47th AIAA Aerospace Sciences Meeting Including The New Horizons Forum and Aerospace Exposition
5 - 8 January 2009, Orlando, Florida
AIAA 2009-202
Preliminary Analysis of the Rocket Plug Nozzle
Combined Cycle (RPNCC) Propulsion System
Dustin Wood1
The University of Alabama in Huntsville, Huntsville, Alabama, 35806
This paper presents research in the development of a new type of Rocket Based
Combined Cycle Propulsion System at the University of Alabama in Huntsville. The Rocket
Plug Nozzle Combined Cycle (RPNCC) configuration integrates an air-breathing propulsion
system within a rocket-driven plug nozzle so that the air-breathing system exhausts through
the plug base. Research is focused on assessing the feasibility of the RPNCC for space access
and high-speed atmospheric flight. Analysis of this unique propulsion system is performed
using analytical and computational methods combined with NASA wind tunnel data. An
analytical method-of-characteristics code is currently being modified to model the airbreathing engine plume exhausting through the plug base. The modified code will be used to
predict RPNCC performance and complement the computational predictions. The modified
code will also become part of a suite of codes to design and optimize flight vehicles at a
variety of flight conditions and thrust levels. The RPNCC concept is described and results
are presented of the computational studies of the rocket and air-breathing plume
interactions. The modifications to the analytical code are described and a preliminary
assessment of the impact of the RPNCC system on the overall propulsion design of a highspeed missile is discussed.
Nomenclature
RPNCC
RBCC
UAH
ADAPT
CFD
CCP
Isp
CAV
2-D
NPR
CEC
MOC
BLIMPJ
C*
NASA
MSFC
γ
ν
µ
M
θ
β
φ
Po
1
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Rocket Plug Nozzle Combined Cycle
Rocket Based Combined Cycle
University of Alabama in Huntsville
Aerospike Design and Performance Tool
Computational Fluid Dynamics
Combined Cycle Propulsion
Specific Impulse
Common Aerial Vehicle
Two Dimensional
Nozzle Pressure Ratio, chamber pressure to ambient pressure (Pc/Pa)
Chemical Equilibrium Code
Method of Characteristics
Boundary Layer Integral Matrix Procedure, Version – J
Characteristic Velocity or Combustion Efficiency
National Aeronautics and Space Administration
Marshal Space Flight Center
Specific Heat Ratio
Prandtl Meyer Function
Mach Angle
Mach Number
Deflection Angle
Shock Wave Angle
Slip Line Turning Angle
Stagnation Pressure
Master’s Student, Mechanical & Aerospace Engineering, Huntsville, AL, AIAA Student Member.
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Copyright © 2009 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.
P
RMF
dj
dr
Tj/Tj*
=
=
=
=
=
Static Pressure
Jet Momentum Flux
Inner Nozzle Exit Diameter
Reference Diameter or Base Diameter
Jet Static Temperature Ratio
I. Introduction
HE Rocket Plug Nozzle Combined Cycle (RPNCC) Propulsion System is a new type of Rocket Based
Combined Cycle (RBCC) configuration that integrates an air-breathing propulsion system within a plug nozzle.
University of Alabama in Huntsville (UAH) personnel are evaluating integration of the RPNCC system into flight
vehicles and the resultant impact on overall mission performance. System level analyses are being performed using
a modified analytical code called the Aerospike Design and Performance Tool (ADAPT)1 with other multidisciplinary design optimization tools to quantify the benefits of this unique propulsion system concept for fulfilling
a range of missions. Analyses over the last two years have primarily consisted of computational fluid dynamics
(CFD) simulations of the fundamental physics of the interacting exhaust plumes. On a standard workstation each
CFD simulation takes over 8 hours to run. This is much too long for use as part of a vehicle design and optimization
code. However, the modified ADAPT code will provide rapid calculation of the plume interaction at the plug base
and estimates of engine system performance to allow for rapid analysis of multiple designs and missions. The
purpose of the current research presented in this paper is development and implement modifications to ADAPT that
will enable analyses of the RPNCC performance. Results should provide the impetus and justification for continued
testing and analytical work.
