^{1,a)}and Alessandro Gomez

^{1,b)}

### Abstract

Opposed-jet flows have been shown to provide a valuable means to study a variety of combustion problems, but have been limited to either laminar or modestly turbulent conditions. With the ultimate goal of developing a burner for laboratory flames reaching turbulence regimes of relevance to practical systems, we characterized highly turbulent, strained, isothermal, opposed-jet flows using particle image velocimetry (PIV). The bulk strain rate was kept at and specially designed and properly positioned turbulence generation plates in the incoming streams boosted the turbulence intensity to well above 20%, under conditions that are amenable to flame stabilization. The data were analyzed with proper orthogonal decomposition (POD) and a novel statistical analysis conditioned to the instantaneous position of the stagnation surface. Both POD and the conditional analysis were found to be valuable tools allowing for the separation of the truly turbulent fluctuations from potential artifacts introduced by relatively low-frequency, large-scale instabilities that would otherwise partly mask the turbulence. These instabilities cause the stagnation surface to wobble with both an axial oscillation and a precession motion about the system axis of symmetry. Once these artifacts are removed, the longitudinal integral length scales are found to decrease as one approaches the stagnation line, as a consequence of the strained flow field, with the corresponding outer scale turbulentReynolds number following a similar trend. The Taylor scale Reynolds number is found to be roughly constant throughout the flow field at about 200, with a value virtually independent of the data analysis technique. The novel conditional statistics allowed for the identification of highly convoluted stagnation lines and, in some cases, of strong three-dimensional effects, that can be screened, as they typically yield more than one stagnation line in the flow field. The ability to lock on the instantaneous stagnation line, at the intersection of the stagnation surface with the PIV measurement plane, is particularly useful in the combustion context, since the flame is aerodynamically stabilized in the vicinity of the stagnation surface. Estimates of the ratio of the mean residence time (inverse strain rate) to the vortex turnover time yield values greater than unity. The conditional mean velocity gradient suggests that, in contrast to the existing literature, the highest gradients are around the system centerline, which would result in a higher probability of flameextinction in that region under chemically reacting conditions. The compactness of the domain and the short mean residence time render the system well suited to direct numerical simulation, more so than conventional jet flames.

We are indebted to Dr. Kailasnath Purushothaman for technical discussions, to Mr. Bruno Coriton for technical discussions and for providing high-speed movies of the flow for our examination, and to Nick Bernardo for technical assistance in the construction of the hardware. The support of DARPA under Grant No. DAAD19-01-1-0664 (Dr. Richard J. Paur, Contract Monitor) is gratefully acknowledged.

I. INTRODUCTION

II. EXPERIMENTAL SETUP

III. RESULTS AND DISCUSSION

A. Nonconditional statistics

B. POD analysis

C. Stagnation line conditional statistics (SLCS)

1. Stagnation line tracking and critical pointanalysis

2. Conditional statistics coordinate system

D. Comparison among the three data processing

E. Relative merits of POD versus SLCS

IV. CONCLUSIONS

### Key Topics

- Turbulent flows
- 78.0
- Flames
- 27.0
- Flow instabilities
- 22.0
- Reynolds stress modeling
- 20.0
- Data analysis
- 15.0

## Figures

Schematic of the opposed-jet assembly.

Schematic of the opposed-jet assembly.

Phase plot of velocity components at different axial locations along the centerline. Triangles: ; circles: ; squares: . The reference location at corresponds to the mean stagnation plane and the negative sign indicates locations between the mean stagnation plane and the bottom nozzle. Case NN (a); case TN (b); case TB (c).

Phase plot of velocity components at different axial locations along the centerline. Triangles: ; circles: ; squares: . The reference location at corresponds to the mean stagnation plane and the negative sign indicates locations between the mean stagnation plane and the bottom nozzle. Case NN (a); case TN (b); case TB (c).

(a) Radial profiles of mean axial and radial velocity components (TB case) at different distances from the mean stagnation plane assumed as . Circles: ; squares: ; triangles: . (b) rms values along the burner centerline.

(a) Radial profiles of mean axial and radial velocity components (TB case) at different distances from the mean stagnation plane assumed as . Circles: ; squares: ; triangles: . (b) rms values along the burner centerline.

Percentage of the total turbulent kinetic energy vs POD mode (TB case).

Percentage of the total turbulent kinetic energy vs POD mode (TB case).

Vector representations of modes 1 (a) and 2 (b) for case TB. Snapshots of the vector field reconstructed with only modes 0 and 1 (c and d). Snapshots of the vector field reconstructed with only modes 0 and 2 (e and f). TB case. Vector fields are undersampled for readability.

Vector representations of modes 1 (a) and 2 (b) for case TB. Snapshots of the vector field reconstructed with only modes 0 and 1 (c and d). Snapshots of the vector field reconstructed with only modes 0 and 2 (e and f). TB case. Vector fields are undersampled for readability.

Phase plot of the POD coefficients, and , relative to mode 1 (abscissa) and mode 2 (ordinate), respectively. TB case.

Phase plot of the POD coefficients, and , relative to mode 1 (abscissa) and mode 2 (ordinate), respectively. TB case.

Snapshot of the velocity field, represented by the velocity vectors. Superimposed are the flow sectional streamlines originating from the top nozzle and from the bottom nozzle (thin lines). The thick gray line is stagnation line, the white circles are nodes/foci, and the black circles are stagnation points.

