NASA/TM-2003-212094 AIAA-2003-0651 

Fuel Injector Design Optimization for an 

Annular Scramjet Geometry 

Christopher J. Steffen, Jr. 

Glenn Research Center, Cleveland, Ohio 

January 2003 

https://ntrs.nasa.gov/search.jsp?R=20030014706 2018-05-15T15:39:17+00:00Z
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NASA/TM-2003-212094 AIAA-2003-0651 

Fuel Injector Design Optimization for an 

Annular Scramjet Geometry 

Christopher J. Steffen, Jr. 

Glenn Research Center, Cleveland, Ohio 

Prepared for the 

41st Aerospace Sciences Meeting and Exhibit 

sponsored by the American Institute of Aeronautics and Astronautics 

Reno, Nevada, January 6-9, 2003 

National Aeronautics and 

Space Administration 

Glenn Research Center 

January 2003 
This report contains preliminary 

findings, subject to revision as 

analysis proceeds. 

Trade names or manufacturers' names are used in this report for 

identification only. This usage does not constitute an official 

endorsement, either expressed or implied, by the National 

Aeronautics and Space Administration. 

The Propulsion and Power Program at 

NASA Glenn Research Center sponsored this work. 

Available from 

NASA Center for Aerospace Information 

7121 Standard Drive 

National Technical Information Service 

5285 Port Royal Road 

Hanover, MD 21076 Springfield, VA 22100 

Available electronically at http://gltrs.grc.nasa.gov 
Fuel Injector Design Optimization for an 

Annular Scramjet Geometry 

Christopher J. Steffen, Jr.* 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

g.j.steff!;m@grc.nasa,.,gQY 

Abstract 

A four-parameter, three-level, central composite experiment design has been used to optimize the 

configuration of an annular scramjet injector geometry using computational fluid dynamics. The 

computational fluid dynamic solutions played the role of computer experiments, and response surface 

methodology was used to capture the simulation results for mixing efficiency and total pressure recovery 

within the scramjet flowpath. An optimization procedure, based upon the response surface results of 

mixing efficiency, was used to compare the optimal design configuration against the target efficiency 

value of 92.5%. The results of three different optimization procedures are presented and all point to the 

need to look outside the current design space for different injector geometries that can meet or exceed 

the stated mixing efficiency target. 

Introduction 

NASA is presently studying several advanced propulsion systems that promise to provide affordable 

access to space. One concept, the reusable SSTO "GTX," is a rocket-based-combined cycle (RBCC) 

propulsion system. A three-view schematic is shown in Figure 1. An axisymmetric engine design has 

been created with an emphasis placed upon structural and analytical simplicity. The flowpath is defined 

by a fixed cowl and a translating centerbody which allows for the required variable geometry 

(see Figure 1). 

The operational scenario for GTX consists of four modes of propulsion. In the first mode, valid from liftoff 

to about Mach 2.5, the engine operates in a so-called independent ramjet stream (IRS) cycle, where 

rocket thrust is initially used for primary power and as an ignition source for hydrogen fuel injected directly 

into the inlet air. Ignition and combustion of this fuel source results in the formation of a thermal throat in 

the nozzle, and a ramjet mode of operation for the secondary stream. As the Mach number increases, the 

percentage of thrust due to the ramjet alone increases, and around Mach 2.5, the rocket motor is shut off 

and the engine shifts to a pure ramjet mode of operation (second mode). Around Mach 6, it becomes 

more practical to burn at supersonic speeds, and aided by centerbody translation, the engine shifts to a 

scramjet mode (third mode). The rocket is re-ignited around Mach 11 (fourth mode), the centerbody is 

translated to shut the inlet flow completely off, and the engine shifts to a rocket-only propulsion mode for 

the remainder of the ascent. Further details on the operation of this propulsion cycle are available in 

reference. 1 

The single flowpath concept presents a design challenge for the fuel injectors within this air-breathing 

combustor. Parametric CFD analysis can be used in a cost-effective manner to address this problem. 

