Application of a new incompressible flow algorithm to flows in a variety of shear-driven cavity configurations

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A recently developed incompressible flow algorithm by the authors is applied to study flows inside a variety of lid-driven cavity configurations. The new algorithm is based upon the pressure correction approach, but employs a regular grid finite-volume arrangement instead of the usual staggered grid arrangement. The pressure equation is derived such that effects which promote the well-known checkerboard instability are minimized. A relevant compatibility constraint on pressure is satisfied by Neumann boundary conditions obtained using a vector identity. Implemented in a second-order-accurate finite-volume code, the algorithm has been evaluated and validated by computing benchmark shear-driven cavity flows. Several geometric variations of the classical lid-driven square cavity flow are currently considered, for example parallelogram and elbow-shaped cavities. In a parallelogram shaped driven cavity, it is shown that the primary eddy in the "posterior" version is similar to both the "anterior" version examined by several previous investigators and to the classical square cavity flow. However, major differences exist in the secondary flow structure including a very strong oblong-shaped eddy in upstream corner region and no eddy at the downstream corner. In another variation, that of flow in an elbow-shaped cavity, bulk flow near the lid is again similar to that of the square cavity, but the flow pattern in the lower region of the cavity is significantly different. A large counter-rotating eddy occupies most of this region in conjunction with a long "finger" of the primary flow that wraps around it at the outer radius of the elbow.

Original languageEnglish
Pages (from-to)233-238
Number of pages6
JournalAmerican Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED
StatePublished - 1996


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