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NASA Technical Memorandum 106550_ _,.__, _ __ X . ^ 

ICOMP-94-05; AIAA-94-0024 .'..."'. .'."_'._. e$$ r 



Computational Study "of SingFe-Expansion- 
Ramp Nozzles With ExternM Buraing 



Shaye Yungster 

Institute for Computational Mechanics in Propulsion 

Lewis_Research Center _ L 

Cleveland, Ohio 



and 

Charles J, Trefny" 
Lewis Research Center 
Cleveland, Ohio 



Prepared for the 

32nd Aerospace Sciences Meeting 

sponsored by the 

American Institute of Aeronautics and Astronautics 

Reno, Nevada, January 10-13,1994 




National Aeronautics and 
Space Administration 



(NASA-TM-106550) COMPUTATIONAL N94-31229 
STUDY OF SINGLE-EXPANSION-RAMP 

NOZZLES WITH EXTERNAL BURNING „ nr i a c 

(NASA. Lewis Research Center) 28 p Unclas 

G3/34 0004760 



Computational Study of Single-Expansion-Ramp 
Nozzles With External Burning 

Shaye Yungster 

Institute for Computational Mechanics in Propulsion 
NASA Lewis Research Center, Cleveland, OH 44135 

and 
Charles J. Trefny 
NASA Lewis Research Center, Cleveland, OH 44135 



Abstract 

A computational investigation of the effects of external 
burning on the performance of single expansion ramp noz- 
zles (SERN) operating at transonic speeds is presented. 
The study focuses on the effects of external heat addition 
and introduces a simplified injection and mixing model 
based on a control volume analysis. This simplified model 
permits parametric and scaling studies that would have 
been impossible to conduct with a detailed CFD analysis. 
The CFD model is validated by comparing the computed 
pressure distribution and thrust forces, for several nozzle 
configurations, with experimental data. Specific Impulse 
calculations are also presented which indicate that exter- 
nal burning performance can be superior to other meth- 
ods of thrust augmentation at transonic speeds. The ef- 
fects of injection fuel pressure and nozzle pressure ratio oil 
the performance of SERN nozzles with external burning 
are described. The results show trends similar to those re- 
ported in the experimental study, and provide additional 
information that complements the experimental data, im- 
proving our understanding of external burning fiowfields. 
A study of the effect of scale is also presented. The re- 
sults indicate that combustion kinetics do not make the 
flowfield sensitive to scale. 

Introduction 

The possibility of achieving orbital conditions with a 
single-stage vehicle using primarily airbreathing propul- 
sion is being evaluated under the National Aerospace 
Plane program. Ready access to space, a reduction in 
the cost of putting payloads into orbit, and very high 



Copyright ©1994 by the American Institute of Aeronautics and 
Astronautics, Inc. No copyright is asserted in the United States 
under Title 17, U.S. Code. The U.S. Government has a royalty- 
free license to exercise all rights under the copyright claimed herein 
for Governmental purposes. All other rights are reserved by the 
copyright owner. 



speed earth transportation are some of the benefits of 
this technology. The propulsion system of such a vehicle 
will have to cover the total flight spectrum from horizon- 
tal takeoff to orbital speed. Efficient operation at high 
Mach numbers dictates the use of hydrogen as the fuel of 
choice, and a highly integrated vehicle design. An artist's 
conception of a single-stage to orbit "Aerospace Plane" is 
shown in Fig. 1. The entire aft end of the vehicle acts as a 
single expansion ramp nozzle, providing a very high area 
ratio which is exploited at the high nozzle pressure ratios 
associated with high Mach number and altitude. Such 
a vehicle, however, will presumably not incorporate vari- 
able geometry in order to minimize the structural weight. 
Therefore, the large aft-facing area becomes a great lia- 
bility at transonic and low supersonic speeds where low 
airbreathing engine pressure ratios result in a highly over- 
expanded nozzle. 

Figure 2 illustrates a single expansion ramp nozzle op- 
erating at transonic speeds. The exhaust mass flow is 
insufficient to fill the large area-ratio nozzle designed for 
high Mach number operation. The shear layer and shock 
wave system adjust and stabilize in a configuration that 
equalizes the pressure in the nozzle plume and external 
flow. Due to the freestream flow turning around the aero- 
dynamic shape formed by the cowl and the shear layer, 
the resulting pressure acting on the nozzle expansion sur- 
face is below atmospheric pressure, resulting in low thrust 
levels. 

An effective method for improving nozzle performance 
at transonic speeds is based on the concept of external 
burning. Fuel, in this case hydrogen, is injected into 
the external flow and is subsequently mixed and burned 
(Fig. 3), pressurizing the entire expansion surface and 
cow l trailing edge. 

The external burning concept described above depends 
on the controlled combustion of hydrogen and air at 
freestream conditions. Experimental studies aimed at 
determining the effects of hydrogen-air external burning 



on the performance of SERN nozzles were reported in 
Refs. [1] and [2]. These studies indicated the potential for 
specific impulse values in excess of other auxiliary propul- 
sion options such as turbomachinery and rockets. 

The objectives of the present work are to develop CFD 
prediction techniques to analyze the sub-scale and full- 
scale performance of external burning nozzles at transonic 
flight conditions; and to understand how the various pa- 
rameters (such as fuel injection pressure, nozzle pressure 
ratio, Mach number, etc) affect the performance of the 
external burning system. In the following sections, we 
describe first the computational model used, the govern- 
ing equations and numerical method employed. Then, 
several model validation tests are presented followed by 
parametric and scaling studies of several nozzle configu- 
rations. 

Computational Model 

A detailed analysis of the entire external burning flow- 
field would be extremely demanding computationally. 
Such a task must address the details of fuel injection 
and fiameholding, mixing, turbulent boundary layers and 
shear layers, reaction kinetics and their interaction with 
the turbulent flowfield. Furthermore, the external burn- 
ing process creates a large subsonic region that requires 
a computational domain that extends far beyond the ex- 
pansion ramp. The requirement of an extended domain, 
combined with the need to resolve the various detailed 
flow features would result in a very large computational 
grid. The use of finite rate chemistry combined per- 
haps with a probability density function (PDF) model for 
proper treatment of the chemistry-turbulence interaction 
would lead to prohibitively expensive CPU times. 

Previous studies of external burning have been based on 
simplified analytical models, or "engineering" type CFD 
approaches in order to determine trends and provide in- 
sight into the various complex phenomena occurring in 
this type of flow. An overview of past analytical methods 
to investigate external burning flowfields was presented 
in Ref. [1]. 

CFD studies have focused on certain aspects of the 
flowfield. Bittner and McClinton [3] used 2D, 3D, and 
PNS versions of the SPARK code to study the injection, 
ignition and fiameholding characteristics of external burn- 
ing flows. Their study was based on a simplified geometry 
and did not analyze the overall effects of external burn- 
ing on the nozzle performance. Trefny [1] on the other 
hand, ignored the details of the injection and mixing pro- 
cesses to investigate drag reduction by external burning 
on an expansion surface. The injection and mixing in Tre- 
fny's study were modeled as a stream-tube of premixed 
hydrogen-air, and an external heat addition term was re- 
tained in the energy equation. 



The present investigation follows an approach similar to 
that of Ref. [l] but includes a more elaborate flow model, 
and considers the actual nozzle configurations studied ex- 
perimentally in Ref. [2]. The focus is on the global effect 
of external heat addition on nozzle performance, without 
modeling in detail the injection process. Therefore, in the 
present work, the injection and mixing are modeled as a 
stream-tube of premixed hydrogen-air (Fig. 4). 