T
II. Background
Combined Cycle Propulsion (CCP) technology shows promise for next generation launch vehicles, missiles, and
aircraft. The primary benefit of a CCP system is its potential for high efficiency operation over a wide range of flight
conditions. For instance, a launch vehicle powered by an RBCC engine could operate in an air-augmented rocket
mode for takeoff and initial acceleration to around Mach 1.5, transition to ramjet operation for efficient cruise
between Mach 4 – 6, and then transition to scramjet operation. Above Mach 8 where hydrocarbon fueled scramjet
operation is difficult, the engine would operate as a pure rocket to accelerate into orbit. If implemented in
supersonic cruise missiles or air-to-surface missiles the rocket could possibly augment the scramjet for a high-speed
dash. The basic principle is to operate the engine in the propulsion mode that provides the highest specific impulse
(Isp) for that flight condition. Conventional combined cycle systems may provide a performance improvement for
launch vehicles, but the substantial change in flow field conditions makes a system having the rocket internal to the
air breather a challenge both technically and operationally. In addition, the internal rocket engine introduces drag
throughout the entire mission, and the combustion process is complicated by the changes in flow conditions.
Operational complexity with changing geometries for the different flight conditions adds further cost, weight, and
complexity. In the conventional air-augmented rocket mode (Figure 1) the internally mounted rocket accelerates the
vehicle to a velocity at which atmospheric air enters the engine with sufficient flow rate and pressure to mix and
combust with the fuel rich rocket exhaust. These
gas products are then exhausted through the
remainder of the duct and a nozzle to produce
thrust. The duct itself has to be longer than a
normal rocket engine to allow full combustion of
the mixture of inlet air and rocket exhaust.
Additional downstream fuel injection may be
necessary to supplement the rocket exhaust
products. Additional hardware and geometry
changes are also required for flow control. These
internal rocket nozzles, injectors, flame holders,
Figure 1: Air-augmented rocket or RAM rocket mode
and other means for controlling the flow and
combustion are sources of drag, losses and
inefficiencies.
At a flight Mach number around 2 the internal rocket is turned off and the engine transitions to a pure ramjet
mode (Figure 2). The incoming air is compressed to subsonic Mach numbers by shock waves in the inlet.
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Downstream RAM injectors supply fuel that
mixes with the air which is then ignited by flame
holders. A series of injection points and duct
geometries may be required as Mach increases.
For rocket - scramjet combined cycles (Figure
3), the engine transitions to scramjet mode around
Mach 4 – 5. Scramjet operation is similar to a
ramjet, except the inlet geometry must be adjusted
to keep the incoming air supersonic. Another set
of injectors and flame holders are also required to
Figure 2: Ramjet mode
provide adequate mixing and combustion. For
space launch applications, the external inlet is
closed and the internal rocket is operated to attain
orbital altitude (Figure 4).
In alternate combined cycle engine
configurations external rocket engines replace the
air-augmented internal rocket. These rocket
engines are simply attached to the vehicle and are
not integrated with the ramjet/scramjet. One
problem with this approach is that it typically
increases the vehicle cross-sectional area and thus
the aerodynamic drag, especially in the transonic
Figure 3: Scramjet mode
flight regime. More rocket engines may be
required to provide thrust greater than drag, but
this increases the cross-sectional area further.
This performance verses geometry/packaging
tradeoff is a serious concern for combined cycle
engines. Additionally, traditional rocket nozzles
do not operate efficiently over a wide altitude
range. Nozzles designed for the high altitude,
pure rocket mode will not perform well at low
altitudes.
Nozzles that have the ability to
compensate for altitude change are very complex,
requiring moving nozzle exhaust skirts. These
Figure 4: Rocket mode
additional features increase cost and weight,
further complicate integration into flight vehicles,
and can lead to reduced reliability and life.
