# A 3D Numerical Study on Opposed Flow Flame-Spread over Thin Parallel Fuel Sheets of Finite Widths in Microgravity

01 Jan 2017-pp 551-558

TL;DR: In this article, a model of flame spread over an array of fuel sheets of finite width size has been modeled and numerically investigated for opposed, low convective flows in microgravity, and steady flame spread rates were observed for all separation distances up to the separation distance of flame extinction.

Abstract: Flame spread over an array of fuel sheets of finite width size has been modeled and numerically investigated for opposed, low convective flows in microgravity. As opposed to the previous studies based on 2D models, steady flame spread rates were observed for all separation distances up to the separation distance of flame extinction. The flame spread rate increased with decrease in separation distance up to a point where it was maximum, further reduction in separation distance, reduced the flame spread rate. The flammability map as a function of separation distance was also obtained for different fuel widths. While the extinction map qualitatively matches with the flammability map obtained from the 2D model, the flame extinguished at higher oxygen levels with the decrease in fuel width due to radiation heat losses.

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01 Jan 1980

TL;DR: In this article, the authors focus on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms.

Abstract: This book focuses on heat and mass transfer, fluid flow, chemical reaction, and other related processes that occur in engineering equipment, the natural environment, and living organisms. Using simple algebra and elementary calculus, the author develops numerical methods for predicting these processes mainly based on physical considerations. Through this approach, readers will develop a deeper understanding of the underlying physical aspects of heat transfer and fluid flow as well as improve their ability to analyze and interpret computed results.

21,638 citations

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TL;DR: In this paper, heat transfer and gas phase chemical kinetic aspects of the flame spread process are addressed separately for the spread of flames in oxidizing flows that oppose or concur with the direction of propagation.

Abstract: Recent advances in the experimental study of the mechanisms controlling the spread of flames over the surface of combustible solids are summarized in this work. The heat transfer and gas phase chemical kinetic aspects of the flame spread process are addressed separately for the spread of flames in oxidizing flows that oppose or concur with the direction of propagation. The realization that, in most practical situations, the spread of fire in opposed gas flows occurs at near extinction or non-propagating conditions is particularly significant. Under these circumstances, gas phase chemical kinetics plays a critical role and it must be considered if realistic descriptions of the flame spread process are attempted. In the concurrent mode of flame spread, heat transfer from the flame to the unburnt fuel appears to be the primary controlling mechanism. Although gas phase chemcial kinetics is unimportant in the flame spreading process, it is important in the establishment and extension of the diffusion ...

245 citations

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TL;DR: A critical, historical review of the flame spread literature is given in this article, beginning with the first systematic studies of opposed-flow flame spread, including qualitative, simplified, and comprehensive numerical modeling.

Abstract: A critical, historical review of the flame spread literature is given, beginning with the first systematic studies of opposed-flow flame spread. Important modeling effects are described, including qualitative, simplified, μg and comprehensive numerical modeling. A brief discussion of subjects with the potential for further development is also given. Although this review focuses on flame-spread theory the emphasis is on the logical development, not the detailed mathematics.

168 citations

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TL;DR: The Newton–Krylov methods are shown to provide a natural way to incorporate the effects of nonlinearity as well as strong coupling in a way that avoids operator splitting, and the resultant method has excellent convergence properties.

Abstract: The ability to solve the radiative transfer equation in a fast and accurate fashion is central to several important applications in combustion physics, controlled thermonuclear fusion and astrophysics. Most practitioners see the value of using discrete ordinates methods for such applications. However, previous efforts at designing discrete ordinates methods that are both fast and accurate have met with limited success. This is especially so when parts of the application satisfy the free streaming limit in which case most solution strategies become unacceptably diffusive or when parts of the application have high absorption or scattering opacities in which case most solution strategies converge poorly. Designing a single solution strategy that retains second-order accuracy and converges with optimal efficiency in the free streaming limit as well as the optically thick limit is a challenge. Recent results also indicate that schemes that are less than second-order accurate will not retrieve the radiation diffusion limit. In this paper we analyze several of the challenges involved in doing multidimensional numerical radiative transfer. It is realized that genuinely multidimensional discretizations of the radiative transfer equation that are second-order accurate exist. Because such discretizations are more faithful to the physics of the problem they help minimize the diffusion in the free streaming limit. Because they have a more compact stencil, they have superior convergence properties. The ability of the absorption and scattering terms to couple strongly to the advection terms is examined. Based on that we find that operator splitting of the scattering and advection terms damages the convergence in several situations. Newton–Krylov methods are shown to provide a natural way to incorporate the effects of nonlinearity as well as strong coupling in a way that avoids operator splitting. Used by themselves, Newton–Krylov methods converge slowly. However, when the Newton–Krylov methods are used as smoothers within a full approximation scheme multigrid method, the convergence is vastly improved. The combination of a genuinely multidimensional, nonlinearly positive scheme that uses Full Approximation Scheme multigrid in conjunction with the Newton–Krylov method is shown to result in a discrete ordinates method for radiative transfer that is highly accurate and converges very rapidly in all circumstances. Several convergence studies are carried out which show that the resultant method has excellent convergence properties. Moreover, this excellent convergence is retained in the free streaming limit as well as in the limit of high optical depth. The presence of strong scattering terms does not slow down the convergence rate for our method. In fact it is shown that without operator splitting, the presence of a strong scattering opacity enhances the convergence rate in quite the same way that the convergence is enhanced when a high absorption opacity is present! We show that the use of differentiable limiters results in substantial improvement in the convergence rate of the method. By carrying out an accuracy analysis on meshes with increasing resolution it is further shown that the accuracy that one obtains seems rather close to the designed second-order accuracy and does not depend on the specific choice of limiter. The methods for multidimensional radiative transfer that are presented here should improve the accuracy of several radiative transfer calculations while at the same time improving their convergence properties. Because the methods presented here are similar to those used for simulating neutron transport problems and problems involving rarefied gases, those fields should also see improvements in their numerical capabilities by assimilation of the methods presented here.

101 citations

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TL;DR: In this article, a flame spreading over a thermally thin cellulose fuel was studied in a quiescent microgravity environment, and two different extinction limits were found in microgravity for the two thicknesses of fuel.

Abstract: A flame spreading over a thermally thin cellulose fuel was studied in a quiescent microgravity environment. Flame spread over two different fuel thicknesses was studied in ambient oxygen-nitrogen environments from the limiting oxygen concentration to 100 percent oxygen at 1 atm pressure. Comparative normal-gravity tests were also conducted. Gravity was found to play an important role in the mechanism of flame spread. In lower oxygen environments, the buoyant flow induced in normal gravity was found to accelerate the flame spread rate as compared to the microgravity flame spread rates. It was also found to stabilize the flame in oxidizer environments, where microgravity flames in a quiescent environment extinguish. In oxygen-rich environments, however, it was determined that gravity does not play an important role in the flame spread mechanism. Fuel thickness influences the flame spread rate in both normal gravity and microgravity. The flame spread rate varies inversely with fuel thickness in both normal gravity and in an oxygen-rich microgravity environment. In lower oxygen microgravity environments, however, the inverse relationship breaks down because finite-rate kinetics and heat losses become important. Two different extinction limits were found in microgravity for the two thicknesses of fuel. This is in contrast to the normal-gravity extinction limit, which was found to be independent of fuel thickness. In microgravity the flame is quenched because of excessive thermal losses, whereas in normal gravity the flame is extinguished by blowoff.

41 citations

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