环形液体射流：精确约束吸收与横截性的有限时间丧失
Annular liquid jets: exact constraint absorption and finite-time loss of global admissibility
- Escuela de Ingenierías Industriales, Universidad de Málaga（马拉加大学工业工程学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对环形液体射流一维模型，提出通过变量替换恒等吸收代数约束以避免指标降阶退化，采用切比雪夫配点法离散，发现自由端横截性在有限时间内丧失，并纠正了已发表数据中的矛盾。
AI中文摘要：
环形液体射流包围一定体积的气体，当表面张力主导惯性时，会在有限距离处于对称轴上闭合。在该构型的一维模型中，该距离并非边界条件，而是自由端状态的代数约束，既有方案对其在时间上求导，并对所得域长度方程进行推进。我们表明，这种指标降阶使约束未被强制执行，且在稳态极限下退化；我们通过在选择因变量时恒等地吸收约束来避免该问题。简化后的系统不携带约束，并采用切比雪夫配点法进行离散。收敛是几何性的，已发表的稳态数据得以重现，且在配点节点之外评估的残差后验地验证了非稳态解。由此得出三个结果。对于有限厚度的射流，只要自由端是横截的，收敛长度随喷嘴处厚度与半径之比严格减小，这与已发表的表格相矛盾，并将差异定位在自由端的处理上。强迫响应在压力系数中呈共振，但在收敛长度中不呈共振。在强迫作用下，自由端在有限时间内不再横截，因此自由边界降阶为单个标量的做法失效，其参数值被发表为周期响应。在其中一种情况下，计算出的失效时间与已发表记录中一个近垂直段重合，而粗糙离散完全无法检测到该失效。
英文摘要：
An annular liquid jet may enclose a volume of gas and, when surface tension dominates over inertia, close on the symmetry axis at a finite distance. In the one-dimensional membrane model, closure provides an algebraic relation among the state variables at the free end. Earlier domain-adaptive schemes differentiate this relation to obtain an evolution equation for the domain length. We instead absorb the endpoint closure identically in the dependent variable and discretise the reduced system by Chebyshev collocation. Convergence is geometric, published steady data are recovered, and the unsteady calculations are checked by componentwise off-grid residuals, temporal refinement, and an independent upwind finite-difference discretisation. For jets of finite thickness, the convergence length decreases with nozzle thickness when the Froude number, Weber number, nozzle angle, and pressure coefficient are held fixed and the terminal zero remains transversal; this is a parameter-specific model result rather than a universal experimental thickness law. The forced response has a pressure-coefficient maximum near a Strouhal number of 0.093, whereas the convergence-length gain increases monotonically over the globally admissible frequency interval studied. Most importantly, a global positivity check changes the interpretation of the first finite-time event. Under body-force forcing, the mean radius first reaches zero at an interior point while the tracked endpoint remains transversal. The interior contact is quadratic, and the independent finite-difference scheme converges to the same first-contact time. After this event, the tracked endpoint is no longer the first physical closure point, so the single-interval annular-jet representation is no longer globally admissible.
