Aerodynamic Body and Aerodynamic Beam Elements

These elements share the description of the aerodynamics; the former assumes the aerodynamic surface to be rigid, and takes its configuration from a single node, while the latter relies on a three-node beam and uses the same interpolation functions of the beam to compute the configuration at an arbitrary point. The aerodynamic body input format is:

    <normal_arglist> ::= <node_label> 
        [ , rotor , <rotor_label> ] ,
        (Vec3)              <relative_surface_offset> , 
        (OrientationMatrix) <relative_surface_orientation> ,
        (scalar)            <surface_span> ,
        (shape_1D)          <surface_chord> ,
        (shape_1D)          <surface_aerodynamic_center> ,
        (shape_1D)          <surface_b_c_point> ,
        (shape_1D)          <surface_twist> ,
                            <integration_points>
        [ , control , (drive_caller) <control_drive> ] 
        [ , <airfoil_data> ]
        [ , unsteady , { bielawa } ]

The aerodynamic beam input format is:

    <normal_arglist> ::= <beam_label> 
        [ , rotor , <rotor_label> ] ,
        (Vec3)              <relative_surface_offset_1> ,       
        (OrientationMatrix) <relative_surface_orientation_1> ,
        (Vec3)              <relative_surface_offset_2> ,
        (OrientationMatrix) <relative_surface_orientation_2> ,
        (Vec3)              <relative_surface_offset_3> ,       
        (OrientationMatrix) <relative_surface_orientation_3> ,
        (shape_1D)          <surface_chord> ,
        (shape_1D)          <surface_aerodynamic_center> ,
        (shape_1D)          <surface_b_c_point> ,
        (shape_1D)          <surface_twist> ,
                            <integration_points>
        [ , control , (drive_caller) <control_drive> ] 
        [ , <airfoil_data> ]
        [ , unsteady , { bielawa } ]

where

    <airfoil_data> ::= { naca 0012 | rae 9671 | c81 , <c81_data> }

and

    <c81_data> ::= <c81_label> 

    <c81_data> ::= multiple , <airfoil_number> ,
        <c81_label> , <end_point>
        [ ... ]

    <c81_data> ::= interpolated, <airfoil_number> ,
        <c81_label> , <position>
        [ ... ]

The field rotor instructs the element that it is linked to a rotor element; this means that it can get information about the induced velocity and should supply information about the forces it generates. An arbitrary configuration and offset is allowed for both elements with respect to the nodes they are linked to. This means that the aerodynamic beam offsets refer to the position of the nodes, and have nothing to do with offsets related to the structural beam element. The shape entities are used to compute the physical chord, aerodynamic center, velocity measurement point (the point where the kinematic boundary conditions are evaluated) and twist as functions of the dimensionless abscissa along the span. The span of the aerodynamic body element is set by the user; the center-span of the element is assumed to be the end of the offset vector. The span of the aerodynamic beam is computed based on the end of the offset vectors related to nodes 1, 3. The aerodynamic center and the velocity measurement points are measured relative to the centerline of the elements, that is the line in direction 3 of the local frame from the end of the offset vector. This line is assumed to be at the 25% of the airfoil chord when steady aerodynamic coefficients are used (unsteady_flag = 0). The direction 1 is assumed to be the ``reference'' line of the airfoil, from the trailing edge to the leading edge (points ``forward''), while direction 2 is normal to the other two and goes from the lower to the upper side of the airfoil (points ``up''). Figure 8.1 shows the arrangement of the airfoil geometry and properties.

Figure 8.1: Airfoil geometry

The airfoil_data defaults to a builtin NACA 0012 semi-analytical model (FIXME: the unsteady correction is buggy; use the c81 mode instead).

The multiple mode of the c81 data allows to specify more than one airfoil for an aerodynamic element; the transition between airfoils is sharp. The integer airfoil_number indicates how many airfoils are expected; the real end_point indicates where the influence zone for that airfoil ends, expressed in terms of a non-dimensional abscissa spanning $\left(\vphantom{ -1,1 }\right.$ -1, 1$\left.\vphantom{ -1,1 }\right)$ along the reference line, roughly along axis 3 of the aerodynamic reference frame; end_point must not lie outside the element. So, for example, if airfoil NACA 0015 is used in the leftmost part of an element up to 1/4 span, NACA 0012 is used from 1/4 to 3/4 span, and NACA 0009 is used in the remaining rightmost 1/4, the syntax is:

    set: integer naca0015 = 15;
    set: integer naca0012 = 12;
    set: integer naca0009 = 9;
    c81 data: naca0015, "naca0015.c81";
    c81 data: naca0012, "naca0012.c81";
    c81 data: naca0009, "naca0009.c81";
    # beginning of aerodynamic element definition...
        multiple, 3,
            naca0015, -0.5,    # from -1.0 to -0.5
            naca0012,  0.5,    # from -0.5 to  0.5
            naca0009,  1.0,    # from  0.5 to  1.0
    # ...rest of aerodynamic element definition

The interpolated mode of the c81 data allows to specify a smooth transition between different airfoils inside an element. The interpolation occurs at the integration points where the aerodynamic data is required, and it is performed once for all at the beginning of the analysis. Since this operation is time consuming, and essentially unnecessary, the interpolated data can be generated once for all with the utility util/c81merge once the position of the integration point is known, and the multiple mode can be used to directly provide the interpolated data to the aerodynamic element.

FIXME: not implemented yet

Output

Aerodynamic elements, both bodies and beams, write their output with file extension .aer; for each time step the required elements are output. Three different formats are available; the format can be selected only at compile time, and it must be the same for all the elements.

Note: eventually it will freeze; if all the output formats will be maintained, they will be made selectable at run-time.

In any case the label of the element is output first.

Node

The format is:

• the label of the node
• the three components of the force applied to the node
• the three components of the couple applied to the node

When an aerodynamic beam is considered, the output is repeated for each node the element is attached to.

Forces at Gauss points

The output refers to each Gauss integration point; the format is:

• the direction of the wind velocity relative to the element frame
• the lift,
• the drag,
• and the aerodynamic moment per unit length

When an aerodynamic beam is considered, the output is repeated for each portion of beam.

Coefficients at Gauss points

The output refers to each Gauss integration point; the format is:

• the local incidence
• the local yaw angle
• the local Mach number
• the lift,
• the drag,
• and the aerodynamic coefficient

When an aerodynamic beam is considered, the output is repeated for each portion of the beam.