Jet Breakup and Atomization --- Jet Simulation in a Diesel Engine - PowerPoint by gKBl2HMI

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									Mitigation of Cavitation Damage Erosion in Liquid Metal Spallation Targets
Nov. 30 – Dec. 1, 2005, ORNL


 Direct Numerical Simulation of Bubbly and
    Cavitating Flows and Applications to
            Cavitation Mitigation
                        Roman Samulyak, Tianshi Lu

                            In collaboration with
                          James Glimm, Zhiliang Xu

                                 Computational Science Center
                                   Brookhaven National Lab
                                      Upton, NY 11973
 Brookhaven Science Associates
   U.S. Department of Energy                 1
                                Talk outline

   Main ideas of front tracking and the FronTier code
   Direct numerical simulation of cavitating and bubbly flows
     •   Discrete vapor bubble model
     •   Dynamic bubble insertion algorithms
     •   Riemann solution for the phase boundary
     •   Validation of models

   Simulation of multiphase flows in the following applications:
     • Atomization of a high speed jet
     • Neutrino Factory/Muon Collider target
     • Cavitation mitigation in the SNS target

   Conclusions and Future Plans


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  U.S. Department of Energy              2
Main ideas of front tracking

Front Tracking: A hybrid of Eulerian and Lagrange methods
Major components: 1) Front propagation, 2) Wave (smooth region) solution


                                Two separate grids to describe the solution:
                                1. A volume filling rectangular mesh
                                2. A unstructured (N-1) dimensional
                                    Lagrangian mesh to represent interface




  Advantages of explicit interface tracking:
  • Real physics models for interface propagation
  • Different physics / numerical approximations
  in domains separated by interfaces
  • No interfacial diffusion

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  U.S. Department of Energy              3
                               The FronTier Code
FronTier is a parallel 3D multiphysics code based on front tracking
 Physics models include
       Compressible fluid dynamics
       MHD

       Flow in porous media

       Elasto-plastic deformations

 Phase transition models
 Exact and approximate Riemann solvers, realistic EOS models

 Adaptive mesh refinement

Resolving interface tangling by using the grid
based method




    Brookhaven Science Associates
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                    Main FronTier applications

Rayleigh – Taylor and Richtmyer-Meshkov fluid
instabilities



                                 Targets for future
                                 accelerators



                            Tokamak refueling through
                            the ablation of frozen
                            deuterium pellets


                                 Liquid jet
                                 breakup and          Supernova
 Brookhaven Science Associates   atomization
   U.S. Department of Energy                   5       explosion
           Modeling of Bubbly and Cavitating Flows
             using the Method of Front Tracking




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  U.S. Department of Energy     6
         Two models for cavitating and bubbly fluids

     Heterogeneous method (Discrete Bubble Model): Each individual bubble is
      explicitly resolved using FronTier interface tracking technique.


                                                          Stiffened Polytropic
                                                          EOS for liquid



                                                          Polytropic EOS for
                                                          gas (vapor)



 Homogeneous EOS model. The mixture of liquid and vapor is treated as a
pseudofluid (single-component flow); Suitable averaging is performed over a
length scale of several bubbles. Small spatial scales are not resolved.

    Brookhaven Science Associates
      U.S. Department of Energy          7
       Features of the discrete vapor bubble model

   First principles simulation.

 Accurate   description of multiphase systems limited only by numerical errors.

   Resolves small spatial scales of the multiphase system.

 Accurate   treatment of drag, surface tension, viscous, and thermal effects.

 Mass transfer due to phase transition (Riemann problem for the phase
boundary).