Incorporating the various engine modes into one flow path creates a number of operational and packaging
challenges. As the engine transitions between modes, the inlet geometry will have to adapt to accommodate both a
change in flow path height and ensure maximum shock capture at all Mach numbers. The internal geometry will
also have to change shape and dimensions. For combined cycle engines with an internal rocket, this geometry
change may be even more complex for the ram/scramjet modes. The geometric changes will require large, complex
drive mechanisms with an associated weight penalty. Different sets of injection and flame holding devices are
required along the mixing duct for ramjet and scramjet operation, and may also be required for the initial airaugmented rocket operation. These mechanisms and control requirements impose operational penalties on the
system. However, the engine mode transitions must be relatively smooth and avoid sharp changes in thrust. Finally,
the number of engines and the optimum positioning of the engine components and propellant tanks complicates the
design process even further. A new approach is required that eliminates or at least alleviates these operational and
performance limitations.
III. The RPNCC Concept
The Rocket Plug Nozzle Combined Cycle (RPNCC) Propulsion System consists of an external annular plug
nozzle rocket engine surrounding an air-breathing engine (ramjet, scramjet, or a turbo ramjet) placed within the
central plug body (Figure 5). The air-breathing engine exhausts through the plug base such that the interaction
between it and the rocket engines occurs only at the exhaust. There are no internal flow field complexities in the
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operation of the two engines
throughout the flight regime,
as with conventional RBCC
approaches described above.
The RPNCC thus achieves
more efficient packaging,
reduces drag, allows smooth
engine
operating
mode
transitions, provides nozzle
altitude compensation, and
improves overall engine
Figure 5: The RPNCC is a combined nozzle consisting of an aerospike
performance.
engine with an integrated air breathing engine in the plug base.
The aerospike nozzle is an
external expansion nozzle, first proposed by Rocketdyne Corporation, which expands the rocket plume in an
approximately isentropic fashion to the atmospheric pressure at that altitude2. This allows the nozzle expansion to
compensate for pressure changes associated with the increasing altitude of the rocket ascent. Altitude compensation
reduces thrust losses and maintains a nearly optimum performance at any altitude. A drawback to the “Ideal” plug
nozzle is that the fully isentropic expansion requires an excessively long, heavy spike. Since the nozzle pressure
components near the end of the spike contribute very little to the axial thrust, this additional weight reduces some of
the performance gains. An aerospike nozzle is an “Ideal” plug nozzle with the low thrust portion of the end spike
truncated. Shortening the nozzle reduces its weight. However, truncation produces a base region with recirculating
flow that increases the drag, increases heat transfer from the rocket exhaust to the base region, and reduces the
potential performance increase. The base region pressure can be increased by injecting low momentum gas through
the base in a process known as base bleed. Not only does this help in alleviating the loss of performance from
truncating the spike, but it also helps in alleviating some of the heat transferred from the exhaust gases.
The RPNCC approach is a combined cycle propulsion system that provides improved operational characteristics,
improved packaging, increased performance, and weight reduction over the traditional RBCC configurations
described above. By a novel combination of one or more plug nozzle thrusters integrated into the ramjet/scramjet
nozzle skirt near the nozzle exhaust, substantial improvements in performance, cost, and weight are achieved while
reducing complexity. In principle, the RPNCC design allows the rocket engine and the ramjet/scramjet engine to be
independently optimized without the additional complexities and losses in performance associated with the
conventional RBCC configuration. This approach further improves operations. The engines are simpler to operate,
more accessible, more easily refurbished, inspected, and removed/replaced.
The RPNCC configuration incorporates the performance increasing effects of the altitude compensating plug
nozzle while using the exhaust from the internal air breathing core to provide the pressurization in the plug base
(Figure 6). This configuration allows the internal air breathing engine to be optimized and operate separately from
the rocket engines. The rocket and air breathing engine exhaust flows only interact at, and downstream of, the plug
base. This approach
avoids the complexity
of
changing
the
geometry and locations
of the fuel injectors
and burners within the
ramjet/scramjet ducted
rocket. The exhaust
from the central core
can exit through one
large
nozzle,
or
through
an
Figure 6: RPNCC view showing traditional plug nozzle with single and multiple
arrangement of smaller
air breathing engine nozzles exhausting through base.
nozzles or modules, as
illustrated in Figure 6.
