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  VOL.  12, NO. 1,  JANUARY  1975 J.  SPACECRAFT 33 Recent Occurrences of Combustion Instability in  Solid Rocket  Motors—An  Overview A.  L.  KARNESKY, AND  S. E.  CoLuccif Aerojet  Solid  Propulsion Company,  Sacramento,  Calif. There has  been and undoubtedly  will  continue  to be frequent  occurrences  of unacceptable  oscillatory combustion in  the  development  of  high-specific-impulse high-volumetric-loading solid-rocket motors.  Some  of  the  observations of  instability  cannot be explained  quantitatively  using existing  T-burner and stability-prediction procedures.The paper  will  present a  review  of the  extent  and  types  of  oscillatory combustion  encountered in recent  solidrocket motor  development  efforts  at  Aerojet.  The intent is to  illustrate  the prevalence of the  occurrence  of thephenomenon to show  examples  of  each  of  three forms  of  combustion  instability  which  have  plagued  real motors and  to indicate  what  actions  were taken  to reduce or eliminate the  instabilities. Introduction C OMBUSTION  stability  in a  solid propellant rocket motor depends on the  balance  between energy gains  and  losses of  the system. If the system gains exceed the losses, an oscilla-tion  will  be  amplified  in  magnitude;  if the  losses exceed  the gains,  the  opposite occurs. Thus, stabilization  of an  unstablemotor reduces to either diminishing energy source factors (gains) or  increasing  the  effectiveness  of  dissipation mechanisms(losses) in the system. When an instability occurs, thenqualitatively,  gains  exceed losses.Combustion instability is a phenomenon which has plaguedsolid rocket motor development for many years. Its occurrencehas  produced  events ranging  from  unsatisfactory ballistic per- formance  to tolerated pressure oscillations and missile vibration.Catastrophic  failure  of the  motor  or  complete malfunction  of the missile have also resulted. Since combustion instabilityresults  from  an interaction of the burning process with the acoustic  mode in the gas cavity, it is related to the pro-pellant formulation, the changing acoustic cavity and motor operating  conditions.With the ever-changing design  features  and propellant  formu- lations used in solid rocket motors, a variety of instabilitieshave occurred and various cures have been attempted to reduce to an  acceptable level  or  completely eliminate pressure  oscilla- tions. Several motor programs conducted with Aerojet motorsare reviewed where combustion instability occurred duringdevelopment  or  production.  The  intent  is to  provide  an  over- view  of the  various types  of  instabilities  and  what cures havebeen used in the past. Types of Instabilities The oscillatory stability state of a solid rocket motor is thenet sum of those design features that influence the  gain-loss balance. The principal contributing parameters are the motorgeometry, grain configuration, propellant driving potential, andthe inherent losses due to the nozzle, particles, or structure.Current and  future  missile systems are imposing more stringentrequirements on performance and design constraints, i.e., volumeor weight limitations. The designer is therefore limited in the options  available  to  minimize  or  eliminate oscillatory com-bustion by the use of geometry or propellant changes. Presented  as  Paper  73-1296  at the  AIAA/SAE  9th  Propulsion Con- ference,  Las  Vegas,  Nev.,  November  5-7,  1973;  submitted November 29,  1973; revision  received  July  24,  1974. *  Manager,  Applied  Mechanics. t  Senior Engineering  Specialist.  Associate Fellow.  AIAA. Since one of the prime parameters of combustion instability is  the acoustic mode of the gas cavity, it is natural to  classify the various types of instability by the type of mode whichbecame unstable and by the mechanism of interaction of thecombustion  process  with  the  acoustic mode. Over  the  pastdecade, the leading  offender  has been an instability in thelongitudinal  or  organ  pipe  mode  in the  chamber. More recently, with  a  return  to  smokeless propellants,  the  tangential modes of  the chamber have exhibited instability as  well.  