RPMTurbo specializes in linear flow analysis for turbomachinery. Linear flow analysis can be used to analyze the following design problems:

Blade flutter
Jet engine noise
Forced response (blade vibration due to rotor/stator interactions)

A key task in analyzing these problems is determing the unsteady flow. Linear flow analysis can be used to accurately predict the unsteady flow when a single time frequency dominates and the flow perturbations are small. This assumption is valid for many aeroelastic and aeroacoustic problems in turbomachines. Linear flow analysis is 10 to 100 times faster than conventional time domain methods and just as accurate for most cases. RPMTurbo has developed LUFT™ (Linearized Unsteady Flow solver for Turbomachinery) with the following features:

3D URANS (Unsteady Reynolds-Averaged Navier-Stokes) flow modelling
Turbulent flow modelling: Spalart & Allmaras
Accurate analysis: validated method
Exact 3D non-reflecting boundary condition
Efficient parallel linear solver
Multi-row analysis (steady and unsteady)
Equations of state for gas modeling: for example wet steam

RPMTurbo delivers high quality analysis to its clients because we have the ability to modify and tune the flow solver for the client's application. The combination of advanced flow modeling, customized analysis and extensive industry experience gives RPMTurbo's customers a unique advantage.

RPMTurbo also offers software licenses for LUFT. This allows manufacturers to perform design calculations in-house.

The mass flow through tip clearances of free standing rotor blades can have a significant influence on flutter analysis. This is particularly important for long steam turbine blades where the relative flow at the exit of the turbine can be supersonic and the blade deflections of the flutter modes are significantly larger near the tip.

The results of a URANS flutter analysis performed by RPMTurbo of an industrial steam turbine with and without tip clearance are shown below. The first plot shows the aerodynamic damping as a function of blade height for an aeroelastic mode near the least stable mode. Most of the unsteady aerodynamic work which contributes to flutter is done near the tip. The overall aerodynamic damping is equal to the area under the curve and it can be seen that including the tip clearance in the flutter analysis significantly changes the overall aerodynamic damping. The contour plots below show how the tip clearance flow changes the unsteady aerodynamic work done on the blade due to a flutter mode.

Aerodynamic Damping versus Span for a Steam Turbine Blade

Unsteady Aerodynamic Work due to a Flutter Mode near the Tip of the Suction Surface of a Steam Turbine Blade assuming no Tip Clearance (left) and with Tip Clearance (right)

RPMTurbo provides the only commercially available flutter analysis that uses an exact 3D non-reflecting boundary condition. A non-reflecting boundary condition is essential to correctly predict unsteady flow. Flow reflections at the inlet and outlet create non-physical flow waves that travel back towards the blade. This pollutes the solution and gives the wrong answer. One method to determine if the boundary condition at the inlet and outlet is non-reflecting, is to repeat the unsteady flow calculation with the inlet and outlet at different locations. The unsteady flow solution at the profile should not change. Are your unsteady flow calculations independent of the location of the inlet and outlet?

The ASME Turbo Expo 2014 will be held in Düsseldorf on 16-20 June. RPMTurbo, LMZ Power Machines and St Petersburg State Polytechnical University will be presenting a paper titled "Advanced Flutter Analysis of a Long Shrouded Steam Turbine Blade". I hope to see you there. The abstract of the paper is below.

Abstract

An advanced flutter analysis of a final stage turbine row with a new 1.2 meter long shrouded blade is presented. The three-dimensional (3D) unsteady Reynolds Averaged Navier-Stokes (URANS) equations with the Spalart and Allmaras turbulence model were employed to model the flow. The flow entering the last stage is a mixture of saturated vapor and liquid. An equilibrium wet-steam equation of state was used to model the properties of the mixture. Multi-row steady state simulations of the upstream stator row, the turbine row and the extended exhaust section were performed. It was considered important to include the exhaust section in the steady-state simulations in order to accurately predict the pressure profile at the exit of the turbine. The flow simulations were relatively high resolution and the single passage turbine mesh had 798 208 cells. Linearized flow simulations for the turbine row were performed to determine the unsteady aerodynamic work on the blades for the possible aeroelastic modes. An exact 3D non-reflecting boundary condition (3D-NRBC) was applied at the inlet and outlet for the linearized flow simulations to eliminate non-physical reflections at these boundaries. The calculated logarithmic decrement values for the new turbine blade are compared with a reference case for a similar steam turbine blade at a condition known to have a long and safe working history. The new last stage was found to be more stable than the reference case at the flow condition examined.