RPMTurbo has developed a very efficient and accurate 3D linearized viscous flow solver which can solve a typical 3D unsteady flow simulation (450 000 cells) in 20 minutes. RPMTurbo employs this flow solver to perform linear flow analysis for its clients, for example, flutter analysis of steam turbines, gas turbines, and aircraft engines. The fact that RPMTurbo has developed its own flow solvers means, that RPMTurbo can easily perform customized flow analysis and that RPMTurbo fully understands the capabilities of the flow solvers that it employs. This results in high quality flow analysis for the client. RPMTurbo has extensively tested its flow solvers and the results for standard test cases are available online.

The importance of 3D viscous effects on flutter analysis was highlighted in a recent flutter study performed by RPMTurbo. The plot below shows the aerodynamic damping calculated from various flow models (3D viscous, 3D inviscid and 2D viscous) for a compressor stage. The 3D viscous analysis predicts that the blade motion is unstable for some interblade phase angles, while the other flow models predict stable conditions for all interblade phase angles. The reason for the difference is the corner separation which is only predicted by the 3D viscous analysis. The corner separation can be seen in the contour slice of flow Mach number at ten percent blade height shown below.

RPMTurbo has developed a three-dimensional non-reflecting boundary condition for unsteady flow simulations. This boundary condition ensures that outgoing waves exit the flow domain without reflection. Unwanted, non-physical reflections of unsteady waves at the far-field can reduce the accuracy of the simulation.

The non-reflecting boundary condition is applied by decomposing the unsteady flow perturbations into independent waves (unsteady aerodynamic modes). The 3D unsteady aerodynamic modes are determined by performing an eigen analysis on the semi-discretized flow equations at the far-field. This approach is valid for non-uniform and swirling flows.

An example of the unsteady aerodynamic modes as calculated by RPMTurbo's 3D non-reflecting boundary condition is shown below. The figures show the unsteady pressure perturbations of acoustic modes in a 3D annulus calculated by RPMTurbo's non-reflecting boundary condition.

The non-reflecting boundary condition has been extensively tested. The figure below shows the aerodynamic damping versus inter-blade phase angle for a standard test case. The red curve was calculated using the analytical method of Giles, and the green curve was calculated using RPMTurbo's non-reflecting boundary condition.

The early identification of potential flutter problems can have significant economic benefits for the manufacturers of gas turbines, steam turbines and aircraft engines. The following savings can be realised:

• reduction in development costs
• reduction in losses due to development delays
• reduction in the cost of long-term maintenance programs

In the past, 3D unsteady viscous flow modeling has been too computationally expensive to use during the design phase, because hundreds of different cases (various operating points and modes) have to be examined. Manufacturers have had to rely on simplified flow models (e.g. 2D inviscid), reduced order models and empirical data during the design process and 3D viscous flutter analysis was only for research purposes. These simplified models fail to model flutter at off-design operating conditions where the flow has separated, for example stall flutter and choke flutter. Three-dimensional (3D) turbulent flow modeling is necessary to predict accurately separated flow.

RPMTurbo has developed a linearized flow solver that is capable of performing a typical unsteady 3D viscous turbomachinery simulation in 20 minutes. As a result, RPMTurbo can complete a full 3D viscous flutter analysis of hundreds of different cases in a short time-frame. Therefore, 3D viscous flutter analysis can have an impact on the preliminary design and save the manufacturer time and money.