Channel turbulent flow

For flow in an open channel, only turbulent flow is considered because streamline flow occurs in practice only when the liquid is flowing as a thin layer, as discussed in the previous section. The transition from streamline to turbulent flow occurs over the range of Reynolds numbers, updm/p = 4000 — 11,000, where dm is the hydraulic mean diameter discussed earlier under Flow in non-circular ducts. 

Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem Eng 16 359-368... 

Moin, R and J. Kim, Numerical investigation of turbulent channel flow. J. Fluid Mech., 1982.118 341-377. 

For most medium- and large-scale micromanifold structures, where one passage feeds multiple parallel channels, flow traverses through turbulent and transition flows in the micromanifold region. This fluid in turbulent to transition flow also turns in the micromanifold region as it drops flow into parallel microchannels, which are primarily in the laminar flow regime. 

With turbulent channel flow the shear rate near the wall is even higher than with laminar flow. Thus, for example, (du/dy) ju = 0.0395 Re u/D is vaHd for turbulent pipe flow with a hydraulically smooth wall. The conditions in this case are even less favourable for uniform stress on particles, as the layer flowing near the wall (boundary layer thickness 6), in which a substantial change in velocity occurs, decreases with increasing Reynolds number according to 6/D = 25 Re", and is very small. Considering that the channel has to be large in comparison with the particles D >dp,so that there is no interference with flow, e.g. at Re = 2300 and D = 10 dp the related boundary layer thickness becomes only approx. 29% of the particle diameter. It shows that even at Re = 2300 no defined stress can be exerted and therefore channels are not suitable model reactors. 

The flow of jets becomes turbulent at much lower Re numbers than channel flows. Calculating the stress from the mean velocity profiles does not reflect the true situation in turbulent flow. As in the case in most bioreactors, the maximum turbulent stress is determined by the turbulence, which can be calculated using Eqs. (2)-(4). It occurs in free jets after the nozzle, at the edge of the mixing zone. The following is generally valid ... 

These results appear to indicate that flow turbulences in the whole channel can improve the critical heat fluxes. 

Dwyer, O. E., G. Strickland, S. Kalish, and P. J. Schoen, 1973a, Incipient-Boiling Superheat for Sodium in Turbulent Channel Flow Effects of Heat Flux and Flow Rate, Int. Heat Mass Transfer 16 911-984. (4)... 

Hubbard and Lightfoot (HI la) earlier reported a Sc,/3 dependence on the basis of measurements in which the Schmidt number was varied over a very large range. The data did not exclude a lower Reynolds number exponent than 0.88, and reaffirmed the value of the classical Chilton-Colburn equation for practical purposes. Recent measurements on smooth transfer surfaces in turbulent channel flow by Dawson and Trass (D8) also firmly suggest a Sc13 dependence and no explicit dependence of k+ on the friction coefficient, with Sh thus depending on Re0,875. The extensive data of Landau... 

To summarize, a comprehensive understanding of turbulent transport is not yet achieved, and information will be needed from optical as well as from further mass-transfer measurements. The latter will have to be made at high Reynolds numbers (> 50,000 in channel flow) and at very high Schmidt numbers (> 10,000) to yield critical information about the transfer process. 

Calmet, I. and J. Magnaudet (1997). Large-eddy simulation of high-Schmidt number mass transfer in a turbulent channel flow. Physics of Fluids 9,438 155. 

Hughes, T. J. R., A. A. Oberai, and L. Mazzei (2001a). Large eddy simulation of turbulent channel flows by the variational multiscale method. Physics of Fluids 13, 1784-1799. 

Equation (4) states that the linear deposition rate vj is a diffusion controlled boundary layer effect. The quantity Ac is the difference in foulant concentration between the film and that in the bulk flow and c is an appropriate average concentration across the diffusion layer. The last term approximately characterizes the "concentration polarization" effect for a developing concentration boundary layer in either a laminar or turbulent pipe or channel flow. Here, Vq is the permeate flux through the unfouled membrane, 6 the foulant concentration boundary layer thickness and D the diffusion coefficient. 

