pa)

Alternate design strategies to minimize thrust loss:

ALTITUDE COMPENSATION NOZZLES Optimum performance can be
achieved at almost all altitudes
(with aerodynamic boundaries)
(Tests successful– Yet to be deployed)

Plug/Aerospike Nozzle
High altitude Sea level

Interface
boundary
Plug
From Rocket propulsion elements
No outer wall ! (hot-gas ambient air interface) (Bilbraz & Sutton)
Interface expands outward with altitude
Changes pressure distribution on central plug
 Nozzle Design
Performance of conical & shaped (Bell) nozzles is sensitive to altitude (back pressure variation)
Eg: Performance of a nozzle designed for sea-level (high Pa) drops at higher altitude (low Pa)

Alternate design strategies to minimize thrust loss:

ALTITUDE COMPENSATION NOZZLES Optimum performance can be
achieved at almost all altitudes
(with aerodynamic boundaries)
(Tests successful– Yet to be deployed)

Plug/Aerospike Nozzle – Truncated (Reduce length)

High altitude Sea level

Truncated Plug

Recirculation
No outer wall ! (hot-gas ambient air interface)
From Rocket propulsion elements
Interface expands outward with altitude
(Bilbraz & Sutton)
Changes pressure distribution on central plug
 Nozzle Design
Length of different Nozzle types

From Rocket propulsion elements

(Bilbraz & Sutton)

Boundary layer
(A* decreases)
A*
Ae
ε = Ae/A*
Boundary layer effect on Nozzle performance:
A/A* of nozzle changes due to blockage
Opposing force due to Viscous stresses
Shock-BL interaction & Losses
Chemical Propellants
 Propellants
Maximize Specific Impulse = f(Maximize Tc, Pc, Low Molecular weight, M
(or exhaust velocity ue ) and Specific heat ratio γ)

Liquid Rocket Propellants Solid Rocket Propellants

Monopropellants Double base (Homogeneous)

(Single substance + pre-heated Catalyst) Composite (Heterogeneous)
Composite modified Double base
Bipropellants
Nitramine propellants
Liquid fuel + Liquid Oxidizer

Further classification based on

Energy/Storability/Ignition

Internal energy of products < Internal energy of reactants

Heat release
If Heat of formation of products < Heat of formation of reactants
ΔHf, products < ΔHf, reactants
 Propellants
Liquid Rocket Propellants
Monopropellants (Single substance + pre-heated Catalyst)
Hydrazine - N2H4 decomposes to N2, Hydrogen Peroxide - H2O2
H2, NH3 when catalyzed on pre-heated decomposes to H2O, O2
Iridium or Alumina Al2O3 when catalyzed on Silver
Isp ~ 245 s Isp ~ 154 s

Bipropellants (Liquid fuel + Liquid Oxidizer)

Liquid Hydrogen LH2,

Hydrocarbons (HC): Hydrazine
Eg: RP1 (Rocket Propellant 1)(CH1.95) is
kerosene type HC, Methane (CH4)
MMH (Mono Methyl Hydrazine)
UDMH (Unsymmetrical DiMethyl Hydrazine) MMH

Unlike Hydrazine, MMH & UDMH are

soluble in hydrocarbons, more stable
than Hydrazine at higher temperatures UDMH
 Propellants
Liquid Rocket Propellants
Monopropellants (Single substance + pre-heated Catalyst)
Hydrazine - N2H4 decomposes to N2, Hydrogen Peroxide - H2O2
H2, NH3 when catalyzed on pre-heated decomposes to H2O, H2
Iridium or Alumina Al2O3 when catalyzed on Silver
Isp ~ 245 s Isp ~ 154 s

Bipropellants (Liquid fuel + Liquid Oxidizer)

Liquid Hydrogen LH2,

Hydrocarbons (HC):
Eg: RP1 (Rocket Propellant 1)(CH1.95) is
kerosene type HC, Methane (CH4)
Benzene Aniline
MMH (Mono Methyl Hydrazine)
UDMH (Unsymmetrical DiMethyl Hydrazine)
Aniline (C6H7N), Xylidine (C8H11N)

Xylidine
 Propellants
Liquid Rocket Propellants
Monopropellants (Single substance + pre-heated Catalyst)
Hydrazine - N2H4 decomposes to N2, Hydrogen Peroxide - H2O2
H2, NH3 when catalyzed on pre-heated decomposes to H2O, H2
Iridium or Alumina Al2O3 when catalyzed on Silver
Isp ~ 245 s Isp ~ 154 s

