The Unsteady Aerodynamic (UA) models account for flow hysteresis, including unsteady attached flow, trailing-edge flow separation, dynamic stall, and flow reattachment. Dynamic stall refers to rapid aerodynamic changes that may bring about or delay stall behavior :cite:`ad-Branlard:book`. Rapid changes in wind speed (for example, when the blades pass through the tower shadow) cause a sudden detachment and then reattachment of air flow along the airfoil. Such effects at the blade surface cannot be predicted with steady state aerodynamics, but may affect turbine operation, not only when the blades encounter tower shadow, but also during operation in skewed flows and turbulent wind conditions. Dynamic stall effects occur on time scales of the order of the time for the relative wind at the blade to traverse the blade chord, approximately c/\Omega r. For large wind turbines, this might be on the order of 0.5 seconds at the blade root to 0.001 seconds at the blade tip. Dynamic stall can result in high transient forces as the wind speed increases, but stall is delayed.
The different dynamic stall models implemented in AeroDyn are presented below.
See :numref:`airfoil_data_input_file` for a comprehensive description of all the inputs present in the profile input file (including some of the ones repeated below).
The airfoil section coordinate system and main variables are presented in :numref:`fig:UAAirfoilSystem` and further described below:
Definition of aifoil section coordinate system used in the unsteady aerodynamics module
- Aerodynamic Center (AC): point of the airfoil cross section where the aerodynamic forces and moment are assumed to act. Usually close to the 1/4 chord point for a regular airfoil and at the center for a circular cross section
- “3/4” chord point: in the original formulation this point refers to the point on the chord axis located 3/4 chord behind the leading edge. This concept is here generalized to the point located mid-way between the aerodynamic center and the trailing edge, to account for aerodynamic center positions that differ strongly from a 1/4 chord point. The notation 3/4 is kept in this document.
- \omega: rotational speed of the airfoil section (pitching/torsional rate) positive around z.
- \boldsymbol{v}_{ac}: velocity vector at the aerodynamic center \boldsymbol{v}_{ac}=[v_{x,ac}, v_{y,ac}] (coordinates assumed to be expressed in the airfoil section coordinate system)
- \boldsymbol{v}_{34}: velocity vector at the 3/4 chord point \boldsymbol{v}_{34}=[v_{x,34}, v_{y,34}](coordinates assumed to be expressed in the airfoil section coordinate system) The velocity is obtained from the velocity at the 1/4 chord point and the rotational speed of the section: \boldsymbol{v}_{34}=\boldsymbol{v}_{ac}+\omega d_{34} \hat{\boldsymbol{x}}_s where d_{34} is the distance between the aerodynamic center and the 3/4 chord point.
- U_{ac}: velocity norm at the aerodynamic center. U_{ac}=\lVert\boldsymbol{v}_{ac}\rVert=\sqrt{v_{x,ac}^2 + v_{y,ac}^2}
- \alpha_{ac}: angle of attack at the aerodynamic center \alpha_{ac}=\operatorname{atan2}(v_{x,ac},v_{y,ac})
- \alpha_{34}: angle of attack at the 3/4 chord point \alpha_{34}=\operatorname{atan2}(v_{x,34},v_{y,34})
- \boldsymbol{x}: the vector of states used by the continuous formulations
- c: airfoil chord
- C_l^{st}, C_d^{st}, C_m^{st}: static airfoil coefficients
- \alpha_0: angle of attack at zero lift, C_l^{st}(\alpha_0)=0
- \alpha_1: angle of attack close to positive stall.
- \alpha_2: angle of attack close to negative stall.
- C_{l,\alpha}: slope of the steady lift curve about \alpha_0.
- f^{st}_s(\alpha): is the steady separation function, determined from the lift curve C_l^{st}(\alpha) (see below, and e.g. :cite:`ad-Hansen:2004`)
- A_1, A_2, b_1, b_2: are four constants, characteristic of the propagation of the wake vorticity (Wagner constants)
Time constants:
- T_u(t) = \frac{c}{2U_{ac}(t)} \in [0.001, 50]: Time for the flow to go over half the airfoil section. The value is plateaued to avoid unphysical values.
