1. MAE 5350: Gas Turbines Nozzles
Mechanical and Aerospace Engineering Department
Florida Institute of Technology
D. R. Kirk

2. OVERVIEW: NOZZLES
Subsonic Aircraft: Usually a fixed area convergent nozzle is adequate
Can be more complex for noise suppression
Supersonic Aircraft: More complex, variable-area, convergent-divergent device
Two Primary Functions:
Provide required throat area to match mass flow and exit conditions
Efficiently expand high pressure, high temperature gases to atmospheric pressure (convert thermal energy → kinetic energy)

3. SUMMARY: INLETS AND NOZZLES
Expression for thrust that shows dependence on atmospheric pressure and cross-sectional
area at compressor or fan entrance
Engine Characteristics
Nozzle area ratio as a function
of engine parameters
Once nozzle area is set, operating point
of engine depends only on tt

4. REVIEW: OPERATION OF CONVERGING-DIVERGING NOZZLES

5. REVIEW: OPERATION OF CONVERGING-DIVERGING NOZZLES
All practical aerospace nozzles operate in regimes (e)-(g)

6. REVIEW: OPERATION OF C-D NOZZLES
Figure (a) shows the flow through the nozzle when it is completely subsonic (i.e. nozzle isn't choked). The flow accelerates out of the chamber through the converging section, reaching its maximum (subsonic) speed at the throat. The flow then decelerates through the diverging section and exhausts into the ambient as a subsonic jet. Lowering the back pressure in this state increases the flow speed everywhere in the nozzle.
Further lowering pb results in figure (b). The flow pattern is exactly the same as in subsonic flow, except that the flow speed at the throat has just reached Mach 1. Flow through the nozzle is now choked since further reductions in the back pressure can't move the point of M=1 away from the throat. However, the flow pattern in the diverging section does change as the back pressure is lowered further.
As pb is lowered below that needed to just choke the flow a region of supersonic flow forms just downstream of the throat. Unlike a subsonic flow, the supersonic flow accelerates as the area gets bigger. This region of supersonic acceleration is terminated by a normal shock wave. The shock wave produces a near-instantaneous deceleration of the flow to subsonic speed. This subsonic flow then decelerates through the remainder of the diverging section and exhausts as a subsonic jet. In this regime if the back pressure is lowered or raised the length of supersonic flow in the diverging section before the shock wave increases or decreases.

7. REVIEW: OPERATION OF C-D NOZZLES
If pb is lowered enough the supersonic region may be extended all the way down the nozzle until the shock is sitting at the nozzle exit, figure (d). Because of the very long region of acceleration (the entire nozzle length) the flow speed just before the shock will be very large. However, after the shock the flow in the jet will still be subsonic.
Lowering the back pressure further causes the shock to bend out into the jet, figure (e), and a complex pattern of shocks and reflections is set up in the jet which will now involve a mixture of subsonic and supersonic flow, or (if the back pressure is low enough) just supersonic flow. Because the shock is no longer perpendicular to the flow near the nozzle walls, it deflects it inward as it leaves the exit producing an initially contracting jet. We refer to this as over-expanded flow because in this case the pressure at the nozzle exit is lower than that in the ambient (the back pressure)- i.e. the flow has been expanded by the nozzle too much.
A further lowering of the back pressure changes and weakens the wave pattern in the jet. Eventually, the back pressure will be lowered enough so that it is now equal to the pressure at the nozzle exit. In this case, the waves in the jet disappear altogether, figure (f), and the jet will be uniformly supersonic. This situation, since it is often desirable, is referred to as the ‘design condition’, Pe=Pa.

8. REVIEW: OPERATION OF C-D NOZZLES
Finally, if the back pressure is lowered even further we will create a new imbalance between the exit and back pressures (exit pressure greater than back pressure), figure (g). In this situation, called under-expanded, expansion waves that produce gradual turning and acceleration in the jet form at the nozzle exit, initially turning the flow at the jet edges outward in a plume and setting up a different type of complex wave pattern.
Summary Points to Remember:
When flow accelerates (sub or supersonically) pressure always drops
Pressure rises instantaneously across a shock
Pressure falls across an expansion wave
Pressure throughout jet is always same as ambient (i.e. the back pressure) unless jet is supersonic and there are shocks or expansion waves in jet to produce pressure differences

