Recirculating wake zone

The recirculating wake zone is of particular importance for dispersion prediction. The dispersing species can become trapped in the wake region, remaining present at elevated concentrations well after a puff might be expected to have passed. 

FIGURE 4.54 Recirculation zone and flame-spreading region for a fully developed turbulent wake behind a bluff body (after Williams [57]). 

Considering the wake of a flame holder as a stirred reactor may be inconsistent with experimental data. It has been shown [66] that as blowoff is approached, the temperature of the recirculating gases remains essentially constant furthermore, their composition is practically all products. Both of these observations are contrary to what is expected from stirred reactor theory. Conceivably, the primary zone of a gas turbine combustor might approach a state that could be considered completely stirred. Nevertheless, as will be shown, all three theories give essentially the same correlation. 

Zukoski and Marble [70, 71] held that the wake of a flame holder establishes a critical ignition time. Their experiments, as indicated earlier, established that the length of the recirculating zone was determined by the characteristic dimension of the stabilizer. At the blowoff condition, they assumed that the free-stream combustible mixture flowing past the stabilizer had a contact time equal to the ignition time associated with the mixture that is, rw = ri( where rw is the flow contact time with the wake and r, is the ignition time. Since the flow contact time is given by... 

Theoretical studies are primarily concentrated on the treatment of flame blow-off phenomenon and the prediction of flame spreading rates. Dunskii [12] is apparently the first to put forward the phenomenological theory of flame stabilization. The theory is based on the characteristic residence and combustion times in adjoining elementary volumes of fresh mixture and combustion products in the recirculation zone. It was shown in [13] that the criteria of [1, 2, 5] reduce to Dunskii s criterion. Longwell et al. [14] suggested the theory of bluff-body stabilized flames assuming that the recirculation zone in the wake of the baffle is so intensely mixed that it becomes homogeneous. The combustion is described by a second-order rate equation for the reaction of fuel and air. 

So far, the flow patterns around bluff bodies in combustible flows are not understood completely. However, a recirculation zone in the immediate wake of the stabilizer which takes the form of a pair of eddies, similar to isothermal flows, is known to exist. The length Lrz of the recirculation zone differs for 2D and axisymmetric bluff bodies. For 2D bodies (V-gutters, rods, prisms), the measured values of Trz/H range from 3 to 6 depending on the operating conditions of combustor [11], which is considerably larger than for isothermal flows, where Lrz/H 2 [11]. For axisymmetric bluff bodies (discs, cones, cylinders), at low-blockage ratio Lrz/H 2 [32], which is similar to isothermal flows [32, 33], or Lrz/H 2.b-A [34], or even Lrz/H 10-11 [35]. 

Limitations on temperatures of solid materials often cause the methods of stabilization by solid elements, discussed so far, to be impractical. In most applications of stabilization by solid elements the flame is attached in the wake behind the element, so that the solid is not fully exposed to the flame temperature. Representative examples are bluff-body flame stabilizers, such as the stabilizing rods or plates placed normal to the flow in ramjets and afterburners, which were mentioned in Sections 5.1.1 and 10.3.5. A distinctive feature of bluff-body flame stabilization is the presence of a recirculation zone behind the body. Unlike the alternate vortices shed from bluff bodies in cold flow over the Reynolds-number range of practical interest, a well-defined vortex, steady in the mean, is observed to exist just downstream from the stabilizer when combustion occurs. This is a toroidal vortex for an axisymmetric stabilizer or a pair of identical counterrotating line vortices for rodlike stabilizers. The reason for the drastic change in the... 

A characteristic transverse dimension d of the flame holder can be measured more easily than the length / of the recirculation zone. The ratio l/d experimentally has a practically constant value between 5 and 10, independent of flow conditions for hot turbulent wakes. Hence, I d in equation (65), so that d. Of greater interest than the dependence... 

Air from the compressor enters the mixing chamber of the atomizer at sonic velocity and, after interaction with the liquid kerosene stream, emerges as a two-phase mixture, directed vertically upwards. The air flow from the annular stream forms a recirculation zone in the wake of the stabilizer disk. The flame is ignited by an external gas stream and subsequently bums independently as a flame in the open atmosphere. Droplets are initially confined to the air jet from the atomizer nozzle, but some of the finer droplets are taken up by the reverse flow of the stabilizer disk recirculation zone. Previous studies on spray combustion and details of atomizer design are reviewed by Chigier (J). 

Reverse flow measurements in the wake of a stabilizer disk show increases in size and magnitude of the maximum reverse flow velocities within the recirculation zone as a result of combustion. Evidence was found of initial pilot burning in the recirculation zone from combustion of flne droplets transported by the reverse flow. 

Figure 6.5 Top view of canopy. Circles represent cylindrical stems of diameter d. Behind each stem is a recirculation zone (black) of length yd, where y is an 0(1) function Re. The wake downstream of each recirculation zone has length (Co ) 1 (light gray). Where wakes overlap (dark gray), the velocity deficit is the linear sum of individual wake deficits. Particles 1, 2, 3 released together at x = 0 and t = 0 pass through different velocity zones and travel different longitudinal distances (x1,x2,x3) in time, t, such that the spatial variance in the velocity field produces longitudinal dispersion.

Next, consider the wakes downstream of the recirculation zone. White and Nepf [643]derived the following expression for the velocity deficit, uw, in the wake of a cylinder (stem) located at x = 0 and y = 0 within an array of cylinders,... 

Note that the dispersion terms described in equation (6.18) are valid only in the limit of Fickian behavior. From the central limit theorem, this regime is reached when every particle has amply sampled each region (wakes, gaps, recirculation zones). The average time-scale to advect through a wake is (a(u)Yl, and the average time-scale to experience trapping within a recirculation zone is r/ (yad). Then, the Fickian limit is reached at time t r/ (yad) and (fl(M 1. 

Figure 6.6 Measured longitudinal dispersion normalized by velocity and stem diameter, (b) Comparison of observed (dots) and predicted (lines) dispersion for Re,/ = 100. Contribution by the recirculation zones (gray solid line), the wake shear (gray dashed line), and the gaps (black dashed line) and the total dispersion (black solid line) based on equation 6.18 with Co = 1.8, vT = 0.03 cm2s l, t = 7.5 s. These parameters were based on experimental and literature values and were not adjusted to fit the data. From White and Nepf [643]. Reprinted with permission from Cambridge University Press.

The observed longitudinal dispersion will also be influence by stem-wake dispersion. However, for ad < 0.1 (as is the case here), the recirculation zone and gap dispersion will be negligible (White and Nepf 2003 [643]). Further, the stem-wake dispersion can reach Fickian behavior at t > (a(/7 ) 1, or x > a x (see discussion above). For the canopy studied this requires x > 8 cm. Because all measurements were taken more than 50 cm downstream, stem-wake dispersion may be represented by the term shown in (6.18). Additionally using equation (6.8) to replace the velocity ratio in equation (6.27), the total longitudinal dispersion coefficient is,... 

Available experimental results on temperature distribution in plugged SA were analyzed to determine the main characteristics of velocity and temperature profiles of singlephase flow, namely recirculation zone length, coolant flow distribution in SA, coolant temperature rise in the wake, etc. At the same time, it is clear that data currently available provide only rough estimations of SA thermohydraulic characteristics in case of blockage as a function of Reynolds number and blocked flow area. 

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