Inflow definition
- @INFLOW_DEFINITION {
- @INFLOW_NAME {InflowName} {
- @INFLOW_TYPE {InflowType}
- @DYNAMIC_INFLOW_MODEL_DEFINITION {
- @NUMBER_OF_MODES {N}
- }
- @COMMENTS {CommentText}
- }
- }
Introduction
An inflow element is a component of an aerodynamic model. The inflow model is associated with a wing or a rotor and inherits from this wing or rotor a list of lifting lines. At each airstation of the lifting lines, lift and circulation are computed using the two-dimensional unsteady aerodynamic model. In turn, this circulation is convected in the flow and creates an unsteady inflow field, which is computed using on the model defined in the present section. The interaction between the structural dynamics, two-dimensional unsteady aerodynamic, and inflow models is depicted in a schematic manner in fig. 1.
Figure 1. The interaction between the structural dynamics, two-dimensional unsteady aerodynamic, and inflow models.
Two types of inflow model can be defined, depending on the value of the parameter InflowType.
- If InflowType = TWO_DIMENSIONAL, the inflow model is based on the theory for unsteady flow about a 2-D airfoil. This model is a space state formulation of Theodorsen function.
- If InflowType = DYNAMIC_INFLOW, the inflow model is based on the theory for unsteady flow over a circular disk with a pressure jump across that disk. Here again the formulation leads to a space state formulation of the problem, called the Dynamic Inflow Model.
The inflow model inherits the following data from the parent rotor or wing.
- The list of lifting lines associated with this inflow model.
- The inflow model reference length is defined as L_{ref} = L_{w} for wings and L_{ref} = R for rotors, where L_{w} is the wing length and R the rotor radius.
- The inflow model reference velocity is defined as V_{ref} = V_{w} for wings and V_{ref} = ΩR for rotors, where V_{w} is the wing velocity and Ω the rotor angular speed.
- The inflow model reference time is defined as T_{ref} = L_{ref}/V_{ref}.
Dynamic inflow model
If InflowType = DYNAMIC_INFLOW, the number of inflow modes, 0 < N ≤ 48, must be defined and determines the number harmonics for the states used for the solution over the inflow disk. The choice of the number and location of the airstations of the associated lifting lines will greatly affects the accuracy and efficiency of the solution: the number of airstations must be increased as the number of inflow states increases. Table 1 indicates the number of states corresponding to a given number of inflow modes. The computational cost of the inflow model grows with the cube of the number of states.
Number | Number | Number | Number | Number | Number | Number | Number |
---|---|---|---|---|---|---|---|
of modes | of states | of modes | of states | of modes | of states | of modes | of states |
0 | 1 | 1 | 3 | 2 | 6 | 3 | 10 |
4 | 15 | 5 | 21 | 6 | 28 | 7 | 36 |
8 | 45 | 9 | 55 | 10 | 66 | 11 | 78 |
12 | 91 | 13 | 105 | 14 | 120 | 15 | 136 |
16 | 153 | 17 | 171 | 18 | 190 | 19 | 210 |
20 | 231 | 24 | 325 | 28 | 435 | 32 | 561 |
36 | 703 | 40 | 861 | 44 | 1035 | 48 | 1225 |
Table 1: Number of states associated with a specific number of modes.
Axis system
The dynamic inflow model is defined in an inflow frame shown in fig. 2. At first, frame F^{R} = [O, B^{R} = (r_{1}, r_{2}, r_{3})] is defined. If the inflow model is associated with a wing, point O is the wing root point and frame F^{R} the wing root frame. If the inflow model is associated with a rotor, point O is the hub point and frame F^{R} the rotor frame. In both cases, frame F^{R} is a non-rotating frame.
Next, an intermediate axis system is defined as follows: it has its origin at point O, and basis E = (e_{1}, e_{2}, e_{3}) is obtained by a 180 degree rotation of basis R,
e_{1} = r_{1}, e_{2} = - r_{2}, e_{3} = - r_{3},
as depicted in fig. 2. Let V_{∞} denote the far field flow velocity. The non-rotating inflow frame, F^{I} = [O, I = (i_{1}, i_{2}, i_{3})], is then defined as follows: it has its origin at point O, and basis I is obtained as follows
i_{3} = e_{3}, i_{2} = (i_{3} x V_{∞})/||i_{3} x V_{∞}||, i_{1} = i_{2} x i_{3}.
If the far field flow velocity vanishes, i.e. in the hover case, the inflow frame is defined as follows
i_{3} = e_{3}, i_{2} = e_{1}, i_{1} = i_{2} x i_{3}.
Figure 2 also indicates the disk effective angle of attack, α_{e}, and the wake skew angle χ = π/2 - α_{e}.
Figure 2. Axis system used for the dynamic inflow model.
Sensors
Sensors can be defined to extract information about inflow models. The following SensorType and associated FrameName specifications are allowed for beams: STATE. (Default value: STATE).