Wall turbulence

Chen, H. C, Patel, V. C. Near-wall turbulence models for complex flows including separation, AIAA J., vol. 26, pp. 641-648, 1988. 

For steam jacketed, agitated closed reactor ketdes, the overall U usually will range from 40-60 Btu/hr (ft ) ( F). Of course, the significant variables are the degree or type of internal wall turbulence and the viscosity and thermal characteristics of the internal fluid. For water or other liquid cooling in the reactor jacket, the U value usually ranges from 20-30. 

The standard wall function is of limited applicability, being restricted to cases of near-wall turbulence in local equilibrium. Especially the constant shear stress and the local equilibrium assumptions restrict the universality of the standard wall functions. The local equilibrium assumption states that the turbulence kinetic energy production and dissipation are equal in the wall-bounded control volumes. In cases where there is a strong pressure gradient near the wall (increased shear stress) or the flow does not satisfy the local equilibrium condition an alternate model, the nonequilibrium model, is recommended (Kim and Choudhury, 1995). In the nonequilibrium wall function the heat transfer procedure remains exactly the same, but the mean velocity is made more sensitive to pressure gradient effects. 

Dreeben, T. D. and S. B. Pope (1997a). Probability density function and Reynolds-stress modeling of near-wall turbulent flows. Physics of Fluids 9, 154—163. 

PDF/Monte Carlo simulation of near-wall turbulent flows. Journal of Fluid Mechanics 357, 141-166. 

Black TJ (1969) Viscous drag reduction examined in the light of a new model of wall turbulence in Viscous drag reduction ed Wells CS, Plenum Press, New York, p. 383... 

The aim of this work is to estimate more accurately fugitive dust emissions due to wind erosion of exposed aggregate storage piles. The model constructed allows to quantify the temporal evolution in the mass flux when a bed of materials is exposed to a turbulent flow. It is based on the interaction between particles take-off and wall turbulence. The model allows as well to take into account materials having a wide size distribution, which is typical of materials such as coal or ore. Some experimental studies have shown a temporal decrease in the mass flux as the bed contains a wide range of particle sizes. This decrease, due to large particles, is predicted by the model. The rate depends on the flow velocity and the characteristics of the particles. 

J. Jimenez, P. Moin, The minimal flow unit in near wall turbulence, J. Fluid. Mech. 225 (1991) 213-240. 

Kasagi, N., Kuroda, A., and Hirata, M., Numerical Investigation of Near-Wall Turbulent Heat Transfer Taking Into Account the Unsteady Heat Conduction in the Solid Wall , J. of Heat Transfer, Vol. Ill, pp. 385-392, 1989. 

Pain, Y, and Banerjee, S., Numerical simulation of particle interactions with wall turbulence. Phys. Fluids S(10). 2733 (1996a). 

Pan, Y., and Banerjee, S., Numerical investigation of the effects of large particles on wall-turbulence. Submitted for publication (1996b). 

Raupach, M., Antonia, R. and Rajagopalan, S. (1991) Rough-wall turbulent boundary layers, Appl. Mech. Rev. 44(1), 1-25. 

Gampert, L Rensch, A. Polymer concentration and near wall turbulence structure of chemical flow of polymer solutions. In Turbulence Modification and Drag Reduction, Proceedings of the 1996 ASME Fluids Engineering Division Summer Meeting, San Diego, CA, Jul 7-11, 1996 Coleman, H., et al., Eds. ASME New York, 1996 FED-Vol. 237-242, 129-136. 

Sanghi, S. and Aubry, N., Mode interaction models for near-wall turbulence, Fluid Mech., Vol. 247, pp. 455 188, 1993. 

This formula agrees very well with the near-wall temperature profile data of Blackwell et al. [99] obtained in air if Prr= 0.7 and Pr, = 0.88. It should be noted that good agreement with the data was achieved here without consideration of near-wall turbulent Prandtl number variations observed by some investigators [100]. 

The turbulent flow in a pipe is quite different in character from the turbulent flow in a wind tunnel or in the lower atmosphere. In the atmosphere or in the central section of a wind tunnel, the nearest wall is so far away that it has little influence on the flow. This kind of flow, substantiallyj uninfluenced by nearby walls, is called free turbulence. In a typical long pipe, the flow is strongly influenced by the nearby presence of a wall. This kind of flow is often called shear turbulence or wall turbulence. 

Pin-promoters of the type shown in Fig. 3.2a and 3.2b are used in heat exchangers to enhance heat transfer by promoting local wall turbulence and by extending heat transfer area. Find an e q)ression to compute the temperature profile, assuming temperature varies mainly in the x direction. The plate temperature T, fluid temperature T , and heat transfer coefficient h are constant. 

Gomez-Perez CA, Espinosa J, Montenegro Ruiz LC, et al CFD simulation for reduced energy costs in mbular photobioreactors using wall turbulence promoters. Algal Res 12 1-9, 2015. 

Natrajan VK, Yamaguchi E, Christensen KT (2007) Statistical and structural similarities between micro- and macroscale wall turbulence. Microfluid Nanofluid 3 89-100... 

The peculiarities of the structure of wall turbulence and the mechanism of drag reduction by polymer additives. ... 

The Peculiarities of the Structure of Wall Turbulence and the Mechanism of Drag Reduction by Polymer Additives... 

In the very dilute polymer solutions the macromolecules practically do not interact with one another, submolecular structures are absent. In the solution at rest long linear molecules are rolled up into slightly asymmetric balls saturated by the solvent. Their sizes are small as compared with characteristic scales of the wall turbulence. 

The given presentation of the mechanism of the interaction of polymer molecules with turbulent flow admits a peculiar theoretical examination. The presence of polymer addition besides the increase of longitudinal viscosity is resulted in the appearance of such rheological solution properties as elastic plasticity, pseudo-plasticity, anisotropy. In [3] the influence of different rheological fluid characteristics on the wall turbulence is theoretically analyzed within the limits of monoharmonic approximation, which affords to take into account turbulent blows-out. Different variants of rheological behaviour were considered. For all that we succeded to show, that the decrease of turbulent friction arose only in mediums, possessing... 

Using the known solution [61 of the problem of two-dimensional laminar flow of the model polymer solution with stretching for the description of wall turbulent flows, the following approximate expression may be received... 

Filipenko, V.N. The influence of additives on wall turbulent flows. The results in science and technology. VINITI AN USSR, Series Mech. of fluids and gas, 1980, 15, 156-257. 

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