-
- ~~ -- 'rwrSEUIT LASFIAIO FAD-A 196 404/
UNCLASSIFIED TSECURITY CLASSFICATION OF THIS PAGE'
REPORT DOCUMENTATION PAGE Fom Ap0-0ro 88la. REPORT SECURITY
CLASSIFICATION lb RESTRICTIVE MARKINGS
UNCLASS IFI ED = in
2a. SECURITY CLASSIFICATION AUTHORITMImoP A a 3. DISTRIBUTION
/AVAILABILITY OF REPORTml =- 4 : 'IApproved for public release,
distribution
2b. OECLASSIFICATION/DOWNGR t r unl imi ted.
4. PERFORMING ORGANIZATION REP UMBER(S) 5. MONITORING
ORGANIZATION REPORT NUMBER(S)
6a. NAME O ERORMNG ORGANZATION SYMBOL 7a. NAME OF MONITORING
ORGANIZATIONpplied Technology Associates (If applicable) U.S. Army
Ballistic Research Laboratory
ATTN: SLCBR-LF
6c. ADDRESS (City, State, and ZIP Code) 7b. ADDRESS (City,
State, and ZIP Code)
P.O. Box 19434Orlando, FL 32814 Aberdeen Proving Ground, MD
21005-5066
8a. NAME OF FUNDING/SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT
INSTRUMENT IDENTIFICATION NUMBERORGANIZATION (if applicable)
I _DAAA15-86-C-00698c. ADDRESS(City, State, and ZIP Code) 10.
SOURCE OF FUNDING NUMBERS
PROGRAM PROJECT TASK IWORK UNITELEMENT NO. NO. NO. ACCESSION
NO.
00 001 AJ11. TITLE (Include Security Classification)
Base Drag Reduction Using Angled Injection
12. PERSONAL AUTHOR(S)CAVALLERI. R.J.13a. TYPE OF REPORT 13b.
TIME COVERED 114. DATE OF REPORT (Year, Month, Day) 1S. PAGE
COUNTContract Report FROM TO _
16. SUPPLEMENTARY NOTATION
17. COSATI CODES 18. SUBJECT TERMS (Continue on reverse if
necessary and identify by block number
FIELD GROUP SUB-GROUP
19, ABSTRACT (Continue on reverse if necessary and identify by
block number)
Reducing the drag of cannon launched artillery shells is a
potential method of increasingthe range of the shell. The base drag
of the shell is directly related to the base pressurethat exists on
the base region area. A potential method to reduce the base drag is
to employa solid propellant gas generator located in the shell aft
end that injects gas into the baseregion. The mass injected can be
distributed in a number of ways. It can be introducedthrough the
center of the projectile, near the edge of the projectile or a
combination ofthese techniques.
The Phase I SBIR effort concentrated on analyzing the effects of
central injection or edgeinjection and its effect on the base drag.
The injectant was injected at subsonic velocities.The injectant was
considered to be either air or a mixture of air and hydrogen. The
effect of
(Continued on Reverse Side of Form)
20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY
CLASSIFICATION
UUNCLASSIFIED/UNLIMITED 0 SAME AS RPT. [ DTIC USERS
UNCLASSIFIED22a. NAME OF RESPONSIBLE INDIVIDUAL 22b TELEPHONE
(Include Area Code) 22c. OFFICE SYMBOL
Walter B. Sturek (301) 278-4773 .. SLCBR-LF-CDD Form 1473, JUN
86 Previous editions are obsolete. SECURITY CLASSIFICATION OF THIS
PAGE
UNCLASSIFIED
-
19. ABSTRACT (Continued)
injectant temperature was considered for the air injection case.
The air hydrogen mixturewas considered to be both non reacting and
also reacting. A flame sheet combustion model wasemployed for the
reacting flow case. The free stream Mach numbers considered were
1.4, 1.8,and 2.2. The effect of spin on the base drag was also
investigated by including a spin termin the axisymmetric flow
equations.
S.-W
*5
S
S
]. ~
. . .. . .".- ,-
-
REPORT #ATA-87-O01
BASE DRAG REDUCTION USING ANGLED INJECTION
by R.J. CAVALLERI
APPLIED TECHNOLOGY ASSOCIATESP.O. BOX 149434ORLANDO FL 32814
8 JUNE 1987
FINAL REPORT
PREPARED FOR
DEPARTMENT OF THE ARMYBALLISTIC RESEARCH LABORATORIESABERDEEN
PROVING GROUNDABERDEEN, MD 21010
CONTRACT; DAAA15-86-C-0069
M) O ""2 '
.S
" 7 " "v y ' y, ',y ... \% V*. \~
-
t.I TV WI aV W . W.
PROJECT SUMMARY
Reducing the drag of cannon launched artillery shells is
apotential. Moethod of increasing the range.of the shell. The,
asedrag of the shell is directly related to the base pressure
thatexists on the base region area. A potential method to reduce
thebase drag is to mploy a solid propellant gas generator locatedin
the shell aft end that injects gas into the base region.Themass
injected can be distributed,in a number of ways. It can
beintroduced through the center of the projectile, near the edge
ofthe projectile or.a combination of these techniques. ,
The Phase I SBIR effort concentrated on analyzing '-theeffects
of central injection or edge injection andrits effect onthe base
drag. The injectant~was injected at sutsonic velocities)The
injectan was considered to be either air or a mixture of airand
hydrogen. The effect of injectant temperature was consideredfor the
air injection case. The air hydrogen mixture wasconsidered to be
both non reacting and .-alsO reacting. A flamesheet combustion
model was, employed for the reacting flow case.The free stream Mach
numbers considered were 1.4, 1.8, and 2.2.The '-effect of spin on
'thebase drag was 'eIso'investigated byincluding a spin term in the
axisymmetric flow equations.
The results obtained indicate that subsonic base injectioncan be
beneficial in reducing base drag. The, use of edgeinjection gives
higher values of base drag reduction (byapproximately 20%) than
center injection. Use of highertemperature injectant gas also gives
larger values of base dragreduction. It appears thatsmall injection
amounts of burning gasin the base region.,s more teneficial than
large amounts, whichmight blow off the'base bubble.
Details of the optimum injection scheme, however, stillremain to
be determined. In particular, effects of flow channelslocated in
the base region that direct the flow either radiallyinward or
outward may increase or possibly decrease the basepressure and
therefore alter the range of the artillery shell.
Accesion For~NTIS CRA&I
DTIC TAB
Urnannotinced 0
4;
,%,vi",tbl1y Codes
A','ei; or,d/Ior
..... ...... "' - v .. .. . . '. - . . . .
-
TABLE OF CONTENTS
TOPIC PAGE
ABSTRACT ................................ 1GRID GENERATOR
PROGRAM ................. 3GRAPHICS POST PROCESSOR PROGRAM
......... 5ADAPTIVE GRID ........................... 6SPIN
MODIFICATIONS ...................... BEXPERIMENTAL VERIFICATION
............... 10PROBLEM GEOMETRY .......................
