Generalized Stability Criteria for an Opposed-Jet Flameholder

A characteristic time model of flame stabilization has been developed for an opposed-jet combustor. The model indicates a linear relationship between dynamic and chemical processes over a range of blowoff data. The corresponding Damkohler similarity group is on the order of unity. The simplified model also provides a useful phenomenological description of the opposed reacting jet and a practical method of estimating stability limits for an aerodynamic flameholder.


Introduction
P REDICTIVE models that address flame stability, exhaust emissions, and heat release behavior are a useful tool for the design of continuous combustion devices. Although quantitative predictions of turbulent, backmixed combustion have been limited by uncertainties about the fundamental combustion processes, the recent. advent of characteristic time modeling 1 has enabled reliable estimates of combustor performance to be made. The technique relies on the specification of the duration of relevant combustion processes. A comparison of controlling events has been shown to correlate blowoff limits 2 and emissions3 for bluff-bodystabilized combustors.
The present study explores the applicability of the modeling procedure for aerodynamic flameholders. The particular combustor configuration considered employs an opposed-jet flameholder 4 as shown in Fig. 1. The flowfield consists of a turbulent pipe flow of premixed reactants c.onfronted by a small (mj/mnr~l) jet injected at a high velocity along the centerline and in a direction opposite to the main stream. A highly turbulent recirculation zone that anchors the flame is generated along the periphery of the jet. The size and shape of the recirculation zone can be varied by altering the relative · velocity of the main and jet streams. The key feature that distinguishes the opposed-jet from bluff-body flameholders is the influence of the jet composition on flame stability. The combustor operating range can be extended to very lean or rich main stream conditions by using a rich or lean jet respectively. s ' The purpose of this work is to construct a characteristic time model describing the opposed-jet flowfield. The model is then used to determine blowoff conditions in a laboratory opposed-jet combustor. The results are also examined with the aim of clarifying the mechanism of flame stabilization by an opposing jet .

Model Formulation
In an early effort to explain the flameholding characteristics of the opposed jet, Schaffer and CambeJS introduced the concept of a "critical zone" which occupies a small volume at the nose of the flame and determines the overall stability. The strong influence of the jet properties on flame stability suggested that the region contains a homogeneous mixture of the jet and main streams and some recirculated combustion products. Subsequent analyses by Noreen and Martin 6 and Bellamy et al. 7 modeled the critical zone as a well-stirred reactor and used a reactor loading parameter to predict blowoff.
In the present analysis we also assume that the predominant flameholding processes operate in the vicinity of the recirculation zone. The requirement for flame stabilization is that the residence time of the reactants exceeds the mixture ignition time. Our primary task is to evaluate the time scale associated with the governing fluid dynamic and chemical processes. Various simplifying assumptions and empirical relationships for evaluating combustor properties are adopted whenever appropriate to generalize the model and to facilitate the analysis.
The results of Zukoski. and Marble 8 suggest that the fluid dynamic time corresponds to the period for the unburned reactants to travel past the recirculation zone. This period is quantified by assuming it is directly proportional t.o a geometric dimension and inversely proportional to a convective velocity. For small-scale turbulence, the length of the recirculation zone, which is proportional to the jet penetration into the main stream, is the appropriate characteristic dimension. 9 The convective velocity is simply the velocity of the bulk flow past the recirculation zone.
It has recently been shown 1 0 that the upstream penetration of a round turbulent jet into a counterflowing turbulent pipe flow is a function of the momentum flux ratio, Z, of the incoming jet and the main stream. For the high jet momentum regime the penetration distance, xP, is given byw where Z=pj U?df!p,,,U~1 d;n evaluated at. the inlet conditions. The annular flow velocity is approximated by the average main stream velocity adjusted for density changes due to combustion. The chemical reaction Lime coincides with the igni tion phase of the combustion process and depends direclly on the mixture composition. Specification of the properties in t:ie critical flame stabilization zone is thus a prerequisite to determining the time scale. The equivalence ratio is fixed by the relative mass contribution (1;1 1 11n,.) of the jet and main stream tO the critical zone. H ere we adopt a slightly modified form of 1n 1 1m,,, =f(Z) · and calculate the critical zone equivalence ratio,</>,., using the following expression 7 : The critical temperaLUre, T,., co111rolling the reaction rate is determined by substituting the adiabatic flame temperaLUrc, r.d<<Pc>, into the following expression9: (3) which has been fou nd incidemall y to depict the bulk gas temperature in the opposed jet. Following Plee and Mellor, 2 the proportionality between Lhe chemical time, Tcr • and a reciprocal reaction rate evaluated at T,. is expressed as (4) The preexponentia l factor (Tel T 111 ) accounts for the acceleration of the bulk flow due to 0 rising temperatures and segregates the dynamics and chemical processes.

