Improvements to the Solid Performance Program

American Institute of Aeronautics an1

39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference AIAA-2003-4504von Braun CenterHuntsville AL20 – 23 July 2003

IMPROVEMENTS TO THE SOLID PERFORMANCE PROGRAM (SPP)

D. E. Coats*, J.C. French†, S.S. Dunn‡, D.R. Berker§, Software & Engineering Associates, Carson City, NV

Copyright 2003 by Software and Engineering Associates, Inc. PubAeronautics and Astronautics, Inc., with permission.* President, Associate Fellow AIAA† Senior Engineer, member AIAA‡ Vice President§ Senior Engineer

Insulation

d Astronautics

lished by the American Institute of

American Institute of Aeronautics and Astronautics2

ABSTRACT

The Solid Performance Program (SPP) is theJANNAF sponsored design tool for solid rocketmotor development. Software and EngineeringAssociates, Inc. (SEA) has maintained this code, andhas recently released version SPP’02. This versioncontains several improvements that are useful forgrain design and ballistics analysis, visualization andease of use. A new segmented motor option allowsfor a burn rate and multiplier for different axialsections of the grain. A similar dual propellantoption allows the user to specify different burn ratesfor different propellant formulations along the grain,which allows the user to design a motor withdifferent propellant characteristics for boost andsustain. An insulation option allows the user to placeinsulation on the motor case and alerts the user in theanalysis when the insulation is first exposed at anaxial location. Three new grain design macros havebeen included to simplify the input of a burning axialwire embedded in the grain, to carve out an axial slot,and for packing multiple hollow rods of grain(straws) in an empty case. A new perimetercomputation yields the total, burning and insulationexposure of the grain surface at consecutive axialstations and web steps. An additional computationconnects adjacent perimeters to form a finite elementsurface mesh, which when displayed for sequentialtime steps animates the burn-back of the motor grain.A scarfed nozzle option has been added to the nozzleperformance module. An ignition transient option isbeing added to the code along with a three-dimensional two-phase flow solver for the motorcavity. Improvements are also being made to the oneand three dimensional combustion stability modules.

INTRODUCTION

SPP provides a framework that allows the nozzle andmotor performance of most solid rockets to beanalyzed to a reasonable degree of accuracy. Thefundamental aspects of solid propellant rocket motordesign, including propellant characterization, nozzledesign, grain design and ballistics are integrated in asingle code. Thus making it is a good starting placefor developing new solid rocket motor designcapabilities, such as spatially varying grainformulations or unusual grain designs without havingto start from scratch. Once new features areincorporated into SPP, they become available to theentire rocket development community.

This paper discusses additional capabilities which havebeen added since the last open literature discussion of thecode1, options which are currently being added and/or arebeing checked our, and some future plans for the code.Finally, some of the deficiencies of the SPP methodologyand code are discussed.

Current Improvements to Spp’02

Several options have been instituted to allow the user tomore accurately define the grain design. A segmentedmotor option and a similar dual propellant option havebeen included in SPP’02. The segmented motor optionallows the user to specify different burn rate tables foreach user-defined segment of a motor. In contrast, thedual propellant option allows the user to model a motorwith separate boost and sustain propellant formulationswith distinctly different combustion properties. The caseinsulation option has been improved and allows the userto define the 3-D shape and placement of insulation alongthe motor. This imparts not only the spatial effect ofinsulation on the grain burn-back, but also alerts the userwhen it is first exposed. When this option is used inconjunction with the perimeter option, the insulationexposure as a function of both perimeter and surface areais computed.

Another facet of SPP’02 grain design is the inclusion ofnew grain design macros, which assist in generatingseveral unusual motor geometries. The straws macro fitsa user-defined number of straws of grain into a motor,usually for igniter applications. A wire macro allows theuser to define a series of cones that are appropriatelydelayed to impart the effect of burn rate augmentation dueto an axial wire being embedded in the grain. Anadditional simple macro was included to automaticallyinsert a series of prisms, which hollow out an exterioraxial slot along the case of the motor. As there can be onthe order of 100 figures defined per macro, if changeswere made to the design of a motor, it is much simpler tochange a single macro input rather than to have to modify100 separate geometrical shapes.

As a direct result of SEA’s Navy SBIR funding for 3-Dcombustion stability analysis, we have developed severalnew options that compute the perimeter and surface areaexposure of the grain, case and insulation, as well asanimate the dynamics of the burning grain. This involvestwo successive options: first SPP analyzes individualaxial cross sections to compute the perimeter, and thenSPP connects these perimeters together to yield a FEMsurface mesh. The grain design figures that follow weregenerated using the FEM surface mesh option.


