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

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

RD-E-5501_Fan_blade.zip

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: Value
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: Value
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 3. Comparison of Stress after Centrifugal Load in Implicit and Explicit Rotation

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.

Figure 4. Time History Plot of Element Stress

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.