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This investigation evaluates the propagation of premixed flames in narrow channels with isothermal walls. The study is based on the numerical solution of the set of fully-compressible, reacting flow equations that includes viscosity, diffusion, thermal conduction and Arrhenius chemical kinetics. Specifically, channels and pipes with one extreme open and one extreme closed are considered such that a flame is sparked at the closed extreme and propagates towards the open one. The isothermal channel walls are kept at multiple constant temperatures in the range from Tw=300 K to 1200 K. The impact of these isothermal walls on the flame dynamics is studied for multiple radii of the channel (R) and for various thermal expansion ratios (Θ), which approximate the thermal behavior of different fuel mixtures in the system. The flame dynamics in isothermal channels is also compared to that with adiabatic walls, which were previously found to produce exponential flame acceleration at the initial stage of the burning process. The results show that the heat losses at the walls prevent strong acceleration and lead to much slower flame propagation in isothermal channels as compared to adiabatic ones. Four distinctive regimes of premixed burning in isothermal channels have been identified in the Θ−Tw−R space: (i) flame extinction; (ii) linear flame acceleration; (iii) steady or near-steady flame propagation; and (iv) flame oscillations. The physical processes in each of these regimes are discussed, and the corresponding regime diagrams are presented.
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Thermodynamic Relationships for Perfectly Elastic Solids Undergoing Steady-State Heat Flow
Available data on insulating, semiconducting, and metallic solids verify our new model that incorporates steady-state heat flow into a macroscopic, thermodynamic description of solids, with agreement being best for isotropic examples. Our model is based on: (1) mass and energy conservation; (2) Fourier’s law; (3) Stefan–Boltzmann’s law; and (4) rigidity, which is a large, yet heretofore neglected, energy reservoir with no counterpart in gases. To account for rigidity while neglecting dissipation, we consider the ideal, limiting case of a perfectly frictionless elastic solid (PFES) which does not generate heat from stress. Its equation-of-state is independent of the energetics, as in the historic model. We show that pressure-volume work (PdV) in a PFES arises from internal interatomic forces, which are linked to Young’s modulus (Ξ) and a constant (n) accounting for cation coordination. Steady-state conditions are adiabatic since heat content (Q) is constant. Because average temperature is also constant and the thermal gradient is fixed in space, conditions are simultaneously isothermal: Under these dual restrictions, thermal transport properties do not enter into our analysis. We find that adiabatic and isothermal bulk moduli (B) are equal. Moreover, Q/V depends on temperature only. Distinguishing deformation from volume changes elucidates how solids thermally expand. These findings lead to simple descriptions of the two specific heats in solids: ∂ln(cP)/∂P = −1/B; cP = nΞ times thermal expansivity divided by density; cP = cVnΞ/B. Implications of our validated formulae are briefly covered.
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- Award ID(s):
- 2122296
- PAR ID:
- 10322115
- Date Published:
- Journal Name:
- Materials
- Volume:
- 15
- Issue:
- 7
- ISSN:
- 1996-1944
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/ma15072638
