Hydrodynamic vortex

The slow decay of the velocity autocorrelation function towards zero can be explained in terms of the of a hydrodynamic vortex. (Figure adapted from Alder B J and T E Wainwright 1970. Decay of the Velocity tation Function. Physical Review A 1 18-21.)... 

A description of the DAL combining the rear stagnant cap and the hydrodynamic vortexes in its neighborhood appears to be necessary, which is a logical conclusion of a large series of investigations described in Chapter 8. It becomes especially vital in coimection with the problem of intensification of microflotation and in particular in two-stage microflotation. 

The only difference is in the characteristic relaxation time for a hydrodynamic vortex ... 

Under low-frequency excitation, the flame front is wrinkled by velocity modulations (Fig. 5.2.5). The number of undulations is directly linked to frequency. This is true as far as the frequency remains low (in this experiment, between 30 and 400 Hz). The flame deformation is created by hydrodynamic perturbations initiated at the base of the flame and convected along the front. When the velocity modulation amplitude is low, the undulations are sinusoidal and weakly damped as they proceed to the top of the flame. When the modulation amplitude is augmented, a toroidal vortex is generated at the burner outlet and the flame front rolls over the vortex near the burner base. Consumption is fast enough to suppress further winding by the structure as it is convected away from the outlet. This yields a cusp formed toward burnt gases. This process requires some duration and it is obtained when the flame extends over a sufficient axial distance. If the acoustic modulation level remain low (typically v /v < 20%),... 

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

Reactors which generate vortex flows (VFs) are common in both planktonic cellular and biofilm reactor applications due to the mixing provided by the VF. The generation of Taylor vortices in Couette cells has been studied by MRM to characterize the dynamics of hydrodynamic instabilities [56], The presence of the coherent flow structures renders the mass transfer coefficient approaches of limited utility, as in the biofilm capillary reactor, due to the inability to incorporate microscale details of the advection field into the mass transfer coefficient model. 

When an interfacial film has reduced the circulation within a drop, the wake vortex becomes more marked, while the extraction rate falls to that for a stagnant sphere (74) More detailed studies of the hydrodynamics of naturally moving drops have recently been carried out (75). The mass-transfer rate in 2-component systems should correlate 76) with... 

Fig. 2. Hydrodynamic model of flow for flame propagation in a channel (Region 1—potential flow of cold gas, region 2—vortex flow of hot products, region 3—-stagnation zone, region 4— wall).

Starting from the flame front the intensity of the vortices remains constant along each streamline, so that the region filled by combustion products is a rotational one. In some of the previous works mentioned, however, the existence of the stagnation zone behind the flame front has not been accounted for, so that the quantitative conclusions diflier essentially from those of the hydrodynamic model presently under consideration. It should be noted that the boundary streamline of the stagnation zone is a tangential velocity component discontinuity surface or a vortex sheet. As a consequence of the... 

In this form there is a close correspondence with the equations of hydrodynamics, or vortex-free flow of a fluid under the influence of conservative forces. Equation (12) resembles a hydrodynamic continuity equation if a2 is considered to be a density and if the stream velocity v = V(j). As V x v = 0,... 

Like any shear flow, reacting flows are submitted to hydrodynamic modes [273 297] and to vortex formation. 

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