Bipropellants (Liquid fuel + Liquid Oxidizer)

Liquid Hydrogen LH2, Liquid oxygen LO2

Hydrocarbons (HC): Liquid Fluorine, Chlorine,
Eg: RP1 (Rocket Propellant 1)(CH1.95) is N2O4 (DiNitrogen Tetroxide)
kerosene type HC, Methane (CH4) HNO3 (Nitric Acid), IRFNA

MMH (Mono Methyl Hydrazine) HNO3 is corrosive –

UDMH (Unsymmetrical DiMethyl Hydrazine) Corrosion is inhibited by adding
Aniline (C6H7N), Xylidine (C8H11N) Hydrofluoric acid (HF)
Oxygen content is further enhanced by
high % NO2 which gives out red fumes
IRFNA – Inhibited Red Fuming Nitric Acid
Less % NO2  White fuming Nitric Acid (WFMA)
 Propellants
Liquid Rocket Propellants Bipropellants (Liquid fuel +Liquid Oxidizer)
Based on Energy Content (Format : Oxidizer/Fuel)

Isp (seconds) 200 300 400

Missiles RFNA/Aniline LOX/UDMH LOX/LH2

RFNA/Xylidine
N2O4/UDMH
Launch vehicles N2O4/MMH
N2O4/N2H4
LOX/RP
Based on Storability
Depending on application: Launch / Missile / Satellite control we have storage requirements:
Earth storable – Low energy propellants listed above don’t require any special storage conditions
Space storable – Requires low freezing point & High boiling point – Nitric Oxide NO decreases
freezing point of N2O4 – Mixed oxides of Nitrogen (MON)
Based on Ignition
Hypergolic: Readily auto-ignites without energy source
Eg:Amines –NH2 have strong reactivity with HNO3, N2O4, MON, etc)
Non-Hypergolic: Require ignition source for combustion
Eg: kerosene + LOX (semi-cryogenic) , LH2+LOX (cryogenic)
 Propellants
Maximize Specific Impulse = f(Maximize Tc, Pc, Low Molecular weight, M
(or exhaust velocity ue ) and Specific heat ratio γ)

Liquid Rocket Propellants Solid Rocket Propellants

Monopropellants Double base (Homogeneous)

(Single substance + pre-heated Catalyst) Composite (Heterogeneous)
Composite modified Double base
Bipropellants
Nitramine propellants
Liquid fuel + Liquid Oxidizer

Further classification based on

Energy/Storability/Ignition
 Propellants
Solid Rocket Propellants
Double base (Homogeneous) Propellant
Mix Nitroglycerine (NG) + Nitrocellulose (NC) at molecular level (homogenous mixture)

C3H8 C3H5(OH)3 C3H5(ONO2)3 Forms NG (This is both fuel + oxidizer rich)

Propane Glycerol
Replace OH
(C6H5O10)n radicals with (C6H5-xO10-x(ONO2)x)n Forms NC (This is fuel rich)
Cellulose ONO2
(paper)
Combine NG & NC – Forms Colloid
+ Plasticizer (to improve fluidity &
CORDITE prevent self ignition due to impact)
(commercial name) + Carbon black (improve opaqueness to
Isp ~ 200 s prevent radiation heating)
+ Metal powder (Aluminium) to achieve
higher performance
 Propellants
Solid Rocket Propellants
Composite (Heterogeneous) Propellants
Oxidizer crystals dispersed in a organic plastic like fuel binder

Disperse Ammonium Perchlorate AP (NH4ClO4) in Polymer fuel (heterogenous mixture)

AP is an Oxidizer Synthetic Rubber is used as binder

Non-hygroscopic & dissociates easily (to withstand severe thermal and
than other oxidisers like ammonium nitrate AN,
potassium perchlorate / nitrate KP,KN, etc
+ mechanical stresses)