12DESCRIPTION OF THE COMPUTER CODE ....... 14CODE MODIFICATIONS
..................... 15COMBUSTION MODEL .......................
18PARAMETRIC CASES ....................... 20THEORETICAL RESULTS
.................... 22CONCLUSIONS ............................
40REFERENCES ............................. 42
p
-
LIST OF ILLUSTRATIONS
FIGURE TITLE PAGE
1 ARTILLERY SHELL CONFIGURATION ......................... 42
ADAPTED GRID AT 500 ITERATIONS ...................... 73 ADAPTED
GRID AT 1000 ITERATIONS ..................... 84A CENTER INJECTION
GEOMETRY .......................... 1248 EDGE INJECTION GEOMETRY
............................ 135 FLAME SHEET SCHEMATIC
.............................. 196 AIR INJECTION
...................................... 217 EFFECT OF MOLECULAR
WEIGHT ......................... 218 EFFECT OF TEMPERATURE
.............................. 229 BASE PRESSURE VERSUS MACH NUMBER
................... 23
10 VARIATION OF BASE PRESSURE COEFICIENT WITHMACH NUMBER
........................................ 23
11 BASE DRAG VERSUS MASS INJECTION RATIO ............... 2412
CENTER INJECTION ................................... 2513 EDGE
INJECTION ..................................... 2614 EQUIVALENT
BODY CONFIGURATIONS ..................... 2715 EDGE EFFECT OF
ANGLED INJECTION .................... 2816 EFFECT OF INJECTION
TEMPERATURE ..................... 2917 EFFECT OF SPIN CENTER
INJECTION..................... 3018 EFFECT OF SPIN EDGE INJECTION
...................... 3119 CENTER INJECTION WITH HYDROGEN
..................... 3220 EDGE INJECTION WITH HYDROGEN ....
.................... 3321 EDGE AIR AND HYDROGEN WITH COMBUSTION
............... 3522 CENTER INJECTION AIR AND HYDROGEN WITH
COMBUSTION..3623 BASE FORCE TIME
HISTORY............................ 3724 BASE FORCE TIME HISTORY
....... .... . ............... 3825 BASE FORCE TIME HISTORY WITH
INJECTION .............. 3926 POTENTIAL BASE BLEED CONFIGURATIONS
................41
S.C
-
LIST OF TABLES
TABLE DESCRIPTION PAGE
1 TEST FACILITIES CONTACTED................. 112 BENCHMARK
COMPARISON...................... 17
n r
S S *. ~ 'C-.5
-
ABSTRACT
Reducing the drag of cannon launched artillery shells is
apotential method of increasing the range of the shell. The
basedrag of the shell is directly related to the base pressure
thatexists on the base region area. A potential method to reduce
thebase drag is to employ a solid propellant gas generator
locatedin the shell aft end that injects gas into the base region
Themass injected can be distributed in a number of ways. It can
beintroduced through the center of the projectile, near the edge
ofthe projectile or a combination of these techniques.
The Phase I SBIR effort concentrated on analyzi-g theeffects of
central Injection or edge injection and its effect onthe base drag.
The injectant was injected at subsonic velocities.The injectant was
considered to be either air or a mixture of airand hydrogen. The
effect of injectant temperature was consideredfor the air injection
case. The air hydrogen mixture wasconsidered to be both non
reacting and also reacting. A flamesheet combustion model was
employed for the reacting flow case.The free stream Mach numbers
considered were 1.4, 1.8, and 2.2.The effect of spin on the base
drag was also investigated byincluding a spin term In the
axisymmetric flow equations.
2
l%
-
INTRODUCTION
Reducing the drag of a cannon launched artillery shell is
apotential method of increasing the range of the shell. The
basedrag of the shell is directly related to the base pressure
thatexists on the base region area. A generic artillery shell
isillustrated in Figure la. By contouring or boat tailing the
backend of the shell as shown in Figure lb, drag is reduced since
thepressure that occurs on the forward facing base region area
isnot as low as the base pressure and causes a positive
axialpressure force. An alternative approach is to employ a
solidpropellant gas generator that injects gas into the base region
asillustrated in Figure Ic. The mass injected can be distributed
ina number of ways. It can be introduced through the center of
theprojectile, near the edge of the projectile or a combination
ofthese techniques.
The effort to be reported on was purely an analytical studyand
concentrated on central and edge mass injection. Theequations
employed in the study were the axisymmetric NavierStokes equations.
In addition to the theoretical studiesperformed some code
modifications were required and some relevantsoftware for pre and
post processing was developed. Prior todiscussing the theoretical
results the pre and post processorsoftware will be discussed then
the code modifications andfinally the results obtained.
GRID GENERATOR PROGRAM
An IBM PC/AT was used to develope the pre and post
processorcomputer programs. The programs were written in Fortran
and usedthe IBM professional Fortran compiler. The IBM AT was also
usedto communicate with the CRAY X/MP at the Ballistic
ResearchLaboratory using a 1200 baud modem and a terminal
emulatorsoftware program call PC Plot.
The transformation which generates the physical grid wasmodified
to allow for grid point clustering in the horizontal andvertical
direction. Several grid clustering transformations wereincorporated
into the program. They consisted of an axial gridclustering at one
x location and a choice of three verticalclustering techniques.
These are
1. a cosine clustering
2. clustering near the centerline %3. clustering at one vertical
y position
A pre-processor graphics program for grid visualization
wasconstructed. This program was used to determine if
suffucientgrid resolution is achieved for the particular case of
interest.The original mode of operation for this grid program was
to
3 '.1. e r .. " % ,%V-ir %'
-
GENERIC SHELL
FIGURE la
BOAT TAIL
BOAT TAILED SHELL
FIGURE lb
EQU IVALENTr
INJECTANT NOZZLE EI BODY
BASE INJEC'ION CONCEPT NGAS
GENERA 'TOR
FIGURE Ic
ARTILLERY SHELL CONFIGURATIONS
FIGURE I
4 a
% % %% %
- ~%=d~ N K .~. N, - v- - ~ = z ?V = .4.V
-
submit the NASJIN code to the main frame as a batch jobfor an
iterati-n of one time step. The grid generated was thendownloaded
to the IBM-PC and plotted using the grid program. Thismethod of
operation became cumbersome when modifications to thegrid sucii as
clustering parameters were used to change the gridresolutuon. This
mode of operation was then replaced by using theIBM AT to perform
the grid generation. The same grid generatorthat was in the NASJIN
code was implemented on the IBM AT. Afterselecting the appropiate x
and y clustering values, these valueswere then used in the input to
the NASJIN code. This eliminatedthe submission of a number of one
iteration cases with differentclustering values and the downloading
of the resulting grids.Also this approach minimizes computer
charges incurred on themain frame.
