# Analysis

This section enables you to define the analysis parameters. The parameters affecting the finite element algorithm are defined in the Theory Manual, in the FEM code section. In particular, that section defines Linear analysis and the Time domain simulation.

Convergence parameters are only relevant for Analysis mode: Nonlinear (for Linear anlaysis they are NOT used).

This section contains the following parameters.

## General

### Analysis type

Choice of the kind of analysis that will be performed.

Options:

Dynamic (default):

The wind turbine is simulated using Newton's second law and the FEM. This is a realistic simulation of how the wind turbine will behave in real life: the rotational speed (rpm) is constantly changing and the wind turbine is moving and deflecting. The parameter Rotor model is visible.

Since Newton's second law and the FEM are used, the structure will respond to the dynamic loads (i.e. changing in time) applied to it, and how it responds (i.e. how it moves and deforms) will depend on stiffness (flexibility), mass, and damping properties.

Static:

A static analysis is performed, where all velocities, accelerations and inertia forces are zero. Dynamic loads and effects, such as wave loads and turbulence of the wind are ignored. The parameter Rotor model is visible.

All loads are calculated for a fixed rotational velocity of the rotor (rpm), i.e. there is no acceleration and Newton's 2nd law is not used. The parameter Rotor model is NOT visible. This is typically used to investigate and better understand loading. Thus, it is particularly useful in an early phase

### Timestep scheme

Determines how the timestep of the analysis (both load and fem analysis) is set.

Note: The rotation per timestep during a simulation can be observed in the rotor sensor Rotation per timestep.

More information can be found in the Time domain simulation section of the Theory Manual.

Options:

From RPM:

The timestep is calculated from reference values of RPM and rotation per timestep to get a reasonable rotation (of the rotor) per timestep. Rated RPM is normally a good choice.

From TSR:

The timestep is calculated from reference values of TSR, wind speed, and rotation per timestep to get a reasonable rotation (of the rotor) per timestep.

User defined (default):

You set the timestep. No questions asked. The parameter Timestep becomes active.

### Rotation per timestep

When Ashes calculates the time step to be used from TSR, this roation (in degrees) as well as the rotation per timestep are also used. Using the reference TSR and the wind speed given, the time step is calculated so that it has this (approximately) rotation per time step. This parameters is shown only if the Timestep scheme parameter above is set to From TSR.

Generally, the smaller the rotation per time step the more accurate are the results. Typically, 2 degrees (or less) are assumed to give sufficient accuracy. The timestep used in a simulation can be looked up in the Model information dialog - no matter if the timestep is set by the user (you) or is calculated.

• Default value: 2
• Unit: $°$
• Range: 0.1 — 10

### RPM for calculated timestep

When Ashes calculates the time step to be used based on this reference RPM, the reference rotation per timestep is also used. This parameters is shown only if the Timestep scheme parameter above is set to From RPM.

The timestep used in a simulation can be looked up in the Model information dialog - no matter if the timestep is set by the user (you) or is calculated.

• Default value: 10
• Unit:
• Range: 1 — 5000

### TSR for calculated timestep

When Ashes calculates the time step to be used from this reference TSR, this reference wind speed and the reference rotation per time step is also used. This parameters is shown only if the Timestep scheme parameter above is set to From TSR.

The timestep used in a simulation can be looked up in the Model information dialog - no matter if the timestep is set by the user (you) or is calculated.

• Default value: 6
• Unit:
• Range: 1 — 100

### Wind speed for calculated timestep

When Ashes calculates the time step to be used, this reference wind speed as well as the reference rotation per time step are also used. This parameters is shown only if the Timestep scheme parameter above is set to From TSR.

The timestep used in a simulation can be looked up in the Model information dialog - no matter if the timestep is set by the user (you) or is calculated.

• Default value: 10
• Unit: ${\text{m}} \over {\text{s}}$
• Range: 1 — 100

### Timestep

Time step of the time simulation. Lets you set the timestep to be used explicitly. This parameters is shown only if the Timestep scheme parameter above is set to User defined.

The timestep used in a simulation can be looked up in the Model information dialog - no matter if the timestep is set by the user (you) or is calculated.

• Default value: 0.025
• Unit: $\text{s}$
• Range: 1e-06 — 10

### Rotor model

Sets the modeling type of rotors in dynamic analyses.

The parts of the wind turbine can be analyzed as stiff or flexible. This parameter applies to a Dynamic analysis. The analysis can be performed with some or all of the wind turbine parts modelled as being structurally (infinitely) stiff (i.e. rigid). This parameter is not shown if Analysis type is set to Loads only because then the whole wind turbine is stiff.