New Motor Definition Options

Segmented Motor Option

The motor segment option allows the user to defineup to 5 axial segments, which have different burncharacteristics. This option is not compatible withthe dual propellant option, which is discussed in thefollowing section. Each motor segment can have aseparate burn rate definition, which includes thepressure exponent and base burn rate as a functionpressure. If values are only input for the first

segment, they will be applied for all segments. Inaddition, each motor segment has an associated ‘hump’factor table. This table modifies the burn rate as afunction of both web burn and axial distance.

As an example, the ASRM rocket motor SPP test casewas modified to include three segments with slightlydifferent burn rate tables. Figure 1 contains several grainburn back steps of this modified ASRM, and Figure 2 demonstrates the effect of the segmented motoroption on the head end pressure of the motor.

(a) Initial Grain Design (b) Mid-way Through Burn (c) Near Burn-Out

Figure 1. ASRM with Segmented Motor Option

Segmented Motor Option

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ASRM ASRM w/Segmented Option

Figure 2. Comparison of ASRM Pressure Time History With and Without Segmented Motor Option

Dual Propellant Motor Option

The dual propellant option is designed to allow theuser to model a system that has two completelydifferent propellants. This option is not compatiblewith the segmented motor option discussed in theprevious section. The convention assumes that thesystem is composed of propellant A and propellant B,which may have different chemical composition and

burn characteristics. If both propellants exist at the sameaxial location, it is assumed that propellant A is initiallyexposed and propellant A covers propellant B. When thethickness of propellant A burns through, propellant B isexposed. Therefore, the user must specify the thicknessof propellant A as a function of axial distance (if thethickness of propellant A at a particular location is zero, itis assumed that propellant B is exposed). In addition, theuser must specify the burn characteristics, the density, and


the chemical composition of both propellants. TheREACTANTS input processor has been modified toaccept A or B in the Oxidizer/Fuel location, in placeof O or F. The properties of the gas flowing downthe grain are then calculated based on the relativemass flows of each propellant.

The following boost-sustain sample motor (Figure 3) hasa star grain design in the aft end and a radial slot in themiddle. The dual propellant option has been used tospecify different propellant formulations for two sectionsof the motor, divided at the axial location of the radialslot. It can be seen that the aft end burns out much morequickly than head end. The pressure history of the burn isshown in Figure 4.

(a) Initial Grain Design (b) Mid-way Through Burn (c) Near Burn-OutFigure 3. Boost-Sustain Dual Propellant Grain Design

Head Pressure vs. Time

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Figure 4. Pressure History of Boost-Sustain Motor using Dual Propellant Option


Case Insulation Option

The insulation option allows the user to specify aninsulation thickness (Ti) as a function of axial lengthand circumferential angle (θi, see Figure 5). Thisoption effectively alters the geometry of the case forthe grain design module. It should be noted that thecircumferential angle is associated with the inputsymmetry factor, SYMFAC (i.e., if SYMFAC=12,then the angle variation should be between 0 and 30degrees). In addition, an output file is written which

displays the web burn at which the insulation is exposedas a function of axial position and angle. The grain is notallowed to burn beyond the insulation. The ballisticmodule utilizes a Nusselt Number correlation to estimatethe heat transfer in the motor for up to five axial stations.This allows the user to calculate the thermal response ofexposed insulation.

Figure 5. Insulation Definition

The Extended Delta motor is used here as an example. Figure 6 shows the motor burn with no insulation applied.Figure 7 demonstrates the effect of adding insulation to the motor.

(a) Initial Grain Design (b) Mid-way Through Burn (c) Near Burn-Out

Figure 6. Extended Delta Motor (no insulation)

Insulation

Tiθi


(a) Initial Insulation Exposure (b) After Burn-Out

Figure 7. Extended Delta Motor (with insulation)

New Grain Design Macros

SPP allows the user to specify geometric primitivesto define the initial motor cavity2. A primitive can bea prism, cone, sphere, or torus, and can be either a“grain filled” or a “void” region. The order in whichthe primitives are specified determines whether agrain filled primitive fills a void primitive, or if thevoid primitive hollows out the filled primitive. Toburn back the grain, SPP then changes the size of theprimitives (voids expand, grain filled contract), usingappropriate corner rounding, to model the burningsurfaces. Hercules Powder Company firstimplemented this approach for ballistic computationsin 19673.

