Grid Deformation Technique Research Articles

Solution of the Unsteady Euler Equations Using an Implicit Dual-Time Method

An unfactored implicit time-marching method for the solution of the unsteady two-dimensional Euler equations on deforming grids is described. The present work is placed into a multiblock framework and e ts into the development of a generally applicable parallel multiblock e ow solver. The convective terms are discretized using an upwind total variation diminishing scheme, whereas the unsteady governing equations are discretized using an implicit dual-time approach. The large sparse linear system arising from the implicit time discretization at each pseudotime step is solved efe ciently by using a conjugate-gradient-type method with a preconditioning based on a block incomplete lower-upper factorization. Results are shown for a series of pitching airfoil test cases selected from the AGARD aeroelastic cone gurations for the NACA 0012 airfoil. Comparisons with experimental data and previous published results are presented. The efe ciency of the method is demonstrated by looking at the effect of a number of numerical parameters, such as the conjugate gradient tolerance and the size of the global time step and by carrying out a grid ree nement study. Finally, a demonstration test case forthe Williamsairfoil (Williams, B. R., “ An Exact Test Case for the Plane Potential Flow About Two Adjacent Lifting Aerofoils,” National Physical Lab., Aeronautical Research Council, Research Memorandum 3717, London, 1973 )with an oscillating e ap is presented, highlighting the capability of the grid deformation technique.

Flutter analysis of propfans using a three-dimensional Euler solver

A three-dimensional aeroelastic solver is developed and applied to investigate the flutter of a propfan. The unsteady airloads are obtained by solving three-dimensional Euler equations. An implicit-explicit hybrid scheme is used to reduce computational time for the solution of Euler equations. A finite element model is used to obtain structural properties, and a deforming grid technique is used to simulate elastic deformations of the blade. The aeroelastic equations are formulated in normal mode form and are solved for flutter using both the time and frequency domain methods. The analysis is used to calculate the dynamic aeroelastic stability of a single-rotation propfan model for which classical flutter was measured at subsonic relative flows. Comparisons with the experimental data and other calculated results are given.

Numerical analysis of flow through oscillating cascade sections

The design of turbomachinery blades requires the prevention of flutter for all operating conditions. However, flow field predictions used for aeroelastic analysis are not well understood for all flow regimes. The present research focuses on numerical solutions of the Euler and Navier-Stokes equations using an ADI procedure to model two-dimensional, transonic flow through oscillating cascades. The model prescribes harmonic pitching motions for the blade sections for both zero and nonzero interblade phase angles. The code introduces the use of a deforming grid technique for convenient specification of the perioidic boundary conditions. Approximate nonreflecting boundary conditons were coded for the inlet and exit boundary conditions. Sample unsteady solutions were performed for an oscillating cascade and compared to experimental data. Also, test cases were run for a flat plate cascade to compare with the unsteady, small-perturbation, subsonic analysis. The predictions for oscillating cascades with nonzero interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. The zero degree interblade phase angle cases, which were near a resonant condition, differ from the experiment and theory. Studies on reflecting versus nonreflecting inlet and exit boundary conditions show that the treatment of the boundary can have a significant effect on the first harmonic, unsteady pressure distribution for certain flow conditions.