Interfacial instability of liquid films coating the walls of a parallel-plate channel and sheared by a gas flow

The stability and coupling of liquid films coating the walls of a parallel-plate channel and sheared by a pressure-driven gas flow along the channel center plane is studied. The films are susceptible to a long-wavelength instability. For sufficiently low Reynolds numbers and thick gas layers, the dynamic behavior is found to be described by two coupled nonlinear partial differential equations. A linear stability analysis is conducted under the condition that the material properties and the initial undisturbed liquid-film thicknesses are equal. The linear analysis is utilized to determine whether the interfaces are predominantly destabilized by the variations of the shear stress or by the pressure gradient acting upon them. The analysis of the weakly nonlinear equations performed for this case shows that instabilities corresponding to a vanishing Reynolds number are absent from the system. Moreover, for this configuration, the patterns emerging along the two interfaces are found to be identical in the long-time limit, implying that the films are fully synchronized. A different setup, where the liquid films have identical material properties but their undisturbed thicknesses differ, is studied numerically. The results show that, even for this configuration, the interfacial waves remain phase-synchronized and closely correlated for an extended period of time. These findings are particularly relevant for gaseous flow through narrow ducts with liquid-coated walls.     

A Nyström-based finite element method on polygonal elements

We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in the local space on each mesh cell are evaluated via Nyström discretizations of associated integral equations, allowing for curvilinear polygons and non-polynomial boundary data. Several experiments demonstrate the approximation quality of interpolated functions in these spaces.     

INCAP – applying short-term flexibility to control inventories

Inventory based capacity control (INCAP) is a very simple method that allows inventory levels to be effectively controlled by using short-term capacity flexibility in make-to-stock settings. Moreover, INCAP can be used for finished goods inventories as well as for semi-finished goods inventories. The basic idea is to define upper and lower inventory limits and to adjust capacities if the inventory level reaches either limit. Should the inventory fall below the lower limit, capacity is increased to prevent stock-outs. Similarly, in order to avoid excess inventories the capacity is decreased should the inventory rise above the upper limit. INCAP is thus able to control inventory levels within a defined inventory range. In order to do so, it applies short term measures like over-time or extra shifts to increase capacities and cancels work hours or shifts to decrease capacities. Simulation experiments based on data from the automotive industry show that INCAP is able to improve the performance of a manufacturing system in that it significantly reduces the inventory levels necessary for guaranteeing a satisfactory service level. Overall, INCAP is found to be a straightforward but powerful method, able to cope both with uncertainties in production output as well as with varying demand. However, some restrictions do apply: INCAP depends not only on a minimum level of short-term capacity flexibility, but also in the standard set-up presented here it is limited to make-to-stock environments with similar products.