A grain design macro allows the user to define acommon grain design problem, such as the star or thedogbone cross-section, using a minimal number ofinputs. The macro then automatically generates allthe geometric primitives required to hollow out therequested shape. This is of great utility when a slightchange is made to the design – only the macrodefinition needs to be changed instead of every userentered geometric primitive. Here we present severalnew grain design macros that are included in SPP’02:straws, wires and external axial slots.

Multiple Straw-Like Grains

This grain design involves utilizing multiple hollowrods of propellant (hence “straws”), which areinserted loosely into a combustion chamber. Theoriginal intent of this grain design was for designingan igniter, and the number of straws added to thechamber directly affects its effectiveness. While thegrain design of a single straw is straightforward, the

number of straws included can be significantly different.The program computes the tightest hexagonal packing fora given straw and case radius, and places the straws in a60° symmetry section. If the user specifies a number ofstraws which is greater than the code determines may bepacked into the case, a warning flag is issued. However,the computation is allowed to proceed utilizing themaximum determined number of straws allowed and across-sectional area multiplication factor equal to the ratioof the requested number of straws to the maximumallowed number of straws. The usefulness of this macrobecomes apparent when one considers having to inputover 100 rods definitions in the input file. Figure 8 is aside view of 100 bundled straws, Figure 9 shows thecross-section of how this “straw” igniter burns, andFigure 10 shows the corresponding pressure history. Theamount of propellant burnt as a function of web can becomputed analytically:

( )[ ]2= − + − −o i o iV W R R L R R Wπ (1)

V is the volume of the propellant burnt, W is the distancethe web is burnt back (typically proportional to time), Rois the outer straw radius, Ri is the inner straw radius, and Lis the length of the straw. Note that 2 ≤ −o iW R R , asthe straw burns on both the inner and outer surfaces.Since the length is typically much longer than the radius,a good approximation can be made by:

( )= −o iV W R R Lπ (2)

This indicates that the amount of propellant burnt ismainly a linear function (wrt W), which implies that thechamber pressure should be relatively constant and this isshown to be the case in Figure 10.

Insulation


Figure 8. 100 Straw Grains

Figure 9. Grain Burn-Back Evolution of 100 “Straw” Grains in Igniter Case

Head End Pressure Time History

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Figure 10. “Straws” Igniter Head End Pressure Time History


Axial Wire Macro

While embedding a metal wire axially within thepropellant may appear to be an exotic grain designoption, it can be quite useful. The metal wireconducts heat into the grain faster than wouldotherwise be possible. The end effect is that the wireappears to burn faster than the propellant burn rate.In this context, burning implies that the wire materialregresses at a faster rate than the surroundingpropellant at the same pressure. Simple end-burnergrain designs can maintain a constant thrust over anextended period of time, but usually at the cost of alow-pressure chamber design due to the reducedamount of surface area (see Figure 11). When a wireis embedded axially in the end-burning motor and

begins to regress, it changes the flat burning plane into acone, increasing the exposed burning surface area andthus the pressure also (see Figure 12). Once the tail endof the cone has burnt out to the case, the exposed surfacearea becomes constant until burn-out, and the constantthrust characteristic of the end-burner is regained, but at ahigher pressure (and thrust) and shorter action time. Thehalf-angle of the cone generated by the burning wire canbe computed by examining the web step for both the wireand the propellant. The cone angle formed is the arcsineof the ratio of the burn rate of the propellant to theregression rate of the wire. This angle is equivalent tothat of Snell’s law in optics and acoustics.

Figure 11. Web Step of End Burner

Figure 12. Web Step of End Burner with Embedded Axial Wire

Modeling this seemingly simple wire in SPP iscomplicated due to the fashion in which SPP definesoutwardly burning cones. The logical procedurewould be to place a cone next to the end-burningplane, and allow the cone to grow into end burningplane. Unfortunately, when SPP burns conesoutward, all of the sharp corners are rounded,including the tip of the cone. To correctly impart theeffect of the cones, it is necessary to establish a seriesof cones that slightly overlap to account for therounding at the cone tip. These cones are then filledback in using a large grain filled cylinder. This grainfilled cylinder then burns inward at the wire burningrate to expose the cone and end of the burning wire,without exposing the tip of the cone.

In the test case of an actual motor that SEA modeled, over300 cones were required. This denotes the utility of themacro, which only requires knowledge of where the wireis to start (X, Y and Z), and its radius. If any of theseparameters changed, without the macro the user would ofhad to modify all 300 cone definitions by hand. The wiremay also be given an overall initial burn delay, in case itis not initially exposed. We could have chosen to modifythe SPP geometry code to allow for a non-corner-roundedcone tip, but this would have required a major change toone of the core subroutines, and implementing a macro togenerate the same result was deemed a simpler and morerobust approach.