A second simplification used in this work is related 
to the three-dimensional nature of the flowfield. SERN 
nozzles operating at transonic speeds without external 
burning are characterized by strong three-dimensional ef- 
fects. The low pressure in the nozzle plume gives rise to 
a transverse flow from the surrounding higher pressure 
air. When external burning is used, however, the net ef- 
fect is to pressurize the nozzle plume and external flow 
to atmospheric levels or higher. As a result, the three- 
dimensional relieving effect is much weaker. Therefore, it 
is reasonable to assume that SERN nozzles that include 
external burning can be adequately modeled using a 2D 
formulation. 
Injection and Mixing Model 

The external burning fuel injection configuration con- 
sidered here is the same as that used in the experimental 
studies of Refs. [1] and [2]. A single row of normal fuel 
injectors was located along the external cowl surface, as 
shown schematically in Fig. 5. The fuel injection scheme 
consisted of 21 choked orifices, each d = 0.060 inches in 
diameter with a spacing s = 0.381 inches apart, resulting 
in a spacing ratio s/d = 6.35. 

In the present work, the injection process is modeled 
as a uniform stream-tube of premixed hydrogen-air. The 
performance of external burning is theoretically a func- 
tion of the equivalence ratio of this fueled stream. This 
external burning equivalence ratio cannot be practically 
measured and will not be uniform for some distance fol- 
lowing the normal injection of fuel. Therefore, a method 
of estimating a "global" equivalence ratio needs to be de- 
vised. This is done based on a jet penetration correlation 
and a control volume analysis around a single hydrogen 
injector. 

The jet penetration height, y P , is determined from the 
correlation developed by Povinelli [4], which gives an 
equation that describes the outer boundary of the injec- 
tant, defined as a 0.5% concentration by volume. For 
sonic orifices this correlation is given by 



^ = 1.12(^i)- 483 (?+0.5)' 281 
d peff a 



Peff = ^Pt,NS 



(1) 



(2) 



where j?t,/ is the fuel injector total pressure, p e ff is an 
effective back pressure taken to be 2/3 of the stagnation 



pressure behind a normal shock, pt,NS, at the freestream 
Mach number. The parameter x denotes the distance 
downstream of the orifice centerline. This distance is a 
free parameter for which an appropriate value must be 
chosen. For x/d greater than about 20, the jet penetra- 
tion is a relatively weak function of x/d because of its 
.281 exponent. An x/d of 30 was therefore chosen for all 
subsequent calculations [1]. 

Once the jet penetration has been estimated, the prop- 
erties of the hydrogen-air stream-tube can be computed 
using a control volume analysis. Figure 5 shows a control 
volume around a single fuel injector. The central assump- 
tions used in the analysis are: 1) the flow coming out of 
the exit area A e has a uniform composition; and 2) the 
height of the hydrogen-air stream-tube exiting the control 
volume is equal to the jet penetration y p . Therefore the 
exit area A e is given by 



A e = y p s 



(3) 



where s is the spacing between the orifices. Thus each 
orifice fuels a stream-tube of air of cross-section Ai. The 
capture area Ai remains to be determined. 

Considering the control volume delimited by the cowl 
surface and the mixing boundary streamline, conservation 
of mass gives 

rh a + rhf = rh e (4) 

where 

TTla = PaU a Ai (5) 

m e = PeU e A e (6) 

where p a and u a are the density and velocity of the in- 
coming air respectively. Similarly, p e and u e denote the 
density and velocity of the mixture exiting through A e . 
The parameter rhf denotes the fuel mass flow rate. Now, 
considering conservation of mass for the whole control 
volume having inflow and exit area A 

rh e + p a u a {A - A e ) + m s -rhf - p a u a A = (7) 

where m s is the mass flow of air through the side of the 
control volume. Rearranging, and using Eq (4) we obtain 



Assuming that the fueled stream-tube exit pressure, p e 
is equal to the air pressure, p e = p a , and defining the 
fuel-air ratio / = rhf/rh a we have 



ih s = p a v> a (A e - A{) 



(8) 



Conservation of momentum, assuming that no net 
thrust is produced by the fuel injection process, can be 
written as 

(p a - Pe)A e = m e u e + rh s u a + p a u a (A - A e )u a - 

™, a U a - p a V, a {A - AijUa (9) 



using Eq (8) we obtain 

{Pa — Pe)A e = m e W e - Th a U a 



U e = 



(1 + /) 



Eqs. (4) and (6) can then be written as 
ihf rh a . Ai . _ rhe 

Ae Ai Ae Ae 



m e 

Te 



= PeUe = 



PeW e Up 
RT e 1 + / 



(11) 



(12) 



(13) 



where T is the temperature, and W the molecular weight. 
We will also assume that the fueled stream-tube exit tem- 
perature, T e is equal to the air temperature T e = T a . The 
fuel-air ratio can be written 



/ = 



nit 

A, 



A 
A, Va 



m 



(14) 



Finally, we obtain the following equation for the capture 
area ratio Ai/A e 



The ^£/j^i\ _ Pa W ' u <* 

Ae Ai [ A e '~ RT a 1 + / 



(15) 



The molecular weight of the fueled stream-tube, W e , is 
a function of the fuel-air ratio which in turn depends on 
the capture area ratio through Eq (14). Equation (15) is 
solved graphically for Ai/A e as shown in Fig 6. The left- 
hand side of Eq (15) is denoted by rhi n and the right-hand 
side by rhout- The left-and right-hand sides of Eq. (15) 
are evaluated for several assumed values of Ai/A e and 
plotted. The crossover pont represents the solution. The 
capture area ratio decreases with increasing fuel pres- 
sure. In the present stdy, its value was in the range 
0.5 < Ai/Ae < 0.9. Once the capture area ratio is known, 
the fuel-air ratio is obtained from Eq (14), and the global 
equivalence ratio, (f>, of the fueled stream-tube is obtained 
from the following equation (valid for hydrogen fuel only) 



4> = 34.4704/ 
The following relations are also used 

A e y/T^ffypS 



and 



a7-°- 532 ^ ( T ) 



(16) 



(17) 



(18) 



where C v is the orifice flow coefficient, T t j is the fuel in- 
jector total temperature, and pt and T t are the freestream 
(10) total pressure and temperature respectively. A* is the 



sonic area, and the ratio A" I A is a function only of the 
freestream Mach number. In Eqs. (17) and (18), the pres- 
sure is in psi, and the temperature is in degrees Rankine. 
Code Description 

The computational study of SERN nozzles with exter- 
nal burning was carried out using an in-house developed 
two-dimensional CFD code [5]. As mentioned in the in- 
troduction, a two-dimensional approach is adequate for 
this type of problem. This code solves the multi-species 
Reynolds-Averaged Navier-Stokes equations with finite- 
rate chemistry. It is a multiblock, fully implicit finite dif- 
ference code based on the LU-SSOR factorization scheme. 
The spatial discretization is based on the second order 
total variation diminishing (TVD) scheme developed by 
Yee [6]. In the present study, a symmetric TVD scheme 
with a minmod type limiter was used. A detailed descrip- 
tion of the code can be found in Yungster [5]. 

The analysis of SERN nozzles that do not include ex- 
ternal burning was carried out using a three-dimensional 
code called MAWLUS, developed by Chitsomboon [7]. 
Some salient features of MAWLUS are: finite volume, 
fully implicit, LXJ factorization, central differencing, and 
multi-block methodology. Artificial viscosity terms are 
added to stabilize the central differencing scheme. 

The turbulence model used in the present study is 
based on the approach of Georgiadis et al [8] in which 
two algebraic models, one optimized for wall-bounded 
flows, and the other developed for unbounded flows are 
linked into a single model. For wall-bounded flow re- 
gions, the Baldwin-Lomax [9] turbulence model is used. 
In the unbounded regions, such as free shear layers, the 
Thomas [10] model is used. To provide a smooth tran- 
sition from the bounded and unbounded regions, a link 
methodology similar to that proposed in Ref. [8] was em- 
ployed. When using standard algebraic turbulent mod- 
els, unrealistically high turbulent viscosities are often ob- 
tained, particularly in flows involving several streams and 
wall boundaries. As a result, it is usually necessary to 
artificially limit the maximum value that the turbulent 
eddy viscosity can have. By using the present approach, 
the artificial limiting of the eddy viscosity was not re- 
quired. This is an important issue for the scaling studies 
described later in the paper. Constant turbulent Schmidt 
and Prandtl numbers were assumed (Pr t = Sc t = 0.9). 

