Keywords: turbulent swirling flows, turbulence modelling, URANS, RSM, LES, DES.

Owing to their importance in a broad range of applications, swirling flows have been the subject of intensive experimental, analytical and numerical investigations over many years [1,2,3,4,5,6,7]. The application of swirling flow in industrial gas turbine combustors is of particular interest to the current work. Lean, premixed, dry, low emission combustors exhibit flows that can be substantially different from non-premixed ones, due to a significantly larger degree of swirl acquired by the flow.

A vortex breakdown recirculation zone along the swirl axis can be seen as an abrupt transition between an upstream super-critical flow and a downstream sub-critical flow [8]. The criticality of the swirling flow describes whether the axial flow velocity exceeds the relative phase velocity of upstream-directed inertia waves (super-critical flow) or vice versa (sub-critical flow). The influence of the downstream conditions can hence be transmitted upstream where the flow is sub-critical, but only affects the local flow at the exit where it is super-critical.

Although many analytical and numerical investigations have been conducted to address vortex breakdown and the criticality of the vortex core in confined turbulent flows [1,2,3,4,5,6,7] much of this work is based upon simplifying assumptions such as inviscid flow and axisymmetry. These studies have revealed much about the behaviour of vortical flows but they fall short of delivering quantitative information that can be used in the design of combustors. Only a CFD-based approach that deals with turbulence heat release and the complexities of the geometry can address the key details relevant to the state of the vortex core. CFD suffers, however, from numerical errors due to flow and geometry complexities and practical grid resolution and the need for physical models for combustion and turbulence. Thus, if CFD methods are to be used effectively in the design of swirl combustor, validation is required to understand the impact of the numerical and modelling deficiencies. This is the scope of the present study.

The present work aims to provide a detailed validation of a broad range of advanced turbulence modelling strategies for this bracket of flows problems. For validating the results, the experimental data of Escudier and Keller is [9] utilised, which is obtained at a water-test rig, for flows exhibiting similar characteristics to those typically encountered in gas turbine combustors.

The analysis is based on the commercial general-purpose CFD code ANSYS-CFX [10]. For modelling the turbulence, the Reynolds stress model-based (RSM) [11], unsteady Reynolds averaged numerical simulations (URANS), large eddy simulations (LES) [12] and detached eddy simulations (DES) [13] approaches are adopted. It is observed that better results are obtained using the RSM based URANS approach. DES is also observed to perform better than LES. The rather unsatisfactory performance of LES may be attributed to inaccuracies in formulating the boundary conditions, and/or because there was too coarse a cut-off scale for the simple sub-grid model adopted. Although the present work shows that remarkable improvements can be achieved compared with traditional RANS-based approaches, comparisons between the predictions and the measurements indicate that further improvements are necessary in order to achieve a satisfactory predictive capability for turbulent swirling flows.

1

J.K. Harwey, "Some observations of the vortex breakdown phenomenon", Journal of Fluid Mechanics, 14, 585-592, 1962. doi:10.1017/S0022112062001470

2

O. Lucca-Negro and T. O'Doherty, "Vortex breakdown: a review", Progress in Energy and Combustion Science, 27, 431-481, 2001. doi:10.1016/S0360-1285(00)00022-8

3

S. Hogg and M.A. Leschziner, "Computation of highly swirling confined flow with a Reynolds stress turbulence model", AIAA J., 27, 57-63, 1989. doi:10.2514/3.10094

4

D.G. Sloan, P.J. Smith and L.D. Smoot, "Modelling of swirl in turbulent flow systems", Progress in Energy and Combust. Science, 12, 163-250, 1986. doi:10.1016/0360-1285(86)90016-X

5

R.E. Spall and T.B. Gatski, "Numerical calculations of three-dimensional turbulent vortex breakdown", International Journal of Num. Meths. Fluids, 20, 307-318, 1995. doi:10.1002/fld.1650200404

6

R. Weber, F. Boysan, J. Swithenbank and P.A. Roberts, "Computation of near field aerodynamics of swirling expanding flows", Proc. 21st Symp. (Int.) Combustion, The Combustion Institute, Pittsburgh, PA, 1435-1443, 1986. doi:10.1016/S0082-0784(88)80376-X

7

A.C. Benim, "Finite element analysis of confined swirling flows", International Journal of Numerical Methods Fluids, 11, 697-717, 1990. doi:10.1002/fld.1650110602

8

T.B. Benjamin, "Theory of vortex breakdown phenomenon", Journal of Fluid Mechanics, 14, 593-629, 1962. doi:10.1017/S0022112062001482

9

M.P. Escudier and J.J. Keller, "Recirculation in swirling flow: a manifestation of vortex breakdown", AIAA Journal, 23, 111-116, 1985. doi:10.2514/3.8878

10

ANSYS-CFX-5.6 Solver Manual, ANSYS Europe, Oxfordshire, UK (2004).

11

C.G. Speziale, S. Sarkar and T.B. Gatski, "Modelling the pressure-strain correlation of turbulence", Journal of Fluid Mechanics, 227, 245-272, 1991. doi:10.1017/S0022112091000101

12

P. Sagaut, "Large Eddy Simulation for Incompressible Flows - An Introduction", 2nd Ed. Springer Verlag, Berlin, 2002.

13

F.R. Menter, M. Kuntz and R. Langtry, "Ten years of industrial experience with the SST turbulence model", in: K. Hanjalic, Y. Nagano and M. Tummers (Eds.) Turbulence, Heat and Mass Transfer 4, Begell House, New York, 625-632, 2003.

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