Labyrinth seals are commonly used in rotating equipment to restrict cooling flow between rotating and stationary components. One of the issues in the design of such seals is the accurate prediction of the temperature rise of the cooling flow due to windage heating effects. Accurate prediction of this heating allows designers to maintain the structural integrity of the engine with the minimum amount of cooling flow, thereby maximizing the efficiency of the engine.

In order to validate the accuracy of FLUENT/UNS for this kind of flow prediction, Fluent's staff analyzed a straight five-fin labyrinth knife seal with a nominal clearance of 1.11 mm between the labyrinth seal and the shroud.¹ The computational model was axisymmetric, with specification of the pressure ratio (1.5) across the seal as imposed boundary conditions. The working fluid was assumed to be air, with density computed via the ideal gas law, and fluid properties (viscosity, thermal conductivity, and heat capacity) expressed as a function of temperature. Turbulence was modeled using the RNG k-e model. The CFD model was run at several different rotor speeds and the windage heating was computed and compared with the experimental data.

Grid Independence Using Adaption

Grid-independent solutions were obtained at each operating speed by using the solution-based mesh adaption capability in FLUENT/UNS. The mesh was adapted based on predicted y+ values and on gradients of total temperature. The initial mesh for each simulation started out with approximately 9400 quadrilateral cells and after adaption the final cell count was approximately 12,500 cells. A typical mesh after the solution-adaptive refinement is shown below.

¹Millward, J.A., Edwards, M.F., "Windage Heating of Air Passing Through Labyrinth Seals", ASME Paper No 94-GT-56.

The FLUENT/UNS predictions yielded good agreement with the measured heat addition due to windage heating.

Temperature prediction showing the effect of windage heating.

Mesh adaption with embedding was used to ensure grid independence of the predictions.

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