Initial simulations can be done to screen the significant design parameters which deserve further study. 

Next, a detailed parametric analysis can be executed such that a polynomial response model can be 

developed to capture the relevant performance parameters. Design optimization, based upon the 

Senior Member, AIAA 

NASAlTM-2003-212094 1 
response surface modeling results, can point towards the optimal injector configuration within the design 

space. This three-step process has been carried out for the GTX combustor geometry, during mode three 

operation. 

Summary of Screening Design Results 

An initial screening design was conducted to investigate the importance of five design parameters 

governing the fuel injector" 

(x,) Injector angle (ainj) relative to wall 

(xJ Injector location (xin), relative to engine station #3 (see Figure 2) 

(x) Flight mach number (Mo) 

(xJ Fuel/Air ratio (<!>inj) 

(xJ Fuel split between axial and transverse injectors (a mixture variable) 

Results of this first phase of analysis clearly indicated that total fuel/air ratio should be maximized and 

axial fuel injector massflow should be minimized for the best mixing efficiency of injector geometry at all 

Mach numbers. Other significant effects were observed, but the sparse nature of the screening design 

obfuscated the results. More to the point, extensive confirmation testing revealed that a probable threeway interaction was lurking in the dataset, yet unresolved with the screening design. The sparse nature of 

the screening design can be appreciated after examining the schematic representation of a half-fractional, 

central composite design shown in Figure 4. 

Objective for RSM Design 

A more focused, second phase of this analysis was undertaken to develop accurate response models for 

both the mixing efficiency and total pressure recovery. This second phase concentrated upon the first four 

parameters discussed above, and fixed the fuel split parameter at one condition (25% step injector75% transverse injector). The second phase was comprised of a central composite experiment design in 

four parameters, shown in Figure 5. This design was capable of resolving the linear, quadratic, two-way 

and three-way interactions that were anticipated. This polynomial regression model, in turn, has been 

used as a surrogate for the costly CFD analysis during the process of design optimization. The 

optimization process sought answers to the following two questions: 1) Which injector geometry yields the 

best integrated performance of mixing efficiency across the scram trajectory? and 2) Can we meet the 

design target efficiency of 92.5% across the scram trajectory with the current injector design philosophy? 

Numerical Methods 

The Navier-Stokes solver used for these solutions was the GASPv4 code. GASP is a 3D, finite volume, 

structured-mesh RANS solver that has been used to analyze many high-speed propulsion flows, including 

scramjet combustors, in steady state or time-dependent fashion. A detailed discussion of the numerical 

methods have been presented elsewhere. 2 

The scramjet flowfield was assumed to be mixing limited, and thus the simulations have been executed 

with frozen chemistry. The GTX combustor geometry was designed as a 2200 annular section, with planar 

endwalls. The scramjet CFD simulations neglect the endwall effect and assumed a full 3600 engine 

geometry. This simplification enabled the computational domain to be limited by the fuel injector 

symmetry requirement. The circumferential distribution of injectors was fixed at three-degrees for the axial 

injectors and six-degrees for the transverse injectors. The percentage of fuel entering the combustor 

through the axial injectors was fixed at 25%. The combustor entrance conditions were specified from 

decoupled axisymmetric inlet simulations, according to the freestream conditions along a prescribed 

trajectory.3 The injectors have been specified as choked, sonic conditions for all cases. The gaseous 

hydrogen fuel was injected with a static temperature that varied with freestream Mach number. The fuel 

temperatures were specified as (1500, 2000, and 2500 OR) at Mach (6.5, 9.25, and 12) respectively. 