Rubber is Polybutadiene
― (CH2 = CH – CH = CH2)n –
Generates HCl gas (non environment friendly)
Alternatives – Ammonium dinitramide (ADN) Terminate chain with OH
HO― (CH2 = CH – CH = CH2)n –OH
Hydroxyl terminated Polybutadiene (HTPB)
Add Metal powders (Al, Boron)
or metal hydrides to increase Alternatives: CTPB, PBAN, etc
hydrogen content and hence
enhance Energy Release !
(solid particles can form deposit in the exhaust)
 Propellants
Solid Rocket Propellants
Composite modified Double base
Double base propellant NO2
|
NG + NC Or Add HMX H2C ― N ― CH2
| |
(cyclo tetra methylene tetra NO2―N N―NO2
Add AP crystals nitramine [C4H8N4(NO2)4]) | |
H2C ― N ― CH2
|
NO2
Higher Isp than Double base propellants – Used for upper stages of solid propellant rockets
NO2
Nitramine propellants | RDX
N
HMX (Her Majesty’s explosive / High-velocity military explosive)
H2C CH2
cyclo tetra methylene tetra nitramine [C4H8N4(NO2)4]
RDX (Research Department explosive) NO2 ―N N―NO2
cyclo tri methylene tri nitramine [C3H6N3(NO2)3]
CH2
Add HMX or RDX to fuel Binder (HTPB) Fuel rich burn

lower temperature exhaust gas (binder acts like coolant)

& less Infra-red radiation
 Propellants
Maximize Specific Impulse = f(Maximize Tc, Pc, Low Molecular weight, M
(or exhaust velocity ue ) and Specific heat ratio γ)

Liquid Rocket Propellants Solid Rocket Propellants

Monopropellants Double base (Homogeneous)

(Single substance + pre-heated Catalyst) Composite (Heterogeneous)
Composite modified Double base
Bipropellants
Nitramine propellants
Liquid fuel + Liquid Oxidizer

Hybrid Propellant (Fuel & Oxidizer in different phases)

Liquid Oxidizer + Solid Fuel

(eg: LOX, HNO3, etc) (eg: Polymers like Polybutadiene based

LOX + LF can be mixed  FLOX PBAN/HTPB, etc)
eg: FLOX-10 has 90% LOX & 10% LF
Higher Isp – lower MW of Combustion products
 Propellants
Heat of formation, ΔHf0 of a substance - Change in enthalpy when 1 mole of the
substance is formed from its constituent elements under standard conditions (1 bar, 298K)
Heat of Combustion, ΔHC of a reaction [Fuel + oxidizer  Products]

Prefer products with large Usually prefer reactants with positive

negative values of ΔH0f or small negative values of ΔH0f
kerosene polymer NC
Al2O3 CO2 H2O CO HCl Hydrazine MMH HMX RDX
OH NO H O

Fuels
Products
NG AN AP HNO3
N2O4

From Rocket Propulsion(K Ramamurthi) Oxidizers

 Propellants
Heat of Combustion, ΔHC of a reaction [Fuel + oxidizer  Products]
Mixture Ratio, MR Gives least Mol.
Wt. of products
MR < Mrstoic Fuel Rich C12H24 + 16 O2 = 12 H2O + 8 CO2 + 4CO

MR = Mrstoic Stoichiometric Ratio C12H24 + 18 O2 = 12 CO2 + 12 H2O Gives highest T02

MR > Mrstoic Oxygen Rich C12H24 + 20 O2 = 12 CO2 + 12 H2O + 2O2

Chamber Temperature
Recall Isp = C*CF/ge where Molecular weight of
products of combustion

Specific Impulse Isp is maximum

for Marginally fuel Rich mixtures
(Tutorial problem:
Effect of Tc/MR on Isp)

N2H4 – O2 performance
(from Hill & Peterson)
Feeding the propellant
Liquid propellant Rockets
 Propellant feeding system (Liquid Propellant Rockets)
Crucial to meter the supply of Propellant to thrust chamber Monopropellant thruster
 Can vary C* and Isp by metering the supply of propellant
 Since Tc and MW of products can be changed Inert
Gas
 High Chamber pressure Pc is crucial to achieve high Isp
Bottle

Feed systems
Pressure
Monopropellant thruster Bipropellant Rockets regulator

Hydrazine
Tank

valve
Injector
Catalyst bed (Iridium/Al2O3)

Thrust
Typical chamber pressures ~1MPa Chamber
(Lower than bipropellant thrust chambers)
Propellant feeding system (Liquid Propellant Rockets)
Feed systems Regulated Mode
Monopropellant thruster Bipropellant Rockets High
pressure
Pressure feed system gas

