### 6.8.3. Case 3: Blade Flutter

Aerodynamic damping calculations are used in the design of turbines, compressors, and fans to predict failures due to blade flutter and to estimate blade life cycles.

Blade flutter and damping calculations can be performed in ANSYS CFX by solving for flow over vibrating blades with prescribed blade displacements. Blade flutter usually occurs at the natural frequency of the blade-disc assembly. This natural frequency can be determined, along with blade displacements (mode shapes), using ANSYS Mechanical prior to performing a flow analysis on the blade. In general, the natural disc frequency of a rotor-disc assembly consists of many modes. However, only a limited number of these modes contribute to flutter and only these modes are considered during a blade flutter simulation setup.

For blade flutter calculations, it is important to consider the aerodynamic effects of adjacent blades. For a rotor-disc assembly consisting of blades, there is a finite number of disc nodal diameters. At nodal diameter , all the blades vibrate in phase with an Interblade Phase Angle (IBPA) of `0`. However, for other nodal diameters, each blade will be out of phase with respect to the others by a finite interblade phase angle value. The interblade phase angle can be computed from the nodal diameter as:

| (6–1)

where for an even number of blades and for an odd number of blades.

In CFX you can set up a full domain transient model to perform a blade flutter simulation. Alternatively, you can use the Fourier Transformation method to perform a blade flutter analysis using a truncated domain with two passages.

The main objective of a blade flutter analysis is to obtain the aerodynamic damping, or work per vibration cycle. Once a transient periodic solution is achieved, you can use the energy balance method to perform the damping calculation. This calculation yields a measure of the system stability at each nodal diameter and blade vibration frequency. The work per vibration cycle can be computed as:

| (6–2)

Where:

- (that is, the period of one vibration cycle)

- is the time at the start of the vibration cycle.

- is the vibration frequency (that is, the Frequency value specified on the Boundary Details tab; see Periodic Displacement in the CFX-Solver Modeling Guide)

- is the fluid pressure

- is the velocity of the blade due to imposed vibrational displacements

- is the surface area (in this case, the surface of the blade)

- is the surface normal unit vector.

Note: Positive values for work indicate that the vibration is damped (for the frequency being studied), whereas negative values indicate that the vibration is undamped.

Aerodynamic damping monitors can be used to monitor aerodynamic damping during a run. The monitor value is calculated according to Equation 6–2 subject to the following modifications and conditions:

- The integration limits are set to encompass an integration interval rather than a vibration cycle. The integration interval size is a multiple of the period of one vibration cycle, the multiple being the value specified for the Integration Multiplier setting, described at Aerodynamic Damping: [Aerodynamic Damping Name]: Integration Multiplier in the CFX-Pre User's Guide. The resulting integral, which represents the work done over the course of one integration interval, is divided by the integration multiplier. For an integration multiplier of one (default), the result is the (unnormalized) aerodynamic damping value. For an integration multiplier greater than one, the result is an average value of (unnormalized) aerodynamic damping (work per vibration cycle) as evaluated over the integration interval (that is, multiple vibration cycles).

- The upper time limit on the integral can be at the end of the last complete integration interval or at the current time step, depending on whether the aerodynamic damping option (described at Aerodynamic Damping: [Aerodynamic Damping Name]: Option in the CFX-Pre User's Guide) is set to `Full Period Integration` or `Moving Integration Interval`, respectively.

- The resulting value (unnormalized aerodynamic damping) is then divided by the specified normalization value, described at Aerodynamic Damping: [Aerodynamic Damping Name]: Normalization in the CFX-Pre User's Guide, to yield a normalized value of aerodynamic damping for the aerodynamic damping monitor.

Note: After a new run is started, an aerodynamic damping monitor reports a value of zero until the required integration interval has passed.

Figure 6.4: Application of Phase-Shifted Boundaries to a Blade Flutter Case

For each component, you must model two instances of the passage, or group of passages, that is repeatable (see Fourier Transformation: Workflow Requirements).

You must specify either the Nodal Diameter or Interblade Phase Angle (IBPA), as well as the modal Frequency to complete the model.

The vibration of the blades with IBPA results in a traveling wave pattern.