- T_{f,0}: Dimensionless time constant associated with leading edge separation. Default is 3.
- T_{p,0}: Dimensionless time constant for the boundary-layer,leading edge pressure gradient. Default is 1.7
Separation function:
The steady separation function, f_s^{st}, is defined as the separation point on a flat plate for a potential Kirchhoff flow :cite:`ad-Hansen:2004`:
\begin{aligned}
\text{Close to $\alpha_0$},
f_s^{st}(\alpha) &= \operatorname{min}\left\{\left[2 \sqrt{ \frac{C_l^{st}(\alpha)}{C_{l,\alpha}(\alpha-\alpha_0) } } -1 \right]^2 , 1 \right\}
,\quad
\text{away from $\alpha_0$},
f_s^{st}(\alpha)=0
\end{aligned}
When \alpha=\alpha_0, f_s^{st}(\alpha_0)=1. Away from \alpha_0, the function drops progressively to 0. As soon as the function reaches 0 on both sides of \alpha_0, then f_s^{st} is kept at the constant value 0.
Note that for UAMod=5, a different separation function is formed.
We define an offset for the C_n function, cn_offset, where
C_{n,offset}=\frac{C_n\left(\alpha^{Lower}\right)+C_n\left(\alpha^{Upper}\right)}{2}. Then, the separation function
is a value between 0 and 1, given by the following equation:
f_s^{st}(\alpha) = \left[ 2 \max\left\{\frac{1}{4} , \sqrt{\frac{C_n^{st}(\alpha) - C_{n,offset}}{C_n^{fullyAttached}(\alpha)-C_{n,offset}}} \right\} -1 \right]^2
with the fully-attached C_n curve defined as C_n between alpha^{Lower} and alpha^{Upper} and linear functions outside of that range:
C_n^{fullyAttached}(\alpha) = \begin{cases} C_n\left(\alpha^{Upper}\right) + C_n^{slope}\left(\alpha^{Upper}\right) \cdot \left(\alpha-\alpha^{Upper}\right) & \alpha>\alpha^{Upper} \\
C_n(\alpha) & \alpha^{Lower}<=\alpha<=\alpha^{Upper} \\
C_n\left(\alpha^{Lower}\right) + C_n^{slope}\left(\alpha^{Lower}\right) \cdot \left(\alpha-\alpha^{Lower}\right) & \alpha<\alpha^{Lower} \end{cases}
Note that to avoid numerical issues at the \pm180 degree boundary, this function changes slope when the separation function is 0 above alpha^{Upper} and below alpha^{Lower}. This allow the fully-attached linear sections to be periodic and avoid numerical issues with large magnitudes of angle of attack.
Inviscid and fully separated lift coefficient:
The inviscid lift coefficient is C_{l,\text{inv}}= C_{l,\alpha} (\alpha-\alpha_0). The fully separated lift coefficient may be modelled in different ways (:cite:`ad-Branlard:book`). In most engineering models, the slope of the fully separated lift coefficient around \alpha_0 is C_{l,\alpha}/2. In the Unsteady AeroDynamics sub-module, the fully separated lift coefficient is derived from the steady separation function as:
\begin{aligned}
C_{l,\text{fs}}(\alpha) = \frac{C_l^{st}(\alpha) - C_{l,\alpha}(\alpha-\alpha_0)f_s^{st}(\alpha)}{1-f_s^{st}(\alpha)}
\text{when $f_s^{st}\neq 1$}
, \qquad
C_{l,\text{fs}}(\alpha) =\frac{C_l^{st}(\alpha)}{2}
\text{when $f_s^{st}=1$}\end{aligned}
The Beddoes-Leishman model account for attached flows and trailing edge stall :cite:`ad-LeishmanBeddoes:1989`.
