Sher Eran, Moshkovich-Makarenko Irena, Moshkovich Yahav, Cukurel Beni
Faculty of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa 3200003, Israel.
Entropy (Basel). 2020 Sep 10;22(9):1011. doi: 10.3390/e22091011.
While considering the deflagration regime, the thermal theory of combustion proposes that the mechanism of heat transfer from the flame exothermic zone to the front neighborhood reactants layer dominates the flame behavior. The introduction of the Fourier law allows a closed solution of the continuity and energy conservation equations to yield the burning velocity. It is, however, clear that this classical solution does not conform to the momentum equation. In the present work, instead of introducing the Fourier law, we suggest the introduction of a simplified version of the Onsager relationship, which accounts for the entropy increase due to the heat transfer process from the front layer to its successive layer. Solving for the burning velocity yields a closed solution that also definitely conforms to the momentum equation. While it is realized that the pressure difference across the flame front in the deflagration regime is very small, we believe that violating the momentum equation is intolerable. Quite a good fitting, similarly to the classic theory predictions, has been obtained between our predictions and some experimentally observed values for the propagation flame deflagration velocity, while here, the momentum equation is strictly conserved.
在考虑爆燃状态时，燃烧热理论提出，从火焰放热区到前沿附近反应物层的热传递机制主导着火焰行为。引入傅里叶定律可以得到连续性方程和能量守恒方程的封闭解，从而得出燃烧速度。然而，很明显，这个经典解并不符合动量方程。在本工作中，我们没有引入傅里叶定律，而是建议引入昂萨格关系的简化版本，该版本考虑了从前层到其后续层的热传递过程导致的熵增加。求解燃烧速度可得到一个封闭解，该解也肯定符合动量方程。虽然认识到在爆燃状态下火焰前沿的压力差非常小，但我们认为违反动量方程是不可容忍的。我们的预测与一些实验观测到的传播火焰爆燃速度值之间取得了与经典理论预测类似的良好拟合，而且在这里，动量方程得到了严格遵守。