Uses high pressure inert gas

to pressurize propellant Pressure
regulator

Regulated mode LF LOX

Blow down mode

Injector

Thrust
Chamber
 Propellant feeding system (Liquid Propellant Rockets)
Feed systems Blow down mode
Pressurized gas
Monopropellant thruster Bipropellant Rockets
in ullage volume

Pressure feed system

Uses high pressure inert gas
to pressurize propellant LF LF

LF LOX
Regulated mode

Blow down mode

Pros: Injector
Simple – Avoids turbomachinery
Cons:
Fuel and oxidant tanks should be designed to withstand Thrust
substantially higher pressures than combustion chamber Chamber

Tank Pressure drops with propellant supply

Used for smaller payload missions requiring low values of Δu & Isp
 Propellant feeding system (Liquid Propellant Rockets)
Feed systems

Monopropellant thruster Bipropellant Rockets

Pressure feed system Pump feed system – Uses pumping system to

Uses high pressure inert gas feed propellant
to pressurize propellant Gas-generator cycle

Staged Combustion cycle

Regulated mode
Expander cycle
Blow down mode

From Hill & Peterson

 Propellant feeding system (Liquid Propellant Rockets)

Bipropellant Rockets Gas

LF LOX
Pump feed system Generator

– Uses pumping system to feed propellant

Gas-generator cycle (Pcc ~ 6 MPa)
P T T P
Staged Combustion cycle

Expander cycle

To exhaust or
Auxiliary nozzle

Gas Generator Cycle

Relatively lower specific impulse

Additional weight due to gas-generator
 Propellant feeding system (Liquid Propellant Rockets)

Bipropellant Rockets Gas

LF LOX
Pump feed system Generator

– Uses pumping system to feed propellant

Gas-generator cycle
P T T P
Staged Combustion cycle (Pcc ~ 45 MPa)

Expander cycle
Exhaust into
main Combustion
chamber

Staged combustion/Topping Cycle

(since combustion takes place in stages)
Relatively higher specific impulse
Useful for waste heat recovery
Lower pressure drop a/c turbines than Gas-
generator cycle
 Propellant feeding system (Liquid Propellant Rockets)

Bipropellant Rockets
Pump feed system LF LOX
– Uses pumping system to feed propellant
Gas-generator cycle
P T T P
Staged Combustion cycle

Expander cycle (Pcc ~ 3 MPa)

Vapour from
regenerative
cooling

Expander Cycle
No Gas-generator
Fuel Vapour formed from regenerative cooling drives the turbine
Simple design + Light weight
Smaller pressure drop a/c turbines – Used for smaller rockets
 Propellant feeding system (Liquid Propellant Rockets)
Feed systems
Monopropellant thruster Bipropellant Rockets

Pressure feed system Pump feed system – Uses pumping system to

Uses high pressure inert gas feed propellant
to pressurize propellant Gas-generator cycle

Regulated mode Staged Combustion cycle

Blow down mode Expander cycle

Gas
Typically the turbopump systems use Centrifugal
LF LOX
Generator
compressor/pump & Axial flow turbine
Eg. Rocketdyne Mark 3 turbopump used in several
P T T P rockets uses Single centrifugal stage & 2-stage axial
flow turbine running at 5 times pump speed (using
gear-reduction unit)
To exhaust or
Auxiliary nozzle
 Propellant feeding system (Liquid Propellant Rockets)
Feed systems

Monopropellant thruster Bipropellant Rockets

Pressure feed system Pump feed system – Uses pumping system to

Uses high pressure inert gas feed propellant
to pressurize propellant Gas-generator cycle

Staged Combustion cycle

Regulated mode
Expander cycle
Blow down mode

Payload ratio vs Velocity increment for Gas-pressurization &

turbopump systems (from Hill & Peterson)
.
Propellant feeding system (Liquid Propellant Rockets)

Example – Estimation of power requirement from Pump

Consider a liquid propellant rocket having a chamber LF
Gas
Generator
LOX

pressure of 10 MPa, generating a thrust of 600 kN with a

specific impulse of 300 s P T T P

Assuming that the Liquid fuel and oxidiser are stored at

0.2MPa, and the supply pressure to combustion chamber to P =10 Mpa
c
be 10% higher than the chamber pressure, estimate the To exhaust or
ρ = 1000 kg/m3
Auxiliary nozzle

power requirement of pump.

