Numerical study of internal wall-bounded turbulent flows

Direct numerical simulation (DNS) of turbulent pipe flow has been performed at Reynolds numbers ranging from Reτ ≈ 170 to 2000. A literature review highlights a need for higher Reynolds number pipe flow DNS data. There have been many numerical studies for internal geometry (pipe and channel) wall-bounded turbulent flows. Many of the numerical data for both pipe and channel flows, which are now readily accessible are at lower Reynolds numbers. At higher Reynolds numbers, there is a lack of pipe flow DNS data as compared to channel flow DNS data. As the highest Reynolds numbers in numerical simulations are starting to overlap the lower region of experiments, validation of both experimental and numerical results is now possible. Moreover, numerical simulations are extremely useful in complementing experimental results in the near-wall region where accurate experimental data are often difficult to obtain. However, available DNS data of internal wall-bounded turbulent flows are performed with different grid resolutions and computational domain sizes, making it difficult to directly compare between them. An undertaking of this thesis involves a systematic study (using constant grid resolutions) of the domain length effect on the convergence of turbulence statistics. Investigations carried out using numerical data from fully developed pipe flow simulations indicate a recommended computational length of 8π pipe radius or half channel height for turbulence statistics to converge. It is hoped that this will serve as a benchmark computational domain length for future numerical simulations performed. A study is also carried out to better understand the similarities and differences of the flow physics between turbulent channel and pipe flows. This is performed using the newly obtained pipe flow DNS data and channel flow DNS data of del ´ Alamo et al. (2004) at a comparable Reynolds number of Reτ ≈ 1000. Different turbulence statistics investigated including mean flow, turbulence intensities, correlations and energy spectra. Comparison of both wall-bounded channel and pipe flows shows little discrepancies in the near-wall region but differences are observed in the outer-region. Although there is abundant literature for both experimental and numerical wall bounded turbulent flows, further analysis reveals discrepancies in the open literature. One of the primary contributing factors that plagues reported results are spatial resolution issues. In this thesis, the numerical data is used to investigate the effects of insufficient spatial resolution in wall-bounded turbulence by averaging the streamwise velocity component in the spanwise direction. A correction scheme is proposed to correct experimental results suffering from insufficient spatial resolution. The correction scheme is applied to attenuated experimental results such as streamwise turbulence intensity and one-dimensional energy spectra and is shown to be effective. The method of using DNS data to analysis and correct experimental results can be extended to other experimental techniques such as particle image velocimetry and laser doppler velocimetry.