Gas flow Simulations with ANSYS-FLUENT for the Design of a Cryogenic Stopping Cell for the low-energy branch of the Super-FRS

at FAIR Frank Morherr¹ for the FRS Ion Catcher-Collaboration:

Faraz Amjad², Samuel Ayet², Peter Dendooven³, Timo Dickel¹ ², Marcel Diwisch¹, Jens Ebert¹, Alfredo Estrade², Fabio Farinon², Hans Geissel¹ ², Florian Greiner¹, Emma Haettner¹ ², Christine Hornung¹, Christian Jesch¹, Nasser Kalantar-Nayestanaki², Ronja Knoebel², Jan Kurcewicz², Johannes Lang¹, Wayne Lippert ¹, Ian Moore⁴, Ivan Mukha², Chiara Nociforo², Martin Petrick¹, Marek Pfuetzner², Stephane Pietri², Wolf-Manisha Ranjan³, Moritz Pascal Reiter¹, Ann-Kathrin Rink¹, Yoshiki Tanaka², Helmut Weick², John Stuart ¹Justus-Liebig-Universität Giessen; ²Helmholtzzentrum für Schwerionenforschung, Darmstadt, Germany; ³KVI, University of Groningen, The Netherlands; ⁴ University of Jyväskylä, Jyväskylä, Finland

Overview

LungGlow2 - Concept Results Outlook

The Cryogenic Stopping Cell: Design and performance

Simulations (rotationally symmetrical)

Situation

Simulations of Gasdynamic/Results References

A Cryogenic Stopping Cell (CSC) has been developed for the low-energy branch of the Super-FRS at FAIR, GSI, Germany. The stopping cell technique is based on the stopping of in-flight separated high energetic ions in a noble gas, Helium in our case. The system design is based on the Super-FRS beam properties. By SIMION simulations the flow of the Ions in the DC-field along the stopping cell length and the ion trajectories along the DC-field of the CSC and the behavior of the RF carpet have been simulated using SIMION code in our group. Until now simulations of the gas flow are missed. Especially the design of the nozzle, where the Ions leave the stopping cell has not been investigated in detail. In the current design a straight extraction nozzle is used. With a laval-nozzle there exists a convergent solution. The goal is, to design an extraction nozzle such, that the gas flow through the nozzle becomes stable for high densities to lead the Ions. So they can be catch by the extraction RFQs. For low densities far away the gas must escape sideward so it is possible to pump it away. The gas dynamics at the extraction nozzle have been simulated using ANSYS Fluent Calculations, they will be combined with ion optics simulations, first results will be presented and allow understanding the behavior of the ions.

[1] Manisha Ranjan: Design and Characterisation of a Cryogenic Stopping Cell for Radioactive Ions, PhD Thesis, University of Groningen, Eur. Phys. Lett. [2] Manisha Ranjan et al: New stopping cell capabilities: RF carpet performance at high gas density and cryogenic operation, EPL, 96 (2011) [3] D. Schäfer: Design and simulation of a cryogenic stopping cell for the low- energy branch of the Super-FRS at FAIR, Master Thesis, Physikalisches Institut, Justus-Liebig-Universität, Giessen (2010) [4] W.R. Plaß, GSI Sci.Rep. 2010/ Eur.Phys. J. Special Topics, 150 (2007) 367 [5] S. Purushothaman et al., GSI Sci. Rep. 2010 (2011) [6] T. Dickel, doctoral thesis, Justus-Liebig-Universität Gießen, 2010 [7] B. Fabian: Fundamentals and Numerical Calculus of Gas Dynamic [8] E. Haettner et al., GSI Sci. Rep. 2010 (2011) [9] V. Varentsov: Gas dyn. cooling of low-energy molecular and ion beams, 2004

Construction of the cryogenic stopping Cell, cooling Channels around are not shown.

Zoomed view of the carpet center. On the left, the 0.6 mm diameter exit hole

Simulation Workflow

Gas dynamics can be taken into account in the simulation in combination with the CFD solver Fluent. The Mesh for the Calculations was done by GAMBIT

Simulation with a Laval-Nozzle

Simulation Procedure • Electric field calculation with FEM- Software Comsol • Gasdynamical calculation with FEM/FVM- Software ANSYS-FLUENT • Outlook: Import of the electric- and gasdynamical Parameters into ITSIM • Simulate each individual particle path

Theoretical description of Gas-Flows Models for Gas Flow Calculations Boltzmann-equation: • Describes the statistical development in time and space of the partical density distribution • Can be used for any gas flow regime • Calculation is very time consuming Continuum description (Navier Stokes equation) • Field description of the gas flow • Is not accurate for very low pressure gases • Can be derived from the Boltzmann equation • Calculation is less time consuming than solving Boltzmann equation Comput. Fluid Dynamics (CFD) (Finite Vol.) Method Continuity equation: Mass conservation: Momentum equation: Momentum conservation

Energy equation: Energy conservation

1. Discretization of the governing equation 2. Equations will be solved in space and time till

solution is steady state 3. Coupled solver: Solves mass-, momentum- and

energy-equation simultaneously

Boundary-Data: Hole: Diameter 0.6mm, length 1mm Solution axisymmetric and steady? Gas: Helium Inflow: Pressure 10000pa Temperature 77K Outflow: Pressure 1pa Temperature 300K

Sutherlands Law: Relationship between the dynamic viscosity η, and the absolute tempera- ture T of an ideal gas.

Here:

Thermal Conductivity: Polynomial with 8 Coefficients Flux Type: Roe-FDS Flow: Second Order Upwind

Potential energy Pressure Friction Heat conduction

Change of Internal- and Kinetic energy

Rectangular Grid

Density (kg/m³):

Velocity magnitude (m/s):

Triangular Grid

Velocity magnitude (m/s):

RFQ-Extraction

Version 1 (pure triangular) Convergent and realistic

Version 2 (mixed) Convergent but unrealistic

Velocity magnitude (m/s):

Static Pressure (Pa):

Problems: Divergence or unrealistic gridshape Solutions

Problem: Lost of Ions

Density (kg/m³):

Velocity magnitude (m/s):

Triangular Grid with Skimmer

10000 Pa 1 Pa