NOZZLE THEORY

Lecture 1

Theory of flow in isentropic nozzles, Convergent nozzle chocking, Nozzle

efficiency, nozzle losses, over and under expanded nozzles, interaction of
nozzle flow with adjacent surfaces, Thrust reversal. Tutorials
 Introduction to Propulsion
Latin words ‘Pro’ (before/forward) + ‘Pellere’ (to drive)
Propulsion → to push or drive an object forward
The forward force is Thrust, generated through some application of Newton’s III law
Jet propulsion classification:
• Air breathing propulsion
Sir Frank Whittle (England 1980) & Dr. Hans Von Ohain (Germany 1936)
• Rocket Propulsion

Air breathing engine

Rocket engine 2
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• The "heart" of a gas turbine engine is the gas generator.
• The compressor, combustor, and turbine are the major components of the gas generator which is common to the
turbojet, turbofan, turboprop, and turboshaft engines.
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• The purpose of a gas generator is to supply high-temperature and high-pressure gas.
• Rockets can be used to propel vehicles beyond earth’s atmosphere
• Converts chemical energy to heat by burning the propellants
• The high energy burnt gases are expanded through a nozzle, whose momentum creates the reaction
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force or thrust for propulsion.
Classification of Rockets

Liquid rocket engine -- Rocket Engine

Solid rocket engine -- Rocket Motor

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 NOZZLES
▪ Aero gas turbines have an exhaust system that passes the turbine discharge gas to atmosphere at a velocity
and direction appropriate to the flight condition.

▪ The main components of exhaust system of a non-after burning engines are Tail cone & Exhaust duct, which are
referred to as Tail pipe & Exhaust nozzle

▪ Tail Pipe: straightens out the flow before the gases passes into the jet pipe.

▪ Along the tail pipe, flow area increases, reducing the flow velocity and hence friction losses.

▪ Exhaust nozzle: The velocity of exhaust gas is increased before discharge to atmosphere

Classification:

1. Convergent or C-D Nozzle

2. Axisymmetric or 2-D Nozzle

3. Fixed Geometry or Variable geometry Nozzle

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 NOZZLE FUNCTIONS
▪ Acceleration of flow to high velocity with minimum total pressure loss

▪ Be matched to other engine components for all engine operating conditions

▪ Provide optimum expansion ratio

▪ Have minimum losses at design and off-design conditions

▪ Permit After burner (A/B) operation (if available) without affecting the main engine operation

▪ Allow cooling of walls if necessary

▪ Provide thrust reversal if necessary

▪ Suppress jet noise and infrared radiation (IR) if desired

▪ Thrust vector control if necessary for maneuvering of military aircrafts [V/STOL]

▪ Do all the above with minimal cost, weight while meeting life and reliability goals
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Schlieren & Shadowgraph images from experiments 29
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 Thrust Reversal

Boeing XB-70A Valkyrie landing with triple drag

chutes

Controllable pitch propellers in turboprop

engines

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Cascade and Clamshell Thrust reverser

located forward of the turbine exhaust nozzle

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Layout of a turbofan engine with two thrust reverse flow streams.
JET NOISE

Exhaust mixing and shock structure.

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Noise of the 1960s and 1990s aero engines
(Airbus Industries)

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 METHODS USED TO DECREASE THE JET NOISE Corrugated perimeter noise suppressor
(rear view).
1. Coating acoustically absorbent lining
2. Reducing the mixing region by increasing the contact area of atmosphere
with the exhaust gases by CORRUGATED or LOBE type noise
suppressors.
CORRUGATED nozzle:
• Breaks jet into smaller jet streams
• Increases the total perimeter of nozzle area
• Promote rapid mixing and
• reduces the size of eddies down linearly with the size of exhaust system
Effects:
• The change in frequency may put some high frequency noise above the
audible range of human ear
• High frequency audible noise are more highly attenuated by atmospheric
absorption than the low frequency noise. 46
METHODS USED TO DECREASE THE JET NOISE
LOBE type nozzle
• The exhaust gases are divided to flow through the lobes and a
small central nozzle.
• These form a number of separate exhaust jets that rapidly mix with
the air entrained by the suppressor lobes
• This principle can be extended by the use of a series of tubes to
give the same overall area as the basic circular nozzle.
• This type of noise suppressors was used by military aircraft and
early commercial aircraft.
Effects:
• But both these methods increased drag and reduced engine
performance, and the multitube approach also increased weight,
sometimes substantially.
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METHODS USED TO DECREASE THE JET NOISE/ IR SIGNATURES
• Turbofan engines are quieter than turbojet engines as the exhaust velocities of both streams of turbofans
are less than those for turbojets.
• To reduce fighters’ infrared signature, nozzle designs were tested to reduce the fully expanded jet
velocity by mixing
(a) core flow with fan flow only,
(b) fan flow with ambient flow only, or
(c) both flows simultaneously.
• Depending on the type of mixing attempted, these designs fell into two broad categories: tabs and
chevrons

