## Inflow definition

@INFLOW_DEFINITION {
@INFLOW_NAME {InflowName} {
@INFLOW_TYPE {InflowType}
@DYNAMIC_INFLOW_MODEL_DEFINITION {
@NUMBER_OF_MODES {N}
}
}
}

### 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.

1. 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.
2. 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.

1. The list of lifting lines associated with this inflow model.
2. The inflow model reference length is defined as Lref = Lw for wings and Lref = R for rotors, where Lw is the wing length and R the rotor radius.
3. The inflow model reference velocity is defined as Vref = Vw for wings and Vref = ΩR for rotors, where Vw is the wing velocity and Ω the rotor angular speed.
4. The inflow model reference time is defined as Tref = Lref/Vref.
• It is possible to attach comments to the definition of the object; these comments have no effect on its definition.
• ### 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.

NumberNumber Number Number NumberNumber Number Number
of modesof states of modes of states of modesof 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

### Axis system

The dynamic inflow model is defined in an inflow frame shown in fig. 2. At first, frame FR = [O, BR = (r1, r2, r3)] is defined. If the inflow model is associated with a wing, point O is the wing root point and frame FR the wing root frame. If the inflow model is associated with a rotor, point O is the hub point and frame FR the rotor frame. In both cases, frame FR is a non-rotating frame.

Next, an intermediate axis system is defined as follows: it has its origin at point O, and basis E = (e1, e2, e3) is obtained by a 180 degree rotation of basis R,

e1 = r1,     e2 = - r2,     e3 = - r3,

as depicted in fig. 2. Let V denote the far field flow velocity. The non-rotating inflow frame, FI = [O, I = (i1, i2, i3)], is then defined as follows: it has its origin at point O, and basis I is obtained as follows

i3 = e3,     i2 = (i3 x V)/||i3 x V||,     i1 = i2 x i3.

If the far field flow velocity vanishes, i.e. in the hover case, the inflow frame is defined as follows

i3 = e3,     i2 = e1,     i1 = i2 x i3.

Figure 2 also indicates the disk effective angle of attack, αe, and the wake skew angle χ = π/2 - αe. ### 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).

No u value or v value are accepted for inflow models.