Two majorclasses of instability in the longitudinal modes have been identified  as being related to the mechanism of the interaction of  the combustion process and the acoustic mode  (i.e.,  pressure-coupled  and  velocity-coupled  instability).  The  acoustic behavior of  a  solid  motor  will  be  reviewed  briefly  with  the  associated forms  of  instability  for  reference. Illustrations  of  these various forms  of  instability  in a  variety  of  motors  will  then  be  reviewed to  provide  a  general  overview  of  what  has  occurred  in  solidrocket motor development programs. A.  Longitudinal  Mode  Instability First  a  little acoustics:  The  interior  gas  flow  passage  of a  solidrocket motor is a confined acoustic cavity. At operating condi-tions, the sonic nozzle throat  forms  essentially a closed endtube (acoustically speaking) and the longitudinal direction of the  motor behaves  as a  closed-closed tube.  For a  simple motorgeometry like a cylindrical bore the acoustic modes are identicalto the organ pipe (closed-closed tube) modes. Figure 1 displays for  a cylindrical  bore,  the conventional pressure modal distribu-tion at two extremes of a standing acoustic wave in a closed-closed tube with the gas density illustrated by the dot density. Fig.  1  Longitudinal  modes.    D  o  w  n   l  o  a   d  e   d   b  y   U   N   I   V   E   R   S   I   T   Y    O   F   T   E   X   A   S   A   T   A   U   S   T   I   N   o  n   J  u  n  e   6 ,   2   0   1   4   |   h   t   t  p  :   /   /  a  r  c .  a   i  a  a .  o  r  g   |   D   O   I  :   1   0 .   2   5   1   4   /   3 .   5   6   9   4   8  34 A.  L. KARNESKY AND S.  E.  COLUCCI J SPACECRAFT Fig. 2  Small  tacticalrocket motor. During  the time  period  between the  first  half  cycle  of oscilla-tion (Fig.  la to  Ib),  the gas  particles  are  accelerated  from one end of the chamber to the other,  with  a resultant particle velocity  which  varies in a  sine  function  distribution. Both  the acoustic  pressure and the  particle  velocity  variations are  super- imposed upon  the mean  chamber  pressure and mean gas  flow in  the  cavity. Analytical  treatments  of  combustion  instability by  McClure et  al., 1  and  more  recently by Culick, 2  have  identified  the interaction  of  the  acoustic  modes,  the  mean  flow,  and the combustion process. Their  analyses have shown  that  in the presence  of the burning  surface  the  oscillating pressure  can add energy to the  acoustic mode.  As previously  indicated,  whenenergy  addition  exceeds  acoustic losses  in the cavity the amplitude  of the  acoustic mode  grows,  or  becomes unstable. In a  similar  sense the  acoustic  particle  velocity, in  conjunctionwith  mean  flow  and  pressure oscillations,  can result in energy added  to the  acoustic mode  which  may  also  result in an increase  in the  oscillations.  In this later  interaction  there  can be an augmentation in the  propellant  burning  rate  resulting in a general  increase  in mean  chamber pressure,  usually  called  ad.c.  shift.  Within these  very  simple  definitions of  pressure-coupled  and velocity-coupled  instabilities those phenomena  maybe  reviewed  as  observed  in  actual solid rocket motors  and some  of the design  changes  made to reduce or eliminate  theiroccurrence. Significance  of instability:  Before  becoming completely lost  in the  instability,  it is worth  noting  the  significance  of  combustioninstability, its range of  severity  and just what  does  it mean to a missile  system.  It  must  be emphasized  that  although we  speak of  an unstable  condition  or instability  implying  a  self  perpetrating increase  in pressure  oscillations,  in actuality  every  oscillation will  increase  only  to a limiting amplitude. In  essence  then the process  is  nonlinear.  The limiting oscillatory  amplitude  may be a few psi or in the  order  of  several hundred psi.The  results  of pressure-coupled longitudinal  mode  instabilityare mechanical vibrations  induced into  the  rocket motor  that may  produce  component  or structural  failure.  