Two sets of runs similar to the motor in Figure 13 werecomputed. In the first set of analyses, 2 to 10 cones were

w∆

1w∆

2w∆

Wire


used, with a ring of wires spaced equally tangentiallyand at halfway between the centerline and the motorcase (see Figure 14a). In the second set of analyses, acone was placed along the centerline, and a ring ofwires was placed equally tangentially but at 2/3’s theradius (Figure 13 has a wire along the centerline and6 wires in a ring about it, and a similar 4 wire cross-section is shown in Figure 14b). The pressure timehistories for these two sets of analyses are shown inFigure 15. Most notably, for the period of time of the

burn when the wire’s effect dominates the graingeometry, the head end (and aft end) pressure not onlyremains constant, but also is invariant with the number ofcones used. An increased number of cones accelerateshow quickly the effect of the wires comes to dominate thesolution, and also steepens the tail off in the pressure.Including a cone at the center of the grain appears topromote acceleration to a wire dominated burn once sevenwires are included, probably due to more efficienthexagonal packing of the wires.

(a) Near ignition (b) Mid-Burn (c) Tail-OffFigure 13. Grain Burn-Back of a 7 Wire Motor

(a) 4 cones with no centered wire (b) 4 cones with centered wireFigure 14. Placement of Cones for Test Cases

(a) Pressure History Without Center Wire (2-10 wire) (b) Pressure History With Center Wires (1-10 wires)

Pressure History: No Centered Wire

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Pressure History: Centered Wire

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Figure 15. Comparison of Motor Pressure History with Varying Numbers of Axial Wires

New Grain Design Analysis Features

Routines within SPP examine axial cross-sections ofthe motor at user defined axial “stations” todetermine the area and moments of the cross-section(Figure 16). When a motor’s grain design has a highdegree of axial cross-sectional symmetry, only thesymmetry section is required for the ballisticsanalysis, which accelerates the computational processand simplifies the input. Each cross section issubdivided into a series of lines perpendicular to the

y-axis (Figure 17). The intersection of the line with thedifferent primitives is used to determine what portions ofeach line extend across the grain. Note that at this pointthe area and moments can be computed using trapezoidalintegration. However, the actual grain surfaces are neverexplicitly evaluated. It is possible to surmise a rough ideaof the grain surface by examining the tops and bottoms ofeach vertical slice (see Figure 17), but there are manypotential pitfalls in evaluating the perimeter by simplyattaching neighboring tops and bottoms.

Figure 16. Axial Cross Sections of Motor Figure 17. Vertical Slices in y-z Plane (Fixed x)

Motor designers often begin with previouslyimplemented grain designs as a starting point. Thedesigner can pick and choose from establisheddesigns in order to design the motor to fit a desiredthrust-time history. There are a number of standardgrain design shapes that can be modeled in SPP’02™using macros to help the user specify these shapes.Macros are defined for the Star, Wagon Wheel,Dogbone, Dendrite, Finocyl, and Conocyl shapes asshown in Figure 18. The Star, Wagon Wheel,Dogbone, and Dendrite macros include a domestreatment, which allows the head end or aft end of adesign to taper from one shape to another. Theseunusual shapes are also difficult to transform into a

surface mesh using a general procedure. The SPP97™code contains several choices for connecting the ends oflines found during the ballistics computations to computethe perimeter. The choices allow the user to specify howtwo sequential perimeters should be attached, such as byincreasing angles or by percentage of perimeter. Theseapproaches often can fail or incorrectly represent thegeometry. These results are primarily used forpresentation rather than engineering purposes. The goalhere was to create a general algorithm yielding both anaccurate perimeter and surface mesh, which could then betransformed into a computational mesh using standardgridding algorithms.

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4 6 8 10 12 14 16 18


a) Conocyl b) Finocyl

c) Dendrite d) Wagon Wheel e) Dogbone

Figure 18. Standard Grain Shapes

Axial Perimeter Computation

One of the benefits of SPP’s original design is thatfor a given axial station it can quickly and accuratelyexamine the full set of geometric primitives for agiven x-y location and return several ranges ofvertical lines parallel to the z axis where the motorgrain or insulation exists. The problem is how to bestconnect the ends of these lines to form the perimeter.The approach is to first define a region, and thenremove everything that is not on the surface of thatregion, leaving only the surface4. This approach issignificantly different from the approach used inSPP97™ to compute the perimeter for 3-D plots5. InSPP’02™, the vertical lines used to performtrapezoidal integration are then used to find theperimeter by attaching the tops or bottoms of thevertical lines. For example, in Figure 19(d), thebottoms of the vertical lines can be attached to form asmooth surface of a star cross-section sector. Whilethis approach works quite well for simple cross-sections, choosing the next correct point using logicis difficult for complicated cross-sections. There areseveral ways to choose which points are connectedon the perimeter. For example, one could connectpoints based on their angular location, or the“closeness” of the neighboring points, resulting insignificantly different perimeters. The followingpresents an approach that eliminates the logic ofchoosing the “next” connecting point on theperimeter. Instead of connecting points, the

perimeter is computed by covering the grain-filled regionwith boxes and triangles. Once the lines inside this regionare removed, only the perimeter remains.

