Ekman layers

Effect of Fluid Viscosity and Inertia The dynamic effect of viscosity on a rotating liquid slurry as found in a sedimenting centrifuge is confined in veiy thin fluid layers, known as Ekman layers. These layers are adjacent to rotating surfaces which are perpendicular to the axis of rotation, such as bowl heads, flanges, and conveyor blades, etc. The thickness of the Ekman layer 6 is of the order... 

The high velocities in the Ekman layers and the thinness of the layers strongly enhance the heat transfer between the gas and the sidewalls. There exist a variety of well-esfablished analytical and experimental correlations for fhe heaf fransfer between gas and a rotating disc (or the wall of fhe vessel). Cobb and Saunders [15] correlated their experimental investigations of fhe average laminar heaf fransfer with the Reynolds number Re = < 2.4 x lO ... 

Although the detailed flow-structure in the vessel is unknown and can be predicted by numerical means, only the basic features of the flame-flow interaction can now be depicted. The interaction is shown schematically in Figure 6.4.7. Each of the Ekman layers formed at the sidewalls by the angular velocity perturbation of the flow induces two recirculation cells—one in front of the flame and one behind it, separated by the flame. The recirculation cell in front of fhe flame is of less importance, as the flow velocities there do not affect the flame. 

Flame-flow interaction in a rotating vessel, showing the generation by the sidewall of two recirculation cells before and after the flame driven by the Ekman layers. 

It is shown that the Ekman layers behind the flame front, generated by the rotational speed changes of the gas owing to expansion, cause flame detachment from the walls and reduction in flame width in the rotating vessels, ultimately causing flame quenching. 

In Chapter 6.4, J. Chomiak and J. Jarosinski discuss the mechanism of flame propagation and quenching in a rofating cylindrical vessel. They explain the observed phenomenon of quenching in ferms of the formation of fhe so-called Ekman layers, which are responsible for the detachment of flames from the walls and the reduction of fheir width. Reduction of the flame speed with increasing angular velocity of rofation is explained in terms of free convection effects driven by centrifugal acceleration. 

Now we consider specification of the Ekman layer. We begin with convective (unstable) conditions. Lamb et al. (1975) derived empiri-... 

Under neutral conditions, L = and so the Monin-Obkuhov length is not an appropriate choice for the vertical length scale. An alternative is to define the scale in terms of the Ekman layer height ujf. Another formulation was proposed by Businger and Ayra (1974) for neutral and stable conditions ... 

In this section we consider the variation of wind with height in the surface and Ekman layers, which constitute the so-called planetary boundary layer. Most of our attention will be devoted to the surface layer, the region in which pollutants are usually first released. The exact vertical distribution of wind velocity depends on a number of parameters, including the surface roughness and the atmospheric stability. 

Since we generally need expressions for Kzz that extend vertically beyond the surface layer, we now consider some available correlations for the entire Ekman layer. 

We note that Myrup and Ranzieri chose the mixed-layer depth z, as the characteristic vertical lengthscale, whereas Shir uses the Ekman layer height, u /f. (Since L = oo under neutral conditions, the Monin-Obukhov length cannot be used as a characteristic length scale.)... 

The atmosphere near the surface of the Earth can be divided into three layers—the free atmosphere, the Ekman layer, and the surface layer. The Ekman layer and the surface layer constitute the so-called planetary boundary layer. The Ekman layer extends to a height of from 300 to 500 m depending on the type of terrain, with the greater thickness corresponding to the more disturbed terrain. 

In the Ekman layer, the wind direction tends to turn clockwise with increasing height in the Northern Hemisphere (counterclockwise in the Southern Hemisphere). The wind speed in the Ekman layer generally increases rapidly with height however, the rate lessens as the free atmosphere is approached. The exact distribution of the wind speed depends on many parameters, particularly the vertical distribution of the horizontal pressure gradient as well as the atmospheric stability. 

Ekman layer, 855 Ekman spii al, f[6, 855 El Nmo/Soiitlrern Oscillation (ENSO), 13 Electi onenti ality equation, 3f[8, 387, 101 ... 

The domain between the surface boundary layer and the free atmosphere is the planetary boundary layer, or the Ekman layer. Lately, it has been referred to more often as the mixed layer. The top of the mixed layer is often well delineated by a solid or broken cloud cover having a stable free atmosphere above, and below whiehturbulerrt motions are confined. 

Bidirectional rotation is employed and rapid acceleration/deceleration (in 1-2 s) is easily achieved at any rotation rate. The Ekman layer thickness, d, from earlier flux growth, should be <0.05 cm, which necessitates rotation rates >20rpm. Horizontal and vertical flow velocities, V and W, are for all rotation rates,... 

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