NASAlTM-2003-212094 2 
All results have been converged so that massflux was constant to within ±1%. The mesh dependence of 

these results has been taken as approximately ±5% based upon three different simulations with a 

coarse/fine grid sequence of (280k/2.24M) cells.' An examination of the run matrix indicates that the 

mixing efficiency results vary by as much as 64% across this design space. The results presented below 

have included an uncertainty associated with the response surface model predictions. The 95% 

confidence interval was seen to be slightly larger than the simulation errors discussed above. Note that 

this confidence interval is strictly valid for a normally distributed error, which is not the case with 

"computer experiments" of this type. Nevertheless, one can treat this bound as a reasonably conservative 

estimate of error since the dominant CFD errors (mesh dependence and iterative convergence) are of 

lesser magnitude. The field of experiment design for "computer experiments" is an active research area, 

and the interested reader is referred elsewhere for further reading. 2 

Two response variables have been modeled with RSM: the mixing efficiency of the hydrogen fuel and the 

total pressure recovery within the combustor. The mixing efficiency was defined as the percentage of 

oxygen that would be present in product water, if the flow was allowed to reach chemical equilibrium 

without further mixing. The species oxygen was chosen instead of hydrogen because all of the conditions 

considered herein are stoichiometric or fuel rich. Total pressure recovery was simply defined as the 

stream-thrust-averaged total pressure at the combustor exit plane, relative to the combustor entrance 

plane. 

Prior analysis has defined the combustor exit plane as the physical engine location called station #3 

(see Figure 3). However, one-dimensional cycle analysis reveals that the combustion process must be 

completed at a specific area ratio which is inversely proportional to the flight Mach number 

(see Figure 6.)t The reason for this is a fixed area profile throughout the mode three operation. To keep 

the Rayleigh losses in check during high Mach number flight, the combustion process must be completed 

at the lowest practical Mach number. 5 This requirement can be expressed in terms of the combustor 

flowpath area ratio. This leads directly to a progressively shorter combustor length to achieve the target 

mixing efficiency. The area profile of the GTX flowpath through the scram combustor is given in Figure 7. 

It is readily apparent that the Mach 12 flight condition has considerably less combustor length than the 

Mach 6 condition, to achieve adequate fuel mixing. This occurs despite a higher Mach number inflow 

condition. The results that follow have been analyzed at the combustor exit locations given by Figure 6 

and Figure 7. 

Response Surface Results 

A statistical analysis of the response data presented in Table 2 was performed using the software Design 

ExpertTM. The response surface model equations for the mixing efficiency and total pressure recovery are 

presented in the appendix, along with the standard error of prediction estimates. Thus far, a single 

confirmation case has been examined, and included in the data of Table 2 (as case #26). The observed 

value of mixing efficiency was (60.2%), while the RSM prediction was (63.8% with 95% confidence 

interval of [55.0%, 71.8%]. The observed value of total pressure recovery was (33.28%), while the RSM 

prediction was (33.54% with 95% confidence interval of [32.24%,34.83%]. 

The major conclusions of the previous work2 .4 are consistent with the new statistical analysis. The primary 

difference is that the surrogate models presented in the appendix have captured a three-way interaction 

that was previously unaccounted for. This results in a much more appropriate polynomial for conducting 

the design optimization. 

Two of the strongest effects present on the data can be seen' in Figure 8. On average, increasing fuel 

equivalence ratio has an expected positive effect upon the mixing efficiency of a given geometry. 

tNote that all flowpath area values have been rationalized by the captured streamtube area (Ac"p). 

I Note that the 3D carpet plot is the response swface, the black dots correspond to data of Table 2, and vertical black bars are the standard-errorof-prediction bounds at 95% confidence. The experiment number from Table 2 has been included for reference purposes. 

NASAITM-2003-212094 3 
Likewise, flight Mach number was inversely proportional to mixing efficiency. These effects are well 

known for the scramjet combustor. Figure 9 shows the total pressure recovery over the same region. 

The statistical analysis, combined with three-dimensional flow visualization, has brought to light an aspect 

of this engineering problem that would likely have been missed by conventional methods. The injector 

geometry (angle and location) and flight Mach number are involved in a three-way interaction. 