Brookhaven Science Associates
  U.S. Department of Energy                8
                           Theory on Bubbly Flows
                         Mass and Momentum Conservation

                    1 p u                     u  ( u 2  p )
                                ,                                 0
                  f c f t x t
                        2
                                                   t      x
                                   f (1   )   g 


                                  The Keller Equation
                                                   2
    1 dR  d R 3        1 dR  dR   1 dR R d  1
                     2
   1     R 2  1              1            pB  p 
    c dt  dt   2  3c dt  dt   c dt c dt  l
                                                  2
                 p g R 3  constant,  p g  pB 
                                                   R

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  U.S. Department of Energy                   9
                           Theory on Bubbly Flows
                                   Dispersion Relation

   k   1  1        1                             c:    low frequency sound speed
 ( )  2 2
       2
                                                 cf:   sound speed in pure fluid
     cf c 1  i   (  ) 2                    B:   resonant frequency
                            B      B           :    damping coefficient


  1                                       1          p               1 3p
       (  g  (1   )  f )(                 ) c      ,     B 
  c 2
                                  g cg  f c f
                                       2        2
                                                        f              R f

                                Steady State Shock Speed

                                    1    1     
                                     2
                                        2  f a
                                   U st c f     Pb

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  U.S. Department of Energy                 10
                                      Linear Wave Propagation
                                                                                          1 3P
                  R  0.06mm,   0.02%                                           fB             54.4 kHz
                                                                                         2R  f

                                                 Dispersion Relation
                      Phase Velocity                      k  k1  ik2                    Attenuation Rate
                                                                                          a  20 log 10 e  k 2
            300                                                              35
                                      theory with =0.7                                                   theory with =0.7
                                      simulation                             30                           simulation
            250                       c in pure fluid
                                                                             25
V (cm/ms)




                                                                 a (dB/cm)
            200                                                              20

                                                                             15
            150
                                                                             10
            100
                                                                             5

            50                                                               0
              0       100    200           300            400                 0      100          200          300            400
                            f (KHz)                                                             f (KHz)
     Brookhaven Science Associates
       U.S. Department of Energy                                11
                           Shock Wave Propagation
      Shock speeds measured from the simulations are within 10% deviation
      from the steady state values.
                                                                      Shock Profile
                                                2.0




                                                1.8
       The oscillation amplitude
        is smaller for gas with                                                          He (  = 1.67 )
        larger .                               1.6
                                                                                         N2 (  = 1.4 )




                                      P (atm)
                                                                                         SF6 (  = 1.09 )


       The oscillation period is               1.4

        longer for larger bubble
        volume fraction.                        1.2




                                                1.0
                                                      0           1             2            3              4
                                                                             t (ms)
                                                      Pa = 1.1 atm, Pb = 1.727 atm, R = 1.18 mm,  = 2.5E-3
                                                      Meardured 40 cm from the interface.
Brookhaven Science Associates
  U.S. Department of Energy                 12
                           Shock Wave Propagation
                        Shock profile of SF6 gas bubbles

                Simulation                             Experiment




   The oscillation period is shorter than        [courtesy of Beylich & Gülhan]
   the experimental value by 28%.
Brookhaven Science Associates
  U.S. Department of Energy                 13
         Dynamic Bubble Insertion Algorithm for
             Direct Numerical Simulation
• A cavitation bubble is dynamically inserted in the center of a rarefaction
wave of critical strength
• A bubbles is dynamically destroyed when the radius becomes smaller
than critical. In simulations, critical radius is determined by the numerical
resolution. With AMR, it is of the same order of magnitude as physical
critical radius.
• There is no data on the distribution of nucleation centers for mercury at
the given conditions. Some estimates within the homogeneous
nucleation theory:
                          2S
  critical radius:   RC 
                          PC
                                 Gb            2S        WCR          16 S 3
nucleation rate:     J  J 0e          , J0  N    , Gb      , WCR 
                                                m                    3  PC 
                                                                                2
                                                          kT
                             
                                       1/2
                  16 S 3
Pc      3kTofln  J Vdt  
Brookhaven Science Associates
                                             Critical pressure necessary to create a
          
