actdisk_info:

• Required paramters

  Parameter	Type	Description
  nsystem	int	Number of systems or rotor groupings
  nrotor	int	Number of rotors in simulation
  nblade	int	Number of unique blade types
  nairfoil	int	Number of airfoil tables to be used
  ref_length	real	Ratio of the physical length to grid length

• Optional Parameters:

  Parameter	Default value	Description
  ref_length_unit	"m"	Unit associated with ref_length
  force_output_unit	N or lb	Units of reported forces in output
  moment_output_unit	N*m or ft*lb	Units of reported moments in output
  ref_density	1.2250	Reference density
  ref_density_unit	kg/m^3	Unit of reference density
  ref_velocity	287.59754	Reference velocity
  ref_velocity_unit	"m/s"	Unit of the reference velocity
  vel_to_mach	0.8451543	Factor to convert solver velocity to Mach number
  system_show	.false.	Flags whether to output system forces at each iteration
  rotor_show	.true.	Flags whether to output rotor forces at each iteration
  implicit_be	.false.	Flag to compute Jacobians of rotor sources

• Detailed Description:

The required keywords and values must be present in the input file or the module will generate an error message and stop. The first three required inputs (nsystem, nrotor, and **nblade) inform the module how many namelists to look for of each corresponding type. For example, nrotor = 2 instructs the module that it should expect to find two distinct actdisk_rotor namelists in the input file. The number of airfoils (nairfoil) is slightly different in that it provides the dimension for the airfoil array, but there will only be one actdisk_airfoil namelist no matter how many airfoils are specified. The last required value is the reference length parameter (ref_length) that is needed to exchange length data to the flow solver in a consistent manner. The reference length is defined by the formula: ref_length = physical length / grid length. The physical length is any meaningful length (e.g. rotor radius, fuselage length, wing chord, etc.) given in full scale units. The grid length is the dimension of the desired physical length in grid units.

The optional values are given default values within the module and therefore do not need to be entered unless one wishes to change the default value. The default values for this namelist are based on the NSU3D non-dimensionalization, the physical freestream conditions are based on sea-level standard conditions, and the default for all units is the SI system.

ref_length_unit: As stated above, the default value is in meters or "m". Other possible units include inches "in" or feet "ft". A full list of dimensional units available is given below.

force_output_unit and moment_output_unit: These determine the units in which the actuator disk forces and moments are reported in the output. The default values depend on the value of ref_length_unit. If ref_length_unit = "ft" or "in", then the settings force_output_unit ="lb" and moment_output_unit =ft*lb are used. For all other values of ref_length_unit the default SI units are used: force_output_unit**= "N" and **moment_output_unit =N*m**. These can be specified differently in the input file if mixing of SI and imperial units is desired.

Reference Values: The default reference values are taken as sea-level values in SI units. Thus, the default reference density is taken as 1.2250 Kg/m^3. The reference velocity is taken as 287.59754 m/s computed as speed_of_sound/sqrt(gamma), following the NSU3D nondimensionalization. Different values can be input to override the default values and any supported units can be used for each individual input. Consistent unit conversion is handled internally by the code. The default value of vel_to_mach = 0.8451543 is calculated as 1/sqrt(gamma) and corresponds to the non-dimensionalization used in NSU3D. This default should not be changed unless gamma is different than the standard air value of 1.4

system_show and ** rotor_show**: The keywords system_show and rotor_show inform the module what data to output at the end of an iteration. By default system output is off and rotor output is true, since most actuator disk runs will have only one rotor. If multiple rotors are present it is usually recommended that system output also be turned on.

actdisk_system:

• Required paramters

  Parameter	Type	Description
  loadtype	int	Type of disk loading

• Optional Parameters:

