Blade tip and tip clearance vortex flow

Underlying Flow Regime 1-02 © copyright ERCOFTAC 2004

Test Case

Measurements performed using a half-wing rectangular plan-form model of a NACA 0012 wing with a rounded tip.

Test data available at 10° angle of attack and Reynolds number based on chord of 4.6 million in an incompressible flow.

Test-case configuration is shown in Figure 2. Note that the use of a large model in the wind-tunnel section implies large wind tunnel blockage and the wind-tunnel walls need to be defined as boundaries in the computational domain. The inflow boundary is rather close to the wing so that the experimental data needs also to be specified at the inflow plane, with a Blasius profile for the missing data points at the location of the measured inlet flow distribution.

The principal measured quantities are global flow patterns by surface oil flow visualisation, blade surface static pressure distributions, pressure field and velocity components by means of a seven hole probe, and triple hot-wire data giving turbulence quantities.

Mean velocity components, pressure and Reynolds stresses are available at a number of planes from 0.59 chord lengths upstream of trailing edge to 0.68 chord lengths downstream.

The key parameter of interest is the location and trajectory of the tip clearance vortex and its decay in the near-field downstream of the wing.

Measurements were performed in the 32 x 48 inch (0.81 x 1.22 m) low-speed wind tunnel at the fluid Mechanics Laboratory of NASA Ames Research Center.

The half wing model has a 3 foot (0.91 m) semi-span and a 4 foot (1.22m) chord, with a NACA 0012 aerofoil section and a rounded tip.

Tests were carried out at a tunnel reference speed of 170 ft/sec giving a chord Reynolds number of 4.6 x 10⁶.

For further details of the test facility and measurement techniques see (Chow, Zilliac and Bradshaw (1997).

The principal measured quantities are global flow patterns by surface oil flow visualisation, blade surface static pressure distributions, pressure field and velocity components by means of a seven hole probe, and triple hot-wire data giving turbulence quantities.

Mean velocity components, pressure and Reynolds stresses are available at a number of planes from 0.59 chord lengths upstream of trailing edge to 0.68 chord lengths downstream.

The experimental data is of exceptionally high quality and the accuracy of the measurements is high:

The flow is close to the target/design flow (10° incidence) and clear information is available about the inlet boundary conditions.

The NACA 0012 aerofoil was manufactured accurately to a precision giving a maximum surface position error of less than 0.01 mm in a 1.22 m chord.

The wing is not in a free boundary, but the wind-tunnel walls can be used as boundaries of the domain.

Accuracy estimates are given for all measured quantities (see Chow, Zilliac and Bradshaw (1997)).

An overview of the methods used has been provided by Dacles-Mariani et al (1995):

The 3D incompressible Navier-Stokes flow solver INS3D-UP was used with a modified form of the Baldwin – Barth one equation turbulence model, in which the production terms were modified.

The code uses an implicit finite difference scheme in generalized curvilinear coordinates and an artificial viscosity formulation. An upwind-biased fifth-order accurate discretization of the convective terms was used and the viscous terms were discretized with a second-order scheme.

The grid resolution was 115 x 157 x 83 in the streamwise, spanwise and surface normal directions (1.5 million nodes). Of the 115 grid points 40 were used in the wake region, and the grid was refined close to all walls and in the core of the vortex.

Initial computations of the blade wing tip flow identified that there were discrepancies between the computed and measured results. Sensitivity tests carried out on smaller problems (wake flow from trailing edge to outlet boundary, and an analytic solution of a free vortex flow) were used to identify the cause of the problems and to quantify numerical accuracy. These studies identified the requirements for grid resolution, and necessary modifications to the turbulence model and the discretisation scheme.

The treatment of the outflow boundary condition were of some consequence in the predictions and studies were carried out with Dirichlet and Neumann outflow conditions (see below).

Contributors: Michael Casey - Sulzer Innotec AG