Clearance mass flows are a major loss mechanism in dry running rotatory positive displacement vacuum pumps. Therefore, a detailed knowledge of the clearance mass flow is crucial to calculate the operation of those pumps. The small clearance heights and the large pressure range of such pumps require a wide range of gas rarefaction parameters to be taken into account. The flow in the clearance can be described as a combined Couette–Poiseuille flow with variable cross section. This is typically done by solving the Stokes equation, but especially at high gas rarefaction parameters, the inertia cannot be neglected any more, which can lead to choking of the flow. A one-dimensional approach for the compressible fluid flow was provided by Shapiro. It is shown that this approach can be carried over for the rarefied gas flow. The problem is solved in bounds for the constant total temperature and compared to experimental investigations by varying the pressure ratio and the circumferential speed of the clearance boundary in a wide range of gas rarefaction parameters.

中文翻译：

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具有可变横截面的全范围气体稀薄的 Couette-Poiseuille 流的一维模拟

间隙质量流量是干式旋转正排量真空泵的主要损失机制。因此，详细了解间隙质量流量对于计算这些泵的运行至关重要。这种泵的小间隙高度和大压力范围需要考虑大范围的气体稀薄参数。间隙中的流动可以描述为具有可变横截面的组合 Couette-Poiseuille 流。这通常通过求解斯托克斯方程来完成，但尤其是在高气体稀薄参数下，不能再忽略惯性，这会导致流动阻塞。Shapiro 提供了一种用于可压缩流体流动的一维方法。结果表明，这种方法可以用于稀薄气流。