Low amplitude instabilities  may be  tolerated,  depending on the  frequency  andthe structural  characteristics  of the  motor.  The  pressure oscilla- tion  will  also  produce  an  oscillatory  force  in the  longitudinaldirection  which  could be transmitted  forward  through the structure  with  resultant mechanical vibration and  possible destruction  of  missile  guidance components. The  significance of  the  motor  instability  to the missile  depends upon  frequency of  oscillation,  mechanical  stiffness  of the  interstage  structure,and the  sensitivity  of upstage components to the inducedmechanical  vibration.Generally speaking,  a  velocity-coupled instability  will  result  in similar mechanical  vibration  of the motor and missile.  In addition,  however,  the augmented burning rate  usually  associated with velocity-coupling  produces  an  increase  in  mean  chamber pressure  and a  decrease  in  motor  firing  duration.  The significance of  the ballistic change  depends  upon the  particular  missile system. The  increase  in  chamber pressure  may result in over pressurization and  rupture  of the  case;  the increased thrust could exceed the  missile  acceleration  limits  and/or the  change  in themotor  duration  can result in  unacceptable  performance of the system.The  severity  of the instability, on the  other  hand,,  and/or the  sensitivity  of the  missile system  may be such  that  the presence  of  instability  does  not  affect  or  compromise  missile performance in any  way.  Hence,  it is  tolerated.  Several  rocket Fig.  3 Illustration of d.c.  shift  effects  on motor  thrust  on small tacticalmotor  quad  tests. motor development  programs have  tolerated  the presence of instabilities  in the  past. Instance  of Instability in Actual  Motor Operation A.  Small Tactical  Motors The rocket  motor  shown  in  Fig.  2 is a small tactical motor less  than  3-in.  in  diam  with an empty fineness  ratio  L/D)  of approximately ten. The grain geometry is a simple  cylindricalperforation and uses a  single  aluminized  propellant. During  thedevelopment  of this  motor, combustion  instability did not  appear to be a problem.  Ballistic anomalies  occurred on two occasionsthat  were  suspected  to be an instability  caused  by the loss of anozzle  insert. In  actuality,  pressure-coupled instability hadoccurred  early in the  motor  firing,  but the  presence  of the instability had been  obscured  by inadequate instrumentation. A  multitude  of  flight  tests  were  conducted  of the missilesystem with  no  detectable  adverse  conditions  resulting  from  the pressure-coupled  instability. The motor program proceeded  into mass  production.  Duringthe  course  of  routine production motor tests,  pressure  anomalies did  occur  in a few lot  acceptance  firings.  The results of one of  these  firings  are shown in  Fig.  3. The  figure  is an  actual oscillograph trace  of the thrust time  histories  of  four  motors fired  simultaneously. The  oscillations observed  are due to ringing of  the thrust  stand,  not an instability. The upper  firing  trace which  shows the large discontinuity is an  occurrence  of a d.c. shift  due to a velocity-coupled instability. The actual thrust oscillations  resulting  from  the instability are almost  obscured by the  frequency  response  of the  test  stand;  however, they  couldbe identified. Several things are  notable  from  the  firing  curve: 1)  the  sudden increase  in  mean  motor  thrust,  2) the limiting of  the thrust  increase,  and 3) the  decrease  in total motorduration.  The instability observed in this motor was attributed to the ejection of a  portion  of the nozzle  throat  which  initiated a pressure pulse in the  motor. A  heavy wall  version of this motor has been used as a testvehicle  to  evaluate suppression devices. The  heavy  wall  con- Fig.  4 Large  dual  thrust  dual  propellant  tactical  motor.    D  o  w  n   l  o  a   d  e   d   b  y   U   N   I   V   E   R   S   I   T   Y    O   F   T   E   X   A   S   A   T   A   U   S   T   I   N   o  n   J  u  n  e   6 ,   2   0   1   4   |   h   t   t  p  :   /   /  a  r  c .  