First, consider the interactive nature of the two geometric features, injector angle and location, at Mach 

6.5 (see Figure 10.) The interactive effect appears as a twist in the surface. Notice how 'the effect of 

injector angle upon mixing efficiency' depended upon whether the injector was placed in the forward 

region (-115 in.) or the aft region (-90 in.). The results reveal that reducing the injection angle will 

improve the mixing in the forward region of the combustor, yet will have the opposite effect if located in 

the aft region. An explanation for this curious effect lies in the flow visualization taken from threedimensional simulation results. 

Consider the effect of different injector geometries at the (Mo = 6.5, <!>;nj = 1.4) condition. Figure 11 

(Case #1) shows multiple cross-sections of the combustor flowfield between engine stations two and 

three. The injector geometry was low-angled (u;nj = 15°) and forward-located (x;nj = -115in.). Contours of 

local equivalence ratio were used to indicate how well the oxygen has mixed with hydrogen fuel. Regions 

that appear as white or light gray are pockets of unmixed oxygen. Likewise, regions of black or dark gray 

are regions of high fuel concentration. Figure 11 clearly presents a well-mixed flow with good fuel 

penetration to the centerline of the annular flowpath. Figure 12 (Case #13) shows a similar figure with 

nearly the same configuration. The only difference from Case #1 was the injection angle (u;nj = 75°). 

One would expect even better fuel penetration for Case #13, and indeed this appears to be the case. 

However, the oxygen-rich flow appears to have been bifurcated into the two un-mixed regions that appear 

in the figure. Consequently, the mixing efficiency was lower than Case #1. To summarize, large injection 

angles are not necessary for the required fuel-jet penetration in the forward region of the combustor for 

the Mach 6.5, (<!>;nj = 1.4) condition. 

Now consider the aft region of the combustor (x;nj = -90 in.).The gap between combustor walls is 

considerably larger in the aft region and the flow is substantially faster due to this area expansion. 

Figure 13 (Case #15) shows the results from the aft-located, low-angled injector at (Mo = 6.5, <!>;nj = 1.4) 

Now one can see that the hydrogen fuel never reaches the flowpath centerline. Instead, an oxygen-rich 

core flow has remained, and affects the overall mixing efficiency. Figure 14 (Case #4) corresponds to the 

aft-located, high-angled injector. One might anticipate that better penetration could substantially improve 

the overall mixing efficiency, as observed. To summarize, large injection angles are necessary for the 

required fuel-jet penetration in the aft region of the combustor at this Mach number and equivalence ratio. 

The difference in behavior discussed above was captured in the two-way interaction between injector 

angle and location. Yet this two-way interaction varies with freestream Mach number (Mo). To appreciate 

this phenomenon, consider the shape of the response surface at (<!>;nj = 1.4, Mo = 12) which is shown in 

Figure 15. Notice that there was very little twist in the surface: increasing injector angle improved mixing 

performance for all injector locations. This is due, in part, to the fact that the combustor inflow condition 

was substantially more difficult to penetrate with the hydrogen fuel jets at all angles. The high-Mach 

results tend to share the same characteristic of an oxygen-rich core flow along the flowpath centerline. 

Another substantial challenge at the high-Mach number limit was alluded to above: the length available 

for complete mixing is approximately 70% shorter than the low-Mach condition. The statistical description 

of the above circumstances can be summarized by saying that the variables (u;nj' x;nj'Mo) are involved in a 

three-way interaction. The interaction can be appreciated in a visual way in Figure 16 by noting the 

change in twist for the three surfaces shown. 

Surrogate-Based Optimization 

The GTX configuration has been designed for an accelerator mission. The scramjet operates in a 

continuous fashion from initiation around Mach 6, to the conclusion about Mach 12. Any performance 

optimization must take this variable operating condition into account. The great advantage of response 

surface methods lies in the ability to explore many different optimization schemes with a surrogate-based 

NASAlTM-2003-212094 4 
approach. Once the regression has been developed and verified, the polynomial representation of 

performance can be used as a surrogate for the complex and time-consuming CFD simulations. For our 

purposes, integration of the mixing performance across the scramjet flight condition can be calculated 

directly for any combination of the design factors. Since we know that the effect of fuel equivalence ratio 

has a net positive effect on mixing performance, we shall explore the results associated with the 

maximum value ($;nj = 1.4). 