The code used for the external burning simulations has 
a generalized chemistry capability. However, since in the 
present study the injection process is not modeled in de- 
tail, the use of a detailed combustion model would be 
superfluous. Instead, we preferred to use a simple com- 
bustion model and leave the rate at which heat is released 
into the flow as a parameter that could be easily adjusted. 
This approach is consistent with our objective of inves- 
tigating the effects of external heat release on the per- 
formance of SERN nozzles, and the effects of scale. The 



combustion model assumes a single reaction 

2tf 2 + 2 + 3.76N 2 - 2H 2 + 3.76JV 2 



(19) 



Therefore, only four species are considered, H 2 , 2 , H 2 0, 
and JV 2 . In the experiments, the only source of ignition for 
the external burning stream was contact with the adja- 
cent hot nozzle exhaust plume. Therefore, in the present 
study, it is assumed that combustion starts at the trailing 
edge of the cowl. The rate of heat release is controlled by 
adjusting the reaction rate constant, Kf, and by assum- 
ing a flame spread angle. Experimental infrared images 
indicated that the flame spread angle remains in the rel- 
atively narrow range of 5° to 15°. In the present study, 
a flame spread angle of 10° was assumed for all the com- 
putations. The reaction rate constant was subsequently 
adjusted to produce pressure distributions similar to that 
obtained in the experiments. A single value for the re- 
action rate constant, Kf = 6000, was used for all the 
computations. 
Force Data Reduction Scheme 

The total force on the nozzle was considered to be the 
sum of three parts: an internal stream thrust, a ramp 
pressure force, and a cowl boat-tail force. The axial and 
normal components of the internal thrust are calculated 
from 

F x ,int = f [pu 2 + (p - p 00 )]dA t (20) 

J exit 



y,int 



■/■' 

Jtzit 



[puv]dA x 



(21) 



The forces on the expansion ramp and boat-tail are com- 
puted by surface integration 



?,,s = J\p- 



Poc]dA x 



\<LA V 



(22) 



(23) 



where S denotes either the expansion ramp surface, or 
the boat-tail surfaces. The forces are normalized by the 
ideal (optimum) thrust coefficient, Fi , which is a function 
of the nozzle pressure ratio, NPR, and the specific heat 
ratio, 7, of the nozzle exhaust flow [11] 



Fi 



Uh 



-W^^iA-S 



(24) 
where A t h denotes the throat area. 

In addition to the net total forces acting on the nozzle, 
a measure of the efficiency of the external burning process 
is needed. Here we use the specific impulse, 7 sp , as the 
figure of merit. I, p is generally defined as the net thrust 
per unit fuel flow, but for the present case, the magnitude 
of the force increment vector due to external burning is 
used. This force is directed at an angle given by its axial 
and normal components. 



SERN Nozzle Configurations 

The experimental investigation of nozzle performance 
and external burning was carried out using the NASA 
Lewis Jet Exit Rig [2]. This test rig, shown schematically 
in Fig. 7, was installed in the NASA Lewis 8' x 6' su- 
personic wind tunnel. The jet exit rig contains flow lines 
internal to the tunnel support strut that allowed a total 
air mass flow rate of 28 pounds-per-second split equally 
between two flow tubes. The hydrogen flow capacity was 
0.4 pounds-per-second through a third flow tube. The 
hydrogen line is split at the flow measurement section to 
provide fuel to both the main combustor and an external 
burning fuel plenum. Up to 25% of the total hydrogen 
flow could be directed into the external burning plenum. 
After passing a flow metering station, the hydrogen and 
air were mixed and burned in the water cooled main com- 
bustor. The combustor was operated at a slightly lean 
fuel-air ratio to yield a temperature of about 3500°i?. 
The combustion products were then expanded through 
the SERN nozzle. 

Two cowl configurations were used with a basic SERN 
nozzle model. A straight cowl was used as a "baseline" 
to determine the effects of cowl deflection and external 
burning. The SERN nozzle configuration with the base- 
line cowl is shown in Figs. 8(a) and (b). It had a 1-inch 
high throat followed by an expansion to an internal area 
ratio of 1.29 at the station where the expansion ramp be- 
gins, x r = 13.75 inches. The expansion ramp was eight 
inches in width, had an initial angle of 17°, and a trailing 
edge angle of 8°. The length of the expansion ramp was 
L = 27.47 inches. Coordinates of the internal flowpath 
and the external expansion ramp are given in Ref. [2]. 

A deflected cowl configuration was designed to reduce 
overexpansion by reducing the internal area ratio, and 
also by generating an oblique shock that would impinge 
on the ramp's initial 17° corner. The throat area and 
location remained the same as the baseline cowl. The 
deflected cowl configuration is shown in Fig. 8(c). The 8° 
deflected portion terminated at the x = 15 inch station, 
extending 1.25 inches beyond the start of the expansion 
ramp. 

In order to enhance flame stability, a flameholder could 
also be attached to the underside of the cowl, as shown 
in Fig. 9. The flameholder, positioned 2.5 inches down- 
stream of the fuel injector, was a wedge with length of 
1-inch and height of 0.5-inch. 

Results 

Code Validation; SERN Nozzles Without 
External Burning 

A three-dimensional computation of a SERN nozzle at 
transonic flight conditions without external burning is 



presented first. The baseline nozzle was considered for 
a flight Mach number of M = 1.2, and a nozzle pressure 
ratio of NPR = 4.97. The stagnation temperature for the 
hot exhaust gas flow is T t = 1783°iif. The composition 
of the hot nozzle flow was determined from the fuel-air 
ratio used in the combustor, which in the present case 
was F/A = 0.021. 

A five block grid consisting of a total of 220,000 points 
was used to model the nozzle and surrounding external 
flow. The domain extended to the trailing edge of the 
expansion ramp in the streamwise direction. Only half of 
the nozzle is computed since it was split at the plane of 
symmetry. 

Figure 10 shows a particle trace plot that demonstrates 
the strong three-dimensional effect created in an overex- 
panded SERN nozzle. The low pressure in the nozzle 
plume gives rise to a transverse flow. Streamlines origi- 
nating from the side of the nozzle are deflected towards 
the symmetry plane. The transverse flow tends to in- 
crease the magnitude of the pressure on the expansion 
ramp surface relative to a two-dimensional case. This is 
shown in Fig. 11 which plots the pressure coefficient on 
the expansion ramp surface as a function of the nondi- 
mensional distance measured from the start of the ex- 
pansion ramp, x r . Results for both the centerline and 
off-centerline (61% semi- width) are compared with both 
the experimental data of Ref. [2] and a two-dimensional 
calculation. The code appears to predict the three di- 
mensional flow reasonably well, however, not enough grid 
points were used in the transverse direction in order to ac- 
curately resolve the flow around the side edges. This cal- 
culation required about 8 hours of CPU time on a CRAY 
YMP. Similar CFD studies of SERN nozzles without ex- 
ternal burning have been performed previously by Yaros 
[12] and Koschel & Rick [13]. 

Attempting to extend this approach to model external 
burning would be prohibitively expensive for the following 
reason: when external burning is used, a large subsonic 
flow region is created which requires a flow domain that 
extends beyond the trailing edge of the expansion ramp. 
This fact combined with the need to improve the resolu- 
tion in the transverse direction and resolve the injector 
and flameholding regions would significantly increase the 
number of points needed. Adding a detailed finite rate 
combustion model to the analysis could easily increase 
by an order of magnitude the computational resources 
needed. For this reason, the external burning flowfields 
are computed using the simplified model previously de- 
scribed. 

