论文标题
多孔羽流的近场形状和稳定性
The near-field shape and stability of a porous plume
论文作者
论文摘要
当将液体注入到充满密度更高的环境流体的多孔培养基中时，注入的液体会形成羽流，由于浮力而升高。在注射点的近场中，羽流可以调节其速度以匹配多孔培养基的浮力速度，即变薄或变厚以节省质量。这些调整是近场羽状形状上的主要控件，而不是与周围流体混合，而环境流体发生在较大的垂直距离上。在这项研究中，我们专注于近场的羽流行为，表明对于中等的注射率，羽流将达到稳态，从而使其与注射点的几个羽宽尺度相匹配。但是，对于非常小的注入率，由于与周围的流体形成鲜明对比，因此稳定的羽流裂开了。近场中羽状的稳定形状仅取决于单个无量纲参数，这是入口速度和浮力速度之间的比率。进行线性稳定性分析，表明对于较小的速度比，可以构建无穷小的扰动，这变得不稳定，而对于中等速度比率，形状被证明是稳定的。最后，我们评论了此类流在多孔地质储层中的CO $ _2 $固存的上下文中的评论。
When a fluid is injected into a porous medium saturated with an ambient fluid of a greater density, the injected fluid forms a plume that rises upwards due to buoyancy. In the near-field of the injection point the plume adjusts its speed to match the buoyancy velocity of the porous medium, either thinning or thickening to conserve mass. These adjustments are the dominant controls on the near-field plume shape, rather than mixing with the ambient fluid, which occurs over larger vertical distances. In this study, we focus on the plume behaviour in the near-field, demonstrating that for moderate injection rates the plume will reach a steady state, whereby it matches the buoyancy velocity over a few plume width-scales from the injection point. However, for very small injection rates an instability occurs in which the steady plume breaks apart due to the insurmountable density contrast with the surrounding fluid. The steady shape of the plume in the near-field only depends on a single dimensionless parameter, which is the ratio between the inlet velocity and the buoyancy velocity. A linear stability analysis is performed, indicating that for small velocity ratios an infinitesimal perturbation can be constructed that becomes unstable, whilst for moderate velocity ratios the shape is shown to be stable. Finally, we comment on the application of such flows to the context of CO$_2$ sequestration in porous geological reservoirs.
