RPMTurbo is an engineering consultancy specializing in linear flow analysis for turbomachinery. Linear flow analysis can be used to analyze the following design problems:

Blade flutter
Jet engine noise
Blade vibration due to interaction with rotating wakes (forced response)

The key to analyzing these problems is calculating 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. RPMTurbo has developed an advanced 3D linearized flow solver with the following features:

Unsteady 3D Navier-Stokes flow modeling
Turbulent flow modeling: Spalart & Allmaras
Accurate analysis: validated method
3D non-reflecting boundary condition
Efficient parallel linear solver: 100 to 1000 times faster than conventional time-domain methods
Multi-row analysis
Equations of state for gas modeling: e.g. wet steam

RPMTurbo can perform customized analysis because RPMTurbo has developed its own steady and linearized flow solvers. RPMTurbo delivers high quality analysis to its clients because it fully understands the capabilities of its flow solvers and the analysis is performed by an expert with more than 10 years of industrial experience. The combination of advanced flow modeling, customized analysis and extensive industry experience gives RPMTurbo's customers a unique advantage.

The reduction of jet engine noise is an important goal for aircraft manufacturers. One of the main components of jet engine noise is tonal noise from the interaction of rotating wakes with downstream blade rows. Tonal noise occurs at discrete frequencies (multiples of the blade passing frequency) and can be analyzed by linearized flow methods.

RPMTurbo can perform 3D linearized flow simulations to predict the amplitude of acoustic modes in a jet engine. The results from the simulations can be represented by a wave plot. The wave plot below shows the amplitude of the outgoing acoustic and vorticity modes generated by an incoming vorticity wave (wake) with 80 nodal diameters which corresponds to the number of blades of the upstream row.

RPMTurbo has developed an exact 3D non-reflecting boundary condition for steady and unsteady flow simulations. The application of the 3D non-reflecting boundary condition is very important for acoustic analysis because the individual acoustic modes can be easily identified. The boundary condition also prevents non-physical reflections at the inlet and outlet which can reduce the accuracy of the linearized flow simulations.

RPMTurbo's acoustic analysis has been validated by examining an internationally recognized acoustic test case.

CAA Benchmark Problem Category 4

Many turbomachinery applications have multiple stages. However, for acoustic and forced response problems, it is usual to assume that the source of unsteady flow is just from the wake of the upstream blade-row. Also, for flutter problems it is usual to assume that the unsteady flow is due to the motion of an isolated blade-row. In reality, unsteady waves are reflected from adjacent rows and also transmitted from blade rows further up or down stream. These reflected and transmitted unsteady waves in multi-row turbomachinery can affect the flutter, acoustic, or forced response behavior of a blade row.

An example of a multi-row wave plot for a stator-rotor-stator combination is shown below. The rotor has a frequency of 30 Hz. Some of the possible acoustic modes generated by the interaction of the first harmonic of the wake (vorticity waves) from the upstream stator and rotor are shown. It can be seen that some of the acoustic modes are reflected back to the original row at a different frequency due to mode scattering (change in nodal diameter).

RPMTurbo can perform a multi-row unsteady wave analysis. Linearised flow simulations are performed for each separate frequency. The unsteady waves at the inlet and outlet are transmitted to adjacent rows and new linearized flow simulations for adjacent rows are performed. One important feature of RPMTurbo's multi-row analysis is the application of an exact 3D non-reflecting boundary condition. This boundary condition ensures that the correct amplitude and phase of each mode is transmitted to the adjacent rows. The boundary condition also prevents non-physical reflections at the inlet and outlet which can reduce the accuracy of the linearized flow simulations.

RPMTurbo presented a paper at the 2010 TURBO EXPO held in Glasgow in June this year. The title of the paper was: Three-Dimensional Non-Reflecting Boundary Condition for Linearized Flow Solvers.

An interesting test case presented by RPMTurbo at the conference was the flutter analysis of a 3D compressor blade row. The aerodynamic damping due to a torsion mode was calculated on three meshes with the inlet and outlet at different locations: 0.2, 1.0 and 2.0 chords from the leading and trailing edge respectively. The steady flow solution on the short domain (0.2 chord) is shown below (left). The aerodynamic damping calculated with the 3D non-reflecting boundary condition is shown in the plot below (right). The three solutions agree well and the solutions are independent of the location of the far-field. This demonstrates that the boundary condition is working correctly.