One of the main problems in generating a computationalgrid from the SPP input is that SPP uses trapezoidalintegration over each cross-section to compute thepropellant volume and surface area for the 1-D ballisticsand moments. The integration algorithm does not requirea visually attractive cross-section – a very rough crosssection is sufficient. In order to generate a computationalgrid, a smooth approximation to the grain’s surface needsto be determined. The gridding code looks fordiscontinuous regions, triggering the code to interpolateseveral new vertical line locations to better approximatethe surface. For example, extra lines are inserted at theleft upper surface of Figure 19(b) to better resolve theintersection with the boundary.

The top and bottom of each line is examined to determineif it is between the top and bottom of the lines to itsimmediate left and right. This is done to divide the graininto rectangles (see Figure 19(c)). The sharp corners ofthe rectangle leave a jagged appearance, so each concavecorner is checked to see if it is within the grain. If it is, atriangle is added to eliminate the concave corners (Figure19(d)), smoothing the boundary. When the interior linesare removed, the surface remains (Figure 19(e)). Thisalgorithm handles double valued regions in the y-z planewithout modification.


(a) Raw Data from SPP (b) Extra Lines Inserted for Resolution of Boundary (c) Minimum Area Boxes Formed (d) Smoothing Triangles Inserted

(e) Interior Lines Removed Leaving Grain Surface

Figure 19. Steps Taken to Compute Grain Perimeter (Extended Delta motor)

The ability to locate the boundary of the grain alsoprovides the ability to compute the perimeter of thegrain’s burning surface, the case wall and theinsulation. From the perimeter at each axial stationthe exposed surface area (total, burning and

insulation) can be computed using trapezoidal integration.Figure 20 shows the surface area plotted versus time forthe Extended Delta motor. Figure 21 shows the effect ofadding insulation: the grain’s burning surface area isreduced as the insulation is exposed (the insulation isincluded as part of the total surface area).

Figure 20. Surface Area vs. Time for Extended DeltaMotor

Figure 21. Surface Area vs. Time for Extended DeltaMotor with Insulation

3-D FEM Surface Mesh Generation

The output from the perimeter algorithm yields asmooth approximation of the grain surface for agiven cross-section. A similar algorithm has beendeveloped which connects the perimeters fromaxially adjacent cross-sections to generate a 3-DFEM surface mesh. The concept behind the 2-Dcross-section perimeter algorithm is to take the outputof SPP (vertical lines segments in the z directionlocated at several locations along the y axis and fixedx location) and find the smallest regions that arefilled with grain by finding the smallest unionsbetween subsequent vertical lines to form boxes (seeFigure 19(c)). The perimeter’s jagged corners arethen smoothed with triangles if they are filled withgrain. In a similar manner, 3-D surface planes can beformed by identifying regions that need to besmoothed with axially connecting triangles (RegionsII and III in Figure 22). For a realistic example,consider the two dendrite perimeters superimposed inFigure 24. These two figures are similar, and onlyvary in the bulge near the case wall (due to the domestreatment). To smoothly transition from one plane’sperimeter to the next, the perimeters that comprisethe neck of the dendrite should be directly connected(projected axially), while the disconnected region atthe bulge should be smoothly connected usingtriangles.

Generally, in order to accomplish this task, the linescomposing the perimeters from two adjacent axiallocations are superimposed on a plane. For eachperimeter line segment, a perpendicular vector ismaintained that points toward the grain, or if the

perimeter line is on the case, the perpendicular vectorpoints out of the case (Figure 23). Lines that are commonto both perimeters are combined. A set of nodes is thenestablished to determine which lines are connected toeach other. For lines on the symmetry boundary,connections are made to the next node on the boundary ina counter-clockwise fashion. The perimeter lines are thentraversed in a counter-clockwise fashion. Each of thelines is traversed twice, once in each direction. When aline is traversed, the cross product of the direction that theline is traversed and a vector associated with the line thatpoints into the grain (or into the motor casing) determinesthe kind of region that is found for each traversed loop.For example, in Figure 23, Region I has only outwardpointing vectors, and as such represents a region thatwould only be projected from one plane to another.Regions II and III have both outward and inward pointingvectors so these perimeters should be connected usingtriangles to create a smooth connection between theregions. If a smooth connection is made, the lines used inthe smoothing will be removed from the set in Region I,which would otherwise have been projected. In RegionIV, there are only inward pointing vectors, indicating thatthis region is filled entirely with grain. For entirely grainfilled regions, any exposed surfaces are already projectedor smoothed by the adjacent regions, and thus noadditional smoothing or projecting triangles are needed.