  Parameter	Default value	Description
  system_name	"System number"	Identification name for this system of rotors
  center_of_gravity	(0.0, 0.0, 0.0)	C.G. coordinates for forces and moments
  cg_unit	"m"	Units of C.G. coordinates
  rotor_list	(1,2,...)	List of rotors belonging to the system (all rotors)
  target_value	0.0	Target thrust for prescribed load cases
  target_unit	"N"	Units of target load
  init_collective	0.0	Initial collective pitch angle of blades (in deg)

• Detailed Description:

  This namelist defines a system or grouping of rotors. A system of rotors enables recording the aggregate forces and moments of the contributing rotors which can be useful for global control. All included rotors must share the same loadtype, and initial collective values, and the target values apply to the aggregate forces and/or moments of the system. The required keyword (loadtype) and value must be present in the input file or the module will generate an error message and stop.

loadtype specifies the type of disk loading. There are currently 4 possible values:

• loadtype=1 : Constant disk loading
• loadtype=2 : Linearly varying loading (in radial direction)
• loadtype=3 : Blade element loading
• loadtype=4 : User prescribed loading

The values loadtype**=1,2 use prescribed loading profiles as shown in the figures below. The loading extends from the blade root to tip locations, as defined by the first and last **chord_sta values in the actdisk_blade namelist. The magnitude of the loading is determined by matching the thrust value specified in the target_value parmeter. Therefore, for loadtype=1,2, the target_value parmeter is required and should be set to the desired thrust of the actuator disk. The resulting power/torque value of the disk, which produces swirl in the wake, is determined by the blade shape and int_collective parameter. In this implementation, the total loading (of which the thrust is a major component) is assumed to be perpendicular to the blade chord at each radial station. Thus, a blade with no twist and init_collective**=0 (default corresponding to no blade pitch) will produce 0 torque or Cq. The blade shape is determined in the **actdisk_blade namelist primarily using the twist parameters. (Omitting the blade parameters produces a flat blade with constant pitch determined by the init_collective value.) The current formulation produces an approximation to the blade local contribution to overall torque and associated wake effects. Given a blade twist distribution, a target torque/moment/Cq value can be obtained by varying the init_collective parameter. Note that the thrust and moment values produced by the actuator disk are independent of the flow field and can be calibrated with a single iteration of the flow solver prior to the flowfield simulation.

Constant (loadtype=1) and linear (loadtype=2) actuator disk loading profiles

Although different blade loading profiles can be implemented, for more complex loading profiles, the user-prescribed loading option loadtype=4 should be used. Under this option, the user supplies a loading value at each loading station along the radial direction of the actuator disk, as determined by the parameters loading_sta and loading under the actdisk_rotor namelist. These loading values correspond to the total local loading vector. The local direction of the loading vector is assumed to be perpendicular to the chord of the local blade station, as determined primarily by the twist and twist_sta values under the actdisk_blade namelist and the init_collective value. Therefore, the local blade pitch angle, determined by the initial collective and blade twist values, corresponds to the actual total loading direction. For example, if a loading distribution is given in terms of thrust and tangential forces on the disk, the total loading vector must be constructed and the magnitude of this vector is used as the local loading value, whereas the blade twist and collective are specified such that the local blade pitch angle matches the constructued total force vector direction.

loadtype=3 specifies the blade element method, where the local loading is deterimed from the local flow conditions and a set of airfoil lookup tables. Note that this method produces actuator disk loading that is dependent on the local flow conditions, whereas the other methods produce constant loading distributions that are independent of changes in the flow field. This setting requires prescribing the blade properties under the actdisk_blade namelist, along with specifying the airfoil table files under the actdisk_airfoil namelist.