T = 600 kN
Take mean density of propellants to be 1000 kg/m3. Isp = 300 s

Ans: ~ 2.2 MW of power from pump

Hence, Turbo-pump system must be used and electric motor/generator is inefficient

 TA session
A high pressure pump-fed liquid propellant rocket based on the gas generator cycle has a vacuum
thrust of 735 kN and a burn duration of 180 secs. The propellants used are N2O4 and UDMH. The
specific impulse is 295 s. The mixture ratio is R = 1.87.
The pressure in the thrust chamber of the rocket is 6 MPa and the propellant supply pressure to the
chamber is 7 MPa.
N2O4 is stored in the propellant tank at a pressure of 0.4 MPa and UDMH is stored at 0.32 MPa.
The density of N2O4 and UDMH are 1400 kg/m3 and 790 kg/m3 respectively at the temperatures
used in the rocket.
Determine:
(a.) Power required to drive N2O4 and UDMH pump.
(b.) If the efficiency of the pump is 60% and the turbine efficiency is 80%, determine the mass flow
rate through the turbine. The gas generator pressure and temperature can be assumed to be 3.5 MPa
and 670 K respectively. The exit pressure of the turbine can be taken as 0.18 MPa.

Assume the molecular mass of the combustion products from the gas generator to be 20.19
kg/kmol, the specific heat of the gas at constant pressure as 1.9 kJ/kg K and the specific heat ratio
of the gases as 1.264.

Ans: UDMH pump 0.735 MW, N2O4 pump 0.765 MW,

Mass flow through turbine = 5.21 kg/s
Combustion Chambers
Of Liquid propellant Rockets
Injectors
Combustion chamber dimensions
 Injectors
Efficient combustion of liquid propellants requires efficient
Injection, Atomization, Mixing before combustion
INJECTORS
Pressure Atomizing
Impinging type (doublet/triplet, etc)
Fuel & oxidizer supplied at high pressure
Types: Shower head / Impinging type/ Swirl

Shower head L/D & sharpness of orifice control discharge

coefficient and hence mass flow rate
Swirl type
Mass ratio of
propellants supplied
nox C d ,ox Aox p ox  ox
MR 
n f C d , f A f p f  f

Cdox/Cdf must be constant over range of Reynolds numbers

From Rocket propulsion (Ramamurthi) & Rocket propulsion elements (Sutton)
 Injectors
Efficient combustion of liquid propellants requires efficient
Injection, Atomization, Mixing before combustion
INJECTORS
Pressure Atomizing Gas-assisted Atomizing
Fuel & oxidizer supplied at high pressure
Low boiling point fuel reach injector in
Types: Shower head / Impinging type/ Swirl gaseous phase
Gas
shear At high velocities (200-300 m/s), the
coaxial gas jet shears the liquid jet (20-
Liquid Jet
30 m/s) promoting atomization

Additional swirl can also be provided to

Shear co-axial injector element liquid oxidizer to assist atomization (Gas
G H2
assisted Swirl-coaxial atomizers)
GH 2

LOx
LOx https://www.youtube.com/watch?v=aa4ATJGRqA0

Flare & step in orifice

From Rocket propulsion (Ramamurthi)
 Combustion Chamber
Combustion chamber Length - It is desirable to be shorter

However, sufficient length must be provided for:

Injection Mixing Vaporization Chemical Reaction
(Atomization)
Of these, vaporization of liquid drops is the slowest
L D2 = D02 - βt
D0 : Initial diameter D0
A* Volume V β : Evaporation constant
β : Increases with increase in the droplet Temperature
Higher for drops with lower molecular mass
(generally due to their higher volatility)
tevap = D02/β Smaller drop sizes & better atomization helps!
 Combustion Chamber
Combustion chamber Length - It is desirable to be shorter

However, sufficient length must be provided for:

Injection Mixing Vaporization Chemical Reaction
Ac (Atomization)
Of these, vaporization of liquid drops is the slowest
L D2 = D02 - βt
D0 : Initial diameter D0
A* Volume V β : Evaporation constant
tevap = D02/β Smaller drop sizes & better atomization helps!
Complete vaporization and Homogeneous MR are preferable
Incomplete vaporization reduces Distribution of Mixture ratio
C* since mixture ratio MRvap is (MR) is also non-uniform
different from MRinjection across combustion chamber
 Combustion Chamber
Combustion chamber Length - It is desirable to be shorter

However, sufficient length must be provided for:

