The AGE Method for Numerical Simulation of Turbulent Shear Flows

Principal Investigator

David Bisset

Dept of Mechanical Engineering

University of Newcastle, and Center for Turbulence Research, Stanford University/NASA-Ames

Projects

g91 - VPP

Computational fluid dynamics (CFD), when based
on the Navier-Stokes equations, may be divided
into three broad classes for turbulent flows. The purest form is direct numerical simulation (DNS), in which the full equations are solved. At the other end of the spectrum, the Reynolds-averaged Navier-Stokes (RANS) equations are solved for mean flow properties while all effects of turbulence are modelled through various auxiliary closures. Compared to the RANS approach, DNS is more accurate, robust and informative, but also far more expensive computationally. The third approach, large eddy simulation (LES), tries to have the best of both worlds by calculating the large scale turbulent motions directly and obtaining the effects of small scale turbulence with a sub-grid-scale model. In suitable flows, LES has accuracy near DNS and speed near RANS.

The principal aim of this project is to continue developing the Advected Grid Explicit or AGE method as a faster type of DNS method. The AGE method is also more versatile than spectral DNS methods in regard to spatially developing flows and a broad range of boundary conditions. In some AGE simulations, however, the small scales have been marginally under-resolved with no ill effects and a large increase in speed, making the AGE method a kind of auto-LES. Another aim of the project is to investigate physical properties of the flows that are simulated.

What are the results to date and the future of this work?

Simulation of turbulent planar jets at Reynolds number 10,000 was continued, with a large domain (x < 40H) focusing on the self-preserving region, and then with a smaller domain (x < 14H) that was better resolved at the jet inlet.

Videos of velocity and pressure isosurfaces were prepared from both planar jet and mixing layer simulations, showing detailed development of the flows and the turbulence structures therein.

Simulation of heat transfer in turbulent mixing layers showed the correct asymmetrical properties (possibly for the first time in a simulation), and allowed the effects of inlet conditions to be studied. The characteristic 'ramp/jump' structure in temperature time series was well displayed.

Appendix B -

A turbulent far-wake, beginning with a 'top hat' mean velocity profile, was simulated satisfactorily. This was the first temporal simulation with the AGE method.

At the Center for Turbulence Research (CTR), Stanford University/NASA-Ames, the initial velocity field from a spectral simulation of the far-wake of a parallel flat plate was made available to start an AGE method simulation. Agreement in results was very close, but the AGE method was around 20 times faster.

Initial results from a low Reynolds number turbulent channel flow agree quite well with earlier spectral simulations at the CTR, though in this case the AGE method is only about half the speed of the spectral.

Future work will include: simulations of far-wakes from various initial conditions in larger domains; efforts to speed up the channel flow calculations; and simulation of a spatially developing boundary layer. Most of this work will be done at Ames, though it is interesting to note that the VPP at ANU is significantly faster (per processor) than the Ames Cray C90s.

What computational techniques are used?

The Advected Grid Explicit (AGE) method, developed by the investigator, is essentially a finite difference solution of the Navier-Stokes equations along with mass continuity and an equation of state. Vectorization on the VPP exceeds 98% in some cases.

Publications

R.A. Antonia, D.K. Bisset, P. Orlandi & B.R. Pearson, Reynolds number dependence of the second-order turbulent pressure structure function, Phys Fluids 11(1), 241-243 (1999).

D.K. Bisset, The AGE method for direct numerical simulation of turbulent shear flow, Int J Numer Meth Fluids 28, 1013-1031 (1998).

D.K. Bisset, Further development of the AGE method, in Numerical Methods for Fluid Dynamics VI, ed. M.J. Baines, Oxford University Computing Laboratory, Oxford 1998.

D.K. Bisset, Numerical simulation of heat transfer in turbulent mixing layers, in Proc 13th Australasian Fluid Mech Conf, eds. M.C. Thompson & K. Hourigan, Monash University, Clayton Vic 1998.

D.K. Bisset & R.A. Antonia, Three-dimensional simulations of turbulent planar jets, in Advances in Turbulence VII, ed. U. Frisch, Kluwer Academic, Dordrecht 1998.

- Appendix B