Another reason for doing the pre and post processinggraphics on
the IBM PC is to make the graphics software mainframeindependent.
Thus when the NASJIN code is ported to anothermainframe the
graphics will not have to be modified for thatmainframe.
GRAPHICS POST PROCESSOR PROGRAM
To display resulting flow field quantities a plottingpackage was
created. This allows visual examination of theresulting flow field
predicted by the NASJIN code. The plots thatare possible with this
program are contour plots, velocity vectorplots and Flow field
profile plots on constant x or y grid lines.The program also has
the ability to allow selecting windows toview the flow field. This
option permits enlarging sections ofthe overall flow field to
examine details of a particularFlowfield region. These changes have
not yet been checked outwith the plot output from the NASJIN code.
The use of thisgraphics program would allow determining the extent
and locationof flow characteristics such as separated flow and
shock waves.This graphics program uses a software package that runs
on theIBM AT called Multi-Halo and is a commercial graphics
package.
The method of operation for the graphics program was tosubmit a
case or a number of cases to the CRAY. After these casesran the
plot file generated by thes cases would be downloaded tothe IBM AT
and the plots generated on the screen. Hard copies ofthese plots
would then be obtained by using a pen plotter. Inattempting to do
this two problems areas surfaced. The first wasthe size of the plot
file. Although the plot file is not large,to download the file
would take on the order of an hour on a 1200baud line. The other
difficulty encountered was the noise on thephone line. During
attempting to download a plot file, noisewould come across the
screen. It is not known if this noiseinterferred with the data that
was transmitted or was onlyrelated to the display on the screen.
Another possibility isthat the PC-PLOT software was inadequate in
filtering of thenoise.
-J}J
-
ADAPTIVE GRID
The incorporation of an adaptive grid capabilty into theNASJIN
code (in fact any CFD code) would enhance the codesability to
resolve regions of high gradients. Also it couldreduce computer cpu
time by allowing use of fewer grid points,since sufficient grid
points would be relocated to high gradientregions from low gradient
regions. In order to accomplish this acopy of the adaptive grid
program was obtained from NASA AMESResearch Center (1).
The adaptive grid program obtained utilizes an existing
flowfield solution to relocate grid points according to local
flowgradients. These flow gradients are utilized in a
tension/torsionspring analogy to redistribute grid points. Spring
tension andtorsion coefficients are additional inputs required by
the code.An iterative (human in the loop) process is required to
determinethe correct combination and magnitude of these
coefficients toachieve an acceptable solution from the adaptive
grid code. Theend objective for the adaptive grid code was to have
the abilityto run the adaptive grid code as a subroutine in the
NASJIN code.The original grid and metrics are provided to the
NASJIN code,and these metrics are recomputed during the solution
process atspecified iteration values.
There are two versions of the NASA Ames two dimensional
adaptive grid code. The first and older version did not have
theability to perform grid adaption unles it was used in a
manual(person in the loop) mode. The second version had a
limitedcapability to perfrom self adaption by adjusting the
requiredspring and torsion constants in only one direction.
Incorporatingeither adaptive grid version into the NASJIN code
required thatthe NASJIN code be stopped during the solution
proceedure, modifythe existing grid to redistribute points in
regions where flowgradients are greatest and then restarting the
code with this newgrid and flowfleld. An interface routine was
required between theadaptive grid subroutine and the NASJIN code.
This necessitatedthe development of an additional subroutine which
would evaluatethe transformation metrics for the modified grid.
Alteration of the adaptive grid routine was necessary tomake
allowances for the additional number of dependent variablescomputed
by the NASJIN code (the specie mass fraction). Codingwas added so
that each of the flow field variables are determinedby
interpolation from the modified grid.
Prior to starting this effort, the inclusion of the adaptivegrid
capability into the NASJIN code was believed to be a simplematter
of employing the NASA Ames adaptive grid code as anadditional
subroutine. The function of this subroutine would beto
automatically adjust the required input values. Afterinitiating
this effort, it was realized that these constants were .%highly
problem dependent. If incorrect values were used theresulting grid
lines would cross. What was believed to be a
6AX w 1i
-
simple matter of addition of a few adaptive grid
relatedsubroutines became in fact a separate developement effort.
Theeffort required deteriming the appropiate values for the
springand torsion constants for the problem of interest and
thenmodifying the adaptive grid code to adjust these values within
'1specified ranges during the solution of the flow field. It wasnot
possible to accomplish this during the Phase I effort.
A partial success for the adaptive grid code was, however,was
obtained. The adaptive grid code was successfully applied tothe
flow over a bluff base having a centered jet. The freestream
'....conditions utilized were Mach=l.5, 14.7 psi at 520
degreesRankine. The jet conditions were Mach 1.85, 29.4 psi
(exitpressure) at 630 degrees Rankine, the injectant was air. The
flowsolution was obtained at 500 time steps and a restart tape was
5written. This restart file along with other required inputsserved
as input data to the adaptive grid routine and the flowwas then
solved for another 500 time steps. A plot of the grid attime steps
of 500 and 1000 iterations is presented in Figures 2and 3.
FIGURE 2
ADAPTED GRID AT 500 ITERATIONS
II t h!ifBASE
- - - ~ CENTERLINE ,XS;:,,
i7 5",:
-
=1W .n .. *a -
FIGURE 3
ADAPTED GRID AT 1000 ITERATIONS
BS-~--
- •
CENTERLINE
SPIN MODIFICATIONS
Analizing the effects of spin on the base flow was achievedby
incorporating additional terms into the two dimensionalaxisymmetric
flow equations. These terms had the effect ofimposing an angular
velocity everywhere throughout the flowfield. This is an
approximation and represented an alternativeapproach to solving the
full set of three dimensional flowequations. If the three
dimensional flow equations were solved aconstant angular velocity
boundary condition would have beenimposed only on the body surface.
Thus the flow field modelemployed for incorporating spin effects is
oversimplified anddoes not represent the true effects of spin. It
does, however,represent a worst case were the spin effects would
beexaggerated. A more realistic approach would have been to
includea e momentum equation and solve for the velocity component
inthis direction. The three dimensional Navier Stokes equations ina
cylindrical co-ordinate system were simplified by neglectingany
flow variation in the circumferential direction and assuminga
constant spin velocity that is independent of axial location.This
simplification leads to the following equations:
continuity: P +- x- + a-u+ =0
at ax 3Y Y
x-momentum:
-++ + L4)+ 2 U L a 3u ax) P_ Y ay ax
-
y-momentum~a 3( U-1L+V 2CU+PiM (u au au u\-2 Lv\w+TX( ay ax) ay
a Y ax Y aS - )- ay y
e-momentum_ 2 Ra Co U ) + - o(P ) + 2 p uW = R 0
where:
The next step is to simplify the e direction equation Fnd
thenobtain a suitable functional form for the angular velocity.