9. KEY EQUATIONS FOR NOZZLE DESIGN
Nozzle area ratio as a function of engine parameters
Once nozzle area is set, operating point of engine depends only on tt
A7 is the throat area, how do we find the exit area of the nozzle?
Found from compressible channel flow relations, recall that M7=1
Set by jet stagnation pressure and ambient

10. ROCKET NOZZLE BEHAVIOR
Low Altitude
OVER-EXPANDED
Pe < Pa
Do not expand beyond Pe=0.4 Pa
Intermediate Altitude
IDEALLY-EXPANDED
Pe = Pa
High Altitude
UNDER-EXPANDED
Pe > Pa

11. SUMMARY Sea Level: Over-Expanded
Rockets operate at this condition at take-off
Intermediate Altitude: Ideally-Expanded
Typically occurs at only 1 point in rocket flight
High Altitude: Under-Expanded

12. EXAMPLE: SPACE SHUTTLE MAIN ENGINE, e~77
Static pressure at exit of Space Shuttle Main Engine nozzle is considerably less than ambient pressure at sea level
Mismatch in pressure gives rise to Mach “disc” in nozzle exhaust
Extremely strong shock wave that creates a region of subsonic flow and produces a characteristic white luminescent glow
Is this nozzle Over- or Under-Expanded?
If this nozzle were to operate at this altitude only, should it be larger or smaller?

13. VARIABLE GEOMETRY AND THRUST VECTORING
PW119
MIG-29 OVT F
up to 15° in any direction

14. NEW TECHNOLOGY (?): Messerschmitt Me 262
World's first operational jet-powered fighter

15. JUMO 004 ENGINE

16. COMMENTS ON NOISE REDUCTION USING NOZZLES
Environmental issues are likely to impose fundamental limitation on air transportation growth in the 21st century
2 major contributors: NOISE and EMISSIONS
Noise
Primarily exhaust jet and fan (whirl) noise
Noise impact of subsonic aircraft is constrains air transportation system through curfews, noise budgets and slot restrictions
Some solutions
Exhaust mixers
Liners that absorb sound
Shaping of stators and fan blade components for low noise

17. SOURCES OF ENGINE NOISE

18. WHY MIX CORE AND FAN FLOWS?
Large velocity gradient
Large shear tends to be noisy
Acoustic noise level scales as U6jet-U8jet

19. INFLUENCE OF BYPASS RATIO: Relative Perceived Noise Level vs
INFLUENCE OF BYPASS RATIO: Relative Perceived Noise Level vs. Bypass Ratio
Increasing bypass ratio increases the fan noise moderately
Increasing bypass ratio decreases the jet noise dramatically

20. PW6000: NOISE SUPPRESSION

21. BOEING / GE 747 NOISE SUPPRESSION

22. CORE-BYPASS MIXING
Mixing of two streams of different Tt increases hprop
How does level of static p at which mixing occurs change mixed-out Pt

23. 3D MIXER LOBE CONCEPT

24. LOBED MIXER FLOW STRUCTURES

25. NOISE SUPPRESSION NOZZLE

26. NOISE SUPPRESSION NOZZLE

27. NOISE CERTIFICATION REQUIREMENTS JET AND TRANSPORT AIRPLANES AT TAKEOFF

28. ENGINE NOISE PERFORMANCE

29. AEROSPIKE APPLICATIONS FOR ROCKETS

30. RADIAL IN-FLOW NOZZLES
Often referred to as spike nozzles
Named for prominent spike centerbody
May be thought of as a bell turned inside out
Nozzle is only one of many possible spike configurations
(a) traditional curved spike with completely external supersonic expansion
(b) similar shape in which part of the expansion occurs internally
(c) design similar to E-D nozzle in which all expansion occurs internally

31. SPIKE NOZZLES Each of spike nozzles features a curved, pointed spike
Most ideal shape
Spike shape allows exhaust gases to expand through isentropic process
Nozzle efficiency is maximized and no energy is lost because of turbulent mixing
Isentropic spike may be most efficient but tends to be prohibitively long and heavy
Replace curve shape by shorter and easier to construct cone ~1% performance loss

32. SPIKE NOZZLE PERFORMANCE

33. SPIKE: EXTERNAL SUPERSONIC COMPRESSION

34. AEROSPIKE NOZZLES
Further subclass of radial in-flow family of spike nozzles is known as aerospike
Go even further by removing pointed spike altogether and replace with a flat base
This configuration is known as a truncated spike

