Flow entrance into a duct with short EPR inserts

6 Flow entrance into a duct with short EPR inserts 

Finite-length porous inserts into a duct are of a special practical importance, Fig. 3.15. The vortical motion can or cannot appear behind the inserts depending on its height h, its length Lh, and the density A. Engineers get thus a means to control the flow. The special case A = oo can be treated as the well-known problem backward facing step . The flow under consideration is so a generalization of the well-known problem. 

No simplification can be used for the problem of the backward facing penetrable step but the full Navier—Stokes equations. Therefore, no solution is available to validate the numerical algorithm. To be aware of it, the numerical algorithm shortly described in the previous section was tested over the whole range of the above-mentioned problems. In this case, the outlet boundary condition (3 = which is associated with the steady flow in an infinite duct, was used. The results of two numerical performances for the flow regime Re = 100 and EPR dimensions h = 0.3 and L x = 1, are shown in Fig. 3.16 the halves of flows in each case are symmetric. Let us analyze them. 

If A = 0, one gets the known problem of the flow entering a duct with smooth walls. This flow is known to gradually change from a uniform velocity distribution to a parabolic profile known for the Poiseuille flow at the entrance region outlet x Lx. No vortices appear in the flow. 

No circulation was found even for penetrable steps with the density A 9. However, yet for A = 10, a short circulation zone begins to appear behind the step (the bottom half of the Fig. 3.16). This circulation grows with the EPR density A. It becomes as large as shown in Fig. 3.16, the upper part for A = 100. There is the extended circulation zone in this case, and the intensity of the recirculation has also been increased by an order of magnitude. 

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