Injection Mixing Vaporization Chemical Reaction
Ac (Atomization)
Of these, vaporization of liquid drops is the slowest
L D2 = D02 - βt
Characteristic Length of C.C, L* = V/A*
A* Volume V Typical L* of liquid propellant rockets ~ 0.8 – 1.2 m
Typical chamber cross-sectional area Ac/A* ~ 3
Average residence time of fluid element in C.C, Δt :

For L = 1m, Ac/A* = 3,

T0 = 2500 K, γ = 1.2, R = 300 J/kg K
Δt ~ 8.6 ms
Combustion Chambers
Of Solid propellant Rockets
Burn rate
 Combustion Chamber

Grain nozzle
NG C3H5(NO3)3 NO2
Ald NO – CO CO2, H2O,
NC [C6H10-xO5-x.xNO3]n
ehy NO – NH2 N2, CO, H2
+ Additives
des
NG C3H5(NO3)3 NO2
Ald NO – CO CO2, H2O,
NC [C6H10-xO5-x.xNO3]n
NO – NH2 N2, CO, H2
+ Additives
ehy
des
Aldehydes : - CHO
Foam Fizz Dark Secondary
Zone Zone Zone Luminous Zone

Foam Fizz Dark Secondary

Zone Zone Zone Luminous Zone

Tf

T1
Tf

T Extent of these zones is typically few mm

Ts
(Depends on chamber pressure)
Ti T1

Distance
Ts
Ti
Typical burning mechanism of double base propellant
From Rocket Propulsion(K Ramamurthi)
 Combustion Chamber

Grain nozzle Vielle’s law or

Saint Robert’s law

Surface recession rate or Burning rate of propellant grain: r = a P0n

P0 – combustion chamber pressure
a , n – Empirical constants determined by fitting experimental data
a = f(initial temperature, propellant characteristic)
Burning rate r (cm/s)

n – Pressure exponent (brings out pressure effects

which are dependent on combustion process)

Log-scale

Pressure (atm)
Burning rate of RDX + PolyUrethane binder
composite propellant (from Hill & Peterson)
 Combustion Chamber

Grain nozzle Vielle’s law or

Saint Robert’s law

Surface recession rate or Burning rate of propellant grain: r = a P0n

P0 – combustion chamber pressure
a , n – Empirical constants determined by fitting experimental data

Plateau burning Mesa burning

propellant propellant
ln (r)

n can be varied by modifying chemical reaction in

fizz zone by adding lead compounds

ln (P0)

Burning can be inhibited in specific directions

using Inhibitors:
Eg: Butyl rubber, EthylenePropeleyene Diene
(EPDM), etc.
Inhibitor
 Combustion Chamber

Grain nozzle Vielle’s law or

Saint Robert’s law

Surface recession rate or Burning rate of propellant grain: r = a P0n

P0 – combustion chamber pressure
a , n – Empirical constants determined by fitting experimental data
n – Burning rate exponent (or pressure exponent / combustion index)

Alternate way of expressing the burn rate law:

r = a (P0/P0,ref )n P0,ref is reference pressure

Typical reference pressure is 7 MPa ( ~ 70 atm)

Corresponding value of constant a at 7 Mpa ( ~ 70 atm) is represented as a70

Burning law at any pressure based on a70 can be written as:

r = a70 (P0/70 )n
 Combustion Chamber

Grain nozzle

Combustion Chamber pressure & Burning stability

A*
Rate at which mass is generated from
propellant surface

Rate at which hot gases leave the

Surface area nozzle
Sb m 2
Rate of mass accumulation in combustion chamber:

ρp : Propellant density
Sb: Propellant burning surface area
r : Burning rate = aP0n
 Combustion Chamber

Grain nozzle

Combustion Chamber pressure & Burning stability

A*
Rate at which mass is generated from
propellant surface

Rate at which hot gases leave the

Surface area nozzle
Sb m 2
Rate of mass accumulation in combustion chamber:

ρ0 : Instantaneous STATIC gas density

V0: Instantaneous volume

𝑟𝑆𝑏 = 𝑎𝑃0𝑛 𝑆𝑏
 Combustion Chamber

Grain nozzle

Combustion Chamber pressure & Burning stability

A*
Rate at which mass is generated from
propellant surface

Rate at which hot gases leave the

Surface area nozzle
Sb m 2
Rate of mass accumulation in combustion chamber:

=0 (Constant pressure combustion, Equilibrium Pressure

P= constant & T is almost constant)
 Combustion Chamber

Grain nozzle

Combustion Chamber pressure & Burning stability

A*
Rate at which mass is generated from
propellant surface

Rate at which hot gases leave the

Surface area
nozzle
Sb m2
1
𝑆𝑏 1−𝑛
𝑃0 = 𝑎𝐶 ∗ 𝜌𝑝
𝐴∗

Note that ρ0 << ρp (Same expression can be

O(1 kg/m3) << O(103 kg/m3) obtained if dm/dtaccumulation is
equated to zero in the derivation)
 Combustion Chamber
Equilibrium pressure
Flame spread

Electric or
pyrogen igniter Local ignition area

Chamber pressure (or thrust) variation with time From Rocket propulsion (K.Ramamurthi)

OA - Ignition delay time

Local Pressure
AB - Ignition rise time peak (or spike)
(Local ignition, Flame spread) P B’
C
BB’ - Chamber filling
0.75Pmax
Pressure / Thrust
B
P – Local pressure spike
(spurt due to increased
burn rate of propellant) Tail off
period
CD – Tail off period
A 0.1P 0.1Pmax
AD – Action time max D
AC – Burning time O
Time
 Combustion Chamber
Equilibrium pressure Thrust

Both Chamber pressure & Thrust depend on Sb i.e. Burning surface area
Sb can be changed by varying propellant grain configuration

a. Neutral
a. Neutral
Neutral burning (constant Sb)

Pressure / Thrust
a. Neutral
inhibited
inhibited
inhibited

b. Progressive
Progressive burning (increasing Sb)
b. Progressive
inhibited
b. Progressive

inhibited
inhibited
Time

c. Regressive(decreasing S )
Regressive burning b
c. Regressive
 Combustion Chamber
Alternate grain configurations
(See Hill & Peterson, K. Ramamurthi, Bilbraz & Sutton for additional details)

Varying star angle can give different thrust

variation – neutral/progressive/regressive

Rocket motor case

Insulation at
edge of grain
Inhibitor
(Prevents axial
burning)

Wagon wheel grain

From Rocket propulsion by K. Ramamurthi

Estimate surface area variation with time to estimate the pressure variation
Ensure that the configuration is strong enough – Avoid propellant grain cracks due
to thermal stresses during burning process
 Combustion Chamber
Combustion Chamber pressure & Burning stability A*

Surface area
Sb m2
Burning rate exponent n determines burning stability
For what values of n (> 1 or < 1) is combustion stable?

Nozzle flow rate

Rate at which hot 𝑚ሶ
gases leave the nozzle

= ∝ 𝑃0
n<1 Operating point
n>1

Rate at which mass is generated Gas generation rate

from propellant surface

= ∝ 𝑃0𝑛
𝑃0
 Combustion Chamber
Combustion Chamber pressure & Burning stability A*

Surface area
Burning rate exponent n determines burning stability Sb m2
For what values of n (> 1 or < 1) is combustion stable?
At operating point =

Consider marginal decrease of

pressure from equilibrium pressure, Peq

For n > 1 >

Gas generation < nozzle flow rate Operating point
 Pressure further departs from Peq (UNSTABLE)

For n < 1 <

Gas generation > nozzle flow rate
 Pressure increases & returns to Peq (STABLE)
Typical values: 0.4 < n < 0.7 Equilibrium pressure 𝑃0
Peq
 Combustion Chamber
A*
Combustion Chamber pressure & Burning stability

Surface area
Sb m2

Burning rate also depends on initial temperature of the

propellant grain (Dependence on a)

As n  1, Pressure becomes much

more sensitive to a which is a
function of initial temperature

Higher initial temperature of the

propellant grain  lower burning
time
Typical variation of chamber pressure for
different initial grain temperatures
From Rocket propulsion elements (Bilbraz & Sutton)
 Combustion Chamber

Burning rate can be enhanced by high

velocity flow of combustion gases over
propellant surface – Erosive burning

Turbulent mixing and convective heat

transfer enhances the initial burning rates

Reduction of flow and thrust at the end

of burning

Web thickness

Left over propellant

is called sliver
Erosive burning
From Rocket propulsion elements (Bilbraz & Sutton)

Erosive burning causes early burnout of the web & exposes insulation sooner