Rearranging the terms on the 0 equation there is obtained:
(apu aPu+PU\+Wa~w+ + ay ax PUx - 0RO
the first term is zero since it is the steady state
continuityequation. This leaves the equation:
,u p w + =-Re'r
Assuming that the w velocity component is of the form:
w = Ay"
and substituting this into the e equation:
rho v ( An y"-- + Ay- - ') = R. :%
in order for the term on the left side of the equation to bezero
n = -1 and A must be a constant. The constant A can bedetermined
using the velocity at the body surface wt.
wt = fI yb = A/yb
9
A. -.P % or -' KP *%~~/* ( - C ' qr - 9
-
where D is the angular spin rate. This gives for the value of
A:
A = Q yb 2
The end result for the circumferential velocity equation is
then:
W = Q
This equation should also be a solution of the viscous RHS of
thetheta equation. Substituting this into the RHS does in
factindicate that it satisfies the equation. On the centerline
thisequation is indeterminate, therefore when the
verticalco-ordinate is less than the body radius it was assumed
that thefluid undergoes solid body rotation. The form for w used in
thisregion is :
w = n r:
Using these forms for the w velocity, at the body surface the
wvelocity is continuous. The equations used in the NASJIN
codeemployed this w velocity equation to asses the effects of spin
onbase pressure.
EXPERIMENTAL VERIFICATION
The experimental verification of results predicted by theNASJIN
code would serve to establish a confidence level for thecode. To
accomplish this an experimental program thatinvestigates the
effects of base injection location (i.e centeror edge injection)
and the effects of combustion would berequired. A survey was made
to determine the availability of windtunnel facilities where
injection tests with combustion could beperformed. The objective of
the experimental program is to gatherdetailed flow field data
necessary to validate the code. Theexperiments would be designed to
supplement deficiencies inavailable test data. The primary goal is
to define the pertinentflow and geometry parameters which minimize
the projectile basedrag. A literature survey was performed to
determine the extentof existing data relevant to the problem of
interest. The surveyshowed that there is substantial experimental
scatter and lack ofagreement between prior theoretical models. Also
the influence ofseveral important flow parameters such as discrete
injection, andmodel spin is either totally lacking or does not
cover asufficiently wide range of interest. Available test
facilitiesfor full scale experiments were examined on the basis
ofsuitability, availability and cost. A list summarizing theresults
of the available wind tunnel facilities is given in Table
10 A
-
appropiate faciltly to perform the tests is that at
GeneralApplied Science Laboratories.
Table 1
Test Facilities Contacted
Facility Test Flow Comments Cost//Location Section Conditions
Basis
General Applied Combustion $9000/wkScience, N.Y. 8"x10" M = 2.7
Testing
Naval SurfaceWeapons Center 16"x18" .3
-
PROBLEM GEOMETRY
The geometry employed for the center injection cases
isillustrated in Figure 4a and the geometry employed for the
edgeInjection cases Is illustrated in Figure 4b. The number of
gridpoints used for each of these configurations is listed in
thefigure. Typically 100 points were used in the axial direction
and50 grid points in the vertical direction. A cartesian grid
wasspecified with suitable clustering transformations employed
toresolve flow details in the vicinity of the corner and
injectorareas.
15
14
55 Grid Points
13
UPPER BOUNDARY
12
CENTER INJECTION GEOMETRY8
INFLOW PLANE
7
*~ 6
OUTFLOW BOUNDARY
5
100 Grid Points4
3 39 Grid PointsBODY
2-
rb = 2.5 21 Grid PointsI-\
\\\ 2. r1.25 INJECTANT NOZZLE
0 1 2 3 4 5 6 7 5I 52 53 54 55
x - inches
CENTER INJECTION GEOMETRYFIGURE 4a
12
-
I
14
13 -75 Grid Points
12 EDGE INJECTION GEOMETRY
7 INFLOW PLANE
6
5
4 100 Grid Points
335 Grid Points BODY OUTFLOW BOUNDARY
9 Grid Points2 11 Grid points
0 X.87 38frid Points- -
0 I 2 3 4 5 6 7 8 51 52 53 54 55
x - inches
EDGE INJECTION GEOMETRY
FIGURE 4b
13 .
-
DESCRIPTION OF THE COMPUTER CODE
the computer code used to perform the parametric studies
istermed NASJIN which is an acronym for Navier Stokes JetINjection.
The equations employed in the code are the twodimensional
axisymmetric unsteady two specie Navier Stokesequations. These
equations are given below:
au + IF 1 3 (oG) +OH 0a a lr + - r n=O Two Dimensional Flow
n=1 Axi-symmetric Flow
P Puv + Ixrp U Pv2 + aU - PV - rr
pe (Pe + arr)v + TxrU +Pf pvf + m
PU2 + a X 0)
S PUV + xr 08
(pe + aXX)U +Txr v + x 0
puf + x 0
where= density
u = axial velocity
v = vertical velocity
e = internal energy
f = specie mas fraction
m = mass fraction rate of change
't -r € )r %f = stress components
This code has evolved over a number of years and is based onwork
performed in references 4,5 and 6. The equations are solvedusing
the explicit technique of MacCormack (7). There are fiveindependent
variables which are solved for, the density, xvelocity, y velocity,
total energy and the specie mass fraction.The flow is not
considered to have a constant total temperature.Therefore at the
inflow plane or base injection plane the static
temperature is specified as a function of y. liias results ina
total temperature and therefore a total energy variation in
thevertical direction.
14
-
CODE MODIFICATIONS
A significant modification that was required to the code
wasimplementing a subsonic inflow boundary condition for
theinjected mass. This was done using an additional subroutine.
Twoapproaches were tried, the first was to assume a total
injectionpressure that was only slightly larger than the static
pressurein the base region. Using these two pressures the injectant
Machnumber was then computed. The injectant mass flow ratio "I"
wasspecified and also the injectant total temperature. Using
thetotal temperature and the Mach number the injectant
statictemperature and velocity was then compited. Using the
staticpressure and the static temperature the injectant density
wasthen calculated. An estimate for the mass injectant flow
rateratio "I," was then computed using the velocity, density
andinjectant area. This value was then compared to the
specfiedinjectant mass flow rate value. The first value was always
lessthan the specfied value (the initial value for the
injectanttotal pressure was chosen so that this was always the
case). Theinjectant pressure was then increased gradually until
thecalculated value for the mass injection was greater than
thespecified value. The correct value for the injectant
conditionswas then interpolated on. These values were then used to
computea new estimate for the mass injectant parameter. If the
twovalues agreed to within 2%, the iteration was stopped, if not
thetotal pressure increment for the injectant was decreased and
theprocess was started over again. This approach appeared to
workuntil at about 9000 iterations it broke down. Large values
ofbase pressure were obtained. The reason for the occurence was
notresolved. Because of this a second approach was also
pursued.
