论文标题
恒定速度的球形幻灯片建模
Modelling of a spherical deflagration at constant speed
论文作者
论文摘要
我们在本文中构建了一个数值解决方案程序，以计算从点源以恒定膨胀速度扩展的球形火焰引起的流动，并具有瞬时化学反应。该溶液应该是自相似的，并且流动在三个区域中分裂：一个内部区域，该区域由静止气体组成，该区域是静止区，一个中间区域，该区域是规则的，最初的气氛由静止的新鲜气体组成。中间区域由反应性冲击（内侧）和所谓的前体休克（外侧）界定，为此写下了兰宁 - 霍尼奥特条件。该区域中的解决方案由两个普通微分方程来控制，这些方程是通过数值求解的。我们表明，对于任何可接受的前体冲击速度，将这种数值分辨率与跳跃条件的开发相结合的结构是独特的，并且在中间区域中的压力，密度和速度剖面降低。此外，反应性休克速度大于冲击外侧的速度，这与这两个量的差异是所谓的火焰速度，即化学反应在新鲜气体中进行的（相对）速度的（相对）速度。最后，我们还从数值上观察到，给出火焰速度作为前体冲击速度的函数正在增加。这允许将分辨率嵌入类似牛顿的过程中，以计算给定火焰速度的流量（而不是给定的前体冲击速度）。所得的数值算法应用于化学计量氢空气混合物。关键词。球形火焰，反应式Euler方程，Riemann问题燃烧区域（恒定状态）中间区（常规溶液）未燃烧区（恒定初始状态）W B W 2 W 1 W 1 W 0反应性冲击，R = $σ$ r t。前体冲击，r = $σ$ p t。 w =（$ρ$，u，p）：局部流体状态。图1.1。解决方案的结构。 1。问题位置。我们在初始恒定组成的反应性无限大气中解决了火焰传播。该点火原本应该在一个点（被选为r 3的起源）发生，并且该流量应该满足球形对称属性：密度$ρ$，压力p，内部能量E和熵S仅取决于距离r的距离r与原点和速度读取u = ur/r，r = ur/r，r reve in r in r s in r sane r sane r sane r sane r sane r spector vector vector vector。火焰应该是无限薄的，并以恒定的速度移动。该流程受Euler方程的约束，我们寻求具有以下结构的解决方案：
We build in this paper a numerical solution procedure to compute the flow induced by a spherical flame expanding from a point source at a constant expansion velocity, with an instantaneous chemical reaction. The solution is supposed to be self-similar and the flow is split in three zones: an inner zone composed of burnt gases at rest, an intermediate zone where the solution is regular and the initial atmosphere composed of fresh gases at rest. The intermediate zone is bounded by the reactive shock (inner side) and the so-called precursor shock (outer side), for which Rankine-Hugoniot conditions are written; the solution in this zone is governed by two ordinary differential equations which are solved numerically. We show that, for any admissible precursor shock speed, the construction combining this numerical resolution with the exploitation of jump conditions is unique, and yields decreasing pressure, density and velocity profiles in the intermediate zone. In addition, the reactive shock speed is larger than the velocity on the outer side of the shock, which is consistent with the fact that the difference of these two quantities is the so-called flame velocity, i.e. the (relative) velocity at which the chemical reaction progresses in the fresh gases. Finally, we also observe numerically that the function giving the flame velocity as a function of the precursor shock speed is increasing; this allows to embed the resolution in a Newton-like procedure to compute the flow for a given flame speed (instead of for a given precursor shock speed). The resulting numerical algorithm is applied to stoichiometric hydrogen-air mixtures. Key words. spherical flames, reactive Euler equations, Riemann problems burnt zone (constant state) intermediate zone (regular solution) unburnt zone (constant initial state) W b W 2 W 1 W 0 reactive shock, r = $σ$ r t. precursor shock, r = $σ$ p t. W = ($ρ$, u, p): local fluid state. Fig. 1.1. Structure of the solution. 1. Problem position. We address the flame propagation in a reactive infinite atmosphere of initial constant composition. The ignition is supposed to occur at a single point (chosen to be the origin of R 3) and the flow is supposed to satisfy a spherical symmetry property: the density $ρ$, the pressure p, the internal energy e and the entropy s only depend on the distance r to the origin and the velocity reads u = ur/r, where r stands for the position vector. The flame is supposed to be infinitely thin and to move at a constant speed. The flow is governed by the Euler equations, and we seek a solution with the following structure:
