On the importance of generating accurate turbulent boundary condition for unsteady simulations

Abstract

Turbulence is generally characterized by random, chaotic motion and has always been a challenging problem for fluid dynamists. Several methods for generating turbulent boundary conditions for computational fluid dynamics are in use today. One of the methods is by adding random white-noise to the averaged velocity profiles to generate turbulence in the flow field, which can be considered as the simplest and inexpensive method. Recently, another method has been introduced, which is based upon a digital filter to generate turbulent inflow data. This paper presents a comparison of the digital filter-based turbulent inflow data generation technique with three different methods within the framework of the large eddy simulations technique using the fifth- and second-order accurate methods in space and time, respectively. The case for comparison/analysis is a sonic jet of air injected transversely into a supersonic (Mach 1.6) stream of air, for which experimental and classical large eddy simulation data were available. It is demonstrated that the random white-noise-based turbulent inflow data dissipate immediately in the computational domain, giving incorrect velocity and pressure profiles. At the same time, the importance of two-point Exponential correlation used in the digital filter-based technique is demonstrated by scaling the random white-noise with the Reynolds stress tensor and ignoring the correlation. This improved the results compared with pure random white-noise, but still exhibits a high initial dissipation rate because the energy is not distributed over the required range of wavenumbers. It is demonstrated that the digital filter-based turbulent inflow data generation technique provides a reliable, accurate and consistent turbulent boundary layer in the flow field, which is required for the capture of correct flow physics. It is also demonstrated that the computational cost involved in all the methods presented is almost identical.

Keywords:

• turbulence
• digital filter
• compressible flows
• jet in supersonic cross-flow
• turbulent mixing

Acknowledgements

The simulations presented in this paper have been carried out on the Cranfield University's Astral supercomputer. The authors would like to acknowledge the financial support for this project from EPSRC under the Doctoral Training Accounts (DTA) scheme.