Another advantage of the RPNCC concept is that the plug nozzle thrusters are integrated into the nozzle region
which reduces any additional cross-sectional area and thus form drag. This improvement is achieved by taking
advantage of the shape of the air-breathing ramjet/scramjet exhaust nozzle configuration to “nest” the aerospike/plug
nozzle engines. Further performance improvement is attained by matching, to the extent feasible, the plug rocket
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and air breathing engine flow velocities and pressures, while minimizing the angular changes in the flow field that
produce shock interaction losses.
IV. RPNCC Applications
The RPNCC engine could be applied in a variety of vehicles to satisfy the requirements of a wide range of
missions. It offers the capability to quickly augment air breathing engine thrust by turning on or throttling the rocket
system. Thus, military reconnaissance/strike aircraft, reusable space launch vehicles, and long rang missile systems
are just a few of the possible vehicles that could benefit from inclusion of a RPNCC system.
In a preliminary analysis, both rocket and RPNCC-powered vehicles were used to fulfill the Air Force’s Prompt
Global Strike CAV delivery mission. This analysis showed the vehicle using the RPNCC propulsion system could
potentially accomplish the same mission with a 23% smaller gross lift-off weight than the conventional rocketpowered system baseline.
A fundamental advantage of the RPNCC approach is that it would allow parallel and concurrent development of
the plug nozzle rocket and core hypersonic air breathing engine system, rather than the more complex, lengthier, and
higher cost iterative development of conventional RBCC systems. This approach could reduce required research
funding, provide earlier system availability, reduce production cost, increase operability, and decrease maintenance
costs relative to comparative RBCC systems.
V. Computational Results
Analysis over the last two years has primarily consisted of CFD simulations of the fundamental physics of the
interacting exhaust plumes. Cold flow 2-D and axisymmetric CFD simulations were performed to see if the
combined performance of a ramjet and the aerospike would be affected by the plume interactions. This situation
would occur when transitioning from one mode to another. The simulations were made with an external flow
representing a flight speed of Mach = 2.5 at approximately 45,000 ft, which would be a possible flight condition for
transition from rocket mode to ramjet mode. The chamber pressures were approximately 1000 psi and 150 psi for
the aerospike and the ramjet, respectively. Two sets of cases were run. In the first, the thrust of the ramjet was kept
at 100% of its maximal thrust, while the thrust of the aerospike was set to 100%, 75%, 50%, 25%, and 0% of its
maximal thrust. In the second run, the thrust of the aerospike was kept constant while the ramjet thrust was varied.
A non-dimensional performance factor was developed by dividing the thrust of the combined nozzle configuration
(Taerospike+ramjet) by the sum of the thrust of the individual components computed independently (Taerospike + Tramjet). If
there were no interaction between the plug nozzle and the ramjet, this parameter would equal 1. Preliminary results
showed that the ramjet flow does not influence the plug nozzle performance even for low aerospike thrust levels.
The aerospike flow does not affect
the ramjet flow for ramjet thrust
level of 100%, 75%, and 50%. At
25% ramjet thrust, the flow
separates in a very small region near
the wall and the exit plane of the
ramjet nozzle as can be seen in
Figure
7.
However,
this
phenomenon did not reduce thrust.
This flow separation occurs for the
Separation
aerospike thrust set to its maximum
Point
value; the flow interference could be
reduced or eliminated when the
aerospike is operated at a lower
thrust level. Figure 8 shows the
interactions between the external
inflow and the plumes at maximum
chamber pressures for the aerospike
Figure 7: CFD predicted Mach number distribution in the RPNCC
and the ramjet. The under-expanded
flow field at maximum chamber pressures for the aerospike and 25%
flow at the exit of the aerospike
chamber pressure for the ramjet with a Mach 2.5 external stream.
nozzle expands right at the exit and
is then immediately pushed back by
the external flow.