The second approach was to express the mass flow as afunction of
the injectant conditions using the expression for theinjection mass
flow ratio.
(puA).
=m b
Using the equation for a perfect gas, the definition of the
Machnumber, and speed of sound an expression for the injectant
Machnumber can be obtained.
,0
M.= I --_kT '
i j J
Note: The pressure used in this equation was an average
pressureat the first flow field interior grid point over the
injectantexit area.
15
-
This expression is solved for the Mach Number using an
iterationprocess. A value for the injectant total temperature is
specifiedand assumed to be constant. An estimate for the injectant
statictemperature (Tj = Tcj) is assumed. The above expression is
usedto compute the Mach number. The static temperature is
updatedusing the new value of Mach Number. A second value for the
MachNumber is determined and compared to the first. This process
isrepeated until there is no change in the value for the
MachNumber. Typically this required 8 iterations. After the
MachNumber is determined the static temperature is computed,
theinjectant velocity and then the injectant density. This
secondapproach was successful.
The second routine that was added to the code was one
thatcomputes the force on the projectile base. The integration of
thebase pressure used a simple trapezoidel integration
technique.Separate values for the static force and injectant
momentum werecomputed. The injectant momentum force is not include
in the baseforce results and would contribute an additional 10% to
the baseforce for injectant values greater than I=.04.
In addition to the above two modifications to the computercode a
major restructuring of the code was performed. This
majorrestructuring was to replace all the double array
subscriptedvariables with a single array. The effect of this is to
increasethe vector length. During the process of performing the
coderestructuring any coding that inhibited do loop vectorization
wasremoved from the loop.
The major differences between the two versions of the codeare
that the single array version has no 'IF' statements insidethe
inner DO loops and has a vector length of NNX (number ofpoints in
the x direction) times NNY (number of points in the ydirection).
For example for a 100 (NNX) by 50 (NNY) grid the oldversion had a
maximum vector length of 100 (the x dimensionlength). The new
version now has a vector length of 1500(NNX*NNY). This allows use
of the maximum length vector permittedby the CRAY processors.
The changes to the code where made on the IBM AT. The codewas
then was compiled on the IBM PC AT to locate and correct anyFORTRAN
syntax errors. Typically it took about 20 minutes tocompile the
4500 lines of code on the IBM AT. The code was thenloaded onto the
CDC CYBERNET system and benchmarks betwcen theold version and the
new single array version were made. Theresults from the single
array version were compared to resultsfrom a previous version of
the code. Both sets of results were inagreement indicating that
there were no coding errors introducedas a result of the code
changes.
16
-
pp
The results of these benchmarks are given in Table 2.Typically
the new single array version runs about three timesfaster on the
Cray XM/P and three times faster on the CYBER 205.This new version
of the code does not have the subsonic injectionboundary condition
routine or the base force routine.
Table 2
Benchmark Comparison
(Performed on CDC Cybernet System)
CPU Execution Time in Seconds
Version Original Single Optimized SingleCode Array Array
Computer s
CYBER 205 337.6 110.1
CRAY X-MP/24 80-90* 46.85 28.6
(These times do not include compilation time)
CPU Breakdown on Cray X-MP/24
Routine Single Optimized SingleArray Array
NASJIN 1.246 1.209TRAN .120 .116THERMD 4.667 .964BC 2.690
2.634SIDE .873 .861STP 16.560 3.450SOLVR 8.030 8.116SMOOTH 4.044
3.239STRESS 5.446 5.166FLUXES 2.180 1.916PRINT .905 .868Other -089
.061
Total CPU time (seconds) 46.85 28.6 U
Benchmark case was a 60x40 grid run for 1000 time steps
* Estimated: The original version required 139 seconds on
aCRAY-i S/2000. The CRAY X-MP/24 was not avaiable for thisoriginal
benchmark.
17
-
COMBUSTION MODEL
The Phase I effort considered the effects of combustion
byemploying a flame sheet hydrogen air combustion model (8). Inthis
type of combustion model the chemical kinetics employed arethose of
chemical equilibrium or an infinitely fast chemicalreaction. This
is a useful model of a single constituent fuelcombustion process
that is essentially a simplified treatment oflocal chemical
equilibrium. This identical approach has beenemployed in references
5 and 6 for analysis of a hydrogen fueledscramjet combustor. The
model can be illustrated by considering ahydrogen air system.
Restricting the treatment to problems with amaximum temperature of
less than 2500=K, an examination of thepertinent equilibrium
constants reveals that it is reasonable toneglect all reactions
involving nitrogen and that the existenceof the radicals of oxygen
and hydrogen (i.e., 0, H and OH) can beneglected. Thus, only the
simple overall reaction
H2 + 1/2 02 zH 20
with the related equilibrium constantH0
K = /2P H P 0 1/22 02
must be considered. Furthermore, for T < 25000 K, K, 1, soit
can be asserted that either the concentration of hydrogen oroxygen
must be essentially zero in certain regions of the flow.Thus, we
come to the flame sheet model where the flow is dividedinto two
regions: one where there is no fuel and one where thereis no
oxygen. The boundary between the two is the "flame sheet"where the
concentration of both hydrogen and oxygen is zero. This"flame
sheet" occurs at the locus of points where the ratio ofoxygen atoms
to hydrogen atoms is stoichiometric. This model isillustrated in
Figure 5.
The flame sheet model is an equilibrium chemistry
model.Therefore, a flame sheet dynamic equilibrium combustion model
canbe considered to be an extreme case where the highest degree
ofheat release is obtained both from a chemical kinetics and
fluiddynamics model. This would then represent one extreme for
theflow phenomena under investigation.
18 ,.18
-
te
FLAME SHEET
AIR
, ..
02, N2 * H20
t2' 2 ' 2
COMBUSTION PRODUCTS
PLUS EXCESS FUEL
INJECTOR WALL S
FLAME SHEET SCHEMATIC
FICURE 5
The method of solution for the flame sheet model model is
tofirst compute the flow field fluid dynamics for a single
timestep. This determines the amount of fuel that is diffused and
,kconvected by the flow field during this time step. Next theamount
of oxygen and nitrogen present at each grid point isdetermined.
This is done using the relations:
Yom = (1.0-YH2) * .232 and YN2 = 1.0-YH-Yo2
The .232 value in the above relation is the gram atom weight
ofoxygen present in the amount of air and is determined by
thefollowing calculation:
Gram atom weight of air =
W= Number of oxygen atoms x oxygen atomic weight +Number of
nitrogen atoms x nitrogen atomic weight xnumber of nitrogen atoms
for each atom of oxygen
= 2 x (16) + 2 x 14.0 x 3.76 = 137.28
Wo2/W = 32/137.28 = .232
The local stoichiometric ratio at each grid point is
determinedbased on the local hydrogen and oxygen composition: S
Ys = (2.016/16.00) Yoz
A comparison is made to determine if the amount of hydrogen
present is greater or less than Ys.. If the amount of
hydrogen
19 .