Snapshot of the velocity field, represented by the velocity vectors. Superimposed are the flow sectional streamlines originating from the top nozzle and from the bottom nozzle (thin lines). The thick gray line is stagnation line, the white circles are nodes/foci, and the black circles are stagnation points.

Instantaneous sectional streamlines superimposed to vector field in the presence of strong three-dimensional effects. Superimposed are the flow sectional streamlines originating from the top nozzle and from the bottom nozzle (thin lines). The thick gray line is stagnation line, the white circles are nodes/foci, and the black circles are stagnation points.

Instantaneous sectional streamlines superimposed to vector field in the presence of strong three-dimensional effects. Superimposed are the flow sectional streamlines originating from the top nozzle and from the bottom nozzle (thin lines). The thick gray line is stagnation line, the white circles are nodes/foci, and the black circles are stagnation points.

Histograms of the intercept of the stagnation line with the centerline for the three cases: NN, no plate (plain line), TN, plate in top burner (dashed line), and TB plate on both sides (dotted line).

Histograms of the intercept of the stagnation line with the centerline for the three cases: NN, no plate (plain line), TN, plate in top burner (dashed line), and TB plate on both sides (dotted line).

Coordinate system for conditional statistics showing (a) the mean stagnation streamline and its intersection with the instantaneous stagnation line and (b) three instantaneous realizations of the stagnation lines, some velocity vectors tangent to the stagnation line and their components along x and z, u and v, respectively.

Coordinate system for conditional statistics showing (a) the mean stagnation streamline and its intersection with the instantaneous stagnation line and (b) three instantaneous realizations of the stagnation lines, some velocity vectors tangent to the stagnation line and their components along x and z, u and v, respectively.

Comparison of the three data analyses. Axial (a) and radial (b) velocity fluctuations along the centerline (burner axis): nonconditional statistics (solid black), POD (dotted gray), and SLCS (dashed black).

Comparison of the three data analyses. Axial (a) and radial (b) velocity fluctuations along the centerline (burner axis): nonconditional statistics (solid black), POD (dotted gray), and SLCS (dashed black).

Comparison of the three data analyses for the radial profiles of axial and radial velocity fluctuations. [(a) and (b)] Radial profiles at different distances from the mean stagnation line assumed as . Circles: ; squares: ; triangles: . (a) Nonconditional statistics. (b) POD filtered statistics. (c) Conditional statistics (gray) vs nonconditional statistics (black) along the stagnation line. Circles: axial velocity fluctuation; triangles: radial velocity fluctuations.

Comparison of the three data analyses for the radial profiles of axial and radial velocity fluctuations. [(a) and (b)] Radial profiles at different distances from the mean stagnation line assumed as . Circles: ; squares: ; triangles: . (a) Nonconditional statistics. (b) POD filtered statistics. (c) Conditional statistics (gray) vs nonconditional statistics (black) along the stagnation line. Circles: axial velocity fluctuation; triangles: radial velocity fluctuations.

Comparison of the three data analyses for the axial profiles for the nonconditional (plain line), POD (dotted line), and conditional (dashed line) estimates of the longitudinal integral scale (a), transversal Taylor scale (b), integral scale based Reynolds number (c), and Taylor scale based Reynolds number (d).

Comparison of the three data analyses for the axial profiles for the nonconditional (plain line), POD (dotted line), and conditional (dashed line) estimates of the longitudinal integral scale (a), transversal Taylor scale (b), integral scale based Reynolds number (c), and Taylor scale based Reynolds number (d).

Profiles of axial and radial velocity gradients along the stagnation line. (a) Nonconditional statistics. (b) POD filtered statistics. (c) Conditional mean and rms velocity gradient.

Profiles of axial and radial velocity gradients along the stagnation line. (a) Nonconditional statistics. (b) POD filtered statistics. (c) Conditional mean and rms velocity gradient.

Profiles of axial and radial velocity gradients along the stagnation streamline. (a) Nonconditional statistics. (b) POD filtered statistics. (c) Conditional mean and rms velocity gradient.

Profiles of axial and radial velocity gradients along the stagnation streamline. (a) Nonconditional statistics. (b) POD filtered statistics. (c) Conditional mean and rms velocity gradient.

Coordinate system for local conditional statistics. (a) One instantaneous realization of the stagnation line, two stagnation points, the stagnation point local sectional streamlines, and vortex. (b) Local stagnation line, local stagnation streamline, the stagnation point local sectional streamlines (thin lines), stagnation point (black circle), local coordinate system (s,n), and respective direction vectors (black).

Coordinate system for local conditional statistics. (a) One instantaneous realization of the stagnation line, two stagnation points, the stagnation point local sectional streamlines, and vortex. (b) Local stagnation line, local stagnation streamline, the stagnation point local sectional streamlines (thin lines), stagnation point (black circle), local coordinate system (s,n), and respective direction vectors (black).

Axial and radial velocity rms profiles along the local instantaneous stagnation line (a) and local instantaneous stagnation streamline (b).

Axial and radial velocity rms profiles along the local instantaneous stagnation line (a) and local instantaneous stagnation streamline (b).

Velocity gradients along the local instantaneous stagnation line (a) and local instantaneous stagnation streamline (b).

Velocity gradients along the local instantaneous stagnation line (a) and local instantaneous stagnation streamline (b).

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