# Presentation: 724771

## Targetry Simulation with Front Tracking 

**And Embedded Boundary Method **

**Jian         Du**
- SUNY at Stony Brook

**Neutrino Factory and Muon Collider Collaboration**
**UCLA January 28 ,2007**

- Collaborators:
**Roman Samulyak**, Computational Sciences Center, BNL
**James Glimm**,        SBU/CSC

## Talk outline 

***   Code Validation through Jet Distortion in transverse B field**
***   Target Simulation **
**     *****  simulation of the interaction of the mercury jet with a proton pulse**
**     *****  inclusion of bubble collapsing effects**
***    Conclusion**

- Talk outline

**Full system of MHD equations**

**Low magnetic Re approximation**
**& charge neutrality**

**  ****Implemented in FronTier**
**   ****Riemann Problem for interface propagation**
**   ****MUSCL scheme for interior state updating**
**   ****Different EOS modeling**
**   ****Embedded Boundary Method for elliptic equation**

## Jet distortion (previous work)

**[1****] ****S.Oshima, R. Yamane, Y.Moshimaru, T.Matsuoka, The shape of a liquid metal jet under a non-uniform magnetic field. JCME Int. J., 30(1987),437-448**

## Simulations of the Muon Collider Target

**       ****bubble is explicitly resolved using FronTier interface tracking technique.**

-    **Homogeneous EOS model. Suitable average properties are determined and the mixture is     **
**      ****treated as a pseudofluid that obeys an equation of  single-component flow. Need conductivity    **
**      ****model.**

**Polytropic EOS for gas (vapor)**

**Stiffened Polytropic EOS for liquid**

**(2) Different  EOS models used**

**Simulations of the Muon Collider Target**

**(1) Experimental Setting**

## :  the conductivity of the mixed phase

- :  the conductivity of the liquid
- :  volume fraction of the liquid

**(3)  Simulations with Homogeneous Model**

##   Simulations with Homogeneous Model

**  ****Simulations with Homogeneous Model**

**Density Profile for no MHD, MHD with Bruggeman Model, MHD with               **
**                ****linear Model, from top to bottom at T = 0.15ms**

**Jet expansion velocity  and cross section density profile at t = 0.1 ms for different magnetic field **

##   Density Plot and Expansion Comparison

**  ****Density Plot and Expansion Comparison**

- Density distribution

- Jet Expansion Velocity

- Conclusions:
- 2D and 3D simulations agree well,both indicate strong restriction of
-       15 Tesla field on jet expansion and cavitation forming
- 2.    Linear and Bruggeman Models have similar jet expansion
- 3.    Bruggeman model gives larger cavitation region

## 4.  Simulations with Heterogeneous Model

**Density Profile for no MHD(top), with MHD (bottom,B=15 Tesla) at T = 0.15ms Initial R_b=1.5 x (mesh size)****,****distance 2 x (mesh size)****,****P_critical = -100 bar**

**Density Profile for no MHD(top), with MHD (bottom,B=15 Tesla) at T = 0.15ms Initial R_b=3 x (mesh size)****,****distance 3.5 x (mesh size)****,****P_critical = -400 bar**

## Comparison of hetero- and homogenized EOS models

**  ****1)  heterogeneous models give uniform jet expansion for different insertion parameters;**
**  ****2)  homogeneous model give larger expansion; **
**  ****3)****  ****Surface instabilities as in the experiments, have not been obtained in all simulations**

**Comparison of hetero- and homogenized EOS models**

- b1 – b4 stand for different bubble radius

## 5. Open problems:

** ****Is MHD reduction of the jet expansion  as strong as in simulations?**
**  ****in the smooth jet, strong azimuthal currents tend to cause strong MHD**
**  ****effects **
** ****If surface instabilities are present, what is the MHD effect on spikes  **
**  ****or when the topology is significantly different from the smooth jet**

**5. Open problems:**

## 6. Surface instability study: problem set-up 

- Possible Cause:
** ****Turbulence nature of the jet**
**  ****Incomplete thermodynamics model (homogeneous)**
**  ****Unresolved bubble evolution (heterogeneous)**

**1D bubble collapsing&rebounding is simulated with spherical geometry and P,rho, v  are coupled into higher dimension cases**

##   1D bubble collapsing & Keller’s equation

- Radius vs. Time

- Pressure Profile at  t =0.0035 ms

**Pressure profile at rebounding stage of 1D simulation is used as input**
**for the 2D simulations (P****bub****=1.0e-4bar, P****amb****=100bar)**

##   2D Simulations with bubble rebounding

**  ****2D Simulations with bubble rebounding**

**Density Profile **

**T = 0.0005ms          T=0.0035ms           T=0.0045ms**

**Perturbation tip position Vs. Time**

**  ****Surface perturbation quickly develops with bubble rebounding**
**  ****Perturbation velocity can reach about 160m/s**
**  ****Similar 3D hydro and MHD simulations are underway**

## Conclusions

**Using the multi-scale approach, verified the important role of bubble collapsing  in jet breakup**
**3D  hydro & MHD simulations with bubble insertion are underway and important to study the MHD effects on jet breakup**

**Conclusions**