Validation of LTRAN2-HI by comparison with unsteady transonic experiment

Here is the disturbance velocity potential, M^ is the freestream Mach number, and 6 is the airfoil thickness-tochord ratio. For the purpose of flutter analysis, industrial users have indicated the need to perform accurate calculations in a frequency range up to A: =1.0, a reduced frequency violating the "low-frequency" assumption. Therefore an objective of the present study is to extend the range of reduced frequency for improved LTRAN2 applicability. The modifications made to the code in this study involve the addition of high-frequency time-dependent terms in the calculation of the pressure coefficient as well as the wake and downstream boundary conditions. The low-frequency governing equation is retained, however. Several other researchers" have performed similar modifications to LTRAN2, adding high-frequency terms to the boundary conditions of the numerical algorithm. Their results indicate that under subsonic flow conditions, improved agreement with linear theory in amplitudes and phase angles of lift and moment coefficients is obtained at higher frequencies with the modified code. However, to truly demonstrate the merit of the modified code, calculations done under transonic flow conditions should be compared with experimental results. Hence this study was undertaken to modify the existing code LTRAN2 and to evaluate the effects of these changes by comparison with experimental data. The experimental test case for comparison, performed by Davis and Malcolm, is a NACA 64A010 airfoil, pitching about quarter chord, at a Mach number of 0.8 over a range of reduced frequencies up to 0.6. This case was chosen based on the following criteria: 1) the availability of good test data, 2) the presence of a moderate strength shock wave, 3) the absence of strong separation effects in the experiments.