Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model

TLDR

Many turbulence treatments ignore kinematic viscosity effects, making exact wall boundary conditions unsuitable for low‑Reynolds‑number flows such as rapid expansions or near transition. The study aims to develop a single transport model from the Navier–Stokes equations that accurately predicts skin friction, heat transfer, and fluctuating kinetic energy in transitional and turbulent regimes. A new turbulence model, derived from the Navier–Stokes equations and constructed via a Taylor‑series expansion of near‑wall shear stress, kinetic energy, and dissipation, preserves the correct balance between dissipation and molecular diffusion and is applied to fully developed turbulent channel flow and flat‑plate boundary‑layer flow. Skin‑friction, mean‑velocity, turbulent‑shear‑stress, and turbulent‑kinetic‑energy distributions predicted by the model agree with experimental data and with the Jones–Launder theory.

Abstract

2~5 However, the effects of the kinematic viscosity on the turbulence structure were ignored in many of these treatments. Consequently, the exact boundary conditions at the wall cannot be used when the turbulence Reynolds number is not high as, e.g., in flows with rapid expansions or near the transition/turbulence interface. The general goal of the present investigation was to develop a single transport model from the Navier-Stokes equation for accurate predictions of skin friction, heat transfer, and fluctuating kinetic energy distributions in transitional and turbulent flow regimes. As a first step toward this general goal, a new turbulence model valid down to the solid wall is formulated in this paper. Turbulence model equations which provide predictions of the flow within the viscous layer adjacent to the wall have been proposed by several investigators.3'4'6'7 Although the general approach of the present model is the same as that of Jones and Launder,3 the detailed proposals are substantially different. In the present study, the Taylor series expansion technique was used to systematically investigate the proper behavior of the turbulent shear stress and the kinetic energy and its rate of dissipation near a solid wall. The results were used in developing a new turbulence model which retains the proper physical behavior of the balance between the dissipation and the molecular diffusion of the turbulent kinetic energy at the solid wall. The model was applied to the problems of a fully developed turbulent channel flow and of a turbulent boundary-layer flow over a flat plate. Results on skin friction, the distribution of mean velocity, turbulent shear stress, and turbulent kinetic energy will be presented and compared with available experimental data and with the theory of Jones and Launder.