The goal of the optimization is to discover which injector geometry (u;njl X;nj) yields the highest net mixing 

performance across the Mach number range of interest. This geometry must maximize the following 

condition 

12 

f17mi.x(a;nJ,x;nJ,Mo,t'AnJ = 1.4)dMo 6.5 

for all injector geometry combinations (u;njl X;nj). Figure 17 shows the graphical image of this condition, and 

the maximum value (75°, -107.5 in.) is shown with a black dot. Now the mixing performance of this 

optimal injector geometry can be compared to our stated target performance, shown in Figure 18. The 

message from this optimization was clear: no geometric injector configuration within this design space 

can achieve the mixing goal of 92.5% efficiency. Although the performance at the lower Mach numbers is 

encouraging, the performance rapidly declines to unacceptable levels. 

Other optimization strategies can be explored be permitting more than one geometric configuration to be 

utilized. Two additional attempts have been made, by segmenting the Mach range into multiple segments 

and repeating the optimization process outlined above. The results, shown in Figure 19, demonstrate that 

incremental improvements can be made by using one low-angled injector for the first half of the Mach 

range and a large-angled injector for the high-speed range. The improvement available by changing to 

three or more separate geometries was negligible. The two-segment optimal design utilized a 

(15°, -112 in.) injector for the first half of the trajectory, and a (75°, -110 in.) injector second half of the 

trajectory. The inescapable conclusion here is that we must pursue injector designs beyond this design 

space to achieve the mixing efficiency required at the high Mach flight conditions. 

Finally, little mention has been made of the response surface results concerning the total pressure 

recovery within the scramjet combustor. At the initiation of the present work, it was my expectation that 

several different injector configurations would be capable of achieving the desired mixing results. The 

total pressure recovery was envisioned as a discriminator that would play an important role in definition of 

the optimal design. Until mixing performance improvements are realized, this data will be of secondary 

importance to our goal of meeting the target efficiencies. 

Conclusions 

Statistical Design of Experiments has provided a framework for conducting an efficient and thorough 

study of the GTX scramjet fuel mixing process. Initial dominant effects were revealed with a five-factor 

screening design. A detailed four-factor central composite design was used to explore the performance 

variation across the design space and develop a response surface model capable of resolving a 

suspected three-way variable interaction. An effective surrogate model was assembled to capture the 

mixing efficiency results from the twenty-five CFD simulations. This surrogate model provided a costeffective means of exploring several injector design optimization strategies. The design for maximizing 

mixing efficiency was observed to be a two-geometry configuration that utilized a (15°, -112 in.) injector 

for the first half of the scramjet trajectory, and a (75°, -110 in.) injector for the remainder. However, 

optimization results clearly indicate that the performance capabilities of this injector design fall short of the 

target during high-Mach scramjet operation. Other design configurations should be included in future 

analysis of this annular scramjet combustor. 

NASAlTM-2003-212094 5 
Future Work 

To date, the GTX scramjet injector design strategy has utilized the simple approach of flush wall injection. 

This strategy has several clear advantages, including an unobtrusive design, a long history of both 

experimental and computational analysis, and an accepted design strategy for layout. Other programs 

have demonstrated better mixing characteristics by incorporating a mechanism that can enhance 

streamwise vortical motion and improve the near field mixing of hydrogen fuel jets. The design challenge 

for a RBCC engine like GTX is to preserve the unobstructed flowpath, and geometric simplicity while 

generating this vortical flow. Deployable hardware and fixed flow obstructions will be given a low priority 

due to the inherent complications just discussed. However, the GTX flowpath does present the scramjet 

designer with a SUdden-expansion feature at the combustor inflow plane. The interaction of angled fuel 

injection from the edge of this sudden expansion is the subject of a current research effort. 