Optional parameters:

The optional values are given default values within the module and therefore do not need to be entered unless one wishes to change the default value. The keyword system_name allows the user to provide a more meaningful name to associate with the system rather than particular system. The keyword center_of_gravity expects three real numbers which denote the physical x, y, and z coordinates of the system center of gravity. Note that these coordinates are normalized by the ref_length value and therefore may or may not be the same as the grid x, y, and z coordinates. The point specified for the center of gravity is where forces and moments for the system will be resolved and as a result is also the point where trim targets are applied (if enabled). The keyword rotor_list is only required when there is more than one system, otherwise the default value is to include all rotors. It is important to note that the default value lists rotors in order of appearance.

actdisk_rotor:

• Required paramters

  Parameter	Type	Description
  rotation_rate	real	Angular velocity of rotor
  shaft_axis	3 reals	Direction vector of rotor shaft
  zero_azimuth_axis	3 reals	Direction vector of zero azimuth direction
  blade_count	(int, int,...)	Number of blades per blade type

• Optional Parameters:

  Parameter	Default value	Description
  rotor_name	"Rotor number"	Identification name for this rotor
  rotation_unit	"rpm"	Units of rotation rate
  hub_coord	(0.,0.,0.)	Hub coordinates (i.e. center of rotation)
  hub_unit	"m"	Units of hub coordinates
  nradial	200	Number of sources in radial direction
  nnormal	720	Number of sources in azimuthal (normal) direction
  naxis	1	Number of sources in axial direction
  axis	(0., 0.)	End points of acuator cylinder in axial direction
  axis_unit	1	Units of axis values
  blade_list	( 1 )	List of blade types used by this rotor
  loading_sta	(real,real,...)	Radial positions of loading stations (required for loadtype=4)
  station_unit	"m"	Units of loadjint stations
  loading	(real,real,...)	Loads at prescribed radial stations (required for loadtype=4)
  loading_unit	"Pa"	Units of loading values

• Detailed Description:

  This namelist is used to define the properties of each rotor. When nrotor = 1 this namelist should appear only once in the input file, but for nrotor > 1 this namelist will appear nrotor times. Although a system can possess multiple rotors, an individual rotor can only belong to one system. A rotor definition will typically only have one blade type, but here is generalized so that it can have multiple blade types (for example in order to model a rotor with a damaged blade).

  The required keywords and values must be present in the input file or the module will generate an error message and stop. The keyword rotation_rate not only specifies the rate of rotation, but also the direction of rotation. A positive value indicates that the rotor spins counter-clockwise when viewed from above and a negative value indicates the rotor spins clockwise from above. Note that, while the rotatio_rate is important for the blade-element loading (loadtype**=3) for the other prescribed loadings it is still required although only for normalizing the reported thrust and moment coefficients, and will not affect the computed flow field.

  The keyword shaft_axis is used to define the direction of positive thrust, as well as the rotation vector of the rotorto which applies the rotation_rate. The keyword zero_azimuth_axis defines the general direction of the psi=0 location for cyclic pitching parameters. An illustration of this axis is provided in the figure below. Technically, zero_azimuth_axis is irrelevent for propeller simulations, where no cyclic variations are assumed. Both of these axes are unit vectors, but the module automatically normalizes any vector provided. In addition, the module will adjust the zero azimuth axis such that it is perpendicular to the shaft axis, so it is not necessary to be exactly perpendicular when defining it.

The keyword blade_count is used to define how many blades are present for each type. For simplicity, 99% of rotors have identical blades within the tolerance of minor imperfections, so in most situations the blade count will be equal to the number of rotor blades. For some unique rotors and situations, it may be desirable to define more than one type of blade for a rotor. If this is the case, then blade count will be an array that will list how many blades of each type are present. For example in order to model a four bladed rotor that has sustained some damage affecting the aerodynamics of one blade, one could define a standard blade and a damaged blade and set blade_count(1:2) = 3, 1.

The keyword rotor_name allows the user to provide a more meaningful name to associate with the rotor. The keyword hub_coord expects three real numbers which denote the physical x, y, z coordinates of the rotor center of rotation. hub_coord is normalized by ref_length, so the values may or may not be equal to the hub coordinates specified in grid units. The point specified for the hub coordinates is where forces and moments for the rotor will be resolved.

