Stagnation point flow

Underlying Flow Regime 3-12 © copyright ERCOFTAC 2004

Test Case

Brief description of the study test case

Despite several studies about stagnation point flows, a comparison between CFD results and separate experimental data seems to be rare. Some measurements, which unfortunately are not separately published, are found in the paper of Kato and Launder (1993). We have therefore aimed at a test case where sufficient CFD calculations are applied to. This is the case for a VKI experiment, a high-pressure gas turbine rotor blade reported in Camci and Arts (1985a, 1985b, 1990). Medic and Durbin (2002) compare several modifications of the turbulence model with these measurements.

Examined is the transonic compressible flow through a gas turbine blade cascade, where the predicted heat transfer coefficient is of particular interest. The experimental data are compared with the predicted heat transfer coefficient. The turbulent kinetic energy, as a result of different modified two-equation is compared separately.

Test Case Experiments

The considered test case refers to a high-pressure turbine rotor blade in the VKI short duration isentropic compression tube. In the high-speed, compressible flow environment of this facility wall heat flux measurements were performed with and without film cooling. The comparison with CFD results, however, considers only the data without film cooling. Test facility, model and measurement technique are outlined in Camci and Arts (1985a, 1985b, 1990). For a full description of the cascade geometry reference is to be made to Consigny and Richards (1983). For the experimental set-up blades with a chord length of 80 mm, pitch-to-chord ratio of 0.67 and stagger angle of 38.5° were used. The inlet condition of the flow was the following: Mach number M_in = 0.25, Reynolds number Re_Cin = 8.5×10⁵, inflow angle = 30° and the free-stream total temperature T_0∞ = 409.5 K. The Mach number at the exit is M_ex,is = 0.92. Furthermore, the temperature of the wall was 298 K. The description of the blade geometry can be found in Camci and Arts (1985a, 1985b, 1990).

The ambient turbulence intensity at inlet was equal to Tu_in = 5% and the length scale was estimated via C_μ^3/4k^3/2/ε as ≈ 1 cm. The free-stream turbulence intensity was measured by means of a VKI constant temperature hot-wire anemometer. If Tu_in would be set to zero, then no noticeable effect from the stagnation point anomaly on heat transfer prediction could be seen. However, turbomachines prevail always a certain amount of ambient turbulence at inlet.

The isentropic Mach number was inferred from static pressure measurements. In Camci and Arts (1985b) the accuracy of the of the pressure reading is given with ±0.7% and the one of the temperature with ±0.5%. The local heat flux was deduced from the corresponding time-dependant surface temperature evolution, provided by 45 platinum thin films deposited on the blade surface. The temperature/wall heat flux conversion was obtained from an electrical analogy, see Schultz and Jones (1973), Ligrani et al. (1982). The heat transfer coefficient h_t is then defined as the ratio between of measured wall heat flux q_w over the difference between free stream recovery and local wall temperature, T_0∞ T_w (recovery factor: 0.896). The flow temperatures were measured using fine tungsten wires and thermocouples. According to Camci and Arts (1985b) the accuracy of the heat transfer coefficient h_t lies within ±5%.

CFD Methods

In order to evaluate the performance of the different turbulence models, Medic and Durbin (2002) used the commercial software package STAR-CD (STAR-CD 1999). This implicit general purpose solver is based on the finite volume concept using a variation of the SIMPLE method (see e.g. Malalasekera & Versteeg, 1996). The turbulence model equations were decoupled form the main flow calculation and solved sequentially. The models are incorporated into the solver via user defined subroutines (v²-f and k-ω model, respectively). However, the built-in k-ε model was used without any modifications with the exception of the time scale bound which was also incorporated via a subroutine. In the case for the Kato-Launder k-ε model, only the production term P_k had to be altered.

Contributors: Beat Ribi - MAN Turbomaschinen AG Schweiz