35. TRUNCATED AEROSPIKE NOZZLES
Disadvantage of "flat" plug is turbulent wake forms aft of base at high altitudes resulting in high base drag and reduced efficiency
Alleviated by introducing a "base bleed," or secondary subsonic flow
Circulation of this secondary flow and its interaction with the engine exhaust creates an "aerodynamic spike" that behaves much like the ideal, isentropic spike
Secondary flow re-circulates upward pushing on base to produce additional thrust
It is this artificial aerodynamic spike for which the aerospike nozzle is named

36. LINEAR AEROSPIKE NOZZLE
Still another variation of aerospike nozzle is linear (instead of annular)
Linear Aerospike pioneered by Rocketdyne (now division of Boeing) in 1970’s
Places combustion chambers in a line along two sides of nozzle
Approach results in more versatile design
Use of lower-cost modular combustors
Modules can be combined in varying configurations depending on application.

37. X-33 LINEAR AEROSPIKE NOZZLE

38. ALTITUDE COMPENSATION: ANNULAR

39. ALTITUDE COMPENSATION: BELL
Ideal situation would be to have size of nozzle bell increase as altitude increases
Altitude Adaptive Nozzles:
Dual-Bell Nozzle
Inserts, fixed and ejectable
Gas injection
Variable geometry (two-position)

40. WHAT IS BEING SHOWN HERE?

41. DETAILS: OVER-EXPANDED DESCRIPTION
The rocket's nozzle is designed to be efficient at altitudes above sea level, and, at engine start, the flow is over-expanded, that is, the exhaust gas pressure, pe, is higher than the supersonic isentropic exit pressure but lower than the ambient pressure, pa. This causes an oblique shock to form at the exit plane (A) of the nozzle. To reach ambient pressure, the gases undergo compression as they move away from the nozzle exit and pass through the oblique shock wave standing at the exit plane. The flow that has passed through the shock wave will be turned towards the center line (2). At the same time, the oblique shock wave, directed toward the center line of the nozzle, cannot penetrate the center plane since the center plane acts like a streamline. This causes the oblique shock wave to be reflected outward (B) from the center plane. The gas flow goes through this reflected shock and is further compressed but the flow is now turned parallel (3) to the centerline. This causes the pressure of the exhaust gases to increase above the ambient pressure. The reflected shock wave (see diagram below) now hits the free jet boundary called a contact discontinuity (or the boundary where the outer edge of the gas flow meets the free stream air). Pressure is the same across this boundary and so is the direction of the flow. Since the flow is at a higher pressure than ambient pressure, the pressure must reduce. Thus, at the reflected shock wave-contact discontinuity intersection, expansion waves of the Prandtl-Meyer (P-M) type are set up (C) to reduce the pressure to pa. These expansion waves are directed towards the centerline of the nozzle. The gas flow passing through the Prandtl-Meyer expansion waves turn away from the centerline (4). The Prandtl-Meyer expansion waves in turn reflect from the center plane towards the contact discontinuity (D). The gas flow passing through the reflected Prandtl-Meyer waves is now turned back parallel to the centerline but undergoes a further reduction of pressure.

42. DETAILS: OVER-EXPANDED DESCRIPTION
The reflected Prandtl-Meyer waves now meet the contact discontinuity and reflect from the contact discontinuity towards the centerline as Prandtl-Meyer compression waves (E). This allows the gas flow to pass through the Prandtl-Meyer compression waves and increase its pressure to ambient pressure, but passage through the compression waves turns the flow back towards the centerline (6). The Prandtl-Meyer compression waves now reflect from the center plane as compression waves (F) further increasing the pressure above ambient, but turning the flow parallel to the nozzle centerline (7). The flow process is now back to when the flow had just passed through the reflected shock wave (B), i.e., the flow pressure is above ambient and the flow is parallel to the centerline (3). This process of expansion-compression wave formation begins anew and continues until the pressure of the gases are the same as the ambient pressure and the flow is parallel to the centerline of the nozzle. These expansion and compression waves that interact with each other, leads to the diamond patterns seen. Ideally, this process would continue without end; but a turbulent shear layer created by the large velocity differences across the contact discontinuity will dissipate the wave patterns (see the diamond pattern for the SR-71 Blackbird at the beginning of this section). At very high altitudes where the ambient pressure is less than the exhaust pressure of the gases, the flow is underexpanded (see diagram below) - the exhaust gases are exiting the nozzle at pressures below the supersonic isentropic exit pressure which is also the ambient pressure. Thus, the flow (3 below) is at the same condition (pexhaust > pa) as the flow was after it passed through the reflected oblique shock wave when the rocket was at sea level (see above, A). To reach ambient pressure, the exhaust gases expand via Prandtl-Meyer expansion waves (waves between sections 3 and 4, below). This expansion occurs by the gases turning away from the centerline of the rocket engine (4). Therefore, the exhaust plume is seen to billow out from the rocket nozzle. The rest of the process ( , below) is the same as the 4-D-5-E-6-F-7 process explained above for the overexpanded nozzle.

