Calculation of Dose from Nuclear Thermal Rockets to Astronauts

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Calculation of Dose from Nuclear Thermal Rockets
to Astronauts

• Joe Yurko (Aeronautics/Astronautics, MIT)
• Prof. Andrew Kadak (Nuclear Engineering, MIT)

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However, the previous picture will look more like
this

• A BACKFLOW PLUME exists around the rocket!

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Overview

• What is NTR propulsion?
• What are we concerned about?
• Analysis Methodology
• What causes backflow?
• Can we model and predict backflow?
• Future Work

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Nuclear Thermal Rockets (NTR)

• A working fluid, usually hydrogen, is heated in a
  high temperature nuclear reactor, and then
  expands through a rocket nozzle to create thrust
• At least twice as efficient as chemical rockets
• Space Shuttle Main Engine Specific Impulse (Isp)
  is 453 seconds
• NTRs Isp range between 800-900 seconds
• Allows fast transport to Mars and beyond for
  manned and unmanned missions
• Reduces trip time to Mars by as much as ½ to 1/3

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Development NERVA

• Designed and fired, in the open, 20 NTRs in the
  late 1960s, until cancellation in 1973
• NRX-A6 ran for planned 60 minute duration at full
  power (1160 MW)

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Motivation

• Backflow around rockets have been witnessed by
  astronauts as the Shuttle ascends into space
• NTR exhaust consists of the hydrogen propellant
  and also fission products due to erosion
• Concern is, if fission products are present in
  backflow region they will radiate the crew!
• Priority to know level of radiation the crew will
  be exposed to from backflow
• Need to determine make-up of backflow region!

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BACKFLOW

• The exhaust is traveling at high Mach numbers at
  the nozzles exit, so what causes it to turn
  backwards?
• First, the nozzle is under-expanded
• The ambient pressure is less than the exit
  pressure of the flow
• As the flow exits the nozzle it undergoes a
  series of Expansion Fans

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• The expansion fan is an isentropic process that
  increases the flows Mach Number and reduces the
  pressure
• This causes the flow to turn away from the nozzle
  center-line (as seen in the picture in the
  previous slide)
• Conceptually expansion fans are the opposite of
  shockwaves

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Boundary Layers

• Are result of viscous forces between the flow and
  a surface
• Are regions where the flows velocity is less
  than the main flow

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Why Boundary Layers are important

• In reference frame of particles, other particles
  can be traveling in any random direction (Kinetic
  Theory of Gases)
• The speed the particles are moving at for a given
  temperature is called the thermal velocity
• In supersonic flows, when the overall stream
  velocity is incorporated, the resultant direction
  is in the direction of the main flow

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• In subsonic flows, the thermal velocity is not
  dominated by the stream velocity
• Thus particles are able to travel in directions
  other than the main stream direction
• For the subsonic boundary layer of a nozzle in
  the exit plane, particles leave and continue in
  their random directions and combined with the
  under-expanded nozzle turning effect, particles
  can enter the backflow region
• Therefore, the main region of interest is the
  subsonic boundary layer!

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Modeling

• At nozzle lip, density of flow drops orders of
  magnitude
• As the flow turns, it experiences continuum,
  transition, and free molecular regimes
• Because of non-equilibrium effects of the
  transition and free-molecular regimes,
  conventional fluid dynamics methods, namely the
  Navier-Stokes equations are no longer valid
• Therefore, need to use a particle approach, that
  models the gas on the molecular level

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Direct Simulation Monte Carlo (DSMC)

• Computer modeling technique of a real gas flow by
  thousands of simulated molecules
• Velocity components and position coordinates of
  the simulated molecules are concurrently followed
  through representative collisions and boundary
  interactions in simulated physical space
• The simulated region is divided into cells and
  time is advanced in discrete time steps ?t
• At each time step every particle is first moved,
  according to the equation of motion
• Then the particle-particle interactions
  (collisions) are taken into account
• DSMC has been experimentally proven to accurately
  model rarefied flows

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Previous Studies

• Many studies have applied DSMC methods to look at
  the nozzle-lip effect in chemical, electrical,
  and nuclear rockets, but not with dose
  consequences
• The major finding is that heavy particles do not
  enter the backflow region
• The question of which particles enter the
  backflow region, is then reduced to a question of
  molecular weight

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Approximations

• DSMC methods are expensive and very time
  consuming, especially when modeling the backflow
  region around the entire spacecraft
• Approximations that give Order-of-Magnitude
  estimates in real time, can give great insight
  into this phenomenon
• In the continuum regime, the flow is modeled
  using the Simons model, which is a source flow
  analysis, valid in the far field where the flow
  behaves as if it were diverging radially from a
  point source
• The model determines the flow angle of the
  boundary layer, then determines the local density
  by relating it to the plume center line density