Code Validation; SERN Nozzles With External 
Burning 

Computations of several external burning nozzle config- 
urations studied experimentally in Ref. [2] are presented 



first. The computational domain that is used for the ex- 
ternal burning study is schematically shown in Fig. 4. At 
the inflow boundary of the SERN nozzle the total pres- 
sure, total temperature and flow angle are specified, and a 
zero pressure gradient is assumed. The composition of the 
gases entering the nozzle is obtained from the fuel-air ra- 
tio used in the combustor upstream of the nozzle. At the 
inflow boundary of the external flow the pressure, temper- 
ature, and flow velocity are specified. The composition of 
the fueled stream-tube was determined from the global 
equivalence ratio obtained from the control volume anal- 
ysis. All wall surfaces are treated as non-catalytic, no-slip 
boundaries, and a constant wall temperature T w = 300°^ 
was assumed based on experimental data. The bottom 
surface is treated as a free boundary. The downstream 
boundary needs to be treated more carefully due to the 
subsonic region created by the external burning process. 
The subsonic region is embedded between two supersonic 
streams; one consisting of the exhaust plume, and the 
other consisting of the freestream flow. Far downstream 
of the expansion ramp trailing edge, the pressure field 
tends to become uniform, with the pressure field in the 
supersonic streams imposed on the subsonic stream. In 
the present study, the outflow boundary condition was 
applied at a distance \L downstream of the expansion 
ramp trailing edge. 

Four cases were considered for the code validation. The 
flow conditions and geometry used are given in Table 1. 
In addition, the following parameters were used in all four 
cases: nozzle total temperature, T nft = 3500°.R, and ex- 
ternal burning fuel total temperature, Tg 3 = 518°ii. 

The first case investigated is the baseline nozzle without 
flameholder. Several grids having different spacings and 
number of points were examined. The computational do- 
main was divided into 3 blocks, as shown in Fig. 12. The 
first and second blocks cover the internal nozzle and ex- 
ternal flow up to the cowl tip respectively, and the third 
block covers the entire domain from the cowl tip down- 
stream. For the baseline nozzle, 70 grid points in the hor- 
izontal direction were sufficient to accurately resolve the 
fiowfield in the internal nozzle (block-1), and this num- 
ber was not changed. Similarly, the fiowfield around the 
cowl (block-2) was adequately modeled with 41 points in 
the horizontal direction. The number of points used in 
the vertical direction and the total number of points used 
for the third block was varied. Exponentially stretched 
increments in the vertical direction were used for all the 
grids. The values of y + for points nearest to the wall, for 
the fine grid, were below 5. 

Figure 13 shows the pressure coefficient on the ex- 
pansion ramp surface as a function of the nondimen- 
sional distance (measured from the start of the expan- 
sion ramp x r ) for three different grids. The results are 
compared with experimental data given at the centerline 



and off-centerline (61% semi-width) location. The station 
(x - x r )/L = corresponds to the the start of the expan- 
sion ramp, and the station (x - x r )/L = 1 corresponds 
to its trailing edge. A coarse and a fine grid were inves- 
tigated in addition to a fine, solution-adapted grid. All 
three grids give reasonably accurate results, but the finer 
grids give a better resolution of the double peak. The 
use of an adapted grid resulted in only a small improve- 
ment in the solution and does not justify the associated 
computational overhead. In all subsequent calculations, 
a distribution of points based on the fine grid was used. 

In order to understand the effects of external burning 
on the pressure distribution along the expansion ramp, it 
is useful to view contour plots of various properties and 
compare them to the flow without external burning. Fig- 
ure 14 shows contour plots for temperature, Mach number 
and pressure for the baseline nozzle with and without ex- 
ternal burning 1 . Figure 14(a) presents temperature con- 
tour plots showing the high temperature external burning 
plume. The combustion process in the external stream 
creates a subsonic flow region embedded in two super- 
sonic streams: one consisting of the exhaust plume and 
the other consisting of the freestream flow, as shown in 
fig. 14(b). The subsonic flow region is attained solely by 
the large increase in the sonic velocity due to combus- 
tion. The subsonic flow region created by the external 
burning process has important implications. In addition 
to local high pressure regions created by external burn- 
ing, information can now propagate upstream through 
this subsonic zone, and higher back pressure levels can 
be imposed also along the entire expansion ramp surface. 
The local high pressure created by the external burning 
plume can be strong enough to cause boundary layer sep- 
aration. This appears to be the case for the present flow 
conditions, as seen in the Mach number contour plot and 
the pressure coefficient plot (fig. 13). A small separation 
bubble appears around the station (x - x T )/L = 0.2. The 
pressure increase behaves like a classic separated bound- 
ary layer, with a pressure rise due to the separation shock 
followed by a pressure plateau and a second jump due to 
the reattachment shock. The subsequent pressure varia- 
tions are a result of reflected waves from the shear layer 
and further interactions with the external burning plume. 
Figure 14(c) shows the effect of external burning on the 
pressure field. Note the localized high pressure areas and 
the pressurization of almost the entire fiowfield to atmo- 
spheric levels. Also, note that the pressure at the exit 
boundary is nearly uniform, consistent with our treat- 
ment of the outflow boundary condition. 

The second case investigated considered the deflected 
cowl without flameholder. The internal block required 
105 grid points in the horizontal direction. The extra grid 



J The results shown in Fig. 14 without external burning give only 
qualitative information, since they do not include 3D effects 



points were needed to resolve the internal shock. The rest 
of the grid used a distribution of points similar to that 
used for the baseline cowl. Figure 15 shows the pressure 
coefficient on the expansion ramp surface. The computed 
results appear to predict the general trend observed in the 
experiments, however, the computed peak values appear 
to be slightly damped. The pressure spike near station 
(x - x r )/L = is caused by the oblique shock generated 
by the deflected cowl impinging slightly ahead of the 17° 
expansion ramp corner. 

The next two cases considered the deflected cowl with 
the flameholder shown in Fig. 9. A fourth block was 
added to the grid topology. Figure 16 shows the pres- 
sure coefficient for the M = 1.8 case. Once again, the 
computed pressure distribution is in close agreement with 
the experiments, however, the pressure peak appears to 
be overpredicted. Figure 17 presents results for the same 
configuration at M = 1.2. The agreement with the ex- 
periments is not as good as in the previous cases, but the 
general trend is well predicted by the computations. It 
should be pointed out that the first pressure peak, which 
is underpredicted, is experimentally observed along the 
centerline but not at the off-center location. A typical 
computation required approximately 90 minutes of CPU 
time on the CRAY YMP. 

Figure 18 shows a qualitative comparison for this case 
between experimental infrared images and computational 
results (temperature contours). The bright spots around 
the nozzle exit are due to hot metal radiation, as well as 
the bright area near the uncooled end of the expansion 
ramp surface. Surface reflections may be responsible for 
some of the bright spots not observed in the CFD result. 

The individual terms comprising the axial and normal 
forces for the four cases discussed above are shown in 
Fig. 19. The internal, ramp, and boat-tail parts of the 
total force are displayed in bar charts and compared with 
the experimental results of Ref. [2] with and without ex- 
ternal burning. Three observations must be made re- 
garding this figure. First, the boat-tail pressures were 
not measured in Ref. [2], but they were estimated using 
the projected areas and a base pressure assumption. The 
values obtained in the present work provide a better ap- 
proximation to these forces and they have been used to 
complement the other forces obtained from Ref. [2]. Sec- 
ond, since experimental pressure measurements extended 
only up to station (a; - x r )/L = 0.61, the CFD ramp sur- 
face pressure was integrated up to this point also. Third, 
following Ref. [2], the flameholder forces have been ne- 
glected. This is due to the fact that, in the experiment, a 
disproportionately large flameholder was required at the 
model scale to stabilize the flame. If these forces, were 
included, the results would not be representative of the 
full scale nozzle. 

From this figure it is clear that external burning in- 



creases the ramp and cowl boat-tail forces in both the 
axial and normal directions. The effect of external burn- 
ing is more pronounced in the normal forces. Negative 
nozzle normal force is detrimental to vehicle performance 
because additional lift, and therefore induced drag, is re- 
quired to counteract it. Also, the resultant nose-up mo- 
ment must be compensated for, usually by control surface 
deflection with an associated drag penalty. 

