Nozzles for Hypersonic Propulsion

1
Nozzles for Hypersonic Propulsion

• September 11, 2007
• L. Jacobsen
• GoHypersonic Inc.

2
Contents

• Introduction
• Scramjet Nozzle Configurations
• Component Design
• Component Performance
• Component Analysis
• Performance Measures
• Experimental Validation

3
Introduction

• This section of the course covers nozzles for
  hypersonic propulsion systems. This, in general
  means nozzles for scramjets and combined cycle
  engines. Scramjet nozzles will be covered here.
• Nozzles (expansion component)
• Major scramjet thrust-producing component.
• Take high-pressure flow from combustor exit and
  expands it to near-atmospheric pressure.
• A good scramjet nozzle design
• Efficiently accelerates flow over a wide range of
  supersonic inflow conditions from the exit of the
  combustor.
• Contributes to the balance of the net
  engine-integrated vehicle pitching moments over
  all flight conditions.

Freestream Flow
Inlet
Isolator
Combustor
Nozzle
Ideal Scramjet Engine
4
Introduction Design and Analysis

• Typical scramjet nozzle flowlines are usually
  generated at a particular design point
• Flight speed.
• Equivalence ratio.
• Flowline generation methods usually involve the
  Method of Characteristics (MOC) or Maximum Thrust
  Rao contours and Boundary Layer (BL) theory.
• Good reviews of these topics are provided in
  Refs. 1-5
• Higher-fidelity methods can take into account
• Non-uniform entrance conditions.
• Vehicle external/nozzle internal interactions in
  highly asymmetric configurations.
• Nonequilibrium thermochemical effects.
• Base drag in over expanded flowfields.

5
Scramjet Nozzle Configurations

• Typical scramjet nozzle designs are significantly
  driven by engine-vehicle configuration factors
• Engine type and corresponding vehicle outer mold
  lines.
• Combustor design.
• Combined cycle aspects.
• Vehicle mission.

6
Nozzle Configurations SERN

• Planar-type engines used in NASP and X-43 use a
  Single Expansion Ramp Nozzle (SERN).
• Typically generated using 2D flow.
• Considered to be structurally light but twice as
  long as conventional nozzle.
• Strong normal force must be designed carefully to
  counteract inlet-vehicle pitching moments.
• Allows considerable engine isolation from
  fuselage.
• Good configuration for the implementation of
  variable geometry.

7
Nozzle Configurations Inward-Turning

• Inward-turning engine configurations such as
  those used in the SCRAM, Falcon, and HyCAUSE
  programs have used techniques such as
• Streamline tracing through axisymmetric nozzle
  flowfields.
• Transitional nozzle shapes using 3D MOC.

HTV-3X
8
Scramjet Nozzle Configurations

• Combustor design
• Round/Rectangular.
• Multi-stage combustor definition of combustor
  exit/nozzle entrance can vary with flight speed!

• Combustor design
• Round/Rectangular.
• Multi-stage combustor definition of combustor
  exit/nozzle entrance can vary with flight speed!

Low-speed combustor
Low-speed nozzle
High-speed combustor
High-speed Nozzle
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Scramjet Nozzle Configurations

• Combined cycle aspects
• Rocket or turbojet placement and integration
  requirements can drive nozzle length and rate of
  expansion.
• Vehicle mission can also play an important role
• Horizontal Take-off/Landing (vehicle pitching may
  require scarf or highly 3D nozzle).
• Vertical takeoff or missile (dropped from a
  plane) can offer axisymmetric solutions.

TJ Engine
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Component Design

• There are several design methods commonly used to
  produce nozzle designs for scramjet engines
• Minimum length contours using the Method Of
  Characteristics (MOC)
• Truncated perfect nozzles via MOC
• 3D nozzle quadrant defined contours via MOC
• Maximum thrust Rao nozzles
• MOC and CFD are also typically used to assess the
  performance of nozzle flowlines.

11
Primer on the Method of Characteristics

• Characteristic lines are Mach lines.
• µ sin-1(1/M)
• The Method of Characteristics (MOC) is a
  practical way for solving supersonic flow.
• Hyperbolic flow equations permit 2 real
  characteristics to exist.
• For 2D irrotational flow one can derive from the
  full velocity potential equations,
• With compatibility relations

y
C
µ
V
A
?
Streamline
µ
C-
x
(Along C-)
(Along C)
Based on Discussion in Ref 1.
12
Primer on the Method of Characteristics

• Note ?(M) is the Prandtl-Meyer function, which
  for calorically perfect gas is
• To apply MOC one must note the region of
  influence and region of dependence of point A.
  (Disturbances do not travel upstream).

µ1
?2
µ2
?2 ?(M2) - ?(M1)
A
Influence
Mgt1
Dependence
13
Component Design Minimum Length

• Minimum length nozzle contours
• Defined using the Method Of Characteristics (MOC)
  in axisymmetric or 2D flow.
• Key is initial turning angle.
• n(M) represents the Prandtl-Meyer function
• Mi is the inflow Mach number (?(Mi) 0 for Mach
  1)
• Me is the desired uniform exit flow mach number

14
Component Design Minimum Length

• Truncated minimum length nozzles can create very
  short scramjet nozzles.

Figure 11.12 from Ref 1.
15
Component Design Truncated Perfect

• Nozzle contours generated using a circular arc at
  the throat joined to a parabolic curve provide a
  good means for creating a high-performing
  scramjet nozzle contour (Ref 6).
• MOC used here to simulate flow over surface.
• Performance (specific impulse) within less than a
  percent of maximum thrust Rao nozzle for some
  cases. (Ref 7)

?t
?e
Rt
re
rt
16
Component Design 3D MOC

• Numeric schemes were also developed in the 60s
  and 70s for solving 3D MOC in nozzle flowfields
  (Ref 6).
• Used in SCRAM Program.