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• The transition and free-molecular regions are
  modeled by replacing the continuous transition
  from continuum to transition to free-molecular,
  with discontinuity surfaces where the flow
  immediately passes from continuum to
  free-molecular
• The flux of these discontinuity surfaces is
  determined and the number density of particles
  that reach the backflow is then known

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Key Equations for Approximation Model

• Simons Equation ?(r,?)/? K(R/r)2 f(?)
• K, the plume normalization constant, is
  determined from continuity considerations
• K sqrt( (?1)/(?-1) ) p2/(8 ?82)
• Function f(?) relates the local density ?(r,?),
  to the plume center line density
• f(?) cos( p/2 ?/?8) 2/(?-1) for 0 ?
  ?0
• f(?) f(?0)exp-ß(?-?0) for ?0 ?
  ?8
• Flow originates from the isentropic core for
  angles ??0 and from the boundary layer for
  angles ?0lt??8

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Discontinuity Surfaces

• The number density dnp at a point p(x,y,z) due to
  molecules leaving an elemental volume dt adjacent
  to the discontinuity surface is proportional to
  nt
• Where nt (NA ? K f(?) ) / (MW(Ae/A)(r/Re)2)
• Shows that the number density leaving the
  discontinuity surfaces is dependant on the
  turning angle and is inversely proportional to
  the molecular weight of the particle
• Thus, heavier particles will have lower number
  densities leaving the discontinuity surfaces

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MIT Analysis Approach

• Apply Approximations and DSMC method to NERVA
  test data
• Use Approximations to estimate region around
  spacecraft where number densities of fission
  products will have significant effect
• Apply DSMC method to this region to get exact
  number densities of fission products
• Calculate dose backflow cloud emits to crew and
  give appropriate distance crew should be away
  from nozzle

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Current Work

• Working on developing Approximation code in
  MATLAB, that will give quick and accurate
  descriptions of particle number densities in
  backflow region
• Locating appropriate DSMC software or modify code
  to this specific application to include
  radiological effects

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FUTURE WORK

• Get NERVA test data
• Apply analysis method to NERVA data
• Plasma effects?
• Some concern that ionization will occur because
  of high reactor temperatures and radiation in
  nozzle
• If this is true, ionized heavy fission products
  could be pushed into backflow by electric
  fields
• Presence and influence of effect needs to be
  evaluated

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Possibilities for design

• If it is shown that the backflow cloud poses no
  significant threat to crew safety, because the
  fission products are too heavy to reach the
  backflow region, then technology from the 1960s
  could be re-used
• However, if threat is serious, new fuel designs
  are needed to reduce erosion in reactor
• Better Nozzles?
• Because backflow is mainly determined by subsonic
  boundary layer any change in nozzle design would
  have to occur in this very small region
• Experiments have shown different nozzle lip
  shapes effect number fluxes and flow angles into
  backflow region

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Review

• Discussed why we need NTR and why we are worried
  about backflow
• Discussed the causes of backflow and methods to
  model it
• Showed the plan for determining if new fuels are
  needed or if technology from the NERVA program
  could be re-used

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Key References

• Boyd, I.D., Penko, P.F., and Meissner, D. L.,
  Numerical And Experimental Investigations of
  Rarefied Nozzle and Plume Flows of Nitrogen,
  AIAA paper 91-1363, June 1991.
• Chung, C.H., De Witt, K.J., Jeng, D.R., and Penko
  P.F., DSMC Analysis of Species Separation in
  Rarefied Nozzle Flows, AIAA paper 92-2859, July
  1992.
• Chung, C.H., Kim, S.C., Stubbs, R.M., and De
  Witt, K.J., Analysis of Plume Backflow Around a
  Nozzle Lip in a Nuclear Rocket, AIAA paper
  93-2497, June 1993.
• Gatsonis, N.A., Buzby, J., Yin, X., and Mauk, B.,
  Modeling Nuclear Thermal Rocket Plume
  Effluents, AIAA paper 96-1850, June 1996.
• Jenkins, R.M., Ciucci, A., Cochran Jr., J. E.,
  Simplified Model for Calculation of Backflow
  Contamination from Rocket Exhausts in Vacuum,
  AIAA J., Spacecraft and Rockets, Vol. 31, No. 2,
  March-April 1994.
• Kuharski, R.A., A Quick Accurate Model of Nozzle
  Backflow, AIAA-1991-608.
• Simons, G.A., Effect of Nozzle Boundary Layers
  on Rocket Exhaust Plumes, AIAA J., Technical
  Notes, Vol. 10, pp. 1534-1535, 1972.

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Questions?