RD-E: 5501 Fan Blade Rotation Initialization

The /LOAD/CENTRI option in Radioss is used to create the centrifugal force field on fan blades.

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)
Centrifugal force field (/LOAD/CENTRI)
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 $[\frac{rad}{s}]$ . 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 $[\frac{rad}{s}]$ 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.

Figure 1.

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.

	Command	Comments
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 $A x = b$ 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.
Nonlinear Solver Method	/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

The input files used in this example include:

<install_directory>/hwsolvers/demos/radioss/example/55_Fan_Blade_Out_FBO/1_Initialize_rotation_stress/*

Model Description

Four fan blades are rotating at a steady state condition at 1000 RPM inside a simplified case. The base of each blade is attached to a rigid body which is constrained in all directions except rotation about the z axis. The stress in the blades caused by the steady-state rotation needs to be correctly modeled before other loads can be applied to the blades. The blades are assumed to be made of titanium with a constant 5mm thickness. The case is made of steel with varying thickness.

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

/MAT/PLAS_JOHNS, isotropic elasto-plastic material using the Johnson-Cook material model. ¹

Blade Titanium Material Properties
Density: $4.43 e - 9 \frac{M g}{m m^{3}}$
Young's modulus: 113400 $[MPa]$
Poisson's ratio: 0.342
Yield stress: 1098 $[MPa]$
Plastic hardening parameter: 1092 $[MPa]$
Plastic hardening exponent: 0.93

Case Steel Material Properties
Density: $7.9 e - 9 \frac{M g}{m m^{3}}$
Young's modulus: 210000 $[MPa]$
Poisson's ratio: 0.3
Yield stress: 200 $[MPa]$
Plastic hardening parameter: 450 $[MPa]$
Plastic hardening exponent: 0.5
Maximum stress: 425 $[MPa]$

Boundary conditions:

Blade Center constrained all directions, except Rz
Imposed Rotational Speed = 1000 = 104.72 $[\frac{rad}{s}]$
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.