# RD-E: 5501 Fan Blade Rotation Initialization

In a second Engine file an initial velocity is applied to the model and a /SENSOR is used to deactivate the /LOAD/CENTRI force and apply an imposed velocity to the blades center of rotation.

## Options and Keywords Used

• Centrifugal force pre-load in rotating structures
• Rotational velocity about an axis
• Sensor activation
• Implicit followed by Explicit simulations
• Implicit simulation options (Implicit Solution)
• Rotational velocity about an axis (/INIV/AXIS/Z/1)
• Load activation and deactivation (/SENSOR/TIME, /SENSOR/NOT)
• Boundary Condition removal in Engine file (/BCSR)
• Johnson-Cook failure model (/FAIL/JOHNSON)

The centrifugal force field is applied to the blades using the /LOAD/CENTRI option with a linear ramp function with a maximum value of 104.72 $\left[\frac{\text{rad}}{\text{s}}\right]$. Since you want to obtain a steady-state rotation condition, use /LOAD/CENTRI option Ivar=1, the variation of velocity is not taken into account.

When the second Engine file starts, an initial and constant imposed rotational velocity of 104.72 $\left[\frac{\text{rad}}{\text{s}}\right]$ is applied to the blades. The imposed velocity (/IMPVEL) is activated using a time activated sensor (/SENSOR/TIME) at t=0.1 seconds. A sensor TYPE=NOT (/SENSOR/NOT) is used to turn off the centrifugal force when the imposed velocity is turned on. The /SENSOR/NOT activation state is opposite of the sensor it references and; thus, it will be on from time = 0 – 0.1 seconds.

To keep the implicit solution in static equilibrium, a fully-constrained boundary condition (/BCS) is used on the main node of the rigid body that connects the base nodes of the blades. This fully-constrained boundary condition is removed in a second Engine file when rotation begins.

Engine File 1
To activate the implicit solution, the following options are used.
Print Info /PRINT/-1

/IMPL/PRINT/NONL/-1

Printout frequency for nonlinear computation.
Linear Solver Method /IMPL/SOLVER/3 N=3 for direct solver. Uses BCS in SMP and MUMPS in SPMD.

Linear solver is also used in nonlinear iteration. It is used to resolve $Ax=b$ in each iteration of nonlinear cycle.

Nonlinear Solver Method /IMPL/NONLIN/1

0, 12, 0.01, 0.01

N=1 (default) used with Modified Newton method.

Itol=12: use relative residual in energy (Ioli=0.01 as tolerance) and in force (Iolj=0.01 as tolerance) as termination criteria.

/IMPL/LSEARCH/1

20, 1.0E-03

Line search methods for nonlinear analysis.

N=1: use standard line-searches minimizing energy residual

MAX_ls=20 (default): maximum line search iteration number is 20

TOL_ls=1e-3 (default): tolerance for line search iteration is 1e-3

Time Step /IMPL/DTINI

0.01E+00

Use to define initial time step for nonlinear implicit analysis.
/IMPL/DT/STOP

0.01E-04,0.03E+00

Implicit analysis will be stopped if DT_min=0.01e-4, and once DT_max=0.03 is reached, computation will continue with this maximum time step.
/IMPL/DT/2

6,0.00E+00,20,0.67E+00,0.11E+01

Implicit time step control .

Desired convergence iteration number is 6 (default).

Set maximum convergence iteration number 20 (default).

Decreasing time step factor set to 0.67 (default).

Max. scale factor for increasing the time step set to 1.1 (default).

Engine File 2
The initial rotational velocity is applied to the blade using the Engine option /INIV/AXIS/Z/1 and the z rotational boundary condition is released using /BCSR/ROT/Z to allow the blades to rotate.
# initialize the explicit rotation
/RUN/fbo_case/2
0.200
…
# apply initial rotational velocity
/INIV/AXIS/Z/1
0
0 0 0 104.72
1 3650
# remove z rotation boundary condition on main node of rigid body (node ID 5)
/BCSR/ROT/Z
5            

## Input Files

Before you begin, copy the file(s) used in this example to your working directory.

## Model Description

Units: mm, s, Mg, N, and MPa

/MAT/PLAS_JOHNS, isotropic elasto-plastic material using the Johnson-Cook material model. 1
Density
$4.43e-9\frac{Mg}{m{m}^{3}}$
Young's modulus
113400 $\left[\mathrm{MPa}\right]$
Poisson's ratio
0.342
Yield stress
1098 $\left[\mathrm{MPa}\right]$
Plastic hardening parameter
1092 $\left[\mathrm{MPa}\right]$
Plastic hardening exponent
0.93
Case Steel Material Properties
Density
$7.9e-9\frac{Mg}{m{m}^{3}}$
Young's modulus
210000 $\left[\mathrm{MPa}\right]$
Poisson's ratio
0.3
Yield stress
200 $\left[\mathrm{MPa}\right]$
Plastic hardening parameter
450 $\left[\mathrm{MPa}\right]$
Plastic hardening exponent
0.5
Maximum stress
425 $\left[\mathrm{MPa}\right]$
Boundary conditions:
• Blade Center constrained all directions, except Rz
• Imposed Rotational Speed = 1000 = 104.72 $\left[\frac{\text{rad}}{\text{s}}\right]$
• Edges of case are fully constrained in X, Y, Z directions

### Model Method

The purpose of the analysis is to initialize the centrifugal force field and stress on the blades from a 1000 RPM rotation. One method to initialize the centrifugal force would be to slowly increase to rotational speed from 0 to 1000 RPM. However, for explicit simulations this can be very time consuming. To reduce the simulation time, the implicit solution method and the /LOAD/CENTRI option in Radioss can be used to create the centrifugal force field. Using a second Engine file, an initial rotational velocity is applied to the blades and a /SENSOR is used to turn off the centrifugal force field and turn on an imposed velocity, (/IMPVEL). Now that the blades are rotating, the stress remains constant which means the blades are in steady-state rotation.

## Results

In Figure 3, the contour plot of the left side show the stress after applying the centrifugal force using /LOAD/CENTRI. The contour plot on the right shows that after 0.1 seconds of rotation at 1000 RPM the stress is still the same and thus, the blade is in a steady-state rotation condition. This demonstrates that the correct pre-load is applied.
Figure 4 demonstrates that the stress in the elements remains constant from 0.1 – 0.2 seconds during the steady-state rotation. This shows that the /LOAD/CENTRI creates the correct centrifugal force.

### Conclusion

Now that the force on the blades is correctly applied and the blades are rotating in a steady-state condition, a fan blade out simulation or blade impact by a bird or hailstone could be completed.