To simplify this greatly, when the two perimeters aremerged, y locations that are within a user-specifiedtolerance are combined. Likewise, z locations that arewithin the same user specified tolerance are alsocombined. A list of points is then kept for each of the ylocations, which comprise the z locations where linesconnect. To traverse the lines, the next line will be


attached to a point in the previous, current or next ylocation node list. By examining the previous andcurrent point, one can then ascertain which point to

move to next for the “most” counter-clockwise line towhich the current line is attached.

Figure 22. Two Perimeters Dividing the Motor Section into Four Regions

Figure 23. Unit Vectors Perpendicular to Perimeter Pointing in Direction of Grain

Figure 24. Superposition of Dendrite Perimeters from Growing Domes Treatment

The burn-back of a double conocyl motor grain and adendrite motor grain are shown in Figure 25 andFigure 26. The double conocyl is a particularlyinteresting case; at an axial location in the middle ofthe cones there geometrically may be as many as fiveseparate perimeters in a symmetry section that the

FEM mesh generator is able to correctly attach. SPPoutputs the surface mesh for a user-specified number ofsectors. The output can be directly read by theGeneralized Mesh Viewer (GMV), a maintained publicdomain graphics program available at:

http://laws.lanl.gov/XCM/gmv/GMVHome.html.

I

II

III

IV

I

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Perimeter 2

Perimeter 1

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http://laws.lanl.gov/XCM/gmv/GMVHome.html


A second output file can be generated to animate theburn-back using Tecplot™, a commercially available

plotting package.

Figure 25. Conocyl Motor Burn-Back

Figure 26. Dendrite with Domes Treatment Burn-Back

Scarfed Nozzle Capability

SPP’02™ has been modified to compute the thrust on ascarfed nozzle. The restriction on this option is that the scarfangle is less than the Mach angle as measured from the wallpoint. This restriction is due to the fact that the performance ofthe scarfed nozzle is computed after regular nozzle calculation.The table below shows the output from the scarfed nozzleoption.

S C A R F E D N O Z Z L E S U M M A R Y

SCARFING ANGLE 63.7000 DEG63.7000 DEG

FROM Z 3.45457 IN0.08775 M

R 0.75338 IN0.01914 M

TO Z 7.32675 IN0.18610 M

R 1.16037 IN0.02947 M

FULL AREA 2.34086E+01IN**2 1.51018E-02 M**2

AREA SCARFED 9.83033E+00 IN**26.34193E-03 M**2

FULL AXIAL THRUST 6.34822E+01 LBF2.82369E+02 N

AXIAL THRUST 3.11859E+01 LBF1.38715E+02 N

LATERAL FORCE 1.50166E+02 LBF6.67937E+02 N

TOTAL FORCE (RMS) 1.53370E+02 LBF6.82189E+02 N

FORCE DIRECTION 78.2678 DEG78.2678 DEG

CENTER OF FORCE (R) 0.46955 IN0.01193 M

CENTER OF FORCE (Z) 5.11381 IN0.12989 M

TORQUE ABOUT X-AXIS 7.82562E+02 IN-LBF8.84132E+01 N-M

1) The coordinate system is R-Z, with the origin at the throat and the Z-axis along the centerline

2) The region examined is from the most forward intersection of the scarfangle to the exit (i.e., for the above example the SCARF analysis startsat Z=3.45457 in, R=.75338 in, and ends at the exit lip, Z=7.32675in,R=1.16037 in)

3) The FULL AREA is the entire surface area between the above twopoints, ignoring the scarfed portion


4) The AREA SCARFED is the actual surface area between theabove two points considering the scarfed portion

5) The FULL AXIAL THRUST is the thrust between the abovetwo points, ignoring the scarfed portion

6) The AXIAL THRUST is the true thrust between the above twopoints considering the scarfed portion

7) The LATERAL FORCE is the true force in the radial directionbetween the above two points considering the scarfed portion

