Effects of Buoyancy and Forcing on Transitioning and Turbulent - PDF document

Effects of Buoyancy and Forcing on Transitioning and Turbulent Circular Jet Flames Joseph W. Nichols, James J. Riley, Peter J. Schmid University of Washington Nov. 24, 2003 Supported by the NASA Microgravity Research Division

Outline • Numerical Method • Axisymmetric Simulations – Parametric study – 3D instabilities not captured • Fully 3D Simulations – Enhanced instability – Flow visualizations reveal 3D structure of instabilities • Linear Stability Analysis c � 2003 Joseph W. Nichols 1

Round Fuel Jet Outlet Collar Lateral x r θ d Inlet u 0 Figure 1: Computational Domain c � 2003 Joseph W. Nichols 2

Numerical Method • Compressible Navier-Stokes with Low Mach Number Approximation (McMurtry et al. ) • One step, Arrhenius-type reaction • Predictor-Corrector scheme (Najm et al. ) handles large density ratios • Staggered 6th order compact schemes • Centerline treated with asymptotic expansions (Constantinescu et al. ) c � 2003 Joseph W. Nichols 3

Axisymmetric Simulations u 0 Figure 2: Density contours, Fr = √ gd c � 2003 Joseph W. Nichols 4

Buoyancy Effects • Buoyancy produces instability • Disturbance source – Round-off – Outlet pressure fluctuations • Slightly buoyant and non-buoyant flames differ significantly (Bahadori et al. ) – Perturbation magnitudes – 3D instabilities c � 2003 Joseph W. Nichols 5

3D DNS: Normal gravity Figure 3: Temperature, Fr = 5 c � 2003 Joseph W. Nichols 6

3D DNS: Zero gravity Figure 4: Temperature, Fr = ∞ c � 2003 Joseph W. Nichols 7

Linear Stability Analysis • Guides an understanding of instabilities • Linearized low Mach number equations u x ( r ) , ¯ • Parallel mean flow ¯ T ( r ) • Primitive variable formulation • Spatially growing disturbances (1) ω ∈ R , α ∈ C c � 2003 Joseph W. Nichols 8

Eigenvalue Spectrum Figure 5: Spatial eigenvalues c � 2003 Joseph W. Nichols 9

Conclusions • Buoyancy greatly enhances instability in circular jet flames • Buoyant instabilities are highly three dimensional • Introducing buoyancy into the linear stability problem produces additional instability modes c � 2003 Joseph W. Nichols 10