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Yelocity-based lift coefficient calculations

2. THEORETICAL BACKGROUND

The lift force L can be obtained from the Kutta-Joukowski theorem (2):

^L = P^WR^r    (1)

where, p fluid density, W_R freestream velocity with respect to the fluid, r circulation of the velocity which can be defined as:

^r = f^V'^ds    (2)

where, jV is a closed loop integral around the airfoil, \/fluid velocity at a given integration point and ds a vector tangent to the loop.

Thus, the information about the velocity field around the airfoil is enough to calculate the lift force (with the assumption of constant fluid density). Furthermore, knowing the chord c one can easily calculate the lift coefficient C_L using the following formula:

^WR

L = C_LP~c    (3)

The method was successfully used for PIV-based measurements presented for example in (4) and (5).

3. CFD SIMMULATIONS

The CFD results (3) have been chosen as the reference data for testing the airfoil load extraction algorithms based on Kutta-Joukowski theorem. A series of CFD simulations supporting the design of a new test section of the modernised wind tunnel at the Institute of Turobmachinery have been performed. Analyses of a virtual wind tunnel were performed in the ANSYS CFX software. Flow around the airfoil (standardised airfoil NACA0012 with chord length c=0.1m) placed inside the test section was investigated. Simulations were run for wide rangę of the angles of attack (0-17°) with the freestream flow velocity at the inlet W_R=11m/s, airfoil chord=0.1m, corresponding to Re=80x10⁵, whereas M=0.03.

A flow around infinitely long profile was simulated. In order to run this kind of simulation in the ANSYS CFX software, a thin geometry representing the cross-section of a wind tunnel with an airfoil was meshed with one element layer across its depth. The symmetry boundary condition was applied then to the side walls of quasi-3D slice-shaped fluid domain. Simulation results obtained for such a geometry are perfect input data for the designed method as it concerns 2-dimensional aerodynamic profile sections.