8) The TOTAL FORCE is the RMS of the AXIAL THRUST &LATERAL FORCE

9) The FORCE DIRECTION is the angle measured from thecenterline where the TOTAL FORCE is acting

10) The CENTER OF FORCE (R) is the radial coordinate where thetorque is acting

11) The CENTER OF FORCE (Z) is the axial coordinate where thetorque is acting

12) The TORQUE ABOUT X-AXIS is the total torque about the Xaxis (Pitching torque)

WORK IN PROGRESS

There are three major works in progress for the SPPcode. The first is the addition of a true ignitiontransient module, the second is the addition of athree-dimensional flow solver for the motor cavity,and the third is the implementation of a multi-dimensional non-linear combustion stabilitycapability. The ignition transient model is currentlybeing checked out and will be available in the nearfuture. The three-dimensional flow solver has beenwritten and will be integrated into SPP in the currentyear. The multi-dimensional non-linear combustionstability module is under development and should becompleted in 2005. Brief descriptions of thesemodules follows.

Ignition Transient Module(ITM)

Many 1D-ignition simulation codes have been writtensince the original Peretz et al6 work. After review, theIgnition Transient module in SPP was based in part on theSHARP1D-IT code of Rozanski7 and the updated NPP97™ code8. Both the Roe and Van Leer upwind fluxsplitting schemes are used. For the Roe schemeformulation, the discrete phase is treated as an equivalentcalorically perfect gas. In the Van Leer scheme, the two-phase flow equations are solved with the particulate flowcarried as a separate discrete phase. The combined gas-particle solution is formulated using the unsteady one-dimensional flow equations in strong conservation formin order to capture the igniter shock:

E / t F / x W R / x∂ ∂ + ∂ ∂ = + ∂ ∂ (3)

where

E U Ae

ρ= ρ

( )

2

U

F U p A

e p U

ρ

= ρ +

+

where ( ) 212e p / 1 U+ γ − + ρ and the source (injection)

terms are

p ig2 21

2 w ig

p p r w w ig pig ig

Sr mW pdA U fA m / A

SrC T Q A m C T

ρ +

= − + ρ

ρ − +

g

0R G A

GU k T / x=

+ ∂ ∂( )G 4 / 3 U / x= µ∂ ∂

and f is a friction coefficient for the bore flow alongwetted surface area Aw, and mig is the specified ignitermass flow. These equations are solved in the ITMmodule using a modern Roe flux vector-splittingtechnique. The ITM allows the igniter gas to be injectedanywhere along the motor bore with a specified injectionvelocity and direction. This capability is necessary forigniters that are not located at the head end of the boreand/or fire upstream into the bore.

The gas/droplet flow emitted by the igniter and later fromsegments of from propellant that have ignited supply theconvective Qc and radiative Qr heat fluxes which heat the


propellant grain to the point of ignition. It iscommon to predict when the propellant will ignite bysolving the 1-D heat conduction equations andimposing an ignition criterion such as critical surfacetemperature. Assuming constant thermal diffusivity,α, and conductivity, k, in the propellant, the variationof propellant temperature, Tp, with depth, y, and time,t, is determined by either numerically from

2 2p pT / t T / y R∂ ∂ = α ∂ ∂ − (4)

where

rR Q / y= ∂ ∂ c rQ Q Q= +

( ) ( )0 roQ t Q Y 0, t Q Q∞= = = +

subject to the boundary conditions

( ) ( )p p poT y,0 T , t T= ∞ =

( ) ( )p oY 0T / t Q t / k

−∂ ∂ = − or

( ) ( ) ( )o g sQ t h T t T t= −

The ITM has two heat transfer models to calculate thefilm coefficient, h. The model due to Cohen9 hasprovisions for calculating the film coefficient for bothmetallized and non-metallized igniter flows. The otherheat transfer option due to Lu and Kuo10 does not.

Figure 27 and Figure 28 show the pressure field for theignition transient for two different motors. The firstmotor is the Space Shuttle RSRM motor while the secondis an annular motor with and aft end igniter which firesforward. The igniter shock and its reflections are clearlyseen in both figures. The fit to measured data for theRSRM is very good, Figure 29. The comparison to datafor the annular motor, not shown, is good but indicatesthat more work needs to be done in characterizing thistype of igniter.