Figure 5.1 Closeup, overhead view of a plume released isokinetically into a turbulent boundary layer in an open-channel flow. Flow direction is from left to right.

The sample data presented in this chapter were collected for fairly simple flow conditions. The flow was a unidirectional open-channel flow without large-scale flow meander, and the release condition was isokinetic in the direction of the bulk flow. Thus, chemical filaments were advected by the bulk flow in the stream-wise direction, while turbulent mixing acted to expand the plume size and dilute the chemical concentration. Changes in the flow and release conditions lead to significant variation in the plume characteristics and structure. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

What is turbulent flow We will use the simple illustration of a free-surface flow given in Figure 5.1 to describe the essential points of the turbulence phenomena. Turbulent open-channel flow can be described with a temporal mean velocity profile that reaches a steady value with turbulent eddies superimposed on it. These turbulent eddies are continually moving about in three dimensions, restricted only by the boundaries of the flow, such that they are eliminated from the temporal mean velocity profile, u in Figure 5.1. It is this temporal mean velocity profile that is normally sketched in turbulent flows. 

Nezu, L, and Nakagawa, H. (1993). Turbulence in Open Channel Flow. Balkema, Rotterdam, The Netherlands. 

It is not possible to calculate Edis for a natural river from first principles alone. However, starting from experiments with uniform channel flow, Fischer et al. (1979) developed concepts to relate dis to other characteristic parameters of the river flow such as u, Ez, Ey, which were introduced to describe turbulent mixing in the river. There are two qualitative arguments for the way Edis should depend on other river parameters ... 

J. Mantzaras, C. Appel, P. Benz, and U. Dogwiler. Numerical Modelling of Turbulent Catalytically Stabilized Channel Flow Combustion. Catalysis Today, 59 3-17,2000. 

Laminar flow reactors are equipped with microstructured reaction chambers that have the desired low Reynolds numbers due to their small dimensions. Mass transport perpendicular to the laminar channel flow is dominated by diffusion, a phenomenon known as dispersion. Without the influence of diffusion, laminar flow reactors could not be used in heterogeneous catalysis. There would be no mass transport from the bulk flow to the walls as laminar flow, in contrast to turbulent flow, cannot mix the flow macroscopically. 

Y. Nino, M.H. Garcia, Experiments on particle-turbulence interactions in the near-wall region of an open channel flow Implications for sediment transport, J. Fluid Mech. 326 (1996) 285-319. 

Figure 11 Schematic diagram of the experimental facility for simultaneous measurement of turbulent velocity field and free-surface wave amplitude in an open channel flow using PIV (Li et al., 2005c).

Figure 13 plots an example of the processed PIV frame. The turbulent velocity field and its boundaries, solid wall, and liquid-free surface are simultaneously shown in Figure 13. The turbulence structures such as the coherent vortical structure near the bottom wall and its modification after release from the no-slip boundary condition near the free surface of the open-channel flow, and the evolvement of the free-surface wave can be seen in Figure 13. This simultaneous measurement technique for free-surface level and velocity field of the liquid phase using PIV has been successfully applied to the investigation of wave-turbulence interaction of a low-speed plane liquid wall-jet flow (Li et al., 2005d), and the characteristics of a swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall (Li et al., 2006c).

An extended version of the hybrid technique of PIV/LIF/SIT is reported by Kitagawa et al. (2005), in which the PTV technique is employed to measure the velocity field in liquid phase and track the velocity distribution of dispersed bubbles, in addition to the SIT measurement of bubbles shape and location in a microbubble-laden turbulent channel flow. It is well known that microbubbles injected into the turbulent boundary layer developing on a solid wall have a significant skin friction reduction effect. To investigate the interactions between the injected microbubbles (the void fraction is actually low but... 

The velocity vectors of the liquid phase and bubbles are accurately detected after the abovementioned data-processing procedures, so that the characteristics of turbulence in a channel flow modified by microbubbles injection and the bubble-turbulence interactions are able to be explored statistically (Kitagawa et al., 2005). 

Experimental investigations of turbulence diffusion. A factor in transportation of sediment in open channel flow. J Applied Mechanics, 12 A91-A100. 

---