a   i  a  a .  o  r  g   |   D   O   I  :   1   0 .   2   5   1   4   /   3 .   5   6   9   4   8  JANUARY  1975 COMBUSTION  INSTABILITY IN  SOLID  ROCKET MOTORS 35 Fig.  5  Illustration  of pressure and  velocity coupled instability  on large tactical  motor. figuration  contained  a pulsing  device  and  provisions  for  high frequency  pressure measurements. The motor was stable  until pulsed.  A  pressure pulse  of  approximately  50 psi was  induced into  the motor at 1.0 sec. Following the  pulse, pressure oscillations  grew  to approximately 240 psi and an  increase  inmean pressure of 900 psi  occurred.  It had been concluded  that this motor  configuration was  stable  until  pulsed, instabilityoccurred either  from  the  direct pressure pulse  or the  ejection of  material through  the  throat. B.  Large Tactical Motor Both pressure-coupled and velocity-coupled instabilities  were encountered  during  the development and  qualification  program of  a  dual  thrust,  dual  grain tactical motor having a diameter of  over  fourteen  inches,  shown in  cross section  in  Fig.  4. This  motor used an  aluminized  propellant in the  boost phase and a  very  slow  burning nonaluminized  propellant  in  sustain. During the development  period,  both pressure and  velocity- coupled  instabilities  were  encountered as illustrated on  Fig.  5. Pressure-coupled instabilities  during  the  boost phase  were  quitenumerous and  occurred almost  routinely.  Various changes  in the propellant  oxidizer  particle  size  and  aluminum  particle  size were  tried.  Eventually  the  motor  was  stabilized  by  changes  inthe  boost  propellant  formulation. Velocity  coupled  instabilities during sustain especially  near  tailoff  were  more  random  in occurrence. These continued to occur  even  through the  produc- tion program  and  sporadically  in missile  flight  tests. Recently,  during  a test of a production motor, an instability was  observed to accompany the  ejection  of a piece of materialthrough  the nozzle  throat  which  led to various  speculations. To  verify  (or  refute)  that  an instability  could  be  initiated  bythe ejection of a piece of  material  (i.e.,  igniter  case  insulation), and to  determine  the approximate  size  of  ejecta  required to trigger  an  instability,  a special  pulse test  was conducted. In  this test,  it was planned to  eject silica-filled  polyurethane  plug cylinders  of  three  different  sizes  at  three  different  times during the sustain  phase.  It was  found,  however,  that  a velocity coupled  longitudinal  mode  instability was  initiated  by theejection of the second cylindrical plug having a  length  and diameter  of  0.75  in. A  copy  of the  actual pressure  and  thrusttrace  as replayed  from  the  tape recorder  is shown on  Fig.  6. In addition to the pressure oscillations it can be seen that the mean  pressure  was  increased considerably  which resulted  from the burning  rate augmentation caused  by the instability. When 14.2 14.5 Fig.  6  Growth  of  instability  caused  by  plug  ejection. the  third  plug was  launched,  the chamber pressure had already decreased  to ambient, hence  measurements  were  meaningless. The sequence of mechanical  events  that occurred to  launch the plug  into  the  freestream  shall not be  described  in detail here.  Briefly,  however, a squib was used to initiate red dot powder:  the  ensuing  pressure rise  ruptures  a burst diaphragm and drives a  piston  forward  until it  reaches  its mechanical stop  or snubber plate. This, in  turn, drives  a  plug  into the gasstream  at an initial velocity  (muzzle  velocity)  considerably greater than  the  local stream  velocity  at the  forward  end of the chamber.  The  average  plug velocity  in  passage  through the chamber  may be calculated  from  the measured time  delay between  the  first  indication  of  pressure  rise  following  squib initiation  and the  start  of  pressure  oscillations.  