Figure 27. RSRM Ignition Transient Calculated Pressure Field

Figure 28. Annular Motor With Forward Facing Aft Igniter Calculated Pressure Field

Figure 29. RSRM Ignition Transient Comparison

Three-Dimensional Chamber Flow Solver

The three-dimensional chamber flowfield solver hasbeen written and has been tested as a standalonecomputer program. It is currently being integratedinto the SPP and will allow the user to compute thechamber flowfield in a quasi-steady manner at anypoint in the burnback. The code is a two phase Eulersolver which treats both the gas and discrete phasesin an Eulerian manner. The intended uses for the

module are for three-dimensional combustion stabilitycalculations and for investigations of three-dimensionaleffects on motor performance. Figure 30 showsstreamline traces for a Minuteman II second stage motor.


Figure 30. 3-D Streamline Traces For Minuteman II Second Stage Motor


For simple grain geometries, the SPP will have a self-contained grid generation capability. For the morecomplicated geometries, the user can export thesurface element grid and use one of the manycommercially available grid generators to build thecomputational mesh.

Non-Linear Combustion Stability Model

SEA is under an SBIR contract to the Navy todevelop a multidimensional non-linear combustionstability capability within the SPP code. The non-linear models being developed are due to Culick andYang11 and G. Flandro12,13. Dr. J. French ispresenting the status of that work in this meeting14.

SUMMARY AND CONCLUSIONS

Herein we have demonstrated the new capabilitiesincorporated into SPP’02: segmented and dualpropellant options, case wall insulation, several newgrain design macros including axial wires embeddedin the grain, and the perimeter and FEM surface meshcomputations. In the future we plan to add 3D CFD,automated grid generation and a non-linearcombustion stability analysis to predict pressure limitamplitudes.

ACKNOWLEDGEMENTS

The authors would like to thank the customers whohave supported the development of SPP and inparticular, Dr. Fred Blomshield of the Naval AirWarfare Center, China Lake, CA for his support ofthe improvements to the combustion stability moduleof SPP.

REFERENCES 1 Dunn, S. S., Coats, D. E., “3-D Grain Design andBallistics Analysis Using the SPP97 Code”, 33rd

AIAA / ASME / SAE / ASEE Joint PropulsionConference, AIAA paper 97-3340, Seattle, WA,1997.2 Dunn et al. Op cit.3 Barron, J.G., Jr.; Cook, K. S., Johnson, W.C.,“Grain Design and Internal Ballistics EvaluationProgram (IBM 7094 FORTRAN IV), Program No.64101 (AD 818321), Hercules Powder Co., BacchusWorks (Magna, UT), July 1967.4 French, J.C., “Mark 90 Grain Design TangentialMode Stability Analysis: Final Report”, ContractReport for Alliant Ammunition & Powder Company,Purchase Order AR0448, August 2000.

5 Coats, D. E., Dunn, S. S., “SPP97™ NozzlePerformance User’s Manual”, Software and EngineeringAssociates, Inc, Carson City, NV, January 1998.6 Perez, A., Kuo, K. K., Caveny, L., and Summerfield,M., “Starting Transient of Solid Propellant Rocket Motorswith High Internal Gas Velocities”, AIAA Journal, Vol.11 No. 12, Dec. 1973, pp 1719-277 Rozanski, J. D., "SHARP1D-IT A Computer Code ForSimulating Ignition Transients Using A One-DimensionalFlow Field', Thiokol TWR-40255, March 1990.8 Coats, D. E., Dang, A. D., and Dunn, S. S. “NozzlelessPerformance Program, NPP 97”, Software andEngineering Associates, Inc., Carson City, NV, 19979 Cohen, N., “Ballistic Predictions for Mass-AugmentedSolid Rocket Motors,” ADRPL-TR-71-13310 Lu, Y., and Kuo, K. K., ”Ignition/Thrust TransientInternal Ballistic (ITTIB) Code, User’s Manual”,Pennsylvania State University, Prepared for ThiokolCorp., Advanced Technologies, May 199211 Culick, F. E. C. and Yang, V., “Prediction of theStability of Unsteady Motions in Solid Propellant RocketMotors”, Chapter 18 in Nonsteady Burning andCombustion Stability of Solid Propellants, Progress inAstronautics and Aeronautics, Vol. 1433, 199212 Flandro, G. A., “Approximate Analysis of NonlinearInstability with Shock Waves”, AIAA-82-1220, 18th JointPropulsion Conference, Cleveland, OH, June 198213 Flandro, G. A., “Energy Balance Analysis of NonlinearCombustion Stability”, Journal of Propulsion and Power,Vol. 1, No. 3, pp210-221, May-June 198514 French, J., ”Non-Linear Combustion StabilityPrediction of SRM’s Using SPP/SSP“, AIAA-2003-4668,39th Joint Propulsion Conference, Huntsville AL, July2003

Improvements to the Solid Performance Program

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