Note that with stiff blades, you will have to manually input the location of the center of mass of the blades. This location is always assumed to be aligned with the main shaft

Options:

Flexible (default):

The rotor will be modeled using fully flexible elements, where bending/axial/torsional stiffness is taken from the blade structural specifications, or computed from the blade's airfoil geometry. More parameters can be configured on the Rotor and Blade parts.

Stiff:

The blades are modeled as stiff. The rest of the RNA (Main shaft etc.) and the support structure will remain flexible. The rotor as a whole will move as if fixed to the end of the mainshaft, also accounting for the relative velocity of the rotor to the incoming wind. No internal flexing or dynamics of the blades will be accounted for.

### Distance from hub to CM of blades

The horizontal distance from the hub node to the center of mass of the blades when the blades are stiff.

• Default value: 1.5
• Unit: $\text{m}$
• Range: 0 — 100

### Analysis mode

The finite element analysis can be performed linearly or nonlinearly. Note: This parameter is set to Nonlinear and disabled for floaters, since floaters always should be analyzed nonlinearly.

Nonlinear analysis

- a nonlinear analysis algorithm is used - particularly Newton-Rhapson iterations

- Euler-Bernoulli beam elements with a corotated coordinate system are used for all elements

- works well (is accurate) for unlimited deformations/deflections (both translations and rotations)

- ALWAYS use nonlinear analysis for a (rotating) rotor where the blades are flexible (the parameter Rotor model set to Flexible)

- ALWAYS use nonlinear analysis for floaters

Linear analysis

- a linear analysis algorithm is used

- normal Euler-Bernoulli beam elements are used for the support structure whereas Euler-Bernoulli beam elements with a corotated coordinate system are still used for blades and main shaft (unless Stiff blades are used, in which case the baldes are not modelled with finite elements)

- stiffness properties are constant (not changed/updated)

- typically faster than nonlinear analysis

- will be inaccurate for large translations or rotations. Thus, should only be used for small deflections/deformations.

- works well for a simulation with a rotation rotor only if the blades are stiff - the parameter Rotor model set to Stiff (i.e. not modelled with finte elements)

- NEVER use linear analysis for floaters

- Note: A rotor modelled flexible can give trustworthy results if it is not rotating (i.e. stopped) and the deformations are small. This should be accomplished by turning on the Bearings locked parameter in the Main shaft.

References:

Euler-Bernoulli beam theory in Wikipedia

Options:

Nonlinear (default):

The solver is nonlinear and the elements are corrotational. This is the recommended alternative.

Linear:

The solver is linear and the elements are linear. This is typically faster than nonlinear.

### Numerical integration method

The numerical method used to solve the dynamic system.

The Hughes Hilbert Taylor method is a modification of the Newmark-beta method that enables the use of numerical damping. More information about the numerical methods is given in the theory manual, in the Time domain simulation section.

Options:

HHT-alpha (default):

The Hughes Hilbert Taylor modified Newmark-beta method is used

Newmark-beta:

The Newmark beta method is used.

### HHT-alpha factor

The numerical damping factor used in the HHT numerical integration method. The value must be negative, or zero.

Setting this factor to 0 implies no numerical damping. This is discouraged since it often leads to numerical problems (non-convergence).

The min value -0.333 gives maximum damping. The damping of a natural mode shape increases for increasing natural frequencises.

This parameter is not relevant and thus hidden if the Numerical integration method is Newmark-beta (see Damping).

Note: In addition to numerical damping there can be material damping.

• Default value: -0.025
• Unit:
• Range: -0.333 — 0

### Beta factor

The beta factor in the Newmark-beta numerical integration method.

This factor is hidden if the Numerical integration method is HHT-alpha, since it is calculated from the alpha factor and cannot be set directly.

• Default value: 0.25
• Unit:
• Range: 0 — 1

### Gamma factor

The gamma factor in the Newmark-beta numerical integration method.

This factor is hidden if the Numerical integration method is HHT-alpha, since it is calculated from the alpha factor and cannot be set directly.

• Default value: 0.5
• Unit:
• Range: 0 — 1

### Default element type

Sets the default type of beam elements to use. Some parts of the model might override this setting, and use a different type. The type of each element can be seen by right-clicking it, or in the Information pane one the part.

Options:

Euler-Bernoulli (default):

Ordinary Euler-Bernoulli beam elements. Also called engineer's beam or classical beam.

Timoshenko:

Timoshenko beam elements. The Timoshenko element accounts for shear deformations, which are of importance for short beams.

