Flow structure in a short chamber of a labyrinth seal with a backward-facing step

The paper studies the direction of the main vortex in a short chamber with a backward-facing step. The starting-point of the work was a computational issue observed during CFD-based modeling of labyrinth gas seals. The predicted main vortex in a sealing cavity with a backward-facing step could develop either counter-clockwise or clockwise depending on the iteration step size of a pseudo-transient coupled CFD solver. First, the paper presents a comprehensive theoretical analysis of the flow structure in a generic chamber with a backward-facing step to isolate the possible sources of numerical uncertainties, among them computational grid, turbulence model, boundary and initial conditions, and solution algorithm. For the studied chamber configuration, the non-unique steady-state solutions could be observed in all model formulations depending on the iteration step sizes. Based upon these results, the observed computational issue is an example of spurious numerical behavior. Solely segregated SIMPLE-type solvers and coupled pseudo-transient solvers without multigrid algorithm have produced a unique flow structure. The second part of the paper describes the effect of the vortex direction on the performance characteristics of a short staggered labyrinth seal. The vortex direction can significantly alter aerodynamic forces arising within the seal clearance. Experimental results have been used to validate the predictions and to confirm the uniqueness and stability of the steady-state flow structure in the chamber. Discussion on the verification of CFD solutions in practical computations is provided.