UFR 1-02 Evaluation
Blade tip and tip clearance vortex flow
Underlying Flow Regime 1-02 © copyright ERCOFTAC 2004
Comparison of CFD calculations with Experiments
Figures 3, 4 and 5 provide some key comparisons between computed quantities and experimental data. Further details can be found in the work of Dacles-Mariani et al (1995).
Based on computations with a single code and a single turbulence model, some conclusions relevant to best practice advice for this test case has been provided by Dacles-Mariani et al (1995), as follows:
- High-order discretization schemes were found to be essential in reducing numerical dissipation and achieving reasonable agreement with measured vortex profiles. In particular the flow field immediately surrounding the vortex core is sensitive to grid resolution, turbulence modeling and numerical dissipation.
- A grid cell aspect ratio close to unity is required in the vicinity of the core of the vortex.
- A minimum of 15 to 20 grid points are needed across the vortex core to resolve the high velocity gradients. A lower grid density can be used in the streamwise direction.
- A total of 1.5 million grid points were found to give good agreement for this case, with local refinement of the grid in areas of high gradients and in the known location of the vortex core.
- A y+ of the first grid point above the wing surface between 0.1 and 0.4 gave accurate results for the boundary layers with a modified Baldwin-Barth model.
- An empirical modification of the production term in the Baldwin-Barth model was needed to avoid an over-prediction of the level of turbulent viscosity in the vortex core.
- The boundary layer in the experiments was tripped near to the leading edge so the sensitivity to transition modeling was not examined, simply
- The detail of the shear layer detachment at the wing tip (in a region of adverse pressure gradient) is significantly affected by the choice of turbulence models, as in other adverse pressure gradient situations.
- The interaction of the trailing vortex with the outflow boundary condition identified that a Neumann outflow pressure boundary condition was preferable to a Dirichlet condition. The problem here originated because the measured outlet static pressure conditions were used for the downstream boundary condition and the precise location of the vortex core was not the same in the test data as in the simulation, leading to inconsistencies on the downstream boundary. This problem would not normally occur in a simulation where no a priori information is available on the downstream boundary.
As no other simulations are available for this UFR it is not possible to give more conclusions and recommendations on which model to use for this particular case. In particular some of the more recent successful turbulence models have not been examined (Spalart Almaras, Menter SST, V2F model of Durbin).
A survey of the technical literature on CFD simulations has been made to identify other recommendations for best practice taken from other recent CFD studies of wingtip vortices:
A study of supersonic wing-tip vortices on a wing with a blunt tip and sharp edges was carried out with the following conclusions:
- Grids of circa 0.5, 1.5 and 3.0 million grid points were used and the finest mesh adequately reproduced the principal features of the flow.
- Grid point clustering in the stream-wise direction at the wing leading and trailing edges, in the lateral direction at the wing surfaces and in the vertical direction towards the wing tip were found to be useful.
- Simulations with Euler equations, laminar Navier Stokes and k_epsilon N-S were carried out. All of the simulations were successful at locating the distance of the vortex core away from the blade, but the penetration of the vortex along the height of the blade was slightly underestimated.
- All of the simulations (Euler, laminar N-S and K-epsilon N-S) were able to predict the total pressure distribution through the vortex, but the K-epsilon simulations closely reproduced the measurements. The static pressure distribution in the vortex core was poorly reproduced with laminar and Euler calculations, but was well reproduced with the K-epsilon N-S simulations.
- The k-epsilon N-S simulations were less accurate with the prediction of the stream-wise velocity and static pressure in the core of the vortex, whereby a 20% deficit in the stream-wise velocities in the vortex core was predicted by the k-epsilon model.
Hsiao and Pauley (1998)
This study concerns the tip vortex formation over a rectangular hydrofoil with a round tip section.
- A sufficiently dense grid must exist near to the tip-vortex core and the blade surface to adequately resolve the tip vortex and predict boundary layer effects. Adaptive grids would be ideal for this, but in this study, the grid was defined with a H-H topology with additional grid clustering near to the blade tip on the suction side of the blade.
- The predictions with an algebraic Baldwin-Barth turbulence model lead to good predictions of the roll-up of the vortex near to the blade tip but to excessive dissipation in the vortex flow downstream of the blade.
- A wake-like profile in the axial velocity within the tip vortex downstream of the blade was found at low angle of attack and a jet-like profile at high angle of attack.
Snyder and Spall (2000)
This study examines a wing with a blunt flat-ended wing tip.
- A coarse grid with 0.8 million cells and a fine grid with 1.6 million cells were made and no significant differences were observed in the results.
- The primary tip vortex generated by the tip leakage flow was well modeled by both RSM and Spalart Almaras turbulence models.
- Multiple secondary vortex structures were observed near to the wing tip, related to the entrainment of the shear layers on the blades into the wing tip vortex. Qualitative flow patterns for these secondary vortices were independent of the turbulence model used (RSM model versus Spalart and Almaras model), although in detail the Spalart Almaras model produced larger secondary vortices.
- The S-A model demonstrated that on this flat-ended blade the shear layers from the blades are swept as a secondary vortex into the primary tip clearance vortex.
Wallin and Girimaji (2000)
These authors studied the detail of the development of an isolated tip vortex
- The flow in the core of the vortex approaches solid body rotation, and thus the production of the turbulence is suppressed giving a strongly stabilized structure. Standard eddy viscosity models, such as the k-epsilon method, are unable to describe the turbulence in rotation dominated flows satisfactorily. The k-epsilon model strongly overpredicts the vortex decay rate.
- Reynolds stress transport models (differential and algebraic) successfully predict the strong suppression of the turbulence in the rotation dominated vortex core and a reasonable decay of the vortex. An explicit algebraic Reynolds stress model (EARSM) based on the full RSM Sarkar-Gatski model gives predictions in line with observations.
© copyright ERCOFTAC 2004
Contributors: Michael Casey - Sulzer Innotec AG