Streakline

For massless particles, only a postprocessing of the result field is needed, where so-called streaklines that follow the given vector field are calculated. If the particles have a certain mass, additional equations have to be solved. 

Fig. 5. Mixing in the partitioned pipe mixer, (a) Schematic view of the mixer geometry one element of the mixer is shown, and the mixer comprises several such elements joined together, (b) KAM surfaces in flow bounding regions of regular flow, (c) A and B show examples of experimentally obtained streaklines undeformed streaklines pass through KAM tubes, whereas streaklines in the chaotic region are well mixed. The white arrows indicate the location of a companion streak-tube. (Khakhar, Franjione, and Ottino, 1987 Kusch and Ottino, 1992).

Consider a flow visualization study in which a small patch of dye is injected instantaneously into the flowing fluid. This will tag an element of the fluid and, by following the course of the dye, the path of the tagged element of fluid is observed. If, however, the dye is introduced continuously, a streakline will be observed. A streakline is the locus of all particles that have passed through a specified fixed point, namely the point at which the dye is injected. 

Although in general, particle paths, streaklines and streamlines are different, they are all the same for steady flow. As flow visualization experiments provide either the particle path or the streakline through the point of dye injection, interpretation is easy for steady flow but requires caution with unsteady flow. 

Figure 2.14 Experimental visualization of the unstable manifold in an open flow as the streakline pattern produced by dye injected in the wake of a cylinder (Sommerer et al., 1996).

To assess the effectiveness of the controllers designed, several visualization techniques are employed. First, massless dye particles are injected in the flow their motion traces the streaklines of the flow. Second, heavier particles simulating droplets in combustion applications are injected in the flow, and their motion is followed. Third, the distribution of a passive scalar is calculated to analyze diffusive mixing. 

Figure 9.5 Streakline plots of mixing controllers with different parameters (a) downstream sensor at x = 5 (b) downstream sensor at x = 10 (c) jet exit sensor with delay = 200 and (d) jet exit sensor with delay = 500.

Figure 9.6 The dispersion of particles with different Stokes numbers streaklines (6) St = 0.1 (c) St = 1 and (d) St = 10.

Fig. 18.32 Streaklines coloured by velocity of gas flow past a sphere in the region of low Reynolds numbers...

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