The standard κ-ϵ equations and other turbulence models are evaluated with respect to their applicability in swirling, recirculating flows. The turbulence models are formulated on the basis of two separate viewpoints. The first perspective assumes that an isotropic eddy viscosity and the modified Boussinesq hypothesis adequately describe the stress distributions, and that the source of predictive error is a consequence of the modeled terms in the κ-ϵ equations. Both stabilizing and destabilizing Richardson number corrections are incorporated to investigate this line of reasoning. A second viewpoint proposes that the eddy viscosity approach is inherently inadequate and that a redistribution of the stress magnitudes is necessary. Investigation of higher-order closure is pursued on the level of an algebraic stress closure. Various turbulence model predictions are compared with experimental data from a variety of isothermal, confined studies. Supportive swirl comparisons are also performed for a laminar flow case, as well as reacting flow cases. Parallel predictions or contributions from other sources are also consulted where appropriate. Predictive accuracy was found to be a partial function of inlet boundary conditions and numerical diffusion. Despite prediction sensitivity to inlet conditions and numerics, the data comparisons delineate the relative advantages and disadvantages of the various modifications. Possible research avenues in the area of computational modeling of strongly swirling, recirculating flows are reviewed and discussed.

Bubbles, Drops, and Particles

Turbulence models and their applications to the prediction of internal flows: a review

The addition of a sufficiently high degree of swirl to flow going into a circular pipe produces a limited region of reversed flow. Such a vortex breakdown, as it is termed, represents a zone of transition from a supercritical to a subcritical flow state. If the flow remains subcritical, an unavoidable consequence is that the geometry and conditions downstream directly affect the upstream flow up to, and including, the breakdown region. Laser Dopper anemometer measurements of the swirl and axial velocity components, as well as the corresponding streamline patterns, are presented for water flow in a model based upon the geometry of a swirl combustor. It is shown that a strong exit contraction (55 percent of the diameter) has practically no influence on a flow which reverts to supercritical, whereas even a weak contraction (15 percent of the diameter) has a significant influence on a flow which remains subcritical. It is argued that a cold flow is likely to be totally unrepresentative of a reacting flow through the same geometry, and, also, that great care has to be taken over the boundary conditions to be imposed for the numerical computation of subcritical flows. 20 references.

Recirculation in swirling flow - A manifestation of vortex breakdown

Six flowfield configurations are investigated with sidewall angles of 90 and 45 deg, and swirl vane angles of 0, 45, and 70 deg. It is found that central recirculation zones occur for the swirling flow cases investigated, which extend from the inlet to x/D = 1.7, where x is the axial polar coordinate, and D is the test section diameter. Five-hole pitot probe pressure measurements are used to determine time-mean velocities, and corresponding flow situations are predicted and compared to results of experimental data. Excellent agreement is found for the nonswirling flow, although poor agreement is found for swirling flow cases, especially near the inlet. The discrepancy is attributed to the lack of realism in the turbulence model, and/or to inaccurate specification of time-mean velocity and turbulence energy distributions at the inlet.

Mean Flowfields in Axisymmetric Combustor Geometries with Swirl

A new approach was developed and tested for alleviating the substantial convergence difficulty which results from implementation of the QUICK differencing scheme into a TEACH-type computer code. It is relatively simple, and the resulting CPU time and number of numerical iterations required to obtain a solution compare favorably with a previously recommended method. This approach has been employed in developing a computer code for calculating the pressure drop for a specified incompressible flow leakage rate in a labyrinth seal. The numerical model is widely applicable and does not require an estimate of the kinetic energy carry-over coefficient for example, whose value is often uncertain. Good agreement with measurements is demonstrated for both straight-through and stepped labyrinths. These new detailed results are examined, and several suggestions are offered for the advancement of simple analytical leakage as well as rotordynamic stability models.

Prediction of Incompressible Flow in Labyrinth Seals

The paper reports research restricted to steady turbulence flow in axisymmetric geometries under low speed and nonreacting conditions. Numerical computations are performed for a basic two-dimensional axisymmetrical flow field similar to that found in a conventional gas turbine combustor. Calculations include a stairstep boundary representation of the expansion flow, a conventional k-epsilon turbulence model and realistic accomodation of swirl effects. A preliminary evaluation of the accuracy of computed flowfields is accomplished by comparisons with flow visualizations using neutrally-buoyant helium-filled soap bubbles as tracer particles. Comparisons of calculated results show good agreement, and it is found that a problem in swirling flows is the accuracy with which the sizes and shapes of the recirculation zones may be predicted, which may be attributed to the quality of the turbulence model.

D. G. Lilley

Papers

On the prediction of swirling flowfields found in axisymmetric combustor geometries