# Presentation: 108858

## MERIT Project Review December 12, 2005, BNL, Upton NY

**MHD Studies of Mercury Jet Target**
**Roman Samulyak**
*Center for Data Intensive Computing*
*Brookhaven National Laboratory*
*U.S. Department of Energy*
*rosamu@bnl.gov*

## Talk Outline

-  Brief summary of modeling and simulation of hydro and MHD processes in the mercury jet target
-  Studies of the distortion of the mercury jet entering a 15 T magnetic solenoid
-  Collaboration with UCLA computational MHD group
-  Conclusions and future plans

## Brief summary of modeling and simulation 

**Brief summary of modeling and simulation **

-  Developed MHD code for compressible multiphase flows (more details in Jian Du’s talk)
-  Developed EOS homogeneous and heterogeneous models for phase transition (cavitation) and the Riemann solver for the phase boundary
-  Studied surface instabilities, jet breakup, and cavitation
-  MHD forces reduce both jet expansion, instabilities, and cavitation
-    (will be discussed in Jian Du’s talk)

- Jet surface instabilities

- Cavitation in the mercury jet and thimble

## Mercury jet entering magnetic field.Schematic of the problem.

**Mercury jet entering magnetic field.****Schematic of the problem.**

**Magnetic field of the 15 T solenoid is given in the tabular format**

## Incompressible steady state formulation of the problem

**Incompressible steady state formulation of the problem**

## Direct numerical simulation approach (FronTier):

**Direct numerical simulation approach (FronTier):**

**Semi-analytical / semi-numerical approach:**

-  Construct an initial unperturbed jet along the B=0 trajectory
-  Use the time dependent compressible code with a realistic EOS and evolve the jet into a steady state

-  Seek for a solution of the incompressible steady state system of equations in form of expansion series
-  Reduce the system to a series of ODE’s for leading order terms
-  Solve numerically ODE’s
- Ref.: S. Oshima, R. Yamane, Y. Mochimary, T. Matsuoka, JSME International Journal, Vol. 30, No. 261, 1987

## Results: Aspect ratio of the jet cross-section

**Results: Aspect ratio of the jet cross-section**

**B = 15 T****V0 = 25 m/s**

## Results: Aspect ratio of the jet cross-section

**Results: Aspect ratio of the jet cross-section**

**B = 15 T****V0 = 25 m/s**

## Summary of results 

-  Jet distortion (aspect ratio) strongly depends on the angle with the solenoid axes (it increases at larger angles)
-  Jet aspect ratio increases at smaller jet velocities (at least if the change of velocity is small compared to the reference velocity of 25 m/s)
-  Jet aspect ratio increases in nozzle is placed further from the solenoid center
- Typical values of the jet aspect ratio in the center of the soleniod:
- Rmax/R0 = 1.35  at V = 25 m/s, alpha = 100 mrad, B = 15 T
- Rmax/R0 = 1.09  at V = 25 m/s, alpha = 50 mrad, B = 15 T

## Consequences of the jet distortion 

-  The cross-section of the mercury jet interaction with the proton pulse is significantly reduced. This reduces particle production rate
-  In order to avoid these undesirable consequences, the angle between the magnetic field and the solenoid axes needs to be reduced. This imposes new hardware design constraints.
-  Verification of results by an independent method. Collaboration with Neil Morley of UCLA computational MHD group.

## UCLA code: HIMAG 

- The code has been written for complex geometries using unstructured meshes. Flexibility in choosing a mesh: Hexahedral, Tetrahedral, Prismatic cells can be used.
- An arbitrary set of conducting walls maybe specified. Free surface flows are modeled using the Level Set method. **Multiple solid materials** can be simulated
- Graphical interfaces are available to assist users from problem setup to post-processing.
- A preliminary turbulence and heat transfer modeling capability now exists.

**UCLA code: HIMAG **

## Simulation of free surface flows

- HIMAG uses the Level Set method to capture free surfaces

*Examples of HIMAG simulations:*

## UCLA jet simulation setup

- The magnetic axis of the solenoid is horizontal. Magnetic field simulated as 24 x 78 windings with 7200 A spaced uniformly in ID 20 cm and OD 80 cm and axial length 1 m
- 100 mrad and 33 mrad tilt angle
- Inlet velocity 20 m/s
- Injection point of the jet is located at -5cm below the magnetic axis and -50cm from the solenoid center.
- The inlet electric potential condition is Phi = 0, trying to simulate disturbances from a perfectly conducting nozzle
- MHD forces are turned off at the exit two diameter before the computational boundary
- Computational area 2.5 x 2.5 x 100 cm with 100 x 100 x 200 computational cells.

## 100 mrad tilt angle

**100 mrad tilt angle**

- z = 0 cm

- z = 20 cm

- z = 40 cm

- z = 50 cm

- z = 30 cm

- z = 60 cm

**Aspect ratio = 1.4 in the solenoid center**

## 33 mrad tilt angle

- z = 2.5 cm

- z = 20 cm

- z = 60 cm

- z = 40 cm

- z = 80 cm

- z = 98 cm

**33 mrad tilt angle**

## Summary of Neil Morley’s results and design parameters change

-  Confirmed the distortion of the jet in the 15 T solenoid. Jet evolution exhibited the same features: reduction of the aspect ratio with the increase of the jet velocity, sensitivity to the nozzle placement, and the angle of the jet with the solenoid axis.
-  Good quantitative agreement was achieved by independent studies.
-  **In order to reduce the jet distortion, the angle between the magnetic field and the solenoid axes for future experiments has been reduced to 33 mrad. **
-  Another possible solution is the use of an elliptic nozzle to compensate for the MHD distortion. This option must be investigated by means of numerical simulation.

## Conclusions and Future Plans

**Conclusions and Future Plans**

-  Deformation of the mercury jet entering a magnetic field has been studied
-  Collaboration with Neil Morley on studies of incompressible free surface jets flows in pipes in the magnetic field
-  Further development of mathematical models and software libraries for the FronTier-MHD code
-  Study the jet splash in the magnetic field using the heterogeneous (discrete bubble model) for cavitation
-  3D numerical simulations of the mercury jet interacting with a proton pulse in a magnetic field will be continued using the FronTier-MHD code