Two variants are implemented in the Unsteady Aerodynamic module. These two (compressible) models are currently described in the following reference: :cite:`ad-AeroDyn:manualUnsteady`. The models use C_n and C_c as main physical quantities. The models use discrete states and cannot be used with linearization.
The 4-states (incompressible) dynamic stall model as implemented in OpenFAST is described in :cite:`ad-Branlard:2022` (the model differs slithgly from the original formulation from Hansen-Gaunaa-Madsen (HGM) :cite:`ad-Hansen:2004`).
The model is enabled using UAMod=4. The model uses C_l as main physical quantity.
Linearization of the model is available.
NOTE: this model might require smaller time steps until a stiff integrator is implemented in AeroDyn-UA.
State equation: The state equation of the model is:
\begin{aligned}
\dot{x}_1 &= - T_u^{-1} b_1\, x_1 + T_u^{-1} b_1 A_1 \alpha_{34}\nonumber \\
\dot{x}_2 &= - T_u^{-1} b_2\, x_2 + T_u^{-1} b_2 A_2 \alpha_{34}\nonumber \\
\dot{x}_3 &= - T_p^{-1} x_3 + T_p^{-1} C_l^p \nonumber \\
\dot{x}_4 &= - T_f^{-1} x_4 + T_f^{-1} f_s^{st}(\alpha_F) ,\qquad x_4 \in[0,1]
\nonumber
\end{aligned}
with
\begin{aligned}
\alpha_E(t) & =\alpha_{34}(t)(1-A_1-A_2)+ x_1(t) + x_2(t) \nonumber \\
C_{L}^p(t) & =C_{l,\alpha} \, \left(\alpha_E(t)-\alpha_0\right) + \pi T_u(t) \omega(t) \nonumber \\
\alpha_F(t) & =\frac{x_3(t)}{C_{l,\alpha}}+\alpha_0 \nonumber
\end{aligned}
Output equation: The unsteady airfoil coefficients C_{l,\text{dyn}}, C_{d,\text{dyn}}, C_{m,\text{dyn}} are obtained from the states as follows:
\begin{aligned}
C_{l,\text{dyn}}(t) &= C_{l,\text{circ}} + \pi T_u \omega \\
% C_{d,\text{dyn}}(t) &= C_d(\alpha_E) + (\alpha_{ac}-\alpha_E) C_{l,\text{dyn}} + \left[ C_d(\alpha_E)-C_d(\alpha_0)\right ] \Delta C_{d,f}'' \\
C_{d,\text{dyn}}(t) &= C_d(\alpha_E) + \left[(\alpha_{ac}-\alpha_E) +T_u \omega \right]C_{l,\text{circ}} + \left[ C_d(\alpha_E)-C_d(\alpha_0)\right ] \Delta C_{d,f}'' \\
% C_{m,\text{dyn}}(t) &= C_m(\alpha_E) + C_{l,\text{dyn}} \Delta C_{m,f}'' - \frac{\pi}{2} T_u \omega\\
C_{m,\text{dyn}}(t) &= C_m(\alpha_E) - \frac{\pi}{2} T_u \omega\\
\end{aligned}
with:
\begin{aligned}
\Delta C_{d,f}'' &= \frac{\sqrt{f_s^{st}(\alpha_E)}-\sqrt{x_4}}{2} - \frac{f_s^{st}(\alpha_E)-x_4}{4}
,\qquad
x_4\ge 0 \\
C_{l,\text{circ}}&= x_4 (\alpha_E-\alpha_0) C_{l,\alpha} + (1-x_4) C_{l,{\text{fs}}}(\alpha_E)
\end{aligned}
The 5-states (incompressible) dynamic stall model is similar to the Beddoes-Leishman 4-states model (UAMod=4), but
adds a 5th state to represent vortex generation.
It is enabled using UAMod=5. The model uses C_n and C_c as main physical quantities.
Linearization of the model is available.
Oye's dynamic stall model is a one-state (continuous) model, formulated in :cite:`ad-Oye:1991` and described e.g. in :cite:`ad-Branlard:book`. The model attempts to capture trailing edge stall. Linearization of the model is available.