The keyword blade_list is closely associated with blade_count. For a single rotor problem, the keyword blade_list will typically be omitted and will default to blade_list=1. When more than one rotor is present or when multiple blade types are present, the user will have to specify which blade index to apply. Blades are indexed by order of appearance in the input file. In situations where more than one blade type is listed, the module will use the blade with the longest radius to compute the rotor coefficients.

The keywords nradius, nnormal and naxis define the number of momentum sources in each direction of the actuator disk or cylinder. The default values (200, 720, 1) have been found to produce good results and naxis=1 specifies an actuator disk with zero thickness. Spreading the loading over an axial distance using naxis>1 corresponds to the use of an actuator cylinder. In this case, two values for axis(1:2) must be specified to determine the axial extent of the actuator cylinder. The momentum sources are positioned uniformily in the actuator disk/cylinder and positioned in the CFD mesh, where their values are interpolated onto the nearest CFD mesh points. The actuator disk extends from the blade root to tip locations, as defined by the first and last chord_sta values in the actdisk_blade namelist. An illistration of the source locations for an actuator disk is given in the figure below.

• Prescribed loading parameters : The keywords loading and loading_sta are required when user specified loading is employed, corresponding to the setting loadtype=4 in the actdisk_system namelist. In this case, a set of loading stations must be prescribed along with the corresponding loads at each station. The default units for the loads and stations are SI units (Pascal for loads, meters for stations). The stations correspond to radial locations along the blade, between the root and tip, and the loads are assumed to be in the direction normal to the local blade chord, as described above in the actdisk_systyem section. These loading values correspond to the total local loading vector. The local direction of the loading vector is assumed to be perpendicular to the chord of the local blade station, as determined primarily by the twist and twist_sta values under the actdisk_blade namelist and the init_collective value. Therefore, the local blade pitch angle, determined by the initial collective and blade twist values, corresponds to the actual total loading direction. For example, if a loading distribution is given in terms of thrust and tangential forces on the disk, the total loading vector must be constructed and the magnitude of this vector is used as the local loading value, whereas the blade twist and collective are specified such that the local blade pitch angle matches the constructued total force vector direction.

actdisk_blade:

• Required paramters

  Parameter	Type	Description
  chord	(real, real, ...)	Blade chord length values
  chord_sta	(real, real, ...)	Radial positions of chord values
  airfoil	(int, int, ...)	Airfoil ID table (only required for loadtype=3)

• Optional Parameters:

  Parameter	Default value	Description
  blade_name	"Blade number"	Identification name for this Blade
  station_unit	"m"	Units applied to unspecified *_sta_units keywords
  chord_unit	"m"	Units associated with the chord length
  chord_sta_unit	(station_unit)	Units associated with chord table stations
  airfoil_sta	(chord_sta)	Radial positions of the airfoil table
  airfoil_sta_unit	(station_unit)	Units associated with airfoil table stations
  twist	(0.,0.,...)	Blade twist table
  twist_sta	(chord_sta)	Radial positions in the twist table
  twist_unit	"deg"	Units associated with twist
  twist_sta_unit	(station_unit)	Units associated with twist table stations
  sweep	(0.,0.,...)	Blade sweep table
  sweep_sta	(chord_sta)	Radial positions in the sweep table
  sweep_unit	"deg"	Units associated with sweep
  sweep_sta_unit	(station_unit)	Units associated with sweep table stations
  offset	(0.,0.,...)	Blade offset table
  offset_sta	(chord_sta)	Radial positions in the offset table
  offset_unit	"m"	Units associated with offset
  offset_sta_unit	(station_unit)	Units associated with offset table stations

• Detailed Description:

  This namelist is used to define the properties of each blade. When nblade = 1 this namelist should appear only once in the input file, but for nblade > 1 this namelist will appear nblade times. Blades can be shared by more than one rotor and rotors can possess more than one blade type. This namelist consists entirely of blade property tables.