The increase in total axial and normal forces as a per- 
centage of ideal axial force, predicted by the present study 
and by the experimental work of Trefny and Carboni is 
shown in Table 2. With the exception of case-3, for which 
the CFD results overpredict the force increments relative 
to the experiment, the computations differ from the ex- 
perimental values by 10-20%. 

The force increments range from 4% to 14% in the axial 
direction, and from 16% to 58% in the normal direction. 

The effectiveness of external burning is also demon- 
strated in Table 2, which shows the specific impulse ob- 
tained from the present study, and from the results of 
Ref. [2]. The computed I ap values range from 554 to 2722 
seconds, compared with a range from 609 to 2113 seconds 
reported by Trefny and Carboni. The lower I, p values are 
obtained with the baseline cowl. For comparison, the I sp 
of other auxiliary propulsion methods, such as a chemical 
rocket, have an I sp of about 400. One disadvantage of 
external burning is that there is little control, if any, of 
the direction of the total force vector increment. 

Effect of External Burning Fuel Pressure on 
SERN Nozzles 

The variation of external burning performance with fuel 
pressure is shown in Figs. 20-22. The deflected cowl with 
.flameholder at M — 1.2 and a nominal NPR = 6 is con- 
sidered. The pressure distribution on the expansion ramp 
is shown in Fig. 20 for four different fuel injection pres- 
sures. The corresponding global equivalence ratio is also 
indicated in this figure. The net effect of increasing the 
fuel pressure is the reduction of the amount of overex- 
pansion on the initial part of the ramp and the creation 
of a second pressure peak which starts near the trailing 
edge of the expansion ramp and moves upstream with still 
higher values of the fuel pressure. This same trend has 
been observed in the experiments of Ref. [2]. The effect 
on the resulting forces is shown in Fig. 21. The axial and 
normal forces on the expansion ramp and cowl boat-tail 
progressively increase with fuel pressure over this range. 
The pressures on the expansion ramp were integrated up 
to the trailing edge in this case. It should be pointed out 
that at the lowest fuel pressure, the forces are probably 
underestimated. The reduced amount of external heat 
addition cannot raise the pressure to atmospheric levels, 
and therefore, three dimensional effects could be expected 
to increase the normal and axial forces calculated for this 



case. The total axial and normal forces as a function of 
external burning fuel pressure are shown in Fig. 22 and 
are compared with experimental data. Note that the axial 
and normal forces show an increasing trend in both CFD 
and experiment over this fuel injection pressure range, al- 
though at a different rate. One possible source for this 
difference could be the fact that the experimental result 
is based on ramp pressure data up to (x - z r )/L = 0.61. 
The CFD results, however, considered the entire expan- 
sion ramp. Eventually, the force curves of Fig. 22 will 
level out at still higher fuel pressures. The value at which 
this will occur has not been determined. 

Figure 23 shows Mach number contour plots for the 
four fuel pressures. The constraining effect of the ex- 
ternal burning process on the nozzle plume expansion is 
clearly visible in this figure. Note that an increased fuel 
pressure results in a reduction in the initial expansion. 
The external burning plume deflects the shear layer to- 
wards the expansion ramp, creating a converging area for 
the internal nozzle plume. The decrease in area for this 
supersonic stream results in a decrease in Mach number 
which produces the first pressure peak. 

Performance of External Burning as a Function 
of NPR 

The performance of a SERN nozzle over a range of 
nozzle pressure ratios is investigated at two Mach num- 
bers M = 1.2 and M = 1.8. The deflected cowl with a 
flameholder is analyzed for a fixed fuel injector pressure 
of ph 2 = 320.4 for the M = 1.2 case, and ph 2 = 112.9 for 
the M = 1.8 case. Figure 24 shows the variation in the 
pressure coefficient on the expansion ramp with NPR for 
the two Mach numbers. The flat pressure distribution at 
the lowest NPR indicates that the external burning plume 
is effectively preventing any further overexpansion beyond 
the cowl trailing edge. This flat, nearly uniform ambient 
pressure distribution is in agreement with experimental 
observations [2]. As NPR is increased, the pressure on 
the initial portion of the ramp increases accordingly, but 
subsequently drops sharply. The effect of external burn- 
ing on the pressure distribution is felt further downstream 
as the NPR increases. 

Figure 25 shows temperature contours for the four 
NPR values at M = 1.8. The internal nozzle plume 
grows in size with increasing NPR, and is able to pen- 
etrate further downstream against the constraining force 
of the external burning plume. Note that for the lowest 
NPR, a high temperature region is established around 
the cowl boat-tail. At the higher NPRs the high tem- 
perature created by the external burning process cannot 
propagate upstream to the cowl. This may help explain 
the difficulties encountered by Trefny and Carboni [2] in 
stabilizing an external burning flame a high NPR values 
{NPR > 8). 



The nozzle force components for the M = 1.8 case 
is shown in Fig. 26. The internal axial force ratio de- 
creases with NPR because the internal expansion area 
remains constant. The decrease in internal thrust is com- 
pensated for by an increase in the ramp forces due to 
the larger pressures acting on its surface. The magni- 
tude of the boat-tail forces increases initially because at 
NPR = 8.5 the external combustion region does not ex- 
tend back to the cowl region. At higher NPR values, 
boat-tail forces decrease in magnitude as they become 
progressively smaller compared to the ideal axial force. 
The total axial and normal forces as a function of NPR 
are plotted in Fig. 27. They are compared with the ex- 
perimental results of Trefny and Carboni [2] with and 
without external burning. In the experimental study, an 
external burning flame could not be stabilized at NPR 
values greater than 8, as previously mentioned, therefore 
only one data point is plotted. The practical stabiliza- 
tion of an external burning flame at high NPR values 
will require further study. 

Scaling Studies 

The computations presented above considered a 10% 
scale model. There is considerable interest in exploring 
the performance of external burning in a full scale nozzle. 
Two full scale (100%) configurations were studied. In the 
first one, the whole nozzle including the flameholder was 
scaled up by a factor of 10. The second configuration 
takes into account the fact that if a 0.5-inch flameholder 
stabilizes combustion at model scale, then the same 0.5- 
inch step should stabilize a piloting flame at vehicle scale 
if pressure, temperature, velocity and fuel pressure are 
comparable. From a practical standpoint, however, some 
increase in flameholder height would be required since the 
boundary layer and the fueled stream height would scale 
geometrically. The scale factor required for the flame- 
holder is presently unknown but thought to be much less 
than the model scale factor. Therefore, the second 100% 
scale configuration considers a scale up of the entire noz- 
zle except for the flameholder which is kept at 0.5-inch 
height. 

In order to maintain the same resolution of the bound- 
ary layer at full scale, where the Reynolds number is 10 
times larger, the clustering of grid points near the wall 
was increased by a factor of \/l0- This factor will keep 
the value of y + unchanged, since it is proportional to 
the distance from the wall, and to the square root of the 
Reynolds number. 

The kinetics of the combustion process is independent 
of scale, and for the same flow velocity, the flame prop- 
agation angle should be identical also. Therefore, the 
parameters controlling the rate of heat release were not 
modified for the full scale computations. 



8 



Figure 28 shows the pressure coefficient for the 10% 
scale nozzle, the 100% scale nozzle, and the 100% scale 
nozzle with the 0.5-inch flameholder. The data is pre- 
sented for M — 1.2, and M = 1.8. The results indicate 
that there is practically no effect of scale on the pressure 
distribution. The flowfield in the 10% scale nozzle and the 
overall 100% nozzle are nearly identical. Some differences 
are observed when the flameholder is kept at 10% scale 
(0.5-inch). This effect is due to the change in the shear 
layer flow, resulting from a difference in the relative scales 
between the nozzle and flameholder. The Mach number 
contours for the 10% nozzle and the 100% nozzle with the 
10% scale flameholder at Af = 1.2 is shown in Fig. 29. A 
detail of the flow near the flameholder is shown in part 
(c) of Fig. 29. 

