a Numerical Study of Turbulent Pipe Flow

Turbulence in pressure driven pipe flow is numerically simulated from the three-dimensional incompressible Navier -Stokes equations written in rotation form. The velocity and pressure-head fields are represented by truncated Fourier series azimuthally and axially and by Chebyshev series in the radial direction. A fractional time stepping method separates the equations into three parts which evaluate the cross-product, pressure, and viscous terms separately by determining intermediate fields and calculating the correction due to each. Pseudo-spectral operations and fast Fourier transforms are incorporated to evaluate the cross-product. Eigenvector/eigenvalue solutions of the Poisson-like equations involved in the pressure and viscous parts are computed in a pre-processing code and coupled with streamlined matrix multiplications used in production runs. These methods and techniques provide for accuracy and efficiency. Various 2-D and 3-D linear tests of the simulation have conformed to calculated analytical results. Demonstrations of transitions to turbulence by examining 3-D growth in the presence of a 2-D finite amplitude perturbation were in agreement with previous published numerical computations of a similar nature. The calculations have determined that various statistical properties of the generated velocity fields compare favorably with available experimental data for fully developed turbulent flow.