  U.S. Department Energy0                    14
                                              bubble in volume V during time dt
                       Riemann Problem for the
                          Phase Boundary




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  U.S. Department of Energy      15
  Governing Equations and Boundary Conditions

                     
                             ( u )  0
                     t
                      ( u )
                                 ( uu )  p  g
                        t
                      ( E )
                                 ((E  p )u )   2T
                        t
                            Phase Boundary Conditions
                  (Generalized Rankine-Hugoniot Conditions):
                        [ un ]  s[  ]
                        [ un  p]  s[ un ]
                            2


                                         T
                        [ Eun  pun      ]  s[ E ]
                                         n
Brookhaven Science Associates
  U.S. Department of Energy                16
                 Interfacial Thermal Conditions
1. Equal interfacia l temparetu re : Tl  Tv  Ts
           The generalized Hugoniot relation :
              T
           [     ]  M ev ([H ]  V [ p])  M ev L
              n
           L : latent heat; H : Enthalphy; M ev : Mass flux
           V  ( l   v ) / 2;   1 /  .

2. Two cases:
 a) Contact with thermal conduction
 b) Phase boundary
                                                                  T
Contact with thermal conduction:                    M ev  0, (    )0
                                                                  n
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  U.S. Department of Energy                    17
                   Phase Boundary Conditions

                         psat (T)  pv                 A deviation from
  Mass flux : M ev  α                                 Clausius-Clapeyron
                              2πRT                     on vapor side is
  α : evaporation coefficient                          allowed.
  psat (T) : Clausius - Clapeyron equation             Similar to:
                                                       Matsumoto etal.
   pv : vapor pressure                                 (94’)
     kB
  R  ; k B is Boltzmann const.; m is molecular mass
     m




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  U.S. Department of Energy          18
                  Two Characteristic Equations
t  t
                      Phase Boundary             S l S r New Position

                                                        u  c
                              u  c
     t                                                                       x
          S 2              S 1 S f     S 0 S 0    Sb    S1          S2

                           dp        un     2T
                                c       2
                           d      d    n
                           dp        un    2T
                                c      2
                           d      d   n

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  U.S. Department of Energy                 19
        Phase Boundary Propagation
      An Iteration Algorithm.
      1. Solve for mass flux and interfacial temperature by:
                pl  pv                 1     T      T
          l  v       ( l   v )    ( v v   l l )
                     2                  M     n      n
               p (T )  pv
          M  a sat
                    2RT
       2. Solve the characteristic equations with the jump conditions:
                 u v , n  ul , n
          M
                    v  l
                      pv  pl
          M2 
                       v  l
       3. Compare the newly obtained p v and  with the previous iteration to
       determine the convergence of the iteration.
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       Validation Phase Boundary Solutions




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         Applications:
          Liquid jet breakup and atomization
          Neutrino Factory / Muon Collider target
          Cavitation mitigation in SNS target




Brookhaven Science Associates
  U.S. Department of Energy     22
       Liquid Jet breakup and Spray Formation

                                 Breakup Regimes:
                                 1. Rayleigh breakup
                                 2. First wind-induced breakup
                                 3. Second wind-induced breakup
                                 4. Atomization




                                     DROP AND SPARY
                                     FORMATION FROM A
                                     LIQUID JET, S.P.Lin, R,D.
                                     Reitz, Annu. Rev. Fluid
                                     Mech. 1998. 30: 65-105

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  U.S. Department of Energy     23
    Simulation setup and processes influencing
                   atomization


                                • Inlet pressure fluctuation


                                • Cavitation in the nozzle and
                                free surface jet

                                • Boundary rearrangement effect




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  U.S. Department of Energy     24
                             Simulation Results

 Density Plot of Jet Simulation Using Discrete Vapor Bubble Model




 Density Plot of Jet Simulation Using Homogenized EOS Model




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   U.S. Department of Energy           25
Animation of
Simulation
Using Discrete
Bubble Model