Plug  performanceis  summarized  on  Table  1. The  oscillograph record  was used to  obtain  measured  values of  plug performance in the  motor  test at  10.2  and  14.2  sec after  start. These  values were  also  shown on  Table  1 as  well  as measured  and calculated  values  for the  initial  pressure rise. These  appear  to be in good  agreement.  The  average grain diameter, at  .each  of the  burn times,  was  back calculatedusing the  chamber  inside  diameter,  the average burning  rate of  the sustain  propellant  and the time remaining  until  burnout. From  this  and knowledge of the nozzle  throat  diameter,  bore exit  velocities  were  estimated. The average  plug velocity  wascalculated  from  the  measured time  delay of 45.5 and 47.5  msec for  the 0.375 and 0.750-in. diam  plugs, respectively.  This timedelay was  assumed  to consist of the  time  it takes the  plug  to reach  and  constrict  the  nozzle  throat  and the  time  required for  the  pressure  wave to travel  back  to the  forward  domewhere  the transducer is  located  (estimated  as  1/2/).  The  calcu-lated  longitudinal mode  fundamental  frequency  for the known chamber  and nozzle length was  226.8  Hz. The measured fundamental  frequency  was 230 Hz. It should be  noted thatthe  first,  second,  and third harmonics are also present.  These  are evident  from  the  pressure trace shown.Chamber  oscillations begin  after  the  quiescent  period  follow- ing plug ejection corresponding to a total elapsed time  (time delays) of 45.5 and 47.5  msec  as shown on  Table  1.  This Table  1  Plug  performance in motor  test Launchtime, sec10.2 14.2 a Aver. diam.,in.0.3750.75 1.375 Plug length, in. 0.375 0.75 1.50Aver. grain i.d., in.11.024 11.527 12.783 Forward  endExit  bore velocity, fps 119.5 109.292.2Plugvelocity, fps171 167 a Timedelay,msec 45.5 47.5 pressure rise Measured, psia 1 3Calculated psia 0.93.0 5.3   Launch time  after  motor burnout.    D  o  w  n   l  o  a   d  e   d   b  y   U   N   I   V   E   R   S   I   T   Y    O   F   T   E   X   A   S   A   T   A   U   S   T   I   N   o  n   J  u  n  e   6 ,   2   0   1   4   |   h   t   t  p  :   /   /  a  r  c .  a   i  a  a .  o  r  g   |   D   O   I  :   1   0 .   2   5   1   4   /   3 .   5   6   9   4   8  36 A.  L. KARNESKY AND S. E.  COLUCCI J.  SPACECRAFT Fig.  7  Dual  thrust  single  grain  tactical  motor. unstable combustion was triggered by the pressure rise  that occurs as the  plug  passes through and partially  constricts  the nozzle  throat.  The  measured  values of  approximately 1.0  and3.0  psia,  on  Table  1,  compared  very well  with  calculated values using  an  existing  ASPC computer program.  This  program utilized the method-of-characteristics for  unsteady one-dimen-sional  flow  to  trace  the  pressure  wave  along  the  length  of the chamber  upstream of the  throat  to the  forward  dome. Given  thevelocity of the plug, its  trajectory  through the  throat  was calculated based  on the  drag  force  exerted on the plug by theaccelerating  gas  flow.  The  average  plug velocity  of 167  fps (0.75-in.  plug) was  used  for all  plug sizes  in  this calculation. The magnitude of the  pressure  wave  was  determined  by the change in area ratio at the  nozzle  entrance due to the blockage of  the  throat area.  The method-of-characteristics  programassumed  a  constant  velocity  chamber  flow  and  this  did not account  for  mass  addition  effects.  However,  for the  chamber velocity  conditions  existing at these burn times,  mass  addition effects  are small. It  should  be  noted that  at the  launch times of  approximately 10 and  14  sec,  respectively, the  calculated  gas velocity  in the chamber was considerably  less  than  the  measured plug  velocity,  hence the plug could not be  accelerated  by thegas as srcinally assumed, until it was  well  inside  the nozzleregion.  Therefore,  the  same assumptions  were  used  for all  three plug sizes. By using  this program,  the  pressure disturbance  atthe  forward  head,  for the  nominally  1.5 in.  diam plug,  wouldhave been 5.3  psia. Accelefometer  response  measurements were reviewed to obtain  a qualitative assessment of stability  along  with  thepressure  and  thrust  traces.  