State equation: Oye's dynamic stall model uses one state, \boldsymbol{x}=[f_s] where f_s is the unsteady separation function. The state equation is a first-order differential equation:
\begin{aligned}
\frac{df_s(t)}{dt} =- \frac{1}{T_f} f_s(t) + \frac{1}{T_f} f_s^{st}(\alpha_{34}(t))
\end{aligned}
where T_f=T_{f,0} T_u is the time constant of the flow separation and f_s^{st} is the steady state separation function described in :numref:`ua_notations`. The value T_{f,0} is usually chosen around 6 (different from the default value). It is readily seen that f_s reaches the value f_s^{st} when the system is in a steady state (i.e. when \frac{df_s(t)}{dt}=0).
Output equation: The unsteady lift coefficient is computed as a linear combination of the inviscid lift coefficient, C_{l, \text{inv}}, and the fully separated lift coefficient C_{l,\text{fs}}. Both of these lift coefficients are determined from the steady lift coefficient, usually provided as tabulated data, noted C_l^{st}(\alpha), where the superscript st stands for “steady”. The unsteady lift coefficient is modelled as:
\begin{aligned}
C_{l,\text{dyn}}(\alpha_{34} ,t) = f_s(t)\; C_{l,\text{inv}}(\alpha_{34}) + (1-f_s(t))\; C_{l,\text{fs}}(\alpha_{34})
\end{aligned}
where \alpha_{34} is the instantaneous angle of attack at the 3/4 chord. f_s is seen to act as a relaxation factor between the two flow situations.
The Boeing-Vertol is mentioned in the following paper :cite:`ad-Murray:2011`. Details of the model were omitted in this reference, so the documentation presented here is inspired from the implementation done in the vortex code CACTUS, which was reproduced to quasi-identity in AeroDyn. Linearization is not possible with this model.
The model as presented in :cite:`ad-Murray:2011` is an output-only model, where the dynamic angle of attack is determined using the quasi steady angle of attack and the rate of change of the angle of attack:
\alpha_{dyn} = \alpha_{34} - k_1 \gamma \sqrt{\left| \dot{\alpha} T_u\right|}
where k_1 and \gamma are constants of the model. In practice, the implementation is different for the lift and drag coefficients, and for negative and positive stall. The model needs a discrete state to calculate the rate of change of the angle of attack and two discrete states to keep track of whether the model is activated or not.
Airfoil constants:
The constants k_1, for positive and negative rates of angle of attack, are set to:
k_{1,p}= 1 ,\quad k_{1,n} = 1/2
The extent of the transition region is computed as:
\Delta \alpha_\text{max} = \frac{0.9 \operatorname{min}\left(|\alpha_1-\alpha_0|, |\alpha_2-\alpha_0|\right)}{\operatorname{max}(k_{1,p},k_{1,n})}
where \alpha_1 and \alpha_2 are the angle of attack at positive and negative stall respectively (taken as the values from the airfoil input file). The factor 0.9 is a margin to prevent the effective angle of attack to reach \alpha_0 during stall.
Intermediate variables:
The variables \gamma for the lift and drag are computed as function of the thickness to chord ratio of the airfoil t_c and the Mach number M_a (assumed to be 0 in the current implementation):
\begin{aligned}
\gamma_L &= (1.4-6\delta)\left[1-\frac{\text{Ma}-(0.4+5\delta)}{0.9+2.5\delta-(0.4+5\delta)}\right] &&\\
\gamma_D &= (1-2.5\delta) ,&&\text{if}\ \text{Ma} < 0.2 \\
\gamma_D &= (1-2.5\delta)\left[1-\frac{\text{Ma}-0.2}{(0.7+2.5\delta-0.2)}\right] ,&& \text{otherwise}
\end{aligned}
where \delta = 0.06-t_c.