The same
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phenomenon occurs with the ramjet
flow. It is initially under-expanded
at the exit plane, but is immediately
constrained by the aerospike flow
preventing further expansion. The
aerospike flow is strong enough to
act like a convergent tube, which
causes the supersonic ramjet plume
to decelerate to subsonic velocities.
This creates the normal shock
visible in the core flow. There is no
observable flow of the ramjet gases
onto the plug nozzle or penetration
of the plug nozzle plume into the
ramjet nozzle. At these conditions
the ramjet and aerospike nozzle
essentially operate independently.
These results support the contention
that the RPNCC approach would
substantially
increase
the
performance of combined cycle
propulsion systems.
Figure 8: CFD predicted Mach number distribution in the RPNCC
flow field at maximum chamber pressures for the aerospike and the
ramjet with a Mach 2.5 external stream.
VI. ADAPT
The analysis and optimization of vehicle designs incorporating the RPNCC system will require relatively fast
computational tools. The large number of CFD solutions needed is prohibitively expensive and time consuming.
The Aerospike Design and Performance Tool (ADAPT) code was chosen for this purpose1. ADAPT is capable of
predicting the performance of 10 different thruster designs, 10 different aerospike contours, and up to 10 different
off design pressures or nozzle pressure ratios (NPR). This allows 1000 different cases to be run in a fraction of the
time that it would take a single case in CFD to
User Input File
run. ADAPT is a collection of existing, proven
stand-alone tools linked together to form an
integrated analysis tool (Figure 9). The code
predicts performance for several types of altitude
)
as
lg
compensating rocket engine nozzles including
rea
If (
linear, annular, and plug cluster aerospike nozzles
like those in Figure 6. ADAPT can be used in
CEC module
BLIMPJ module
concert with other analysis techniques to optimize
RAO or
MOC module
PERFECT Nozzle
aerospike nozzles over an entire flight envelope.
module
Figure 9 shows that ADAPT uses the individual
Figure 9: ADAPT Logical Structure
stand-alone codes to design and optimize an
aerospike nozzle and calculate its performance
based on a single user defined input file.
The individual stand-alone tools are legacy FORTRAN programs that include: the Chemical Equilibrium Code
(CEC)3, the RAO and PERFECT Nozzle codes4,5, a method of characteristics (MOC) code6, and the Boundary Layer
Model or BLIMPJ code7. The culmination of these individual codes allows ADAPT to save on computational time,
giving it the advantage over CFD in the analysis and optimization process. The thruster (individual cluster modules)
contour can be designed using one of three choices: the RAO nozzle method8, which allows for a maximum thrust
contour for a specified length and nozzle pressure ratio (NPR), i.e. the ratio of chamber pressure to ambient
pressure; the PERFECT nozzle method, which by definition turns the exhaust gases parallel and uniform at a
specified Mach number and area-ratio; or a User Defined contour geometry, which allows for a non-ideal geometry.
This allows ADAPT to analyze both ideal and non-ideal geometries. It can optimize designs based on ideal gas with
a constant ratio of specific heats, γ, or real gas chemistry by having the CEC code generate the exhaust gas
properties and variable ratios of specific heats, which are then used to calculate the isentropic properties at the
thruster’s sonic line. Figure 10 shows the geometry of, and terms associated with an aerospike nozzle. The “Ideal”
ADAPT
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R
Cowl Lip
Sonic Throat
Pa
Pc
D
Spike Wall Contour
Expansion Region
“Ideal” Spike Section
Base Region
Pb
C
0
x
Figure 10: Aerospike Geometry and Nomenclature
Spike contour terminates at a vertex (X) on the axial line, while a truncated aerospike does not and forms a base
region (D to C). A previous modification to the original ADAPT code added a subroutine that accounts for
incomplete combustion and heat losses which resulted in a lower combustion efficiency, C*, than theory predicts.