Conclusions 

A computational investigation of the effects of external 
burning on the performance of SERN nozzles operating at 
transonic speeds was presented. The study focused on the 
effects of external heat addition and introduced a simpli- 
fied injection and mixing model based on a control volume 
analysis. This simplified model permitted parametric and 
scaling studies that would have been prohibitively costly 
to conduct with a detailed CFD analysis. 

While overexpanded SERN nozzles without external 
burning required a full three dimensional analysis, it was 
shown that SERN nozzles that include external burn- 
ing can be adequately modeled using a two-dimensional 
formulation. The CFD methodology was validated by 
comparing the computed pressure distribution and thrust 
forces with experimental data. These comparisons were 
conducted for several nozzle configurations at various flow 
conditions. Good agreement between computational and 
experimental results was obtained. Specific Impulse cal- 
culations were also presented which indicated that exter- 
nal burning performance can be superior to other forms 
of thrust augmentation methods at transonic speeds. The 
results show that external burning can pressurize not only 
the expansion ramp, but also the nozzle cowl surface. 

The effects of injection fuel pressure and nozzle pressure 
ratio on the performance of SERN nozzles with external 
burning were investigated. The external burning process 
was shown to create a large subsonic flow region that 
permits higher back pressure levels to be imposed along 
the expansion ramp. In addition, localized high pres- 
sure regions are created by the external burning process. 
The adverse pressure gradients established, can force the 
boundary layer to separate. This interaction may be a 
major design issue and will require further study. The 
results of the parametric studies produced trends similar 
to those reported in the experimental study, and provided 
additional information that complements the experimen- 
tal data, improving our understanding of external burning 



flowfields. A study of external burning at full scale was 
also presented. The results indicated that the flowfield is 
not very sensitive to scale. 

References 

[1] Trefny, C. J., "Experiments and Analysis Concerning 
the Use of External Burning to Reduce Aerospace Vehicle 
Transonic Drag," NASA TM-105397, Jan. 1992. 
[2] Trefny, C. J. and Carboni, J.D., "Results of a Single- 
Expansion-Ramp Nozzle Experiment With Hot Exhaust 
and External Burning," NASA TM-106390, 1993. 
[3] Bittner, R.D. and McClintori, C.R., "Numerical Study 
of External Burning Flowfields," AIAA paper 91-2392, 
June 1991. 

[4] Povinelli, F.P. and Povinelli, L. A., "Correlation of Sec- 
ondary Sonic and Supersonic Gaseous Jet Penetration 
Into Supersonic Crossflows," NASA TN D-6370, June 
1971. 

[5] Yungster, S., "Numerical Study of Shock- Wave Bound- 
ary Layer Interactions in Premixed Combustible Gases," 
AIAA Journal, Vol. 30, No. 10, 1992, pp. 2379-2387. 
[6] Yee, H.C., Klopfer, G.H. and Montagne, J.-L., "High- 
Resolution Shock-Capturing Schemes for Inviscid and 
Viscous Hypersonic Flows," NASA TM- 100097, Apr. 
1988. 

[7] Chitsomboon, T., private communication, ICOMP- 
NASA Lewis Research Center, Cleveland, OH, March 
1993. 

[8] Georgiadis, N.J., Drummond, J.E. and Leonard, B.P., 
"Development of an Algebraic Turbulence Model for 
Analysis of Propulsion Flows," AIAA paper 92-3861, 
1992. 

[9] Baldwin, B. and Lomax, H., "Thin Layer Approx- 
imation and Algebraic Model for Separated Turbulent 
Flows," AIAA paper 78-257, Jan. 1978. 
[10] Thomas, P.D., "Numerical Method for Predicting 
Flow Characteristics and Performance of Nonaxisymmet- 
ric Nozzles, Theory," NASA CR-3147, Sept. 1979. 
[11] Hill, P.G. and Peterson, C.R., Mechanics and Ther- 
modynamics of Propulsion, 1st ed., Addison-Wesley, 
1965, pp. 354-362. 

[12] Yaros, S., "Use of the PARC Code For Generic NASP 
Nozzles Operating at Off-Design Transonic Conditions," 
AIAA paper 91-2154, June 1991. 
[13] Koschel, W. and Rick, W., "Design Considera- 
tions for Nozzles of Hypersonic Airbreathing Propulsion," 
AIAA paper 91-5019, Dec. 1991. 



Table 1: Code Validation Cases 



Case 


Cowl 


Flameholder 


Mach number 


NPR 


Ph 2 
psi 


Poo 

psi 


{FIAT 


1 


baseline 


no 


1.2 


6.07 


320.0 


6.87 


0.021 


2 


deflected 


no 


1.2 


5.37 


238.4 


6.87 


0.016 


3 


deflected 


yes 


1.8 


8.58 


112.9 


4.0 


0.018 


4 


deflected 


yes 


1.2 


6.45 


320.4 


6.87 


0.02 



I Fuel-air ratio in the combustor (nozzle inlet) 



Table 2: Performance of External Burning 



Case (AF/Fj) x (AF/FQy I sp (sec) 





Experiment 


CFD 


Experiment 


CFD 


Experiment 


CFD 


1 


0.053 


0.047 


0.178 


0.162 


609 


554 


2 


0.136 


0.146 


0.448 


0.545 


1768 


2131 


3 


0.043 


0.063 


0.178 


0.326 


1501 


2722 


4 


0.140 


0.121 


0.584 


0.513 


2113 


1857 



10 





External 
fuel injection 



\JH2 J2 



External flow 

M-0.8 - 2.5 



.*«£$ ."■ External burning^ 

^-combusUon products^ 
#0 



Ftame front 



Fig. 1. Artists conception of a single-stage-to-orbit ve- 
hicle. 



Fig. 3. Schematic of external burning. 



NOZZLE 
EXPANSION 
SURFACE 




SHEAR LAYER 



COWL 

TRAILING 

EDGE 



Tt,P„a 



p z =0 En 9' ne 

fl«VJ 

Cowl **■ 




prembced H2-alr 



„ *f combm«^! model ^ 



K **«rfii" ' 



Moo, Poo, Too 



Flame front 



Fig. 2. Schematic of over-expanded SERN nozzle at 
transonic conditions. 



Fig. 4. Computational model of external burning. 



11 




Pa U a Pa 



p U p 
K a a na 



/^-jL 



m 



cowl surface^, 

A e— ► Pe U e R* 
— ► Pa U a Pa 




u~u. 



mixing boundary streamline 



Fig. 5. Control volume analysis of the flow around the fuel injector. 



0.35 



0.30 



D 



| 0.25 



CO 

en 
o 

E 



0.20 



0.15 









— «n 


\ 










V 1 






*~ 


— Tl 


"•out 








/ 


/ 














































/> 


. — *' 


_^.i 


i 


--- 


*"" 




ir-'' 


■ "'" 


--y 
































f 






















SUPPORT STRUT 
o 8x6 SWT 
o 10x10 SWT 
o 9x15 LSWT 



TEST NOZZLES 
o NASP 
o HSCT/HSR 
a OTHER 



BASE BURNING 
TEST CAPA8UTY 

H.-AIR COMBUSTOR 
(T«„ - 4500 OEG R) 
^- FLOW MEASUREMENT 
STATION 



SIX COMPONENT 
FORCE BALANCE 



-HIGH PRESSURE AIR. FUEL. 
AND COOLING FLOW SYSTEMS 
o TWO 450 PSI AIR LINES 
o GH2 FUEL SYPPLY 
o WATER COOLING 



0.5 0.6 0.7 0.8 0.9 1.0 

VA. 



Fig. 6. Graphic solution of Eq. 15. 



Fig. 7. Schematic of NASA Lewis jet exit rig. 



12 




Throat 



-17° initial angle 
■ Baseline Cowl 



Nozzle Ramp Surface (Upper Wall) 
Coordinates in Table 1(a) 



Combustor Exit "=9.875 X =13.75 

(Nozzle inlet) ' (a) Nozzle geometry with baseline cowl. 