Accelerometers  located  on the  sameside of the motor (in  line), were  used to  confirm  the  postulation (made  earlier)  that the pressure  wave  srcinated  at the aftend of the  motor  (as the plug  passed  through  the  throat)  and takes approximately 2.2 msec  t  =  1/J2/)  to travel  forward  and record  on the  forward  dome  where  the pressure transducer is  located.  Both  the pressure amplitude peaks and  forward and aft  accelerometer disturbances  were  approximately 2.2 msec out of  phase. The motor history described above provides a typical  example of  combustion instability  during  development  and the  reoccur-rence  of  instabilities  in  production.  The pulse  tests  firmly established  the  sensitivity  of the motor to transient pressurepulses and  that  the motor could be triggered  into  instability by the  ejection  of  material through  the nozzle  throat.  The pressure coupled instability  that  occurred in this motor was eventually  eliminated  by a  change  in the  propellant  formula- tion.  Velocity  coupling instability in the sustain  phase  may beavoided  by an  adequate design  to  preclude  the ejection of any significant  size  material  during the  firing. Dual  Thrust Single  Grain  Motor The  previous  motor discussed was a dual  thrust  bipropellant (dual grain)  motor  which  experienced instability. The  next  motor to be  reviewed  is a dual thrust single  propellant  motornominally  8 in.  diam.  The  dual thrust  levels  are  achieved  bythe  interior  grain  geometry as shown in  Fig.  7. The  fore  end of  the  motor  is a circular  bore  and the aft  portion containslarge  surface  area radial  fins.  The high  thrust  portion  of the ballistics  is  obtained  by the  propellant  finned surface  in the aft end. These  burn  out in a  few  seconds  leaving  only  the cylindrical bore  of  propellant  in the  forward  end  for  the  sustain phase  of motor  operation. The  instabilities  which  occurred  were  both  pressure-coupledand velocity-coupled  with  an associated change in  mean ballistics  as shown in  Fig.  8 and an adverse  pressure oscillation. The  instabilities  were  unacceptable  from  the  standpoint  of themissile  and their  elimination  was approached  from  a cut and try  process.  The changes made in motor design  included  minorgrain  geometry  changes, propellant  formulation  variations  in- cluding  oxidizer  particle  size and aluminum  particle  size  changes,as  well  as various attempts to utilize Helmholtz  resonators.This  motor  development  took place  before  the  acceptance  ofthe  jT-burner  as a  laboratory tool  to evaluate  prppellants  for combustion instability. Stability  was eventually  achieved  for the motor  after  approximately 35  motor  tests using various  com-binations  of  grain design  and  propellant  changes. Velocity coupling  was  eliminated  from  the  boost  phase  and  pressure- coupled  instabilities  eliminated  from  the sustain  phase. One of the  trends observed  from  the results of  this programshowed that there  is an  effect  of  particle  size on  stability.Figures  9 and 10 illustrate the change in oscillatory amplitudeand mean  chamber increase  as the  aluminum  particle  size  was increased  and the  particle  size  of the oxidizer  decreased.  Themean  particle  size of the ingredients is shown in  Table  2. Solution  of the stability  problems  for this  motor  was  bothcostly and time consuming. The  utilization  of  technologies 2.5 10.012.5 .0 7.5Time sec Fig.  8  Dual  thrust  single  grain  tactical motor measured chamberpressure. 300 'i.   200   ãi  100 ã s_- ã§< Increasing Aluminum Particle  Size Decreasing  Oxidizer  Particle  Size Fig.  9  Effects  of  various aluminum  and oxidizer particle  sizes  on oscillating amplitude.    D  o  w  n   l  o  a   d  e   d   b  y   U   N   I   V   E   R   S   I   T   Y    O   F   T   E   X   A   S   A   T   A   U   S   T   I   N   o  n   J  u  n  e   6 ,   2   0   1   4   |   h   t   t  p  :   /   /  a  r  c .  a   i  a  a .  o  r  g   |   D   O   I  :   1   0 .   2   5   1   4   /   3 .   5   6   9   4   8


Jul 23, 2017
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