### Use lumped mass

Use lumped mass scheme for nodal masses (as opposed to consistent mass).

• Default value: True
• Unit:

### Inner solver

Experimental feature

Changes the inner equation solver type.

Options:

Gaussian elimination (default):

Gaussian elimination

Gauss-Seidel (experimental):

Gauss-Seidel (experimental)

### Solution acceleration factor

Accelerates (or decelerates) the solution process by multiplying the predicted displacement increment by this factor.

• Default value: 1
• Unit:
• Range: -∞ — ∞

## Damping (structural)

### Structural damping mode

Choice of structural damping.

Note: In addition to the structural damping there can be numerical damping (depending on the value of the HHT-alpha parameter)

Options:

None (default):

There is no structural damping

Rayleigh:

Sum of stiffness proportional and mass proportional damping.

Stiffness proportional:

The damping is proportional to the stiffness

Mass proportional:

The damping is proportional to the mass

### Damping input

The way structural damping is defined.

Damping can be set by damping coefficients explicitly, or implicitly by setting damping ratio for one or two periods (or frequencies). Usually, natural periods of the system is used, but this does not have to be the case.

If Damping ratio(s) is chosen, then Damping ratio 1 and possibly Damping ratio 2, as well as Period 1 and possibly Period 2 are shown. The damping coefficients are calculated from these inputs, see the Info window.

Options:

Damping ratio(s) (default):

Damping ratio(s) for one or two periods is used to define the damping

Explicit coefficient(s):

The mass and/or stiffness coefficient(s) is/are given as input directly

### Mass coefficient

The factor that is multiplied with the mass properties of the element to get the damping effect of the mass

This coefficients is used both for Rayleigh damping and for mass proportional damping.

The Period 1 parameter is also shown, but it is not used in the simulations. It is only used to calculate the corresponding damping ratio and these are presented in the Info window.

• Default value: 0.05
• Unit: ${\text{rad}} \over {\text{s}}$
• Range: 0 — 10

### Stiffness coefficient

The factor that is multiplied with the stiffness properties of the element to get the damping effect of the stiffness

This coefficients is used both for Rayleigh damping and for stiffness proportional damping.

The Period 1 parameter is also shown, but it is not used in the simulations. It is only used to calculate the corresponding damping ratio and these are presented in the Info window.

• Default value: 0.05
• Unit: ${\text{s}} \over {\text{rad}}$
• Range: 0 — 10

### Damping ratio 1

The damping ratio (in percent) at the first period for which the damping is tuned.

100% damping means that the damping is equal to the critical damping.

• Default value: 1
• Unit: $\text{%}$
• Range: 0 — 100

### Period 1

The period for which the first damping ratio (ksi 1) is given.

This period must be greater than the second Rayleigh period to be used.

Note: If the Damping input is Explicit coefficient(s) then this parameter is NOT used in the simulations, but only to calculate the corresponding damping ratio presented in the Info window.

• Default value: 3
• Unit: $\text{s}$
• Range: 0.001 — 1000

### Damping ratio 2

The damping ratio (in percent) at the second period for which the damping is tuned.

100% damping means that the damping is equal to the critical damping.

• Default value: 2
• Unit: $\text{%}$
• Range: 0 — 100

### Period 2

The period for which the second damping ratio (ksi 2) is given.

Note: If the Damping input is Explicit coefficient(s) then this parameter is NOT used in the simulations, but only to calculate the corresponding damping ratio presented in the Info window.

• Default value: 0.3
• Unit: $\text{s}$
• Range: 0.001 — 1000

The loads can be ramped-up from zero to their full values over a given number of timesteps of a given time (duration).

Options:

None:

Number of timesteps (default):

You set the number of timesteps over which the loads are ramped up.

Duration:

You set duration (in seconds) over which the loads are ramped up.

The number of timesteps at the start of the analysis where all loads will be ramped up from zero to the full load value. Ramping the loads will give a smoother start, avoiding abrupt loading which can cause numerical problems. The shape (curve) of the ramp-up is set by the Load ramp-up curve parameter. This parameter is only visible (active) if the Load ramp-up scheme parameter is set to Number of timesteps.

• Default value: 100
• Unit:
• Range: 1 — 10000

The time interval at the start of the analysis where all loads will be ramped up from zero to the full load value. Ramping the loads will give a smoother start, avoiding abrupt loading which can cause numerical problems. The shape (curve) of the ramp-up is set by the Load ramp-up curve parameter. This parameter is only visible (active) if the Load ramp-up scheme parameter is set to Duration.