(b) Baseline Cowl 



Cowl Internal (Lower Wall) y — Straight line 

— 8.875 Radius centered at x=10.125 



- 0.066 Radius 



0.888 



X=10.125 X=13.75 



- Cowl Internal (Lower Wall) 
Coordinates Same as Baseline 
Uptox=12.70 



8 deflection 




Straight line 



~~~f— — 0.063 Radius 
Straight line blend into 8.875 Radius 



x=15.00 



Fig. 8. Schematic of SERN nozzle configurations. 




FUEL INJECTION 

.381" SPACING 

21,.060"DIA. 

(S/d =6.35) 



2.50 (42dla) 



5.50 (92dia) 



Fig. 9. Schematic of flameholder. 



13 




Fig. 10. Particle traces for a SERN nozzle without external burning. M^ = 1.2. 



4.0 



o 




-1.0 



-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 
(x-x r )/L 

Fig. 11. Pressure coefficient on the expansion ramp surface without external burning. 



14 



o 



5.0 
4.0 
3.0 
2.0 
1.0 
0.0 
-1.0 





Fig. 12. Computational grid. 3 blocks 70x93; 40x65; 240x158. 



■ Expi (centerlirje) ; 

' J!xp L _( off— ce n^e rli ne) 

•CFD (22?x'128)" ~T 

— -l-CFDl (309x158) ! 

. --4=-CFdL (3Q$x4 58- adapted) 




-0.4-0.2 O.O 0.2 0.4 0.6 0.8 1.0 
(x-x r )/L 



2.0 



1.0 



o 



0.0 



-1.0 



■Exp. (centerlinei) 
'Exp. (t>ff— cent^riine) 
-|— CFD (229x1 28)| 
-!— CFD (309x158); 
-_CFD-(£o9-xi58-; 



adapted) 




-0.1 0.1 0.3 0.5 

(x-x r )/L 



0.7 



Fig. 13. Pressure coefficient for three grid distributions. Baseline nozzle, no flameholder, Moo = 1-2, NPR = 6.07. 



15 




o 
2 



PQ 



o o 
a s 

OS 
O N 



t 10 
a a 



D Q 

d a 
o a 
b a 
as a 



DQE3QOQQO 

ooannoon 
BoogoasQ 

PSOQOQSD 
N VtOttON7l0 



■ w pj n eg 



O 

S 

o 
o 

(1 

s 









3 
O 



o 
u 

s-l 
3 



ft 

g 

a 
-*■=> 

"3 
c 
o 



ee 




H 

o 
2 



1 


1 h> 




a a q o a 








a 


aoa 


D O 


SS 
























DO o 
















s 












m a 


wow 


U) 


o in 



O*-— NMnnTTmUIBISSN 




o 



C 

e 

•3 
c 
o 
2 



N 

O 

c 

.£ 
"3 

3 

fa* 

<2 

_© 

ft 

o 

e 
o 



ho 



(c) 







O 





"Exp. (denteif-Iine) 



NoEB. 



4.0 



3.0 



2.0 



1.0 



0.0 



-1.0 

-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 

(x-x r )/L 

Fig. 15. Pressure coefficient for deflected cowl without 
fiameholder. M x = 1.2, NPR = 5.37. 



m 



q o n o a oooaaaaaaoapDOOOogaoog 

ainaind inouiDinavioinaviSuiDiAouiamQuio 

O a »- •- M NnBTTKllfllDISSNOBIHOIOO^^NNn 



loaaaosooonoaaasaooo* 




EB on 



o 



4.0 



3.0 



2.0 



1.0 



0.0 




-1.0 



"Exp. (centerline) ! 



Fig. 14. cont. (c) Nondimensional pressure contours 

(p/Poo)- 



-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 
(x-x r )/L 



Fig. 16. Pressure coefficient for deflected cowl with 
fiameholder. M x = 1.8, NPR = 8.58. 



17 



5.0 
4.0 - 
3.0 

o* 2-0 

1.0 

0.0 

-1.0 

-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 

(x-x r )/L 

Fig. 17. Pressure coefficient for deflected cowl with 
flameholder. M x = 1.2, NPR = 6.45. 



\ ; °Exp. (cienteiHine) 


rre)- 




i -CFD ! ] 

_ . .• . . ■ .1. - i. . . 




i i ' ! 
1 i ' ! 






. . ._, 






: *• i i 


_ 1 _/. 




Experimental infrared image 




Computational result (T/Tx,). 



Fig. 18. Qualitative comparison of computed and ex- 
perimental external burning flowfield 



18 



(a) 



' ■ 


Total 


s 


Interna! 


HI Ramp 


D 


Boat-tail 



(b) 





CFD (EB on) 



Exp (EB on) 



Exp (No EB) 



CFD (EB on) 



Exp (EB on) 



Exp (No EB) 





CFD (EB on) 



Exp (EB on) 



Exp (No EB) 



CFD (EB on) 



Exp (EB on) 



Exp (No EB) 



Fig. 19. Nozzle force components obtained with present CFD method, compared with the experimental results of 
Trefny and Carboni. (Note: The forces on the boat-tail were not measured in the experiments. Therefore, the values 
shown are those obtained in the present work.) 

(a) Baseline cowl without flameholder, Moo = 1.2, NPR - 6.08. (b) Deflected cowl without flameholder, M x = 1.2, 
NPR = 5.37. 



19 



(c) 



■ 


Total 


E3 


Internal 


U 


Ramp 


D 


Boat-tail 



(d) 





CFD (EB on) 



Exp (EB on) 



Exp (No EB) 



CFD(EBon) 



Exp (EB on) 



Exp (No EB) 





CFD (EB on) 



Exp (EB on) 



Exp (No EB) 



CFD (EB on) 



Exp (EB on) 



Exp (No EB) 



Fig. 19. continued, (c) Deflected cowl with flameholder, M x = 1.8, NPR = 8.58. (d) Deflected cowl with 
flameholder, M^ = 1.2, NPR = 6.45. 



20 



o 



I 



-|— p„jj= 5p psi 
y— Ph2 =130 psi 



r -p"hi=lSp"ps7 
— p h j 2 =25p psi 



(*=6.52) 
(*=1.14) 
"(¥=1:67)' 
($=4.35) 



4.0 



3.0 



2.0 



1.0 



0.0 



-1.0 

-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 

(x-x r )/L 

Fig. 20. Variation of pressure coefficient with external 
burning fuel pressure. M x = 1.2, NPR = 6. 




I us 



I 

bj* ^bb^ « 

I ? 

1 

i 




1.15 



uT 1.05 

u." 

o 
*■*-» 

o 
a: 



0.95 



< 0.85 



ExtMiHl Burning FihI Pimui'i (psi) 



I 0. 



S -0-2 
4 



B^l 8 

IT Ml B? 

I I 

■J BH _ — 1 

J 1 

I 



0.75 





















CFD 

FXP 










c 














DD 


















aa 


u d 


. 








£1 











































0.0 100.0 200.0 300.0 

External Burning Fuel Pressure (psi) 





0.60 




0.40 




0.20 


>> 




u. 


0.00 









0£. 


-0.20 


p 


-0.40 







u_ 






-0.60 







F 







-0.80 


z 






-1.00 





















CFD 












a 


~EXP" 








DD 


















DO 


or 










[] 










































i 


/ 













EjtariMf Burning Fort PrMturt <p«l) 



-1.20 

0.0 100.0 200.0 300.0 

External Burning Fuel Pressure (psi) 

Fig. 22. Net (total) axial and normal forces as a 
function of external burning fuel pressure. M x = 1-2, 
NPR = 6. 



Fig. 21. Ramp and boat- tail forces variation with ex- 
ternal burning fuel pressure. 



21 



o 



o 

00 



as 

ft. 




10 




CN 


O 


II 


II 


3 


a. 


o 

CM 




II 


II 


ft. 


a? 



5» 

EL 









CM 




1BSSDBBBBBSSQ 



aoaQsagDOOSSB 
aooaaBanoaoao 
aooDsapoDaooB 



a a oa a * 



CM 



o 



Si 

ft. 



II 



o 

CO 



ft. 



X 



