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00 001 AJ11. TITLE (Include Security Classification)

Base Drag Reduction Using Angled Injection

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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

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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.

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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

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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

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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". .