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CHEVRON NOZZLES

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METHODS USED TO DECREASE THE JET NOISE/ IR SIGNATURES
• Tabs are severe protrusions into the flow at the nozzle exit plane.
• Chevrons are also protrusions but of much less severity than tabs.
• The aggressive mixing produced by the tabs greatly reduced low-frequency noise but with the penalty of
tab-induced high-frequency noise.
• Chevrons, which provided a more balanced approach to mixing, reduced low-frequency noise without
significant chevron-induced high-frequency noise.
• Other nozzle designs attempted to shield the core flow by using a scarf fan nozzle and an offset fan
nozzle for mixed flow turbofan engines; mixing of both hot and cold streams greatly reduces the noise.
• Generally, the most successful method employed by numerous aero engine manufacturers is to mix the
hot and cold exhaust streams within the confines of the engine and expel the lower velocity exhaust gas
flow through a single nozzle.
• This single nozzle may also have the corrugated or lobe-type shape

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 Thrust vectoring
• The ability of an aircraft or other vehicle to direct the thrust from its main engine(s) in a direction other than parallel
to the vehicle’s longitudinal axis.
• “a maneuver effector which can be used to augment aerodynamic control moments throughout and
beyond the conventional flight envelop”
• Design challenge: developing a multi-axis thrust-vectored exhaust nozzle that can operate efficiently at all flight
conditions while satisfying the design constraint of low cost, low weight, and minimum impact on radar cross-
section signature
• The technique was originally envisaged to provide upward vertical thrust as a means to give the aircraft VTOL or
short takeoff and landing (STOL) capability.
• use of vectored thrust in combat situations enabled an aircraft to perform various maneuvers and have better rates
of climb not available to conventional-engined planes.
• thrust vectoring can control the aircraft by engine forces, even beyond its stall limit, that is, during “impossible”
post-stall (PS) maneuvers at extremely high nose turn rates
• It is also used as a control mechanism for airships, particularly modern nonrigid airships 51
 Mechanical control
Thrust vectoring
Fluidic control

• Mechanical thrust vectoring includes deflecting the engine nozzle and thus physically changing the
direction of the primary jet.
• Fluidic thrust vectoring involves injecting fluid into or removing it from the boundary layer of a primary jet to
enable vectoring.
• Mechanical thrust vectoring system is heavy and complex, while fluidic thrust vectoring is simple, lightweight,
inexpensive, and free from moving parts (fixed geometry).

engine/nozzle internal thrust vectoring (ITV)

Mechanical control
engine/nozzle external thrust vectoring (ETV).

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Thrust vectoring
engine/nozzle internal thrust vectoring (ITV)
Mechanical control
engine/nozzle external thrust vectoring (ETV).

Pitch control internal thrust vectoring nozzle (ITV)

Turbofan engines
• only pitch control is available • Most currently operational
vectored thrust aircraft use
turbofans with rotating nozzles
or vanes to deflect the exhaust
stream.
• This method can successfully
deflect thrust through as much
as 90o, relative to the aircraft
(a) Normal (Unvectored) operation. (b) Down-pitch operation centerline
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Thrust vectoring
engine/nozzle internal thrust vectoring (ITV)
Mechanical control
engine/nozzle external thrust vectoring (ETV).

External thrust vectoring (ETV)

• ETV is based on post-nozzle exit, that is, (three or

four) jet deflecting vanes that deflect exhaust jet(s)
in the yaw and pitch coordinates, and in a few
designs, also in roll coordinates

(a) 3 Pedals. (b) Side view. (c) 4 Pedals.