>• 
a; 
a: 



3 
O 



o 

XI 

s 

S 



S 



CO 



60 



o 



4.0 



3.0 



2.0 



1.0 



0.0 



-1.0 i- 




-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 
(x-x r )/L 

(a) 



o 



4.0 



3.0 



2.0 



1.0 



0.0 ; -j-- 



-1.0 





1 ' '■ ' 1 

! ! — JNPR=j=6 i | 


k. i'. 


! | ;NPRi8.5 | i 


i^l' 


r ^:^fNPRiU t2~ 1 1 


I i\ 


\ | ; lNPR±18 ! J 


i l\ 


^trt"'H 


i I \ 


\n : i i I 


I i. 


(W \ . ■ .4. . j. . \ 


i ' • Vl"".\ : i i '/ \! 


i i ^M^u ! : /\ ; / i 


j i 
i i 




i i" — i • i 


i i 


! : i i ' I 
± ■ : x_ _L J 



-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 
(x-x r )/L 

(b) 



Fig. 24. Variation of pressure coefficient with nozzle pressure ratio at two Mach numbers: (a) M<x> = 1-2, and (b) 
il^ = 1.8 



23 




»5 
a, 




a? 
ft, 



c4 



a; 
a, 




goggoaaaoooaoagD 
aSaooaasaDoaaaSp 
aaaaooaoaooaagoS 

uiavisiABinsi/ioinaiflQiAo 



a? 
ft, 




od 
II 

fti 
ft, 



N 

N 

o 

s 









o 

s 
o 
u 
tv 
s 

cs 

bb 



C-5 



O 0-6 







m 




6 




8 


MM 


H 








^H 








^H 








H 


^^1 6 


H 3 


1 ^ 


§ 1 


Mi 

1 


I 

9 


o 
o 



8.5 12 

Nozzle Pressure Ratio (NPR) 



1.00 



uT 0.95 



o 



0.90 



< 0.85 



0.80 







^ 


■ 








• >CFD 

•EXP 
- — EXP 


(EB on) 
(EB on) 
(No EB) 









5.0 10.0 15.0 20.0 

Nozzle Pressure Ratio, NPR 



■ 


Internal 


□ Ramp 


D 


Boat-tail 



d 



■ 






a 

o 








9 


w 

9 8 
9 


I'f 

5 


1 

o 











8.5 12 

Nozzle Pressure Ratio (NPR) 



O 



D 



V 



0.25 



0.00 



-0.25 



^ -0.50 

o 

E 

o 

z -0.75 



-1.00 









• 








• -CFD 


(EB on) 




■LXP 
---EXP 


(EB on) 
(No EB) 









5.0 10.0 15.0 20.0 

Nozzle Pressure Ratio, NPR 



Fig. 26. Nozzle force component variation with nozzle Fig. 27. Net (total) axial and normal forces as a func- 
pressure ratio (NPR). M^ = 1.8, ph, = 112.9. tion of nozzle pressure ratio, compared with the experi- 

mental results of Trefny and Carboni with and without 
external burning. M^ = 1.8, ph 2 = 112.9. 



25 



4.0 r- 



o 




-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 

(x-x r )/L 
(a) 



o 



4.0 



3.0 



2.0 



1.0 



0.0 



•1.0 



H 


-J— 1(j% i i ! 
-j — 1 Q0%; i1 00%^FH : 

- -^TODJf f "i TTRSF-TFT 1 
| i i ! 
; i i ! 
! :_ _ i _ _i_ _■_ 







; LmA.i\Li 


,. 1 

t 


' ! : L J_ 



-0.4-0.2 0.0 0.2 0.4 0.6 0.8 1.0 
(x-x r )/L 

(b) 




0.00000 
0.20000 
0.40000 
O.GOOOO 
0.80000 
1.00000 
1.20000 
1.40000 
I.EDODD 
l.BODOO 
Z. 00000 
Z.ZOODO 
Z. 40000 



(a) 




(b) 




(c) 



_. „„ n .. „. A ., a, . . ., Fig. 29. Mach number contours for (a) 10% scale 
Fig. 28. Scaling effect on the pressure coefficient on the ,° , ,, . . nn0f , ,,..,, ir ,ny i * 
° . t> ■„. * j r mo/ i model, and (b) 100% scale model with a 10% scale flame- 
expansion ramp. Results are presented for a 10% scale, ' v ' 

full scale, and a full scale model with a 10% nameholder. ... , ; ; . 

t \ .f t o /•i.n ./ 1 n holder of part (b). 
(a) Moo = 1.8; (b) M^ = 1.2. 



26 



REPORT DOCUMENTATION PAGE 



Form Approved 
OMB No. 0704-0188 



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1. AGENCY USE ONLY (LeaveblanQ 



2. REPORT DATE 

April 1992 



REPORTTYPE AND DATES COVERED 

Technical Memorandum 



4. TITLE AND SUBTITLE 



Computational Study of Single-Expansion-Ramp Nozzles With 
External Burning 



6. AUTHOR(S) 



Shaye Yungster, Charles J. Trefney 



7. PERFORMING ORGANIZATION NAME(S)AND ADDRESS(ES) 

National Aeronautics and Space Administration 
Lewis Research Center 
Cleveland, Ohio 44135-3191 



9. SPONSORING/MONITORING AGENCYNAME(S) AND ADDRESS(ES) 

National Aeronautics and Space Administration 
Washington, D.C. 20546-0001 



5. FUNDING NUMBERS 



WU-505-90-5R 



8. PERFORMING ORGANIZATION 
REPORT NUMBER 



E-8702 



10. SPONSORING/MONITORING 
AGENCY REPORT NUMBER 

NASATM-106550 
ICOMP-94-5 



11. SUPPLEMENTARY NOTES 

Shaye Yungster, Institute for Computational Mechanics in Propulsion, Lewis Research Center (work funded under NASA 
Cooperative Agreement NCC3-233). Charles J. Trefny, NASA Lewis Research Center. ICOMP Program Director, Louis 
Povinelli, (216) 433-58 18. 



12a. DISTRIBUTION/AVAILABILITY STATEMENT 

Unclassified-Unlimited 
Subject Category 34 



12b. DISTRIBUTION CODE 



13. ABSTRACT (Maximum 200 words) 

A computational investigation of the effects of external burning on the performance of single expansion ramp nozzles 
(SERN) operating at transonic speeds is presented. The study focuses on the effects of external heat addition and intro- 
duces a simplified injection and mixing model based on a control volume analysis. This simplified model permits 
parametric and scaling studies that would have been impossible to conduct with a detailed CFD analysis. The CFD model 
is validated by comparing the computed pressure distribution and thrust forces, for several nozzle configurations, with 
experimental data. Specific Impulse calculations are also presented which indicate that external burning performance can 
be superior to other methods of thrust augmentation at transonic speeds. The effects of injection fuel pressure and nozzle 
pressure ratio on the performance of SERN nozzles with external burning are described. The results show trends similar 
to those reported in the experimental study, and provide additional information that complements the experimental data, 
improving our understanding of external burning flowfields. A study of the effect of scale is also presented. The results 
indicate that combustion kinetics do not make the flowfield sensitive to scale. 



14. SUBJECTTERMS 

Transonic drag reduction; External burning 



17. SECURITY CLASSIFICATION 
OF REPORT 

Unclassified 



18. SECURITY CLASSIFICATION 
OF THIS PAGE 

Unclassified 



19. SECURITY CLASSIFICATION 
OF ABSTRACT 

Unclassified 



15. NUMBER OF PAGES 

28 



16. PRICE CODE 

A03 



20. LIMITATION OF ABSTRACT 



NSN 7540-01-280-5500 



Standard Form 298 (Rev. 2-89) 
Prescribed by ANSI Std. Z39-18 
298-102