-
present is greater than the stoichiometric value the amount
ofhydrogen consumed in the reaction is set equal to
thestoichiometric value. The residual amount of hydrogen is
then:
If the amount of hydrogen present is less than the
stoichiometric
value then all of the hydrogen is consumed in the reaction
and
0.0
In the case when there is excess hydrogen, the amount of
oxygenand water are computed from the equation:
((Yo')iriit±. = - 16.0*YS/2.016
(YHzo)- ,.3. = 18.016 * Ys/2.016
or for the case when there is not enough hydrogen for
completecombustion
= (Yo2) 1 ,±z - 16.0*YH2 /2.016
18.016 * YHm/2.016
The results of the above proceedure allow computing the
gascomposition at each grid point. This composition is then used
tocompute the static enthalpy of the mixture. The enthalpy isthen
used in the equation for total energy to compute a newvalue of
temperature after the fuel and air has burned.
PARAMETRIC CASES
The effects that were investigated consisted of determiningthe
impact on base drag of:
1) edge injection in the axial direction2) center injection in
the axial direction3) edge injection at an angle of 4504) effect of
injectant temperature5) effect of spin6) air and hydrogen injection
with no reaction7) air and hydrogen injection with reaction
The effect of injectant conditions on the injection massflow
requirements was estimated as a function of free stream MachNumber.
Results of these calculations are shown in Figures 6, 7and 8. These
curves were generated only to obtain a relativecomparison of
different conditions. It was assumed for all ofthese cases that the
base pressure was constant and equal to 7.0psia and the base area
to injectant area ratio was constant at avalue of 2.5. The figures
indicate that the higher the injectanttemperature and molecular
weight the lower the injectant massflow requirements to obtain the
same value of base pressure.
20
-
T-'T
AIR INJECTION I
Free Stream Mach Number
M 2.6 2.4-2.2 2.0 1.8 1.6 1.4 1.2 1.01.0
0.8-8
0.6-
S0. 4jo70pi
v
0.2-AbA 2.
0. .02 .04 .06 .08 ,I0 .12 .14 f16 .16 .20 .22
Injectast Mass Flow Ratio I r.
AIR INJECTION
FIGURE 6
EFFECT OF MOLECULAR WEIGHT
Free Stream Mach Number
M 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.21.0
1.0-
0.8 . ~ 0
z
0.6 . - 14 M . 1 .
.20
.0
0. .02 .04 .06 .08 .10 .12 .14 .16 .18 .20 .22
Injectant Mass Flow Ratio -I
EFFECT OF MOLECULAR WEIGHTI
21
-
Free Stream Mach NumbeeM 2.6 2.4 2.0 1.8 1.6 1.4 1.2 1.0 0.8
.0
0.8
I •.
0.65P
z
0.2 02A/ A 2.
0.00. .02 .04 .06 .08 .10 .12 .14 .16 .18 .20
Injectant Mass Flow Ratio - I
EFFECT OF TEMPERATURE
THEORETICAL RESULTS FIGURE 8
The majority of the theoretical results obtained from theNASJIN
code were performed on the Ballistic Research LaboratoryCRAY
XMP/48. The computer was accessed over a toll free dial inline at
1200 baud. Typical run times using the original versionof the code
required 30 minutes to 90 minutes depending on thenumber of grid
points and the number of time steps. The 90 minuterun typically was
for 20,000 time steps using a grid with 100points in the x
direction and 55 grid points in the y direction.The turn around
time was either overnight or if a job wassubmitted early in the day
it would be finished by lateafternoon.
The theoretical effort performed focused on determining
theeffects of central injection and edge injection on
projectilebase drag. Prior to performing the injection studies, it
wasdesirable to correlate the results of the code with
experimentaldata when there was no base injection. The computed
base pressurewith no injection are plotted in Figure 9. Also shown
in thefigure are experimental results from NACA report 1051
"AnAnalysis of Base Pressure at Supersonic Velocities and
Comparison -"with Experiment" by Dean R. Chapman. The computed
values of basepressure agree to within 10% of the experimental
values. The basepressures with no injection from AIAA Paper 86-0487
"SupersonicFlow over Cylindrical Afterbodies with Base Bleed" by J.
Sahu arealso shown on the figure. Again these values agree to
within 10%of the experimental values. The original data from NACA
1051 isshown in Figure 10 and covers a wide range of experimental
testconditions and body configurations. Therefore agreement to
within10% is not unreasonable.
NHaving established a confidence level of the code when
there
is no injection, the objective was to determine the
confidencelevel of the code with injection. The base pressures for
cases
22V,; N V1z "kip6,L,
-
6EXPERIMENTAL, DATA (NACA 105114
SCALCULATION
I - + CALCULATION -AIAA 86-0487
120
10
0.0
6
.5 1.0 1.5 2.0 Z.5 3.0
FREE STREAM MACH NUMBER
BASE PRESSURE VERSUS MACH NUMBER
FIGURE 9
o Free-flight, 3
-
with injection again from AIAA Paper 86-0487 "Supersonic
Flowover Cylindrical Afterbodies with Base Bleed" are shown in
Figure11. The results are for a Mach 1.8 center injection case
whereasthe AIAA results are for a Mach nunber of 1.7. Although the
bodysizes and free stream conditions are not the same for these
twocases there is general agreement between the two sets of
results.The minor difference between the current calculations and
the
previous ones is that there is no minimum value for base drag
asthe injection mass ratio "I" increases. The base drag continuesto
decrease as injection increases, indicating the more massinjected
the lower the base drag.
0.30
* COMPUTATION 5.0 " D BODY M 1.80.25
o COMPUTATION M = 1.7
0.20 0 EXPERIMENT M = 1.7
0.15
0.0
0.00 0.01 0.02 0.03 0.04
MASS INJECTION RATIO - I
BASE DRAG VERSUS MASS INJECTION RATIO
FIGURE II
Parametric calculations were then performed for center andedge
injection on the 5.0 inch diameter body of Figure 4. Resultsfor air
injection are shown in Figure 12 for central injectionand Figure 13
for edge injection. Injectant total temperature forthese cases was
the same as the free stream total temperature.Both the value of the
force and the base drag coeffficinet areplotted in the figures. In
general for center injection, as theamount of mass injection
increases the base drag decreases. Thisis true for both central and
edge injection. An exception to thisis the center injection Mach
1.4 case which exhibits a definitepeak at I=.03. The edge injection
results, however, indicate thatat the lower Mach number of 1.4 a
substantial drag reductionoccurs with only a small amount of mass
injection (I=.01). Infact the edge injection actually results in
forces large enoughto generate some degree of thrust. As the free
stream Mach numberincreases the base drag coefficient decreases but
is still largeenough so that there is almost no base drag penalty
incurred. Ingeneral the edge injection results indicate a
potentialimprovement in projectile range may be obtained over that
of
central injection. To determine the degree of
improvementrequires performing trajectory simulations for the
differentinjection techniques.