43. CLAM SHELL THRUST REVERSER

45. Comments on Section 6.23

46. COMPARISON OF CONVERGING vs. DIVERGING NOZZLES
Examine ratio of thrusts, with and without a diverging section
Examine performance benefit of having diverging portion
Metric of comparison:
Excellent Web Site:
Chamber, Pa
Chamber P0
Chamber P0
Converging Nozzle
Converging-Diverging Nozzle

47. COMMENTS: CONVERGING NOZZLE (CTconv)
For nozzle with only a converging section → analysis is straightforward
Pa/P0 is varied in equation
Evaluate at Me = 1
Sonic exit condition
For converging nozzle
Ae/A* = 1

48. THRUST COEFFICIENT, CTconv, FOR CONVERGING NOZZLES
Maximum Thrust Coefficient when Pa = 0 (expansion into a vacuum)
Ae/A*=1

49. COMMENTS: DIVERGING NOZZLE (CT)
Requires more analysis than simple converging nozzle
IMPORTANT POINT: We can not vary Pe/P0 and Ae/A* independently
Connected through Mach Number, Me
Expression for Pe/P0
Vary Pa/P0 and Ae/A*
Given A/A* → 2 Me Solutions
Subsonic and Supersonic

50. MACH NUMBER vs. A/A* Differences in Cp/Cv Amplified as M ↑
For Given A/A* → 2 Solutions
Subsonic and Supersonic Mach
Highly Sensitive Region:
Small Changes in A/A*
→ Large Changes in M

51. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
WHAT DID WE DO HERE?
Set Pa/P0 = 0.05, g = 1.2
For any Ae/A* determine supersonic Me
Using this Me calculate P0/Pe
Calculate CT
Plot CT/CTconv (or T/Tconv) as function of Ae/A* (which is equivalent to plotting CT as a function of Me (supersonic))
Function is Maximized when Pe = Pa

52. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
Maximum Thrust (Pe = Pa)
Diverging Portion Increases Thrust
In terms of calculation, we could allow T/Tconv to become negative, but as we will soon see, we can deal with this part of the curve more realistically
Diverging Portion Reduces Thrust

53. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
Nozzle is Ideally Expanded Pe = Pa
Curve can also tell us where Pe > or < Pa
IF: Pe > Pa Nozzle is Under-Expanded
IF: Pe < Pa Nozzle is Over-Expanded

54. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
Nozzle is Ideally Expanded (Pe = Pa)
Nozzle is Under-Expanded (Pe > Pa)
Nozzle is Over-Expanded (Pe < Pa)

55. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
Nominal Range of Pa/P0
Decreasing Back Pressure or
Increasing Altitude

56. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
Line of Maximum Thrust: Connects Locus of Maxima
For each value of Pa/P0 there is an optimum area ratio for nozzle

57. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
Small Ratios of Pa/P0 Require Very Large Area Ratios

58. EXAMPLE: ROCKET LAUNCH Ae/A* = 20
Burnout (Under-Expanded)
↑ Vertical Flight
Max Thrust (Ideally Expanded)
Launch (Over-Expanded)
Notice we are closer to Optimum Thrust on
Under-Expanded Side

59. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
What can physically happen to supersonic flow in this region?
For this combination of pressure ratios and area ratios, a shock enters nozzle

60. MODEL OF SHOCK IN EXIT PLANE
We can plot shock line by located a shock at exit plane of nozzle
Requires 1 additional equation
Flow across a normal shock to connect conditions
For a given g only one Pa/P0 for which a normal shock will locate in plane of a nozzle of given area ratio Ae/A*

61. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
On this line a normal shock wave
located at exit of nozzle

62. PERFORMANCE CHARACTERISTIC OF A 1-D ISENTROPIC NOZZLE
If Pe reduced substantially below Pa
flow can separate
A rough approximation for this condition is:
Pe/Pa < 0.4
NOTE: Axial thrust direction is not usually altered by separation and CT can actually be increased over non-separated case