Zones stagnation

Dead or stagnation zones with that flat plate dies should be avoided... 

On comparing the two flames, it is evident that the flow structure of the lean limit methane flame fundamentally differs from that of the limit propane one. In the flame coordinate system, the velocity field shows a stagnation zone in the central region of the methane flame bubble, just behind the flame front. In this region, the combustion products move upward with the flame and are not replaced by the new ones produced in the reaction zone. For methane, at the lean limit an accumulation of particle image velocimetry (PIV) seeding particles can be seen within the stagnation core, in... 

PIV velocity measurements made it possible to evaluate the flame temperature field [23], following the method demonstrated in Ref. [25]. The calculated thermal structure of lean limit methane flame is shown in Figure 3.1.7. The differences between the structures of lean limit methane and propane flames are fundamental. The most striking phenomenon seen from Figure 3.1.7 is the low temperature in the stagnation zone (the calculated temperatures near the tube axis seem unrealistically low, probably due to very low gas velocities in the stagnation core). 

High shear forces and stagnation zones should be avoided when processing biodegradable polyesters such as starch compounds because they are sensitive to thermal degradation [12]. 

The photograph taken from the paper of Uberoi (1959) and presented in Fig. 1 shows the shape of the flame front propagating in a plane channel. It shows stagnation zones near the channel walls where the gas rests with respect to the flame front. The stagnation zones are caused by the refraction of stream lines at the extreme points of the flame front. 

Fig. 1. Photograph of flow field and flame front shape from the work by Uberoi (1959). Flame is propagating downward in a vertical tube small particles added to the gaseous mixture indicate streamlines before and behind flame front. One can see stagnation zone close to tube wall.

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... 

Consider the condition, which determines the velocity of the curved flame front propagation in the channel. Inside the stagnation zone filled by combustion products the pressure is constant and is equal to the value at infinity (when x = oo). Because of Bernoulli s integral along the streamline restricting the stagnation zone, the gas motion velocity remains unchanged. Since at x = oo the flow is plane-parallel (ptJO = const, v — 0), distributions of velocity u and of the stream function are associated with the vorticity distribution ... 

Results of numerical integration of Eq. (29) are represented in Fig. 5. For ordinary flames a 0.1-0.2 the flame propagation velocity along the channel is greater than the normal flame velocity by a factor of 1.25-1.40. The stagnation zone in the combustion products occupies about a quarter of the channel cross section. 

A similar procedure can be applied with the negative weight of harmonic added. In this case a critical value emin corresponds to the minimum of the propagation velocity when the jet thickness at x = oo tends to zero, and the stagnation zone occupies the whole channel cross section. One may suggest... 

Fig. 13. Flow field before the flame front in the laboratory coordinate system. (Region 1—potential flow, region 2—vortex flow, region 3—stagnation zone, region 4—channel wall).

The integral Eq. (59) together with the surface shape Eq. (56) would determine the flame propagation velocity along the tube axis as a function of the normal flame velocity and the density ratio a. The width of the stagnation zone could be derived by integration... 

The performed numerical calculations for the case of cylindrical symmetry yielded the same qualitative dependence of the flame surface shape, the propagation velocity, and thickness of the stagnation zone, as iu the case of the plane channel. The quantitative results for the cylindrical tube are somewhat different, e.g., the dimensionless propagation velocity along the tube axis at a real a proves to be 50 percent higher than in the case of plane symmetry. 

A possible design of an extruder for reactive processing is shown in Fig. 4.34.240 Two screws are installed on the same axis inside a common barrel 1 but they have independent drives. This design eliminates stagnation zones, where the extruder is obstructed by the polymeric product. Independent drives for both screws permits the choice of optimal rotation speeds, i. e., to synchronize the polymerization rate with the residence times of the reactive mass in both stages of the process. 

The holes act as sources and sinks for fluid motion [23], They draw the dye from in the surrounding region and expel it in a jet-like action into other parts of the liquid. These jet-like structures are mainly responsible for mixing. Where flow symmetries delineated by the formation of internal stagnation zones exist, mixing is retarded. Best mixing results are obtained for the five-bubble arrangement. 

The stock is pumped through a manifold into the headbox of the paper machine, where the stock flow is decelerated and distributed over the width of the machine. Various baffles and step diffusors are used to avoid vortex flow and stagnation zones. The furnish leaves the headbox through the slice, a narrow gap with controlled profile, and impacts on one or two endless screens, the so-called papermakers wire. Water is removed from the fiber mat by the action of foils and vacuum. 

Effect of Hydraulic Barriers in the Through-Flow and Stagnation Zones... 

Conventional membrane surfaces arc cither flat (as a foil, plate or square channel) or regularly curved (as in a tube or circular channel). Potentially there may be stagnation zones in which carbonaceous materials arc deposited. Moreover, not every site on the membrane surface participates in the catalytic reaction. 

The analysis of the flow picture obtained allows us to distinguish several structural elements of the flow, i.e. initial region, main region, and a possible stagnation zone, all being represented in Figure 3.8. 

Figure 3.8 General structure of the boundary layer (BL) over an easily penetrable roughness 1 - core of the initial region with BLs 2 and 3 4 - external BL 5 and 6 - main and transition regions and 7 - possible stagnation zone.

The uniquenessambient(external) flow of the curve = (ji) is broken at the beginning of the initial region or at the distance where a possible stagnation zone starts. 

A stagnation zone within the droplet EPR can also appear in the main region, i.e. a zone near the wall with no longitudinal motion. It would be of significant practical interest for the spraying cooler theory. Self-similarity (3.42) of the external boundary layer has also been confirmed in terms of the variables used in Section 3.1.4. 

The thermal stagnation zone can happen in the lower part of the droplet layer, over which t(z) has almost reached its possible limit, and so there is no cooling of droplets over the lower part of their trajectories. This means that the density of droplets is too high, and the efficiency of the cooling system can be improved by arranging the spraying nozzles to reach a lesser density of droplets. 

The flow with heat and mass exchanges acting simultaneously is naturally expected to have the same structure, i.e. the initial and main regions and the stagnation zone. It is so possible to find approximate solutions for them by reducing the problem to one-dimensional models. 

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