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.

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

This paper reviews the state of the art of Reynolds number effects in wall-bounded shear-flow turbulence, with particular emphasis on the canonical zero-pressure-gradient boundary layer and two-dimensional channel flow problems. The Reynolds numbers encountered in many practical situations are typically orders of magnitude higher than those studied computationally or even experimentally. High-Reynolds number research facilities are expensive to build and operate and the few existing are heavily scheduled with mostly developmental work. For wind tunnels, additional complications due to compressibility effects are introduced at high speeds. Full computational simulation of high-Reynolds number flows is beyond the reach of current capabilities. Understanding of turbulence and modeling will continue to play vital roles in the computation of high-Reynolds number practical flows using the Reynolds-averaged Navier-Stokes equations. Since the existing knowledge base, accumulated mostly through physical as well as numerical experiments, is skewed towards the low Reynolds numbers, the key question in such high-Reynolds number modeling as well as in devising novel flow control strategies is: what are the Reynolds number effects on the mean and statistical turbulence quantities and on the organized motions? Since the mean flow review of Coles (1962), the coherent structures, in low-Reynolds number wall-bounded flows, have been reviewed several times. However, the Reynolds number effects on the higher-order statistical turbulence quantities and on the coherent structures have not been reviewed thus far, and there are some unresolved aspects of the effects on even the mean flow at very high Reynolds numbers. Furthermore, a considerable volume of experimental and full-simulation data have been accumulated since 1962. The present article aims at further assimilation of those data, pointing to obvious gaps in the present state of knowledge and highlighting the misunderstood as well as the ill-understood aspects of Reynolds number effects.

Reynolds Number Effects in Wall-Bounded Turbulent Flows

A direct numerical simulation (DNS) of the fully developed turbulent channel flow and heat transfer with uniform wall injection and suction was carried out. The Reynolds number, which was based on the channel half-width and the friction velocity averaged on the two walls, was set to be 150, whereas the Prandtl number was 0.71. The walls were assumed to be kept at isothermal but different temperatures. With any buoyancy effect neglected, temperature was considered as a passive scalar. The computation was executed on sufficiently dense grid points by using a spectral method. The statistics obtained include the mean velocity and temperature, Reynolds stresses, and turbulent heat fluxes. Each term in the budget equations of the second-order velocity and temperature correlations and of their destruction rates was also calculated. It is found that the injection decreases the friction coefficient, but tends to stimulate the near-wall turbulence activity so that the Reynolds stresses and turbulent heat fluxes are increased, whereas the suction has an inverse influence.

Direct numerical simulation of turbulent transport with uniform wall injection and suction

The behavior of various terms in the Reynolds-stress transport equations is evaluated in view results of near-wall turbulence characterizations which show that all components of the velocity-pressure gradient correlation vanish at the wall. A methodology for deriving an asymptotically correct model of the velocity-pressure gradient correlation is proposed, and a model capable of approaching the high-Reynolds number model for pressure distribution far from the wall is derived. A parametric study of the model constants introduced by the near-wall closure reveals that one constant in the dissipation-rate equation is Reynolds number-dependent; with this modification, excellent agreement is obtained with measured and simulated near-wall turbulence statistics.

On near-wall turbulent flow modelling

A modified low-Reynolds-number k-e turbulence model is developed in this work. The performance of the proposed model is assessed through testing with fully developed pipe flows and recirculating flow in pipe expansion. Attention is specifically focused on the flow region around the reattachment point. It is shown that the proposed model is capable of correctly predicting the near-wall limiting flow behavior while avoiding occurrence of the singular difficulty near the reattachment point as applying to the recirculating flow in sudden-expansion pipe.

A Modified Low-Reynolds-Number Turbulence Model Applicable to Recirculating Flow in Pipe Expansion

The effect of uniform wall suction on the structure of turbulence in a fully established turbulent pipe flow has been measured, with special attention to the critical layers close to the wall. Uniform suction was introduced into a pipe flow with a Reynolds number of 17250 by means of a porous-walled section 2·2 diameters in length with very fine perforations. The effect of suction on the turbulent energy balance was then measured over the entire cross-section at four axial locations. The results indicate the following.
 The amplitudes of the three principal velocity fluctuation components are reduced by suction, but to differing degrees. Moreover, the effects of suction on the amplitudes of these fluctuations develop at differing rates such that the x-wise components are first affected, then the r-wise and lastly the ϕ-wise components.The suction-induced perturbation in the turbulent structure propagates from the wall to the pipe centre-line with a velocity approximately equal to the friction velocity Uτ.Even with very small rates of fluid extraction the maxima of the terms in the turbulent energy balance occurring close to the wall are drastically reduced. Nevertheless there is no tendency for the location of these maxima to move towards the wall.The general reduction of the level of turbulent energy across the entire section is due to transport of this energy by the augmented mean radial velocity towards the wall, where it is dissipated since the boundary condition inhibits the passage of turbulent energy through the wall.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112079002081

The influence of suction on the structure of turbulence in fully developed pipe flow

/pdf/the-influence-of-suction-on-energy-distribution-in-fully-37i7n9ynuj.pdf

J. A. Miller

Papers

The influence of suction on the structure of turbulence in fully developed pipe flow

The Influence of Suction on Energy Distribution in Fully Established Turbulent Pipe Flow