1. Numerical simulation of particle concentration in a turbulent pipe flow Hans Kuerten Maurice Veenman Joost de Hoogh

2. Contents DNS - model Concentration equations Space and time discretisation Early results Finite volume method Future planning

3. DNS model Direct Numerical Simulation by M. Veenman Axial and tangential direction –Spectral solver Radial direction –Chebychev polynomial expansion Implementation of the concentration equations as a passive scalar

4. Concentration equation Boundary conditions Axial and tangential direction: periodic conditions Radial direction:

5. Adams-Bashforth time integration

6. Simple testing 1. 2. 3. 4.

7. First results Movie clip!

8. Negative concentration

9. Finite volume method Roe’s first order upwind scheme Muscl method (by van Leer) Second/third order depending on parameters r φ z

10. Results Muscl method MovieMovie clip!clip!

11. Different grid New uniform grid –Radial direction: uniform grid –Tangential direction (MUSCL): half the points Velocity Interpolation

12. Mean radius Muscl Fourier 1 st order upwind

13. Things still to do Implement diffusion Compare the model with Brethouwer’s results Look into forces acting on the concentration (e.g. gravity)