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Improved energy normalization function in rocket motor stability calculations

机译：火箭发动机稳定性计算中改进的能量归一化功能

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This work details the derivation of the energy normalization function which arises in motor stability calculations. It starts by identifying the flow parameters that appear in Kirchoff's expression defining the acoustic energy density in a given enclosure. Special care is taken to account for the rotational contributions due to unsteady chamber vorticity. Subsequently, these flow parameters are inserted into the energy normalization function and perturbed to the leading order. The resulting expressions are simplified and asymptotically integrated to obtain the average value of the energy normalization function. This procedure is repeated for two basic geometries pertaining to the circular-port and slab rocket motors, respectively. Our results demonstrate that inclusion of unsteady rotational flow components is critically important for the accurate assessment of energy. We also find that the conventional one-dimensional approach is lacking because it omits unsteady rotational contributions. It under-predicts the energy normalization function by 25% in each of the circular and slab motor cases.
机译：这项工作详细介绍了在电动机稳定性计算中产生的能量归一化函数的推导。它首先确定出现在Kirchoff表达式中的流量参数，该参数定义了给定外壳中的声能密度。要特别注意考虑由于不稳定的腔室涡流而产生的旋转贡献。随后，将这些流量参数插入到能量归一化函数中，并扰动到前导阶数。对所得表达式进行简化并渐近积分，以获得能量归一化函数的平均值。对于分别与圆形端口和平板火箭发动机有关的两个基本几何形状，重复此过程。我们的结果表明，包含不稳定的旋转流分量对于准确评估能量至关重要。我们还发现缺少传统的一维方法，因为它忽略了不稳定的旋转贡献。在圆形和平板电动机的每种情况下，它均低估了25％的能量归一化功能。

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