REPORT 1174 THE STRUCTURE OF TURBULENCE IN FULLY DEVELOPED PIPE FLOW

REPORT 1174 THE STRUCTURE OF TURBULENCE IN FULLY DEVELOPED PIPE FLOW

| BY JOHN LAUFER
This report, authored by John Lauder, investigates the structure of turbulence in fully developed pipe flow using hot-wire anemometry. The study focuses on turbulence and conditions near the wall, measuring relevant mean and statistical quantities such as Reynolds stresses, triple correlations, turbulent dissipation, and energy spectra. Key findings include: 1. **Turbulent Energy Production and Dissipation**: Rates of turbulent energy production, dissipation, and diffusion have sharp maxima near the edge of the laminar sublayer. There is a strong movement of kinetic energy away from this point and an equally strong movement of pressure energy toward it. 2. **Three Regions of Turbulent Field**: - **Wall Proximity**: Turbulence production, diffusion, and viscous action are all of about equal importance. - **Central Region**: Energy diffusion plays the predominant role. - **Region Between (1) and (2)**: Local rate of change of turbulent energy production dominates the energy received by diffusive action. 3. **Energy Balance**: - **Low Reynolds Number Flow**: Energy production and dissipation are approximately balanced throughout the cross-section, except in the center region. The edge of the laminar sublayer is crucial for both energy production and dissipation. - **High Reynolds Number Flow**: Similar energy balance is observed, with significant dissipation at high frequencies. 4. **Energy Spectrum**: - The measured $u'$-spectra indicate that the spectral distributions behave similarly over a wide range of wave numbers, varying as the $-5/3$ power of the wave number $k_1$ over a considerable range. This behavior is consistent with the equilibrium range of the energy spectrum in isotropic fields. The report concludes that while the understanding of turbulence is not yet complete, the study provides valuable insights into the structure of turbulence in fully developed pipe flow, particularly near the wall.This report, authored by John Lauder, investigates the structure of turbulence in fully developed pipe flow using hot-wire anemometry. The study focuses on turbulence and conditions near the wall, measuring relevant mean and statistical quantities such as Reynolds stresses, triple correlations, turbulent dissipation, and energy spectra. Key findings include: 1. **Turbulent Energy Production and Dissipation**: Rates of turbulent energy production, dissipation, and diffusion have sharp maxima near the edge of the laminar sublayer. There is a strong movement of kinetic energy away from this point and an equally strong movement of pressure energy toward it. 2. **Three Regions of Turbulent Field**: - **Wall Proximity**: Turbulence production, diffusion, and viscous action are all of about equal importance. - **Central Region**: Energy diffusion plays the predominant role. - **Region Between (1) and (2)**: Local rate of change of turbulent energy production dominates the energy received by diffusive action. 3. **Energy Balance**: - **Low Reynolds Number Flow**: Energy production and dissipation are approximately balanced throughout the cross-section, except in the center region. The edge of the laminar sublayer is crucial for both energy production and dissipation. - **High Reynolds Number Flow**: Similar energy balance is observed, with significant dissipation at high frequencies. 4. **Energy Spectrum**: - The measured $u'$-spectra indicate that the spectral distributions behave similarly over a wide range of wave numbers, varying as the $-5/3$ power of the wave number $k_1$ over a considerable range. This behavior is consistent with the equilibrium range of the energy spectrum in isotropic fields. The report concludes that while the understanding of turbulence is not yet complete, the study provides valuable insights into the structure of turbulence in fully developed pipe flow, particularly near the wall.
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