 Brookhaven Science Associates
   U.S. Department of Energy     26
        Neutrino Factory / Muon Collider Target




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  U.S. Department of Energy     27
            Numerical simulations of the mercury jet target

Simulation of the mercury jet target interacting with a proton pulse in a
magnetic field
   • Studies of surface instabilities, jet breakup, and cavitation
   • MHD forces reduce both jet expansion, instabilities, and cavitation


        Richtmyer-Meshkov instability of the
        mercury target surface. Single fluid
        EOS (no cavitation)




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      U.S. Department of Energy          28
Cavitation in the mercury jet interacting with the proton pulse




         Initial density              Density at 20 microseconds




 Initial pressure is 16 Kbar              400 microseconds




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                MHD effects in the Mercury Target


   Distortion of the mercury        Stabilizing effect of the magnetic field
   jet by a magnetic field




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  U.S. Department of Energy       30
                   SNS and Cavitation Mitigation




                                        P (r, z)  500e r       0.1z
                                                             2

                                         0                               bar


                  Courtesy of Oak Ridge National Laboratory


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  U.S. Department of Energy           31
Step 1: DNS of pressure wave propagation in the
container: pure mercury

                          Pure Mercury




                                                                               2t
                                                                    t
                                                                
                                              Pw (t )  Pw0 e       
                                                                        cos(       )
                                                                                T



                                                     Pw0  500bar
                                                      940s
                                                    T  70s




 Brookhaven Science Associates
   U.S. Department of Energy             32
Step 2: DNS of pressure wave propagation in the
container: mercury containing gas bubbles

            Bubbly Mercury ( R=1.0mm, =2.5% )




                                                                                  2t
                                                                       t
                                                                   
                                                 Pw (t )  Pw0 e       
                                                                           cos(       )
                                                                                   T



                                                       Pw0  600bar
                                                         50s
                                                       T  12s




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Step 3: Collapse pressure of cavitation bubbles

                                  The Keller Equation
                                                   2
     1 dR  d R 3        1 dR  dR   1 dR R d  1
                      2
    1     R 2  1                1           pB  p 
     c dt  dt   2  3c dt  dt   c dt c dt  l
                                                  2
                  p g R 3  p g 0 R0 ,
                                   3
                                       p g  pB 
                                                   R

                                                  2t
                                 p(t )  P sin(        0 )
                                                   T

                    Empirical formula for P < 10Kbar and T < 1ms

                1                            93.0 P 1.25 pg 0 R0 3 0.50
   Pc ( P, T )  Pc ( P, T , 0  0.63 )      (     ) (        (   ) ) Kbar
                2                             2  f cf
                                                     2
                                                            f cf cfT
                                                                2

 Brookhaven Science Associates
   U.S. Department of Energy                 34
Step 4: Estimation of efficiency of the cavitation damage mitigation


    • Statistical averages of collapsing
    bubbles pressure peaks                                   Pc (   0)
                                                E (  , R) 
                                                             Pc (  , R)
   R0 = 1.0 m
   pg0 = 0.01 bar
                                                E(,R) is independent
                                                of R0 and pg0.




                                                E ~ 40 at R = 0.5 mm
                                                and 0.5% void fraction




  Brookhaven Science Associates
    U.S. Department of Energy              35
                Conclusions and Future Plans

 Developed components enabling the direct numerical simulation of
 cavitating and bubbly flows
       • Discrete vapor bubble model
       • Dynamic bubble insertion algorithms
       • Riemann solution for the phase boundary
    Studied multiphase flows in the following applications:
       • Atomization of a high speed jet
       • Neutrino Factory/Muon Collider target
       • Cavitation mitigation in the SNS target
    Future work:
       • Investigate the influence of the init. bubble size on the simulation.
       • Improve the bubble insertion algorithm - implement a conservative insertion.
       • Studies of accelerator targets and liquid jets


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  U.S. Department of Energy                36

								
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