The MOC code combined with an external expansion method9 draws the aerospike contour to allow for isentropic
expansion and aligns the thruster exhaust angle measured from the cowl lip with the flow angle of the aerospike
contour. The MOC code then calculates the performance and flow field properties of an “ideal” full-length spike or
truncated spike contours. The previous modification also incorporated base pressure calculations for truncated
spikes. The BLIMPJ code calculates the viscous losses in the thruster and along the contour of the aerospike. The
ADAPT code creates input files for each of
the sub-codes so that user intervention is
not required after the ADAPT input file is
read. The output is printed to a summary
file, which includes the spike and thruster
contours, and performance data at each
NPR.
ADAPT predictions have been shown
to compare very well to wind tunnel and
CFD results. CFD simulations of a plug
nozzle at different chamber pressure to
ambient pressure ratios were compared to
data from a NASA MSFC annular
aerospike wind tunnel experiment. Figure
Figure 11: Example NASA MSFC wind tunnel test data
11 shows excellent agreement between the
compared to ADAPT results.
ADAPT results and the experimental data.
VII. Applying the RPNCC Concept to ADAPT
The current version of ADAPT can not model an air breathing core in the base of the aerospike plug. The code
can perform the proper calculations and design optimization for both a conventional bell-rocket nozzle and an
aerospike nozzle separately, but not together (i.e. with the exhaust plumes flowing co-axially around each other).
Also, the flow field calculations from the MOC code stop at the base of the aerospike and/or exit of the bell-nozzle.
It was not required to know what happened to the exhaust gases and plume interactions after the exit plane of the
nozzle for optimization performance data. However, now that an air breather core is replacing the base region of the
truncated aerospike, it is desired to know in which atmospheric and engine operating conditions, will, if at all, cause
separation in the flow along the air-breather nozzle or cause a shock to form in the air-breather nozzle. Modifying
ADAPT to allow for these changes will help reveal in what operating regimes separation will occur, cause a
decrease in performance, or cause a shock to form in the inner nozzle. According to Romine10, the typical internal
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expansion nozzle exit pressure to
ambient pressure ratio (Pe/Pa),
threshold for separation is
correlated with Mach number and
the ratio of specific heats for the
exhaust gases.
The ambient
pressure for the inner nozzle
Expansion Fan
would be the static pressure at the
exit of the adjacent outer nozzle or
aerospike rocket flow, while the
ambient pressure for the outer
aerospike
nozzle
is
the
atmospheric pressure.
This
Oblique Shock
concept is further elaborated using
Brazzel Method to estimate the
base lip pressure.
One issue with modifying the
Figure 12: Subsonic Recirculation at lip of aerospike and air breather.
code to include a rocket exhaust
plume in the plug base was the
Method-of-Characteristics is only applicable to supersonic, continuous flows. Figure 12 shows that in the lip region
between the exit plane of the aerospike and air-breather nozzle a subsonic recirculation region forms. This causes a
discontinuity in the MOC code. This region is also visible in the CFD results (Figure 7). The aerospike exit lip
pressure would be directly affected by any non-zero ambient pressure below the design altitude for the aerospike
contour, and would thus require modeling of the spike flow field in response to that. To alleviate this, it was first
thought to extend the lip out to a sharp edge. This would eliminate the base region and create a slip line when the
two supersonic flows met at the tip. This could be easily modeled and a subroutine added to the main ADAPT code
that would predict at what angle with the horizontal the slip stream makes based on nozzle exit pressures and flow
Mach number. If there were a difference between the exit gas flow angles and accounting for any effects for flow
turning; the 2D Prandtl Meyer (expansion) and shock relations would be adequate to estimate flow turning pressure
effects. The pressures across the slip line would be used to iterate a turning angle to get equal pressures on both
sides of the slip stream11, which could be used to tell if a shock is forming along the inner flow corridor or in the airbreathing nozzle. Equations 1 – 3 are the Prandtl Meyer expansion relations11 for flow turning away from itself,
creating an expansion fan emanating from the edge of the lip as seen in Figure 12. The subscripts 1 and 2 denote
flow upstream and downstream, respectively, of the expansion wave. Depending on the exit pressure and Mach
number of the aerospike and air-breather nozzle the expansion fan will form on either the upper edge for a stronger
aerospike flow, which will turn the external flow in towards the internal flow or the fan will form on the lower edge
for a stronger air-breather flow, which will turn the internal flow outwards.