For a model that has a rotating component:

- A Forward Traveling Wave (FTW) is a wave traveling in the direction of blade rotation, and is associated with a positive IBPA value. Parts (a) and (b) of Figure 6.5: Direction of Forward Traveling Wave show the direction of a FTW for a rotating component.

- A Backward Traveling Wave (BTW) is a wave traveling in the direction opposite to blade rotation, and is associated with a negative IBPA value.

For a model that has only stationary components (for example, a model of a stand-alone stator):

- A Forward Traveling Wave (FTW) is a wave traveling in the direction of increasing sector tag number. Part (c) of Figure 6.5: Direction of Forward Traveling Wave shows the direction of a FTW for a stationary component (in a model having no rotating components).

- A Backward Traveling Wave (BTW) is a wave traveling in the direction of decreasing sector tag number.

In CFX, sector tagging is independent of machine rotation. The sector tag number starts at 1 (one) for the original sector and, as shown in Figure 6.5: Direction of Forward Traveling Wave, increases around the wheel in a direction established using the right hand rule and the global coordinate frame.

Figure 6.5: Direction of Forward Traveling Wave

To compute the magnitude of the nodal diameter, divide the magnitude of the IBPA by the blade pitch in radians. The magnitude of the IBPA can be defined as , where is the time shift between adjacent blades. The blade pitch in radians is , where is the number of blades. The magnitude of the nodal diameter can therefore be computed as .

Note: The size of the computational model for the analysis of a blade flutter case that uses standard periodicity boundary conditions, such as the one illustrated in Figure 6.4: Application of Phase-Shifted Boundaries to a Blade Flutter Case, is heavily dependent on the number of passages and the nodal diameter. For most cases, a large sector of the blade row must be modeled. When you account for the phase shift at periodic boundaries by using the Fourier Transformation method, the computational model only needs to include two passages for any nodal diameter.

Note: If splitter blades are involved, then for the purpose of calculating the magnitude of the nodal diameter, the blade pitch should be measured from one main blade to the next.

Note: For cases where the mesh motion on a given boundary straddles stationary interfaces, there is a risk of mesh folding. In order to prevent this problem, the ANSYS CFX-Solver automatically blends the mesh motion displacement amplitude down to zero on boundary nodes approaching the stationary interfaces. This strategy, referred to as “Zero Displacement Approximation”, is always used because the Fourier Transformation Blade Flutter model requires stationary interfaces. The “Zero Displacement Approximation” might be the cause of solution discrepancies between a Fourier Transformation Blade Flutter model and its equivalent Symmetric Blade Flutter case, for example, when the displacements across stationary interfaces are large compared to displacements elsewhere in the domain.

#### 6.8.3.1. Setting Up a Blade Flutter Simulation

The fundamental input, which is the modal shape of the structure, must be computed and provided in the ANSYS CFX .csv file format (see Profile Data Format in the CFX-Pre User's Guide). This file should contain the coordinates, real modal displacements, and complex modal displacements (only for cyclic symmetry models) at the structural mesh locations. For cyclic symmetry cases (usually involving complex mode shapes), the harmonic index (nodal diameter) should also be provided. A sample .csv mode shape profile is shown below.

    [Name]
    normmodeshape

    [Parameters]
    Ncompt = 3
    Nnodes = 4404
    Harmonic Index = 4
    Mass = 7.25811591 [kg]
    Frequency = 1422.69639 [Hz]
    Maximum Displacement = 2.43392589 [m]

    [Spatial Fields]
    Initial X,Initial Y,Initial Z

    [Data]
    Initial X [m], Initial Y [m], Initial Z [m], node [], norm imag meshdisptot x [], norm imag meshdisptot y [], norm imag meshdisptot z [], norm meshdisptot x [], norm meshdisptot y [], norm meshdisptot z [], Sector Tag []
    2.62491941e-001, -1.55315742e-001, -2.57421546e-002, 2.48000000e+002, 3.58961582e-001, 1.76829070e-001, 7.21225142e-001, -2.96412501e-002, -2.16900989e-001, 5.16302824e-001, 1
    2.63363600e-001, -1.53833091e-001, -2.57421546e-002, 2.49000000e+002, 3.52993071e-001, 1.80246934e-001, 7.36300290e-001, -3.26568820e-002, -2.15245709e-001, 4.98975039e-001, 1
    ...