Appendix 

The response data of Table 2 can readily be turned into a response surface model via regression 

techniques. The following polynomial expression was derived with the Design Expert software. Note that 

a natural logarithm transformation of the mixing efficiency data (rf":::s )was performed prior to modeling; 

the mixing efficiency model is back-transformed via the exponential (EXP) function. 

('l!ci~)= -25.904 + 0.l6767 £linj - 0.50985 xinj - 0.84107 Mo 

+3.3006 ¢\uj - 0.0022317 (Xinjf + 0.040200(Mo)2 

+ 0.0016821 (£linjXinj) -0.012812 (ainjMo) 

+ 0.000044196 (XinjMo) - 0.l9789 (Mo¢\uJ 

- 0.00013416 (ainjXinjMo) 

('TJ",;,x) = 100.0% EXP~~)) l+EXP~~ 

A proper interpretation of this polynomial model of mixing efficiency must include the statistical 

uncertainty E:S%~.L. The 95% confidence interval on future prediction, of the response is defined below. 

Note that the uncertainty estimate is based upon Student'st-distribution (tstudent) and the standard error of 

regression (Strans(y).x) for the transformed data. 6 

Em: c.r. '" ±tstudent Strans(yj-x ; tstudent = 2.16 ; Strans(yj-x = 0.17 

o EXP' trans + E trae-s ) 95YoC.I. '" 100.0 \'l~ - 95VoC.r. 

'lnnx trans trans ) 1 + EXP 'lmix ± E95% C.I. 

Note that a similar set of equations has been developed for the response data corresponding to the total 

pressure recovery. The pressure recovery data did not require any transformation. 

NASA/TM-2003-212094 

(PO~02) = 86.213 - 0.39662 £linj + 0.0020274 (£linjf 

- 0.18151 xinj - 0.0016203 £linjxinj -10.245 Mo 

- 0.0075576 £linjMO + 0.012149 XinjMO 

+ 0.6508 (Mo)2 - 4.3482 ¢\uj - 1.133 Mo ¢\uj 

E95%C.r. % '" ±tstudent S(y).x ; tstudent = 2.l.- S(y).x = 0.60 

(Rl3/ )95%C.I. (Rl3/) 'P02 '" O}-P02 ± E95%C.r. 

6 
References 

1. Trefny, C.J. "An Airbreathing Launch Vehicle Concept for Single Stage to Orbit," AIAA-99-2730, 

35th AIAAlASMEISAEIASEE Joint Propulsion Conference and Exhibit, June 20-23,1999. 

2. Steffen, C.J., Jr., "Response Surface Modeling of Combined-Cycle Propulsion Components Using 

Computational Fluid Dynamics," AIAA-2002-Q542, Reno, NV, 2002. 

3. Hack, K.J., and Riehl, J.P., "Trajectory Development and Optimization of an RBCC-based Launch 

Vehicle," AAS 99-347, AAS/AIAA Astrodynamics Specialist Conference, Girdwood, AK, 16-19 

August, 1999. 

4. Steffen, C.J., Jr., Bond, A.B., and Edwards, J.A., ''Three Dimensional CFD Analysis of the GTX 

Combustor," NASAlTM-2002-211572, prepared for the Joint Subcommittee Meeting sponsored by 

the Joint Army-Navy-NASA-Air Force, Destin, FL, April 2002. 

5. Heiser, W.H., and Pratt, D.T., Hypersonic Airbreathing Propulsion. AIAA Education Series, 

J.S. Przemieniecki, Series Editor-in-Chief, ISBN 1-56347-035-7, 1994, pp. 79-80. 

6. CRC Standard Mathematical Tables, 28th edition, W.H. Beyer, editor, CRC Press, Boca Raton, FL, 

1987. 

<X.inj 

Xinj 

Mo 

ejlinj 

NASAlTM-2003-212094 

Table 1. Central composite design: 

four parameter design space. 

Min Mid 

15° 45° 

Max 

75° 

Fwd (-115 in.) Mid (-102.5 in.) Aft (-90 in.) 