ν (M ) =
(
 γ −1

γ +1
⋅ tan −1 
⋅ (M 2 − 1)  − tan −1 M 2 − 1
γ −1
 γ +1

θ = ν (M 2 ) − ν (M 1 )
 1 

M 
µ = sin −1 
)
(1)
(2)
(3)
Equations 4 - 6 are the oblique shock relations11 for the flow turning in on itself, creating an oblique shock
emanating from the edge of the lip as seen in Figure 12. The shock wave angle, β, can be determined via an explicit
method given in Ref. 12.
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M n1 = M 1 ⋅ sin (β )
M2 =
(4)
M n2
sin (β − θ )
(5)
 M 12 sin 2 (β ) − 1 
tan (θ ) = 2 cot (β ) 2

 M 1 (γ + cos(2 β )) + 2 
(6)
Equations 7 and 8 are the isentropic pressure ratio and normal shock relations11, respectively. They are used to
find the pressure ratios between the upstream and downstream flow of the expansion or shock. The stagnation
pressure, Po, is constant across an isentropic expansion, but not a shock.
γ
Po  γ − 1 2  γ −1
= 1 +
M 
P 
2

(7)
P2
2γ
= 1+
M 2 −1
P1
γ +1 1
(8)
(
)
The shear layer between the flows merely transmits the supersonic flow static pressures at any station along the
slip line. Since, the correlation given by Ref. 10 is dependant upon exit pressure only, which is a function of the
ratio of the nozzle exit area to the sonic throat area (Ae/At) and the specific heat ratio for full nozzle expansions, the
chamber pressure avoiding separation would drop out. However, having the lip extended to a sharp edge would not
be physically practical for weight and structural issues and is only changing the physical specifications of the
aerospike to meet the requirements of the analytical methods. Plus, due to packaging issues the contour of the
aerospike and/or air breather may not be optimum and thus not allow elongated curved surfaces but more of a
conical shape with a truncated lip. Therefore, the lip could remain as a base region and be ignored by the MOC
code which would model each nozzle flow at a time; iterating down to find where the plumes meet and create a slip
line between them. The same principals apply to discovering the difference between the exit gas flow angles and
using the above 2D Prandtl-Meyer and oblique-shock equations directly in the code. The ‘base’ region could be
calculated separately as it is now with the pressure
estimation model for truncated plug nozzles.
Tinf
However, the empirical correlations in ADAPT for
Minf
base pressure calculations are based on the
Pinf
aerospike exit Mach Number and Pressure only and
γinf
do not include any correlation for base bleed.
PB
Therefore another base pressure correlation is
Tj
needed that includes two flow fields running past
Mj
dj
the base, thus Brazzel Method is chosen for this
dB = dr
Pj
purpose13. Equations 9-11 are Brazzel Method for
γj
calculating base pressure with power-on effects.
Figure 13 shows Tj, Mj, Pj, and γj as the inner nozzle
exit plane properties and Tinf, Minf, Pinf, and γinf as
the aerospike flow properties at the base or exit
plane. Assuming that the aerospike flow can be
used as the free-steam flow, the Brazzel Method can
be used to estimate the lip pressure as it would for
Figure 13: Brazzel Method for finding base pressure.
the base region.
