ACCURATE NAVIER-STOKES INVESTIGATION OF TRANSITIONAL AND TURBULENT FLOWS IN A CIRCULAR PIPE

A new fast, accurate, and roundoff-error robust numerical technique fo r integrating unsteady incompressible Navier-Stokes equations in cylin drical coordinates is presented. The algorithm is based on a special c hange of dependent variables which avoids the singularity problem and provides high accuracy and computational efficiency. Accuracy and stab ility of the method are thoroughly tested for the model problem of tra nsitional and turbulent flows in an infinite circular pipe. Verificati on of the algorithm includes two issues. First, spectral characteristi cs of the Hagen-Poiseuille flow stability problem are compared with th ose of the discrete linearized Navier-Stokes operator. Secondly, the r esults of direct Navier-Stokes simulation of all stages of laminar-tur bulent transition in a circular pipe at Reynolds number of 4000 are pr esented. Time evolution of finite-amplitude disturbances of laminar fl ow was calculated until the statistically stationary turbulent flow re gime was established. in addition to common statistical analysis, the possibility of turbulence description by means of velocity fields havi ng certain symmetries is examined, Thus, the algorithm presented seems to be a ready-to-use robust tool for accurate investigation and furth er parametric studies of both transition mechanisms and fully develope d turbulent flow regimes. (C) 1998 Academic Press.