6.5 9.25 12 

1.0 1.2 1.4 

7 
Table 2. Central composite design: run matrix and response variables 

for the 25 cases with an additional confirmation run (#26). 

~ 

-=====- ::;Jt?f] 

-====== <jb;d 

~ -L 

Figure 1. Rocket based combined cycle vehicle geometry: GTX. 

NASAITM-2003-212094 8 
Nozzle 

Translating 

centerbody 

Figure 2. RBCC propulsion system cutaway view. 

Figure 3. Close-up view of the Scramjet combustor 

portion of the GTX flowpath. 

r rJJJ ~IJ trlJ 

x·[J!D m O!~ 

tl~tC~Drt~ -X1~ 

X » 4 

Figure 4. Twenty-seven node fractionated-central-composite 

design used for screening purposes: this design was 

for a five parameter, three level analysis. 

NASAlTM-2003-212094 9 
NASAlTM-2003-212094 

cl.I~' $~ L/ r~ -j/ -X1~ / 

IrI·l. ./ •• 

X4 ----- .. 

Figure 5. Twenty-five node central-composite design 

used to build a more accurate response surface model: 

this design was for a four parameter, three level analysis. 

Combustor Exit Area 

0.45 

0.40 

0.35 

0.30 CI. J 0.25 

J 0.20 

0.15 

0.10 

0.05 

0.00 

5 6 7 8 9 10 11 12 

Freestream Mach number, Mo 

Figure 6. Combustor Exit Area is inversely 

proportional to the flight Mach number. 

0.35 

0.30 

0.25 

J 0.20 

Cl 0.15 

0.10 

0.05 

0.00 

Flowpath Area Profile 

-120 -100 -80 -60 -40 -20 0 

Axial location, relative to Staion#3 (in) 

Figure 7. Combustor area profile: note this plot 

describes the flowpath geometry between 

stations #2 and #3 depicted above. 

10 
_ 8 Mo 

~-------------------------- ~ 

~--____ 10 

----___ 12 

-----

------ ~, 

_~100 

'#10 ]80 

6077mix (%) 

#2-0--~ ~~~-J20 

~.2 1.31.4 

1 .1 ¢ 

Figure 8. Response surface of mixing efficiency, as a function 

of flight Mach number (Mo) and fuel equivalence ratio (cjI). 

11 ¢ ·~.2. _~.3 . . --.1.. 4 ~~45 

#17 ! 40 

35 P03 (% ) 

Figure 9. Response surface of total pressure recovery, as a function 

of flight Mach number (Mo) and fuel equivalence ratio (cjI). 

77mix 

-100 

( . -:uo 

Xinj In) 

// 

// 

Figure 10. Response surface of mixing efficiency as a function 

of injector angle (a;..j) and location (Xinj) for the Mo = 6.5, cjI = 1.4 condition. 

NASA/TM-2003-212094 11 
FWD- 15° 

o 

5 

o 

5 

Figure 11. Case #1 (forward-located and low-angled injection): 

three-dimensional contours of fuel-equivalence ratio. 

Note that the lighter colored regions connote excess oxygen. 

FWD-75° 

~·~ "1.0 

\05 

Figure 12. Case #13 (forward-located and high-angled injection): 

three-dimensional contours of fuel-equivalence ratio. 

~ASAJT~--2003-212094 12 
NASAfTM-2003-212094 

AFT-15 Co 

I I: 

±~J 

Figure 13. Case #15 (aft-located and low-angled injection): 

three-dimensional contours of fuel-equivalence ratio. 

I .' ... $j 

0J 

AFT-75° 

Figure 14. Case #4 (aft-located and high-angled injection): 

three-dimensional contours of fuel-equivalence ratio. 

13 
20 

100 

80 

rJmix (%) 60 

40 

-100 

( . -],10 Xinj In) 

Figure 15. Response surface of mixing efficiency as a function of 

injector angle (amj) and location (Xinj) for the Mo = 12, q, = 1.4 condition. 

rJmix 

-100 

( . -],10 Xinj In) 

Figure 16. Response surface of mixing efficiency: note the different 

"surface twist" at each Mach number. 