• Default value: 3
• Unit: $\text{s}$
• Range: 0 — 1000

Choose how the loads are ramped up: either linearly or exponentially

Options:

Linear:

Linear ramp-up

Exponential:

Exponential ramp-up

Smooth (default):

Smooth start and end, i.e. the derivative is zero at start and end.

## Convergence

### Energy tolerance (absolute)

The exponent of the tolerance of residual energy allowed when continuing nonlinear equilbrium iterations. This value is the exponent, and gives an absolute tolerance (E = 10^value) of the total residual energy required for equilibrium.

This is explained more in details in the Time simulation section of theory manual

• Default value: -6
• Unit:
• Range: -1000 — 1000

### On non-convergence

If the nonlinear equilibrium iterations do not converge within the specified tolerances, Ashes can either abort the simulation or ignore the convergence problem and continue the simulation. Use the "Continue" option with caution!

Options:

Stop simulation (default):

If the nonlinear equilibrium iterations do not converge within the specified tolerances, Ashes stops the simulation.

Continue:

If the nonlinear equilibrium iterations do not converge within the specified tolerances, Ashes continues the simulation. Use this option with caution!

### Maximum iterations

The maximum number of nonlinear iterations performed without achieving the specified tolerances before stopping the simulation.

• Default value: 1000
• Unit:
• Range: 0 — 1e+09

## Special events

### Special event

Choice of a special event

Options:

None (default):

Nothing special

Loss of torque:

Generator torque is lost at a given point in time.This is typically caused by loss of grid, but there can be other causes. Loss of grid typically leads to runaway of the rotro, which means that the rotor accelerates until it the aerodynamic torque is (clos to) zero. In reality, the WT breaks before zero troque is reached, so this is can be a catastrophic event if it is not mitigated fast.

### Loss of torque time

The time at which loss of torque occurs.

• Default value: 10
• Unit:
• Range: 0 — 20000

Choice of what category the load is: force or moment

Options:

None (default):

Force:

The prescribed load is a force

Moment:

The prescribed load is a moment

### Node id

The prescribed force specified in the Prescribed force parameter will be applied to the node with this global id. The global id is auto generated and can be found in the node info window, which can be opened by right-clicking a node. If you enter a non-existing id you will get an error message.

• Default value: 1
• Unit:
• Range: 1 — 100000

The magnitude of the load (given in global coordinates) that will be applied to the node specified in Node id. If the Period of the force is 0.0 then the the magnitude is the constant value of the load.

• Default value: 0 0 0
• Unit:

### Period

The prescribed force specified in the Prescribed force parameter will be varying as a sine wave with this period. If the period is 0 (which is the default value), then the force will be constant.

• Default value: 0
• Unit: $\text{s}$
• Range: 0 — 1000

If set, the static force will be disabled when the simulation time passes this value. A value of 0 will Disable this option.

• Default value: 0
• Unit: $\text{s}$
• Range: -1e+07 — 1e+08

## Statics

This is the number of steps made in a (nonlinear) static analysis. For a linear analysis only 1 step is necessary to get an exact result. For nonlinear static simulations the accuracy will typically increase with an increasing number of steps.

• Default value: 100
• Unit:
• Range: 1 — 10000

### Mass scale factor for static solve

Determines the amount of mass/inertia that is included when finding a static equilibrium before starting the dynamic analysis.

If this scale factor is 0, a pure static nonlinear analysis is performed. A value greater than 0 will scale all mass/inertia with this factor, and a quasi-static analysis will be performed. If a fully static solution doesn't converge, this value should be set to a small value, such as 10-6.

• Default value: 0
• Unit:
• Range: 0 — 1

Gravity loads are applied on all masses.

• Default value: 1
• Unit:

Includes buoyancy loads on the parts of the structure that is submerged.

• Default value: 1
• Unit:

## Misc.

### Statistics start time

The time from which on statistics for sensor data should be calculated and viewed.

• Default value: 0
• Unit: $\text{s}$
• Range: 0 — 1e+06

### Realtime scheme

This parameter addresses a problem that can arise when a (very) small rotor is used (typically wind tunnel scale, i.e. a diameter around 1 m). The typical RPM will then be on the order of thousands and the simulation clock must be slowed down a lot for the visualization to make sense.

Options:

Auto (default):

An appropriate SPEED factor is set when the model is changed and the rotor diameter is so small that the typical observed rpm will be over 20. The SPEED factor is then reduced to get a visualization with approximately 20 (observed) rpm (while the actual rpm is in the 1000's).

User defined:

You set the SPEED factor in the SIMULATION CLOCK widget. No questions asked.