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 Thrust vectoring nozzle
(a) Up pitch (b) Down-pitch.

• If the two nozzles of a twin-engined plane can also be deflected

differentially (one producing up force, the other down force), then it will
provide roll control.
• This type of nozzle may be identified as three-dimensional thrust
vectoring.
• Examples for aircraft using two-dimensional nozzle are Harrier, Boeing X-
32, F-35, Yak-38, and Yak-141.
• Aircraft employing three-dimensional thrust vectoring (pitch and yaw
moments) are F-15, F-16, F-18, MiG-29, MiG-35, Sukhoi Su-30, Su-37,
and Su-47.
• F-22 carries two P&W F119-PW-100, reheated (Afterburner) engines. The
exhaust nozzles move 20◦ in all directions providing 3-D thrust vectoring Thrust vectoring nozzle.
capabilities. (a) Up pitch.
(b) Down-pitch. 55
Su- 27, Su-30, Su-35

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Fluidic control Thrust Vectoring
• Fluidic nozzles, which divert thrust via fluid effects. Air forced into the exhaust stream can affect deflected thrust
of up to 15o.
• Use a secondary air jet to control the direction of the primary jet.
• Extensive experimental studies for utilizing a fluidic injection system (light weight and simple) instead of the
heavy and mechanically complex door system are being carried out.
• It has minimal aircraft observability penalty (or lower radar cross-section).
• Challenges with Fluidic vectoring are in obtaining an effective, efficient system with reasonably linear control
response.
• It has several types, namely, shock vector control, co-flow, counterflow, synthetic jet actuators, and sonic
throat skewing.

1. Shock thrust vector control

• Involves injecting a secondary jet into the primary jet from one of the divergent flaps.
• An oblique shock wave is formed that deflects the primary jet in the pitch plane.
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 Fluidic control Thrust Vectoring
• Both co-flow and counterflow concepts involve the use of a secondary jet together with the Coanda effect.
• Curved reaction surfaces are positioned downstream of the nozzle exit to which the jet may attach according to
the Coanda effect.

• The side onto which the jet attaches is controlled by tangential injection of a secondary jet of air upstream of the
surfaces.

• The resulting thrust vector force is

used to provide useful moments for
aircraft control.

Shock vector, co-flow, and counterflow fluidic thrust

vectoring concepts. 58
 Forces on aircraft for thrust vectoring

• The four forces that influence the aircraft motion are

the lift (L), weight (W), drag (D), and thrust (T).
• The thrust force is inclined at an angle (θ) to the
horizontal.

where ax and ay are the acceleration in the horizontal and vertical directions, respectively

• The first acceleration (ax) controls the forward motion, while the second acceleration (ay) controls the rate of
climb or descent.
• The angle (θ) is the inclination of the exhaust jet stream from the axis of aircraft. For a vertical flight this angle is
90o.
• This angle also develops a pitching moment necessary for nose up or down depending on deflecting the jet
nozzle upward or downward
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 Nozzle performance is ordinarily evaluated by
NOZZLE COEFFICIENTS two dimensionless coefficients

• Gross thrust coefficient

• Discharge or flow coefficient
• Velocity Coefficient
• Angularity coefficient

Gross thrust coefficient (Cfg)

• The ratio of the actual gross thrust Fg actual to the

ideal gross thrust Fg ideal

𝑭𝒈
𝑪𝒇𝒈 =
Ls 𝑭𝒈 𝒊𝒅𝒆𝒂𝒍
• It account for the losses and directionality of the actual nozzle flow
• Thrust loss due to exhaust velocity vector angularity
• Thrust loss due to the reduction in velocity magnitude caused by friction in the boundary layers
• Thrust loss due to loss of mass flow between stations 7 and 9 from leakage through the nozzle walls
• Thrust loss due to flow nonuniformities 60
Nozzle Performance
• Gross thrust for a one-dimensional flow

• Ideal gross thrust corresponding to P9 = P0

• Vs is the isentropic exit velocity based on Pt8 / Po and Tt8

One-dimensional flow of a calorically perfect gas,

• Ideal expansion (P9 = P0) gives a gross thrust coefficient of unity and that both underexpansion (P9 >
Po) and overexpansion (P9 < Po) reduces the gross thrust coefficient below unity.

