Annual Report on 2005 Project

Direct Numerical Simulation of Swirling Jets

This study proposes to investigate swirling jets at moderate to high Reynolds numbers using direct numerical simulation (DNS). DNS involves no turbulence modelling - the governing equations for an incompressible fluid flow are numerically solved with sufficient spatial resolution to account for the dynamics and interactions of all significant length scales of turbulence. The proposed DNS is computationally demanding, both in CPU usage and memory requirements. The computational facilities available at APAC are uniquely suited for this work. The detailed information obtained from the simulations will assist in the development of realistic physical models that explain the complex mechanics of phenoma associated with swirling jets such as the formation of coherent structures, instability and transition to turbulence, vortex breakdown and hysteresis. Computational results will be compared to experimental data. It is expected that the results of this work will be published in the archival literature.

Principal Investigator

Julio Soria
Department of Mechanical Engineering
Monash University

Project

g75

Co-Investigators

John Cater
Department of Engineering
INT

Stefano Wahono
Mechanical Engineering
Monash University

Wolfgang Kollmann
Mechanical and Aeronautical Engineering
University of California, Davis

Phillippa O'Neill
School of Mechanical Engineering
University of Western Australia

RFCD Codes

291801

Significant Achievements, Anticipated Outcomes and Future Work

In this investigation, differential diffusion of scalars in a swirling jet undergoing vortex breakdown is investigated using direct numerical simulation (DNS). A range of swirl numbers and Reynolds numbers are investigated, and a variety of passive scalar diffusion models are considered. The results reveal several mechanisms of mixing enhancement by swirl, dependent on the molecular diffusivity of the scalar. The results are also relevant to the transfer of heat where the differential is due to a difference in the conduction properties of the flow.

The following are the progresses which have been made along the line of the project:

Testing grid sensitivity to find the minimum grid resolution required to completely resolve all the turbulent scales for a typical range of Reynolds number, Schmidt number, and Swirl number. Reynolds number, and swirl number has been chosen to match the experiment of Billant, et al. to validate the code.
Developing and testing modification to the solver to incorporate multiple scalar fields in order to observe how each scalar is preferentially diffused according to their corresponding Schmidt number.
The restart files of each run, which has reached statistically stationary flow, are collected for running later analysis of Lagrangian and Eulerian statistics of the flow field variables and scalar fields.
Development of the stable full 3-dimensional DNS solver has just recently completed. The code is now due for further testing in the APAC machine. Further research will focus on investigation on the coupling between multiple scalars diffusion process and the momentum in the highly complex 3-dimensional vortex breakdown flow.

The study will extend to investigation of differential diffusion of passive scalars in swirling flows on the verge of vortex breakdown. It will involve undertaking a comprehensive theoretical and experimental study. The theoretical component involves a full 3-dimensional Direct Numerical Simulation (DNS) of the flow, while experiments involve flow field measurement using both Multi-Grid Cross Correlation Digital Particle Image Velocimetry (MCCDPIV) and dye-flow visualization using Planar Laser Induced Fluorescence (PLIF) technique.

The DNS data will then be used to develop an analytical model of scalars mixing in non-reacting and reacting swirling jets.

Computational Techniques Used

The computational method is full 3-dimensional Direct Numerical Simulation of swirling jet in cylindrical coordinates. A hybrid spectral finite-difference method numerical scheme has been used to directly solve the Navier-Stokes equations without modelling the flow with any turbulence model. Solutions are obtained using a fifth order upwind biased scheme (Li[4]) for the convective terms and a fourth order central difference scheme for other terms in the axial and radial directions. Radial periodic Fourier series have been used for discretisation in the azimuthal direction. The numerical formulation carefully considers the variation of the azimuthal Fourier modes close to the r = 0 axis (central axis) and exploits the symmetry and pole conditions. A fourth order Runge-Kutta type time integration method is used to advance the simulation in time. Helmholtz equation for the streamfunction and the pressure modes are solved using LU decomposition method and deferred corrections to minimise the bandwidth of the coefficient matrices. The DNS simulation typically requires 500MB of RAM at low Reynolds Number (Re=1200) and approximately 2-3 GB of RAM at moderate to high Reynolds Number (Re>5000). These are the memory requirements for 2-dimensional simulations. The upcoming full 3-dimensional simulations will require a lot more memory. The increase in memory will exponentially scale with increasing Reynolds number. The simulation involves memory intensive operation due to operations of large matrices, FFT, and Gaussian Elimination. Several parametric cases are run simultaneously using a number of different nodes.

Publications, Awards and External Funding

External Funding and Awards

None

Publications

Several publications have been presented in various conferences on the investigation of differential diffusion of multiple passive scalars in 2-dimensional vortex breakdown flow in swirling jet. Some of the papers presented in 2005 are:

Wahono, S., O’Neill, P., Kollmann, W. and Soria, J., “A numerical investigation of differential diffusion in a swirling jet”, Proc. 8th Australasian Heat and Mass Transfer Conference (8AHMTC), Curtin University, Perth, 26-29th July 2005.
Wahono, S., Wolfgang, K., Soria, J., Honnery, D. and O’Neill, P., “Direct numerical simulation of passive scalars mixing in a spatially evolving axisymmetric vortex breakdown flow”, Proc. 5th AIAA - Space Science Conference (5ASSC), RMIT University, September 2005.
Wahono, S., Kollmann, W., Soria, J. and Honnery, D., “Limitations of axisymmetric simulations in swirling jets”, Presented at 7th Biennial Engineering mathematics and Applications Conference (7EMAC), RMIT University, 22-28th September, 2005.
Wahono, S., O’Neill, P., Kollmann, W. Honnery, D. and Soria, J., 'DNS of passive scalars mixing in a spatially evolving axisymmetric vortex breakdown flow.” , March, 2006, Submitted to the Australian Journal of Mechanical Engineering – AJME:8.