24
-
M SYMBOL
1.4
-10
.05
0. .050 .3.4 0
MASIJCIO0AI
.055
-
-. 10
Lo
.05
1.0
C2.2
35
.50 1.4
.150
2506
U7
-
A possible explanation of this is that edge injection ismore
effective in generating an equivalent streamlined body thencenter
injection. This is depicted in Figure 14a and 14b. For thesame
amount of mass flow the center jet injectant has to spreadfurther
than the edge jet injectant to attenuate the expansion ofthe free
stream gas into the centerline region of the body.Therefore, based
on these initial results, it appears that edgeinjection is more
effective in the reduction of base drag thencentral injection.
These results however should be verified byadditional calculations
and experimental wind tunnel tests.
EQQUINLENTBODY
CENTER INJECTION
FIGURE 14aINJECTIO
~~~~~~EQUIVALENTBOYCNIUAONEDGE INJECTIONFIGURE 14b
EQUIVALENT BODY CONFIGU%"TIONSFIGURE 14
-
The effect of injection angle angle for the edge injectioncase
was also investigated. Shown in Figure 15 are the resultsfor
injecting at an angle of +450 and -45. The results indicatethat
angled injection in general detracts from the reducing thebase
drag. There is also a crossover where a negative injectionangle is
initially better than positive injection until at aninjection ratio
of I=.04 where this trend is reversed. Thereason for lookin at this
effect was based on the fact that ifthe injectant was directed at
an angle of 450 up into theoncoming free stream flow, it would
appear as blockage to thisincoming stream and cause an increase in
the projectile lippressure which would in turn cause an increase in
the basepressure. To fully study this effect a three dimensional
computercode is required that would be capable of analyzing
discreetinjection. The area between the discrete injector orifices
wouldallow the higher projectile lip pressure to be communicated
intothe base region, thereby increasing base pressure and
decreasingbase drag.
-. 15
f-4
-. 0505 0 M -1.8 \
Injection Angle
< .00
300 .
0
200
15010. .Al .02 .03 .04 .05 .06
Injection Mass Ratio - I
EDGE INJECTION EFFECT OF ANGLED INJECTION
FIGURE 15
28
-
The effect of injectant temperature was then investigated ata
free stream Mach number of 1.8. The injectant temperature
wasincreased to 11000 R from 8540 R. At the injectant plane
(thebase region station) the injectant static temperature
isspecified and does not have to be equal to the free stream
statictemperature. This difference in static .temperature at
theinjectant plane also gives rise to a variation in the
totalenergy between the external stream and the injectant. The
resultsof these calculations are shown in Figure 16.'In contrast to
theprevious cases where the injectant total temperature was equal
tothe -'free stream total'temperature, there is now a more
distinctoptimum injectant mass flow rate that occurs at I = .03.
Theeffect of increased injectant temperature gives a
furtherreduction in base dr-ag than cold air injection.
-. 10
.05
U
0 854 -
I100 Edge
.1 8 4 C e n t e r
U
0
200
150
.00 .01 . .03 .04 .05 .06
Injection Mass Ratio- I
EFFECT OF INJECTION TEMPERATURE
FIGURE 1629
-
A
The effects of spin on central injection is illustrated inFigure
17 and for edge injection in Figure 18. The spin rateswere 20,000
rpm and 30,000 rpm for the center injection case and10,000 and
20,000 rpm for the edge injection case. Spin causes alowering of
the base pressure as is shown in the figures,apparently the spin
imparts a radial outward velocity to the gasin the base region.
This decreases the density of the base regiongas and therefore also
the base pressure. The central injectionshows a monotonic variation
of the base force with spin. Theeffect of spin on edge injection is
to decrease the erraticbehavior that occurs with no spin.
-. 25
-. 20.
3V
iL
-.5
.00 0 (rpm)
0 20000
30000
" j
-. 05
0
150
1000
00 .00 .01 .02 .03 .04 .05 .06
' Injection Mass Ratio - 1
EFFECT OF SPIN CENTER INJECTION
FIGURE 1730
-
-. 25
H- 1.6
0 (rpm)
-. 15 0 0
£~10000
o 20000
:.0
.00
-.05
01
Ip
S 0 0
200
I so
1031
-
The effects of injecting a mixture of hydrogen and air forthe
center injection case is shown in Figure 19 and for the edgecase in
Figure 20. The amount of hydrogen that was injected is amass
fraction of .007. Although this may seem small the hydrogenmass
fraction for a stoichiometric air hydrogen mixture is .027.Thus the
amount of hydrogen injected is about one fourth thestiochiometric
value. This value was choosen to avoid anexcessive amount of heat
release that may cause the code to gounstable. The results in the
figurts indicate that the hydrogencauses the base force to increase
and base drag to decrease.This agrees with other published work
which indicates that theinjection of light molecular weight gases
in the base region aremore effective in decreasing base drag.
-. 15
M .,0
- .05
m 112 air.00
0 0.00 1.00 i300
• 0.007 .993
250
U
200
15 0 .. 0 .0 600 .0J .02 .03 .04.0.0
INJECTION MASS RATIO I %
CENTER INJECTION WITH HYDROGEN i
.0.
2002
N N
-
:I
-. 15
-. 10 I
05
S .00
a .05M- 1.8
F Fa112 air
350 0 0.00 1.000 .0 0 7 .9 9 3 ,. .
300
.n250.
Cs o 5% -
200
50.0
.00 .01 .02 .03 .04 .05 .06
INJECTION MASS RATIO - I
EDGE INJECTION WITH HYDROGEN
FIGURE 20
33
• . ,j . .*,. ,t ,, ,,
",, ",. "- ". ,f .,-
-
The effects of combustion in the base region is shown inFigure
21 for the edge injection case. The amount of hydrogenthat was
injected is the same as in the previous case (hydrogenmass fraction
= .007). The results in the figure indicate thatthe combustion of
hydrogen in the base region caused the baseforce to decrease and
therefore the base drag to increase. Thisis unexpected since
combustion should cause an increase intemperature and any increase
in temperature would give rise to adecrease in base drag. Possibly
the amount of hydrogen injectedis too small and since it is located
near the edge of theprojectile the combusted gas mixes rapidly and
is in effectquenched by the outer cooler stream.