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American Institute of Aeronautics and Astronautics
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



 T j 
3.5
 RMF 
PB

L
=  *  0.19 + 1.28


2
P∞  T  
 1 + RMF  
dB  

 j 
1 + 2.5 d r  
(9)
2
 xj
 xj
 
+ 0.047(5 − M ∞ )2
+
 
  d B   d B  
RMF =
Tj
T
*
j
γ j ⋅ Pj ⋅ d 2j ⋅ M 2j
γ ∞ ⋅ P∞ ⋅ d r2 ⋅ M ∞2
(10)
γ j +1
=
2
γ j −1
1+
⋅ M 2j
2
(11)
The j-parameters are at the exit of the inner nozzle, RMF is the jet momentum flux ratio of the exit to ambient
conditions, where the ambient conditions are the aerospike flow and Tj/Tj* is the ratio of the jet static temperature
for a given jet Mach number to that at a jet exit Mach number of one. To analyze if Brazzel Method would match
CFD, average values for pressure and Mach number were taken over the nozzle exits from the CFD data, using a
specific heat ratio of 1.4 for air and the inner nozzle diameter as 0.204 meters and the outer diameter, dB, as 0.2308
meters. The reference diameter is equal to dB and Xj is zero because the exit planes of both nozzles are assumed to
be at the same axial location as the base. The CFD gave an average lip pressure to be 3469 Pascals and the Brazzel
Method gave 1491 Pascals. This is more than a 55% difference and may be due to the fact that the CFD is laminar
in all cases and the Brazzel Method is based on experimental correlations, which accounts for turbulence. Also, the
CFD cases are based on cold flow constant specific heat ratio gas, while the Brazzel Method is based on reacting hot
flows which may affect the pressure in the recirculation region at the base. Figure 13 shows the schematic of the
base region using Brazzel Method.
Essentially, to model the slip line and co-axial flows at different pressure ratios, the lip region will be ignored.
The inner nozzle is run at its given chamber pressure, its flow field analyzed and the pressures along the plume are
stored and modeled as a solid boundary for the run of the aerospike nozzle. The aerospike will then be run at its
given chamber pressure and ambient conditions and the pressures along the solid inner plume boundary would
change; these pressures would be
stored and used for the next run of
the inner nozzle. The inner nozzle
would run again and this time the
solid boundary would change due
to the change in the original
plume boundary pressures. Then
the aerospike would run again and
so on until the pressures on either
side of the stream line are equal.
Figure 14 shows the steps
associated with this iterative
method. After a few iterations of
this the plumes would begin to
look like the co-axial corridor we
Figure 14: Iteration Model of Plumes.
see in the CFD results (Figures 7
& 8).
10
American Institute of Aeronautics and Astronautics
092407
VIII. Conclusion
Results from the ADAPT code will be compared to detailed computational fluid dynamics (CFD) analysis of the
exhaust interaction during mode transitions and vehicle/engine integration to help explain some of the more
fundamental plume physics. The modifications made to ADAPT will be used to predict RPNCC exhaust
performance and complement the CFD work already preformed. It will also become part of a suite of codes to
design and optimize flight vehicles at a variety of flight conditions and thrust levels. At the current stage in research
it is unclear if the Brazzel Method will work for calculating the base lip pressure; however, a potential method of
validating the Brazzel Method for this particular configuration would be to run a CFD case with reacting flows or
with average specific heat ratios to save on computation time, for the flows to mimic a reacting flow, and refine the
grid at the base to get more detail out of the calculation in that area. Using the Brazzel Method it may be possible to
determine where separation might occur within the air-breathing nozzle by correlating the pressures along the
internal contour to the pressure found at the base. If the pressures on the contour at the exit plane are similar or
equal to the base pressure, then separation may be possible and a normal shock could form in the air-breathing
nozzle. Using these correlations the ADAPT code will be modified and used to predict multiple flow fields in a
fraction of the time that CFD can.
Acknowledgments
The author of this paper thanks the Alabama Space Grant Consortium for providing the opportunity and funds to
conduct this research for his Master’s Degree. The author acknowledges Sean Entrekin as the author of the RPNCC
concept; Olivier Demaneuf for the preliminary CFD analysis; and Dr. Brian Landrum and Dr. Jim Blackmon for
directing in the preliminary study.
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2
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American Institute of Aeronautics and Astronautics
092407