Results and Discussion
The cha racteristic time model of flame stabilization is tested by comparison 10 lean blowoff data obtained from a bench-scale, propane-fired, opposed-jct com bust or. The with the temperature in K. The correspondence between t he characteristic fluid dynamic time and the chemical reacti on time for the experimental blowoff data is presen1 ed in Fig. 3.
The results indicate a linear correlation of the lean blowoff data from an opposed-jet combustor. Deviations at elevated jet momentum and equivalence ratios are attributed to extrapolating the empirical elements of the model or to im-pre~is~ measurements of q, 1 and <1> 111 • An error in sto1ch1omctry, for example, can be exaggerated over five times in the calculated reaction time. The results of the present simplified a nalysis of a complex reacting, recirculating flowfi eld based on elementary combustion theor y and information available in the literature generally display a good representa1ion of the governing physical and chemical processes in the opposed-jet flamcholder.
lt is noted that little effort was expended toward obtaining the best fit as the goa l was to demonstrate the applicability of the model for the opposed-jct combustor. Improved results could be obtai ned by optimizing the choice of activation energy for the fuel of interest and by determining the effect of heat release on the characteristic length scale. A correction for the freestream acceleration past the obstr ucting jet would further reduce the discrepancies. Finally, a larger data set that excludes ambiguous jet inlet conditions found in earlier work would also improve the cor relation .

Conclusions
A characteristic time model of flame stabilization ha s been developed for an opposed-jet combustor. T he model indicates a linear relationship between dynamic and chemical processes over a range of blowoff data. T he corresponding Damkohler similarity group is on the order of unity. The simpljfied model also provides a useful phenomenological description of the opposed reacting jet and a practical method of estimating stability limits for an aerodynamic nameholder. (TWECS). The results indicate that the confined vortex in the tower of TWECS rotates approximately as a solid body and only supplements total power production, most of which comes from the tower acting as a bluff body. This raises ques tions about the validity of major assumptions that have served as foundations of TWECS theory since ics beginning.

Experimental Facility
T he 1.2-m-high lexan model , which incorporates the basic features of past theoretical and experimental TWECS, as described in the literature, 1 • 3 is shown in Fig. I during flow vis ua lization in the New York University Environmental Wind Tunnel. T he louvers of the tower create a confined vortex from the ambient flow emering the tower. Smoke released horizontally into the bottom inlet region is drawn by a pressure gradient upwards through the duct a nd then vertically th rough the tower and out the tower exit int.o the ambient flow.
F low velocity measurements were made using 0.3-cm-diam pitot tubes positioned from below or through the leeward side of the tower. Flow visualization using tufts on the pitoc tubes allowed them to be secured parallel to the flow at any position. Calibration of the pitot tubes' angular sensitivity ensured that this met hod was sufficiently accurate to elucidate the general structure of the vortex.
Power was measu red with a calibrated turbinedynamometer located in the duct and instrumented to produce simultaneous torque (Q) and angular velocity (w) data. The torque was varied to find the maximum power dissipation (Qw) peak by the t urbine.
Velocity Distribution Inside TWECS Figure 2 is a map of the vortex translational velocity ( v. ) within the tower at the level of the duct exit, composed from measurements at distances of 12.7, 15.2, 17.8, 20.3, and 22.9 cm from the axis a long 12 equally spaced radii. At chis level, V 11 is virtually horizontal. Higher in the tower, Vv has a slight vertical component , which is of greatest value just inside the louvers, and which was compensated by a decrease in the horizontal component value from the continuity equation.
Significantly, throughout the tower, the vortex has a velocity distribution most similar to solid-body rotation, m which, if r is t he distance from the vortex center, V v oc r.
fig. I T W ECS .durin g flow visualization. JI 00 is from the left and is 5.9 m/ s.