## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission
of the Department of Mechanical Engineering for public examination and debate in Auditorium
K216 at Helsinki University of Technology (Espoo, Finland) on the 1^{st} of December, 2006, at 12
noon.

Overview in PDF format (ISBN 951-22-8405-7) [13521 KB]

Dissertation is also available in print (ISBN 951-22-8404-9)

Several aspects of large-eddy simulations (LES) are studied in this thesis. In the first part computational requirements and methods are compared for the calculation of unsteady incompressible flow. Explicit time integration methods are efficient especially in simple flow geometries and with low Reynolds numbers. An Adams-Bashford fractional time-stepping scheme is used in the turbulent channel flow computations.

The Smagorinsky model is a baseline subgrid-scale model used in LES. This and the dynamic version are assessed in a turbulent channel flow. The models do not necessarily improve the results at a low Reynolds number if the calculation is stabilized enough by the molecular or numerical viscous effects. With the second-order central scheme the numerical error is estimated to be greater than the filtered stresses from the momentum equations. This estimate alone suggests that there is no accurate model for instantaneous stresses for the low-order schemes. The main role of the subgrid-scale model is to remove energy from the resolved scales and hence to stabilize the calculation.

LES in any practical application, even at a low-Reynolds number, requires high computational resources. A parallel solver based on a multi-block approach is written, where computational domain is divided between many structured blocks. The blocks assigned to different processors communicate at the boundaries with an MPI standard. The solver is tested with a turbulent cavity and a pipe flow. A linear speed-up and scale-up are achieved with equally balanced processors loads.

A large-eddy simulation of a round jet penetrating normally into a cross-flow is computed. The jet-to-cross-flow velocity ratio is 2.3 at a Reynolds number of 46 700, based on the jet bulk velocity and the jet diameter. The simulation is performed both with a steady and an unsteady boundary condition at the jet inlet pipe. A passive scalar is discretized both with a central and a TVD discretization. The results are compared with each other and the experimental measurements of Crabb, Durão and Whitelaw. The computation reproduced many phenomena present in such a flow, like the shear layer ring vortices and a counter-rotating vortex pair. In general, a reasonable agreement with the measurements was obtained. The unsteady boundary condition at the jet inlet increases the spreading of the jet slightly.

This thesis consists of an overview and of the following 5 publications:

- Majander P., Siikonen T., A comparison of time integration methods in an unsteady low-Reynolds-number flow, International Journal for Numerical Methods in Fluids, vol 39, pp 361-390, 2002. © 2002 John Wiley & Sons. By permission.
- Majander P., Siikonen T., Evaluation of Smagorinsky-based subgrid-scale models in a finite-volume computation, International Journal for Numerical Methods in Fluids, vol 40, pp 735-774, 2002. © 2002 John Wiley & Sons. By permission.
- Majander P., Siikonen T., A parallel multi-block Navier-Stokes solver for large-eddy simulation in complex flows, 8th Finnish Mechanics Days, Espoo, Finland, pp. 395-406, June 12-13, 2003. © 2003 by authors.
- Majander P., Siikonen T., Large-Eddy Simulation of a Round Jet in a Crossflow, Proceedings of the 4th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2004), Jyväskylä, Finland, July 24-28, 2004. © 2004 by authors.
- Majander P., Siikonen T., Large-eddy simulation of a round jet in a cross-flow, International Journal of Heat and Fluid Flow, vol 27, pp 402-415, 2006. © 2006 Elsevier Science. By permission.

Errata of publications 1, 3 and 4

**Keywords:**
large-eddy simulation, jet in a cross-flow

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© 2006 Helsinki University of Technology

Last update 2011-05-26