Figure 7 from Ref 6.
17
Component Design 3D MOC
Figure 9 from Ref 6.
18
Component Design 3D MOC

• This nozzle parametric surface is defined by
• Streamwise Joined circular arc-parabolic
  contours.
• Circumferential hyper-ellipse with varying
  exponents.

Figure 19 from Ref 6.
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Component Design 3D MOC
Figure 20 from Ref 6.
20
Component Design Rao

• Determines contour of the divergence for a
  propulsive nozzle that maximizes thrust.
• Specified nozzle length.
• Constant mass flow rate.
• Constrained maxima problem was solved using
  Lagrange multipliers on isentropic frictionless
  irrotational flow.

21
Component Design Rao
Figure 16.33 from Ref 5.
22
Component Design Rao
Figure 16.34 from Ref 5.
23
Component Performance
x direction

• Note This section is based on the discussion in
  Heiser and Pratt (Ref 8).
• Off-Design
• Underexpanded P4/P0 lt Design
• Overexpanded P4/P0 gt Design
• Control volume analysis Gross Thrust, Feg
• It can be shown that
• Where Sa4 is stream-thrust at station 4.
• Clearly we want to maximize u10.

Fig. 7.9 from Ref. 8
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Component Performance

• Off-design expansion causes loss in thrust
• Over Shocks reduce u10.
• Under Higher u10 reduced due to flow angularity.
• Mitigation of off-design expansion loss is
  sometimes accomplished using variable geometry
• Over
• Thrust gain from reduction of flow angularity and
  shock emanating from the flap trailing edge.
• Partially offset due to new hinge line oblique
  shock.
• Under
• Thrust gain from reduction of flow angularity.
• Partially offset by new flap tip oblique shock.

Fig. 7.10 from Ref. 8
25
Performance Measures
Note This section is based on the discussion in
Heiser and Pratt (Ref 8).

• Adiabatic Expansion Process Efficiency he
• Total Pressure Ratio pe
• Interrelationships

26
Performance Measures

• Velocity Coefficient Cev
• Interrelationships
• Expansion Angularity Coefficient Cea

27
Performance Measures

• Gross Thrust Coefficient Ceg
• Net Thrust Coefficient Cen

28
Performance Measures Chemistry

• Note performance equations so far have been based
  on actual chemical state in the expansion
  process.
• Often performance is based on or referenced to
  equilibrium chemical state This maximizes the
  enthalpy available for exit kinetic energy.
• Depending on reaction rates and flow residence
  times, the actual performance will be somewhere
  between a frozen and equilibrium chemical state.

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Performance Measures Chemistry

• Equilibrium Adiabatic Expansion Efficiency he

Where
and
30
Performance Measures Chemistry

• Equilibrium Expansion Velocity Coefficient Cev
• Equilibrium Expansion Net Thrust Coefficient
  Cen

Where
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Performance Measures Chemistry

• Example calculations from Heiser and Pratt (Ref
  8)
• Constant pressure combustion of Hydrogen fuel
  with air. (Tfuel 1000 ºR)
• Subsequent expansion (Frozen and Equilibrium) to
  freestream static pressure (P0)
• T3 and P3 represent expected operating range at
  the combustor entrance.

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Performance Measures Other Loss

• Fluid dynamic loss mechanisms which lead to
  reduced efficiency
• Wall skin friction and heat transfer.
• Non-uniform and non-constant entrance conditions.
• Off-design free-boundary interaction (e.g. SERN).
• Non-axial exit velocity.

33
Experimental Validation

• To date, not much data available.
• Most experiments are associated with freejet
  engine tests or non-reacting flow.
• X-43, HyFly, HyCAUSE
• Simulation of combined internal exhaust and
  external vehicle flow.
• Issues
• Species concentration measurements in expansion
  process at elevated temperature.
• Understanding influence of H20 and NOX on
  expansion and combustion process. (Ground tests
  vs. flight)
• Base drag in underexpanded nozzles
• Large expansion ratios scramjet nozzles create
  transonic base drag problems.
• Testing with combined cycle systems also needed
  to address this transonic pinch point problem.

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Experimental Validation
35
Experimental Validation

• HyFly was tested at Mach 6.5

Photo Applied Physics Laboratory
36
References

• Anderson, J. D., Modern Compressible Flow With
  Historical perspective, 2nd Edition,
  McGraw-Hill, Inc., 1990.
• Shapiro, A. H., The Dynamics and Thermodynamics
  of Compressible Fluid Flow, Ronald Press, New
  York, 1953.
• Schetz, J. A., Boundary Layer Analysis,
  Prentice-Hall, Inc., New Jersey, 1993.
• Rao, G. V. R., Exhaust Nozzle Contour for
  Optimum Thrust, Jet Propulsion, Vol. 28, 1958,
  pp. 377-382.
• Zucrow, M. J. and Hoffman, J. D., Volume II, Gas
  Dynamics, Multidimensional Flow, Wiley, New
  York, 1977.
• Ransom, V. H., Hoffman, J., D., and Thompson H.
  D., A Second-Order Method of Characteristics for
  Three-Dimensional Supersonic Flow, Volume I,
  Theoretical Development and Results,
  AFAPL-TR-69-98, WPABP, OH, October, 1969.
• Hoffman, J. D., Design of Compressed Truncated
  Perfect Nozzles, Journal of Propulsion, Vol. 3,
  No. 2, pp. 150-156.
• Heiser W. H. and Pratt, D. T., Hypersonic
  Airbreathing Propulsion, AIAA Education Series,
  Washington DC, 1994, pp. 400, 403.