CFD code

The described optimized time discretization has been implemented and tested in an internal GE code. The main features of this code [Holmes et al., 1997] can be summarized as follows:

Multiblock structured meshes

Dual-time stepping for unsteady fbw simulations

Phase lag boundary conditions

Multigrid and local time stepping for convergence acceleration

Adaptive 2nd/4th order (JST) dissipation

k — и model for turbulence modeling

2. Numerical results

The first calculation considered is the propagation of an entropy wave in a periodic duct. The flow is subsonic and inviscid. The initial flow is uniform. At the inlet plane, an entropy wave is specified that convects downstream with fre­quency such that the expected wave length is approximately six times smaller than the length of the duct. At the exit, non-refecting boundary conditions are applied that allow all the outgoing waves to leave the computational domain. The calculations are performed with non-optimized and optimized second or­der temporal discretizations. The number of time steps per unsteady period is varied from 10 to 90. We also perform a calculation with an excessively large number of time steps per period to obtain a solution independent of the size of the time step. This solution is used to compute errors for the calculations with larger time steps. All inner iteration loops for all calculations are fully converged. The grid size is 250 by 50 which is sufficiently fine to resolve the specified wave. Figure 3 shows the density distribution along the duct for the both optimized and non-optimized schemes. Figures 4 and 5 show the ampli­tude and phase errors at the points located at the middle and the exit of the duct. These plots demonstrate that in order to achieve a certain level of the amplitude error one needs approximately twice as many time steps per period for a calculation with non-optimized discretization compared to the optimized one. To maintain the same phase error the number of time steps per period can be reduced by 15% when the optimized discretization is used.

Next, we consider a wake/blade row type calculation where the blade row is a rotor of a three-dimensional high pressure compressor. The wake is modeled by specifying a vorticity wave at the inlet. Again, calculations are performed

AERODYNAMICS