Lagrangian Particle Tracking on Large Unstructured Three-Dimensional Meshes

A prerequisite for the prediction of ice accretion on an aircraft flying through clouds of supercooled liquid water is the accurate determination of the water impingement rate on various components of the aircraft. For this purpose, a droplet impingement module has been developed using the datastructure of the unstructured Navier-Stokes solver TAU. Since nowadays large computational grids are common practice, an efficient algorithm for determination of the droplet trajectories on such grids had to be implemented. This paper describes the physics and details of the implemented numerical algorithm. It summarizes lessons learned during development. The paper concludes with the presentation of code validation results and examples of applications.

[1]  A. Gosman,et al.  A method for particle location and field interpolation on complex, three-dimensional computational meshes , 1997 .

[2]  Neelesh A. Patankar,et al.  Lagrangian numerical simulation of particulate flows , 2001 .

[3]  M. Papadakis,et al.  Experimental Investigation of Water Droplet Impingement on Airfoils, Finite Wings, and an S-duct Engine Inlet , 2002 .

[4]  R. J. Brun,et al.  Procedure for measuring liquid-water content and droplet sizes in supercooled clouds by rotating multicylinder method , 1953 .

[5]  Michael Papadakis,et al.  Water Droplet Impingement on Airfoils and Aircraft Engine Inlets for Icing Analysis , 1991 .

[6]  Robert Haimes,et al.  An analysis of 3-D particle path integration algorithms , 1995 .

[7]  I. Langmuir,et al.  mathematical investigation of water droplet trajectories , 1946 .

[8]  Jose C. F. Pereira,et al.  Efficient computation of particle dispersion in turbulent flows with a stochastic-probabilistic model , 1997 .

[9]  L. Shampine,et al.  A 3(2) pair of Runge - Kutta formulas , 1989 .

[10]  T. Gerhold,et al.  Calculation of Complex Three-Dimensional Configurations Employing the DLR-tau-Code , 1997 .

[11]  Xiaoling Tong,et al.  Eulerian Simulations of Icing Collection Efficiency Using a Singularity Diffusion Model , 2005 .

[12]  J. Dormand,et al.  A family of embedded Runge-Kutta formulae , 1980 .

[13]  R. Lazic,et al.  An efficient algorithm for high accuracy particle tracking in finite elements , 2002 .

[14]  Axel Raichle,et al.  A New Actuator Disk Model for the TAU Code and Application to a Sailplaine with a Folding Engine , 2007 .

[15]  Rainald Löhner.  Robust, Vectorized Search Algorithms for Interpolation on Unstructured Grids , 1995 .

[16]  D. Darmofal,et al.  An Analysis of 3D Particle Path Integration Algorithms , 1996 .

[17]  Alan H. Karp,et al.  A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides , 1990, TOMS.

[18]  Greg F. Naterer,et al.  Multiphase flow with impinging droplets and airstream interaction at a moving gas/solid interface , 2002 .

[19]  Rainald Löhner,et al.  A vectorized particle tracer for unstructured grids , 1990 .

[20]  N. Fueyo,et al.  An efficient particle-locating algorithm for application in arbitrary 2D and 3D grids , 2002 .

[21]  D T Bowden,et al.  ENGINEERING SUMMARY OF AIRFRAME ICING TECHNICAL DATA , 1963 .

[22]  Imre Balásházy,et al.  Simulation of particle trajectories in bifurcating tubes , 1994 .

[23]  M. D. Breer,et al.  Experimental investigation of water impingement on single and multi-element airfoils , 2000 .

[24]  Günther Greiner,et al.  Local Exact Particle Tracing on Unstructured Grids , 2003, Comput. Graph. Forum.

[25]  Genong Li,et al.  An effective particle tracing scheme on structured/unstructured grids in hybrid finite volume/PDF Monte Carlo methods , 2001 .

[26]  Three-dimensional airflow and hydrometeor trajectory calculation with applications , 1985 .

[27]  M. Leschziner,et al.  An improved particle-locating algorithm for Eulerian-Lagrangian computations of two-phase flows in general coordinates , 1999 .

[28]  T. Westermann,et al.  Algorithms for interpolation and localization in irregular 2D meshes , 1988 .