CXinj (d~) 60 40~ 

450 

r12 400 

In rJmix dlMjl50 

6.5 

300 

250 

Figure 17. Mixing efficiency, integrated across the flight trajectory of 

Mo = [6.5,12] at q, = 1.4, for all combinations of the injection geometry (amj, Xinj): 

note the maximum value shown as a black dot. 

NASAITM-2003-212094 14 
Optimal1-lnjector Performance 

~ 100 I~~~~~~ 

e... 

11:0 90 w 

.E '" 80 +--'>-....... 

..., 

~ 70 

~ 

'i! 60 I .......... I a: ...... _- 50+---~-'---r--~--~~ 

6 7 8 9 10 11 12 

Freestream Mach 

---RSM 1-inj 

······-95%CI 

······-95%CI 

- - -target 

Figure 18. Comparison of the mixing performance of the optimal injector design 

and the stated target value of 92.5%, across the Mach number range. 

_100 

~ 

11:0 90 w 

'" c 80 

i 

I 70 

~ 60 

IL 

50 

6 

Optimal2-1njector Performance 

.. - -- -- -- -- .. 

7 8 9 10 11 12 

Freestream Mach 

---RSM2-inj 

- - -target 

·RSM 1-inj 

Figure 19. Comparison of two different optimization strategies: the light gray result 

is the single geometry optimum; the black lines are the two-geometry optimum. 

NASA/TM-2003-212094 15 
REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 0704-0188 

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, 

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this 

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1. AGENCY USE ONLY (Leave blank) 12. REPORT DATE 13. REPORT TYPE AND DATES COVERED 

January 2003 Technical Memorandum 

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS 

Fuel Injector Design Optimization for an Annular Scramjet Geometry 

6. AUTHOR(S) VVBS-22-708-90-46 

Christopher J. Steffen, Jr. 

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION 

REPORT NUMBER 

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field E-13746 

Cleveland, Ohio 44135-3191 

9. SPONSORINGIMONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORINGIMONITORING 

AGENCY REPORT NUMBER 

National Aeronautics and Space Administration 

Washington, NASA TM-2003-212094 DC 20546-0001 

AIAA-2003-0651 

11. SUPPLEMENTARY NOTES 

Prepared for the 41 st Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and 

Astronautics, Reno, Nevada, January 6-9, 2003 (invited). Responsible person, Christopher J. Steffen, Jr., organization 

code 5880, 216-433-8508. 

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE 

Unclassified - Unlimited 

Subject Categories: 15,34, and 64 Distribution: Nonstandard 

Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Infonnation, 301-621~390. 

13. ABSTRACT (Maximum 200 words) 

A four-parameter, three-level, central composite experiment design has been used to optimize the configuration of an 

annular scramjet injector geometry using computational fluid dynamics. The computational fluid dynamic solutions 

played the role of computer experiments, and response surface methodology was used to capture the simulation results 

for mixing efficiency and total pressure recovery within the scramjet flowpath. An optimization procedure, based upon 

the response surface results of mixing efficiency, was used to compare the optimal design configuration against the 

target efficiency value of 92.5 percent. The results of three different optimization procedures are presented and all point 

to the need to look outside the current design space for different injector geometries that can meet or exceed the stated 

mixing efficiency target. 

14. SUBJECT TERMS 15. NUMBER OF PAGES 

Supersonic combustion ramjet engines; Experiment design; computational fluid dynamics; 21 

16. PRICE CODE Rocket-based combined-cycle engines 

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 

OF REPORT OF THIS PAGE 

Unclassified Unclassified 

NSN 7540-01-280-5500 

19. SECURITY CLASSIFICATION 

OF ABSTRACT 

Unclassified 

20. LIMITATION OF ABSTRACT 

Standard Form 298 (Rev. 2-89) 

Prescribed by ANSI Std. Z39-18 

298-102 

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