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Research Papers: Combustion and Reactive Flows

# A Numerical and Analytical Study of Thermally Driven Combustion Oscillations in a Perfectly Stirred Reactor

[+] Author and Article Information
Maria V. Petrova

Reaction Design, 6440 Lusk Boulevard, Suite D205, San Diego, CA 92121mpetrova@reactiondesign.com

Matthew McGarry1

Department of Engineering, University of San Diego, 5998 Alcala Park, Loma Hall, San Diego, CA 92110mmcgarry@sandiego.edu

Hai Wang

Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089haiw@usc.edu

1

Corresponding author.

J. Heat Transfer 130(7), 071201 (May 16, 2008) (8 pages) doi:10.1115/1.2897926 History: Received February 13, 2007; Revised October 17, 2007; Published May 16, 2008

## Abstract

The oscillatory behaviors of methane and hydrogen oxidation in a perfectly stirred reactor (PSR) are examined. The work explores the parameter spaces in which oscillatory combustion and ignition take place using heat transfer coefficient, mean residence time, and reactor wall temperatures as variables. An analytic model was developed using an eigenvalue analysis to determine the nature and stability of these oscillations. Both numerical and analytical studies suggest that combustion oscillations occur at the extinction turning point of the hysteresis curve or the boundary of combustion extinction. These oscillations are found to be driven by the coupling of the heat released from the reaction and the heat dissipation through the reactor wall, and these are unstable, which perhaps explains why they were never or rarely observed experimentally. In the case of hydrogen oxidation, we demonstrate the existence of two additional types of oscillations, namely, hybrid oscillation and oscillatory ignition, both of which occur at or near the turning point of ignition. These oscillations are stable and driven by detailed reaction kinetics. The numerical results for hydrogen oxidation were compared with previous experiments and found to be within $5K$ of the observed wall temperature where oscillations were observed.

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## Figures

Figure 1

Numerical characterization of PSR solution types in the parameter space of effective heat transfer coefficient versus residence time for methane in 11% O2–89%(N2+Ar) mixtures. The parameter space beneath each solid curve represents the condition where combustion is possible. The dashed lines indicate the conditions where combustion oscillations are observed. Argon was used to substitute N2 for ϕ=0.7 and 1.5 to achieve identical adiabatic flame temperature for the three equivalence ratios. Other conditions employed in the computation include V=100cm3, p=1atm, and Tin=Tw=300K.

Figure 2

Oscillatory solutions obtained from numerical simulation for the ϕ=1.5 mixture. The PSR conditions are identical to those in Fig. 1.

Figure 3

Variation of the steady-state burning and frozen temperature solutions as a function of reciprocal mass flow rate (ṁ−1) and mean residence time (τ), computed for the reaction of 2H2+O2 in a PSR (Tw=700K, χ=0.093cal∕Ks, and p=16Torr). The solid lines are obtained with inlet temperature Tin=300K, and dashed lines with Tin=500K. The plot identifies the sustained oscillatory combustion point (filled circle) and the oscillatory ignition region (shaded area). The frequency of oscillatory ignition is also shown as a function of mass flow rate or mean residence time. Values on the residence time axis are those of the steady burning solution and pseudoquenched state during oscillatory ignition.

Figure 4

Numerical characterization of PSR solution types in the parameter space of effective heat transfer coefficient versus mass flow rate, computed for the 2H2+O2 mixture. Reactive solutions are obtained below each dashed curves. The dashed lines indicate the conditions where combustion oscillations are observed. Oscillatory combustion occurs on the boundaries of frozen and reactive solutions. Other PSR conditions are inlet temperature Tin=300K, reactor pressure p=16Torr, and reactor volume V=550cm3.

Figure 5

Numerical characterization of solution types in the parameter space of reactor wall temperature versus mass flow rate, computed for the 2H2+O2 mixture. The mixture is reactive above each curve obtained for a specific value of effective heat transfer coefficient. Other conditions are the same as in Fig. 3.

Figure 6

Analytical solutions of dimensionless temperature (thick line) and trace (thin line) as functions of dimensionless residence time. The inset shows the variation of trace near the oscillatory point.

Figure 7

(a) Representative oscillatory solutions obtained for the 2H2+O2 mixture with mass flow rate m=1mg∕s and effective heat transfer coefficient χ=0.05cal∕sK. Other conditions are the same as in Fig. 3. (b) The temperature difference between the reactor and vessel wall temperature as a function of the vessel wall temperature (adapted from Baulch (3)).

Figure 8

Temperature excess (T−Tw) plotted as a function of wall temperature, computed for the reaction of 2H2+O2 in a PSR with mass flow rate ṁ=5mg∕s (top panel) and ṁ=0.5mg∕s (bottom panel), both with effective heat transfer coefficient χ=0.093cal∕sK. Other conditions are the same as in Fig. 3. In the bottom panel, points (h), (b), and (i) represent hybrid, Hopf bifurcation, and ignition oscillations, respectively.

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