Slight Amount Of Under Expansion Is Better Than Over Expansion In Nozzle Operation
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Discharge or flow coefficient (CD)

• The ratio of the actual mass flow 𝑚ሶ 8 to the ideal mass flow 𝑚ሶ 8 𝑖𝑑𝑒𝑎𝑙 called the discharge coefficient, CD

𝑚ሶ 8 𝜌8 𝐴8𝑒 𝑉8 𝐴8𝑒 • When nozzle is choked, CD attains maximum value,

𝐶𝐷 = = = CDmax
𝑚ሶ 8 𝑖𝑑𝑒𝑎𝑙 𝜌8 𝐴8 𝑉8 𝐴8

Area required to pass the total actual nozzle flow = 𝑨𝟖𝒆

Nozzle physical throat area = 𝑨𝟖
Ls

𝑃𝑡8 𝑃𝑡8
ൗ𝑃 ൗ𝑃
0 0
Convergent nozzle C-D nozzle 62
Velocity coefficient (CV)

▪ The ratio of the actual exit

velocity V9 to the ideal exit

velocity V9i corresponding to Pt9
= Pt8

▪ The effect of frictional loss in the

boundary layer of the nozzle

▪ Mainly a function of the nozzle

ratio A8 /A9 and the half-angle α

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 Angularity coefficient (CA)

1
𝐶𝐴 = න cos 𝛼𝑗 𝑑𝑚ሶ
𝑚ሶ

• It is the axial friction of the nozzle momentum and is

proportional to the thrust loss due to the nonaxial exit of
the exhaust gas
• For a differential element of flow, this coefficient is the

cosine of the local exit flow angle, 𝜶𝒋 .

• The local flow angle 𝛼𝑗 varies from zero at the centerline

to 𝜶 at the outer wall; thus, the nozzle angularity
coefficient is the integral of 𝜶𝒋 across the nozzle.
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 Variable geometry ejector nozzle
VARIABLE GEOMETRY NOZZLES • spring-loaded petals
1. Central plug at nozzle outlet
2. Ejector type nozzle
3. IRIS nozzle

Plug nozzle at design point

• Exact analogue of spike at the inlet
Ejector nozzle with blow-in doors for tertiary air

Iris variable nozzle

• higher performance nozzles

• uses overlapping, hydraulically adjustable
“petals.”
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 ROCKET NOZZLES

• When fired at sea-level

conditions, the nozzle of the third
stage with the highest area ratio
will experience flow separation
and suffer a major performance
loss.
• The second stage will flow full
but the external plume will
contrast; since Pe < Pb there is a
loss in Is and F.

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 ROCKET NOZZLES

❑ The principal difference in the different nozzle configurations is found in the diverging supersonic-
flow section
❑ The wall surface throughout the nozzle should be smooth and shiny to minimize friction, radiation
absorption, and convective heat transfer due to surface roughness.
❑ The first three sketches show conical and bell-shaped nozzles
❑ Although these last three have been ground tested, to date none of them has flown in a space
launch vehicle
❑ The objectives of a good nozzle configuration are to obtain the highest practical Is, minimize inert
nozzle mass, and conserve length (shorter nozzles can reduce vehicle length, vehicle structure, and
vehicle inert mass).

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 Bell, Contoured & Conical Nozzles

Bell nozzle Contoured nozzle

Bell nozzle Conical Nozzle

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Bell, Contoured & Conical Nozzles

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Bell-Shaped Nozzles

(1)
(2)

• Bell consists of two sections

• Near throat, nozzle diverges at relatively large angle (1). Degree of divergence tapers off further downstream
• Near nozzle exit, divergence angle is very small ~2º-8º, (2)
• Minimize weight / maximize performance ~10-25% shorter than conical nozzle
• The contoured shape avoids shock and increase performance.
• Shape is optimum only in a particular altitude.
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Two-Step Nozzles

• Extendible nozzle
• Droppable insert concept
• Dual bell nozzle concept

Extendible nozzle

Droppable insert concept

Dual bell nozzle

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Conical nozzle
Bell nozzle Dual bell nozzle

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