A typical blade flutter calculation, whether made using the symmetric sector model or a reduced model, requires modeling several blade passages, which in turn requires expansion of the structural mode shape. The latter can be accomplished using the Expand Profile Data tool provided in CFX-Pre (see Expand Profile Data in the CFX-Pre User's Guide). This tool can replicate as many copies as required by the model and can expand a cyclic symmetry modal shape using the Harmonic Index provided in the file.

Once the mode shape has been imported, it can be visualized to verify that it is aligned with the existing ANSYS CFX model before using it in a boundary condition. In case the structural mode shape is not aligned with the model, it must be aligned either using a local coordinate frame once imported, or by external means.

It is highly recommended that you use the automated facility for generating boundary conditions from profiles (see Use Profile Data in the CFX-Pre User's Guide) because it will automatically fill in most of the boundary condition details from the available information in the profile. It is imperative that the settings include the intended maximum amplitude for the deformation of the boundary and the wave traveling direction. For real modal shapes, the Interblade Phase Angle (IBPA) or nodal diameter must also be provided.

While setting up a boundary condition using the structural modal shape, keep in mind that there are two ways of setting up a blade flutter case:

- For mode shape displacements that can be used for a wide range of nodal diameters (typically associated with real mode shapes):

  After expanding the profile to the appropriate number of sectors, the mesh motion defined by the mode shapes is entered using the `Periodic Displacement` mesh motion option. You can then run the case with any IBPA or nodal diameter by adjusting the specified Phase Angle or Nodal Diameter.

- For mode shape displacements corresponding to a specific nodal diameter (typically associated with complex mode shapes from cyclic symmetry calculations):

  After instancing the profile to the appropriate number of sectors, the mesh motion defined by the complex mode shapes is entered using the `Periodic Displacement` mesh motion option. The phase angle or the nodal diameter cannot be adjusted because its value is obtained from the expanded profile. To run the case with another IBPA or nodal diameter requires that you specify a corresponding mode shape displacement.

#### 6.8.3.2. Running a Blade Flutter Simulation

When running blade flutter simulations, consider doing some or all of the following:

- Use the `Blended Distance and Small Volumes` stiffness model. For details, see Blended Distance and Small Volumes.

- Run with mesh pre-coarsening, which is a partitioning option for parallel runs. This is particularly appropriate if you experience robustness problems during a run. For details, see Mesh Precoarsening in the CFX-Solver Manager User's Guide.

- Lower the residual target for mesh convergence from 1.0e-04 to 1.0e-05.

- Increase the maximum number of coefficient loops to ensure well-converged mesh motion at every time step.

#### 6.8.3.3. Blade Flutter using Harmonic Analysis

As described above, a blade flutter or aerodynamic damping factor calculation can be performed on two blade passages for a range of nodal diameters using the Fourier-Transformation pitch-change method. The solution is obtained faster than for a full-wheel calculation. A significant further reduction in computational time can be achieved by performing the aerodynamic damping computation using the Harmonic Analysis (HA) (see Harmonic Analysis in the CFX-Solver Theory Guide) solution method, which avoids the need for solving in time over many vibration cycles in order to reach a steady-periodic state.

A blade flutter simulation that uses the HA methodology is set up like a blade flutter simulation that uses the time-marching method, except:

- In the Transient Blade Row Models details view:

  Transient Method > Option should be set to `Harmonic Balance` .

  Transient Method > Number of Modes should be set.

  Typically, one mode is sufficient for a blade flutter calculation; however, for some transonic flow regimes, three modes may be required to accurately resolve the flow.

- In the Solver Control details view, you must specify the maximum number of iterations and the pseudo-time step size. Typically, the size of the time step is equal to the period of the vibration cycle divided by the intended number of time steps per period.

  The period of the vibration cycle is equal to 1/(vibration frequency). A typical number of pseudo-time steps per cycle is between 15 and 30. Recall that the lower the number of pseudo-time steps that can be used while maintaining a stable solution, the more efficient the calculation is with respect to the time marching method.

- The Mesh Deformation option cannot be set to `Periodic Regions of Motion`. For details on the `Periodic Regions of Motion` option, see Periodic Regions of Motion.

Release 18.2 - © ANSYS, Inc. All rights reserved.