**8. References**


18 Advanced Fluid Dynamics

Araki, K. & Moriyama, A. (1981). Theory on Deformation Behavior of a Liquid Droplet

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Beck, J. & Watkins, A. (2002). On the Development of Spray Submodels Based on Droplet

Bendig, L., Raudensky, M. & Horsky, J. (1995). Spray parameters and heat transfer

Bowen, I. & Davies, G. (1951). Technical Report ICT 28. *Shell Research Ltd.,* London,

Bul, Q. (2001). Development of a Fan Spray Nozzle for Continuous Caster Secondary Cooling. *AISE Steel Technology*, Vol. 78, No. 5, (May 2001), pp. 35-38. Camporredondo, J., Castillejos, A., Acosta, F., Gutiérrez, E. & Herrera, M. (2004). Analysis of

Ciofalo, M., Caronia, A., Di Liberto, M. & Puleo, S. (2007). The Nukiyama Curve in Water

Crowe, C., Sharma, M. & Stock, D. (1977). The Particle-Source-In-Cell (PSI-CELL) Model

Crowe, C., Schwarzkopf, J., Sommerfeld, M. & Tsuji, Y. (1998). *Multiphase Flows with Droplets and Particles*, CRC Press LLC, ISBN 0-8493-9469-4. Boca Raton, FL, USA. Deb, S. & Yao, S. (1989). Analysis on Film Boiling Heat Transfer of Impacting Sprays.

Hatta, N., Fujimoto, H., Ishii, R. & Kokado, J. (1991a). Analytical Study of Gas-Particle Two-

Hatta, N., Fujimoto, H. & Ishii, R. (1991b). Numerical Analysis of a Gas-Particle Subsonic Jet

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t terminal T Total

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**8. References**

x, y, z Coordinates directions


**Direct Numerical Simulations of**

S.A. Karabasov1 and V.M. Goloviznin2

*1UK 2Russia* 

*1University of Cambridge Department of Engineering* 

**Compressible Vortex Flow Problems** 

*2Moscow Institute of Nuclear Safety, Russian Academy of Science* 

Vortical flows are one of the most fascinating topics in fluid mechanics. A particular difficulty of modelling such flows at high Reynolds (Re) numbers is the diversity of space

For compressible flows, in particular, there are additional degrees of freedom associated with the shocks and acoustic waves. The latter can have very different characteristic amplitudes and scales in comparison with the vorticity field. In case of high Re-number flows, the disparity of the scales becomes overwhelming and instead of Direct Numerical Simulations (DNS) less drastically expensive Large Eddy Simulations (LES) are used in which large flow scales are explicitly resolved on the grid and the small scales are modelled. For engineering applications, examples of unsteady vortical flows include the interaction of wakes and shocks with the boundary layer in a transonic turbine and vorticity dissipation shed due to the temporal variations in blade circulation that can have a profound loss influence and affect the overall performance of a turbomachine (e.g., Fritsch and Giles, 1992; Michelassi et al, 2003). Another example is dynamics and acoustics of high-speed jet flows that is affected by the jet inflow conditions such as the state of the boundary layer at the nozzle exit (e.g., Bogey and Bailly, 2010). The computational aspects involved in the modelling of such complex flows, typically, include the issues of high-resolution numerical schemes, boundary conditions, non-uniform grids and the choice of subgrid scale

Stepping back from this complexity to more idealised problems, two-dimensional (2D) vortex problems are a key object for testing different modelling strategies. Such reducedorder systems play an important role in the understanding of full-scale flow problems as

One example of such important idealised systems is isolated vortices, their interaction with acoustic waves and also nonlinear dynamics when interacting with each other. In particular, such vortical systems are a classical problem in the theory of sound generation and

The structure of the chapter is the following. In part I, an outline of unsteady computational schemes for vortical flow problems is presented. In part II, the test problem of a stationary inviscid vortex in a periodic box domain is considered and a few numerical solutions

scattering by hydrodynamic non-uniformities (e.g., Kreichnan, 1953; Howe, 1975)

**1. Introduction** 

and time scales that emerge as the flow develops.

parameterization in case of LES modelling.

well as in benchmarking of computational methods.

Yap, C. (n.d. 1987). *Turbulent Heat and Momentum Transfer in Recirculating and Impinging Flows.* Ph.D. Thesis, University of Manchester, Manchester, UK. **2**