The required keywords and values must be present in the input file or the module will generate an error message and stop. The minimum input required to define a blade in the module is a list of radial stations (chord_sta), the chord length at those stations (chord). Additionally, for the blade-element method (i.e. loadtype=3), the airfoil keyword must be used to specify the airfoils used at each station. For specified load cases (i.e. loadtype=1,2,4) the blade planform is not needed. However, the first and last blade stations are used to determine the extent of the actuator disk as shown in the figure above, and therefore at least 2 stations must always be included.

The optional keyword "blade_name" can be used to identify each blade in the place of the default blade numbering.

Blade properties are entered through the use of five tables: chord, airfoil, twist, sweep, and offset. Four of the tables are entered through the use of four keywords: the variable value (tablename), the radial station to apply the variable value (tablename_sta), the units of the variable value (tablename_unit), and the units for the radial station (tablename_sta_unit). The only exception is the airfoil table, which uses indices for the keyword airfoil and therefore does not have a keyword airfoil_unit.

The station variables (tablename_sta) for airfoil, twist, sweep, and offset are optional. If these tables are not present then the station values are assumed to be the same as the values found in chord_sta. The keyword station_unit allows the user to specify the units for all tablename_sta_unit keywords with a single input. It is also acceptable to use the station_unit keyword, but individually set specific tables to be something different.

The keyword twist is used to define any twist that may be present along the span of the blade. More specifically it represents a difference in the pitch of a specific section of the blade with the reference pitch of the blade. A positive value of twist indicates that the local station will have a larger pitch setting than the reference station. The final local pitch value for the blade station is given by the station pitch plus the collective angle, which corresponds to the init_collective value in the actdisk_system namelist when no control law is being used (and can vary dynamically with the application of a control law or trim). If no twist values are specified, a flat blade with no twist is assumed.

The keyword sweep is used to define any sweep that may be present along the span of the blade. A positive value of sweep indicates that the local station is rotated aft of the reference blade line. The keyword offset is used to define the chord-wise position of the aerodynamic center. A positive value of offset indicates that the local station reference point is forward of the blade reference line. An important item to know about sweep and offset is that they do not affect the location of the source terms passed to the flow solver. Sweep affects which components of flow velocity are used to compute the angle of attack and offset influences the computation of the velocity components due to blade motion. In general, sweep and offset will only be used to model a swept tip blade.

For prescribed loading cases (loadtype=1,2,4) the only parameters that are relevant are: chord, chord_sta, twist and twist_sta. As mentioned previously, the twist angle has a different meaning and purpose for blade-element runs versus prescribed loading cases as shown in the figure below. For loadtype=3 blade-element cases, the twist angle is the blade installed angle, shown as theta - theta_0 in the figure, where theta_0 is the initial collective angle. For other loading types, the twist angle is the total force angle, shown as phi+beta in the figure.

actdisk_airfoil:

• Required paramters

  Parameter	Type	Description
  airfoil_file	("char","char",...)	C81 Airfoil Table File Names

• Detailed Description:

  This namelist provides a list of all airfoil files to be read by the module. The airfoil file namelist appears only once no matter how many airfoils are specified by nairfoil. The keyword, nairfoil, defined in actdisk_info defines the dimension of the array airfoil file defined in this namelist.

  This namelist has only one keyword, airfoil_file, which is a one-dimensional array that lists the names of all of the airfoil table files to be read by the module. The index values of this array are referenced by the keyword, airfoil, in the actdisk_blade namelist. This namelist is separate from the blade definition namelist to enable airfoil tables to be reused by different blade definitions. Path names should be acceptable as long as the character string is shorter than 256 characters long. To keep track of the index assigned to each airfoil table, it is recommended that each file be listed on a separate line:

  Airfoil table data is currently read using the C81 format. Additional details on writing a C81 formatted airfoil table are provided in the Appendix under Airfoil Table Format.

Sample C81 Airfoil File