The effects of combustion in the base region is shown inFigure
22 for the center injection case. Again the amount ofhydrogen that
was injected is the same as in the previous casesThe results in the
figure indicate that for the centralinjection, the combustion of a
small amount of hydrogen in thebase region initially causes the
base force to increase (I=.01)and therefore the base drag to
decrease. As the amount of massflow increases, however, this trend
reverses itself and at massinjection ratios greater than .025 the
base force is smaller thanfor the no injection case.
In obtaining these results the base force did not attain asteady
state value. The base force time history for these fourinjection
cases are shown in Figure 23. All of the casesdemonstrated an
almost constant value of base force at earlyvalues of time. At
later values of time this force increased. Itis not known if this
behaviour is due to improper implemenationof the injectant boundary
conditions, downstream boundaryconditions or reflections from the
downstream boundaries thattraveled back to the base region. Each of
these effects can beinvestigated by moving the downstream boundary
or using differentboundary conditions such as characteristics
rather thanextrapolated boundary conditions.
344
TS
1.
a
.W
34"
-
- A
A.
°0p
-. 15
-. 05
0 AIR
0 AIR AND HYDROGEN (F H2 - 007)
35 L AIR AND HYDROGEN WITH COMBUSTION .
300"-
o 250 -- --- ) " '
N.
05
.00 .01 .02 .03 .04 .05 .06
MASS INJECTION RATIO -I
EDGE INJECTION AIR AND HYDROGEN WITH COMBUSTION
FIGURE 21I
3005
-
i-0.05
-- . 15
.00
.05
M 1.8
0 • Alk AND HYDROGEN (F 2 .007)
350 AIR AND HYDROGEN WITH COMBUSTION
300
250
200
150
.00 .01 .02 .03 .04 .05 .06 .INJECTION MASS IO- P O I
CENTER INJECTION - AIR AND HYDROGEN WITH COMBUSTION
FIGURE 2236
S.-. S.j
-
600
500
O I - .01
.0~ -~ I.02
400
200
0. .001 .002 .003 .004 .005 .006 .007
TIME (sec)
1400
1200
1000
800
0 I - .03
-I.04
,
600 -
400
200
0. .001 .002 .003 .004 .005 .006 .007 .008 .009
TIME (sec)BASE FORCE TIME HISTORY
FIGURE 23
37~. SS. ~5- * -. ~ * ~ * * i'. ~ S*.. * k5
-
.40
I
A problem area that surfaced during the performance of
thetheoretical calculations was the base force in some cases did
notreadily converge to a constant value. The degree of
oscillationis depicted in Figure 24 for a case with no injection
and inFigure 25 for a case where the injectant mass flow ratio was
.01and the free stream Mach number was 2.2. This oscillation
isbelieved to be due to applying a constant value of pressure
overthe injection plane where in reality the pressure and
velocityvary over the injection plane. This effect or variation
would bemore dominant for large bodies with sparser grids than
forsmaller diameter bodies with more tightly clustered
grids.Comparison to the no injection case shows that the base
forceconverges very rapidly to a constant value after only about
4000iterations. Except for the peak that occurs at about
5000iterations the value is extremely steady. This indicates
thatfurther work must be done to either smooth the flow in the
baseinjection region or to allow for a variable injectant
conditionsat the injectant plane.
.300 BASE FORCE VERSUS TI [E
m I'M,- 1.4 !
I -0.0
-250
200
150
° IS
3000 6000 9000 ITERATIONS) I~00.,
0.0 .001 .002 .003 .004 .005 .006 .007 .008TIME - SECONDS
BASE FORCE TIME HISTORYFIGURE 24
38 .
-
200 BASE FORCE VERSUS TIME
M= 2.2
190 .
180
17o 0_
21000 ITERATIONS
0.0 .00 .002 .003 .004 .005 .006 .007
TIME SECONDS
BASE FORCE TIME HISTORY WITH INJECTION
FIGURE 25
- -).
3 9 'p.
-
Conclusions
The results obtained indicate that subsonic base injectioncan be
beneficial in reducing base drag. The use of edgeinjection gives
higher values of base drag reduction (byapproximately 20%) than
center injection. Use of highertemperature injectant gas also gives
larger values of base dragreduction. it appears that small
injection amounts of burning gasin the base region is more
beneficial than large amounts, whichmight blow off the base
bubble.
Details of the optimum injection scheme, however, stillremain to
be determined. In particular, effects of flow channelslocated in
the base region that direct the flow either radiallyinward or
outward may increase or possibly decrease the basepressure and
therefore alter the range of the artillery shell.Potential flow
channel concept are illustrated in Figure 26. Theobjective of these
concepts are to direct injectant gas so thatit interacts with
ambient air that is trying to turn the corneror to use bleed paths
to generate small jets which interact withthe gaseous
injectant.
40
.m
-
00
a N z1-4 -z
0 0 aZf -
/ - - n
* _41
0NiV *LI4 - 1
-
REFERENCES A
1. Nakahashi, K. and Diewert, G.S. "A Practical Adaptive
GridMethcd fnv- Complex Fluid-Flow Problems" NASA TM-85890,
June1984
2. Chapman, D.R., "An Analysis of Base Pressure at
SupersonicVelocities and Comparison with Experiment" NACA 1051
1951
3. Sahu, J "Supersonic Flow Over Cylindrical Afterbodies
withBase Bleed" AIAA 86-0487, January 1986
4. Cavalleri, R.J. "Assessment of a Time-Dependent
ComputationalTechnique for Chemical Laser Type Diffuser
FlowfieldCalculations" AIAA Paper 11-6 Presented at the AIAA
Conferenceon Fluid Dynamics of High Power Lasers October, 1978
5. Drummond, J.P. and Weidner, E.H., "Numerical Study of
aScramjet Engine Flowfield", AIAA Journal 1982, Vol. 20 No. 9pp.
1182-1187
6. Drummond, J.P. "Numerical Study of a Ramjet Dump
CombustorFlowfield", AIAA-83-0421, 1983
7. MacCormack. R.W. "The Effect of Viscosity on
HypervelocityImpact Cratering", AIAA Paper 69-354, 1969
8. Schetz, O.A. "Analysis of The Mixing and Combustion of
Gaseousand Particle Laden Jets in an Air Stream", AIAA Paper
69-33,Presented at the AIAA 7th Aerospace Sciences Meeting
January1969
42 4
V
5'
-
LIST OF SYMBOLS
A AreaC L base drag coefficient 2(Fk-F,)/(u:)2Ft, base drag
forceF,,, reference base force (Alp.)I mass injection ratiom mass
flow rateM Mach numberp pressureR gas constantR0 circumferential
viscous termsT temperatureu x direction velocityv y direction
velocityw circumferential velocityx axial distancey vertical
distance
7 ratio of specific heats
0 circumferential co-ordinate1 viscosityP densityA angular
velocity
SUBSCRIPTS
b base valuej injectant valueo injectant supply value00 free
stream condition
w
s--
\* . ,2". .