Update of discrete states (and intermediate variables):
The rate of change of the angle of attack is computed as:
\dot{\alpha} = \frac{\alpha_{34}(t+\Delta t) - \alpha_{34}(t)}{\Delta t}
An additional state was introduced to avoid sudden jump of \dot{\alpha}, by storing its value. Rates that are beyond a fraction of \pi \Delta t are replaced with the values at the previous time step. This feature is not present in the CACTUS implementation.
The dynamic angle of attack offsets (lags) for the lift and drag are computed as:
\begin{aligned}
\Delta \alpha_L &= k_1 \operatorname{min} \left(\gamma_L \sqrt{\dot{|\alpha}T_u|} , \Delta \alpha_\text{max}\right)\\
\Delta \alpha_D &= k_1 \operatorname{min}\left(\gamma_D \sqrt{\dot{|\alpha}T_u|}, \Delta \alpha_\text{max} \right)
\end{aligned}
The value of k_1 is taken as k_{1,n} if \dot{\alpha}(\alpha_{34}-\alpha_0)<0, and taken as k_{1,p} otherwise. The lagged angle of attacks for the lift and drag are:
\begin{aligned}
\alpha_{\text{Lag},L} &= \alpha_{34} - \Delta \alpha_L\operatorname{sign}(\dot{\alpha}) \\
\alpha_{\text{Lag},D} &= \alpha_{34} - \Delta \alpha_D\operatorname{sign}(\dot{\alpha})
\end{aligned}
The distances to positive and negative stall are computed as follows. If \dot{\alpha}(\alpha_{34}-\alpha_0)<0 and the dynamic stall is active:
\Delta_n = \alpha_2 - \alpha_{\text{Lag},D} , \quad \Delta_p = \alpha_{\text{Lag},D} - \alpha_1
If \dot{\alpha}(\alpha_{34}-\alpha_0)<0 and the dynamic stall is not active:
\Delta_n = 0 , \quad \Delta_p = 0
If \dot{\alpha}(\alpha_{34}-\alpha_0)\ge0:
\Delta_n = \alpha_2 - \alpha_{34}, \qquad
\Delta_p = \alpha_{34} - \alpha_1
The effective angle of attack for the lift coefficient is taken as the lagged angle of attack:
\begin{aligned}
\alpha_{e,L} &= \alpha_{\text{Lag},L}
\end{aligned}
The effective angle of attack for the drag coefficient is obtained from the lagged angle of attack and the deltas to stall:
\begin{aligned}
\alpha_{e,D} &= \alpha_{\text{Lag},D}, &&\text{if}\ \Delta_n>T \ \text{or} \ \Delta_p > T \\
\alpha_{e,D} &= \alpha_{34}+(\alpha_{\text{Lag},D}-\alpha_{34}) \frac{\Delta_n}{T} , &&\text{if}\ \Delta_n>0 \ \text{and}\ \Delta_n < T \\
\alpha_{e,D} &= \alpha_{34}+(\alpha_{\text{Lag},D}-\alpha_{34}) \frac{\Delta_p}{T} , &&\text{if}\ \Delta_p>0 \ \text{and}\ \Delta_p < T \\
\alpha_{e,D} &= \alpha_{34} , &&\text{otherwise}
\end{aligned}
where T=2\Delta\alpha_\text{max} is the extent of the "transition" region.
The lift dynamic stall state is activated if \dot{\alpha}(\alpha_{34}-\alpha_0) \ge 0 and if the angle of attack is above \alpha_1 or below \alpha_2. The state is turned off if \dot{\alpha}(\alpha_{34}-\alpha_0) < 0 and the effective angle of attack is below \alpha_1 and above \alpha_2.
The drag dynamic stall state is activated if any of the condition below are true:
\begin{aligned}
&\Delta_n > T \ \text{or }\ \Delta_p > T \\
&\Delta_n > 0 \ \text{and}\ \Delta_n < T \\
&\Delta_p > 0 \ \text{and}\ \Delta_p < T
\end{aligned}
The state is turned off otherwise.
Calculation of outputs: The calculation of the dynamic lift and drag coefficients is done as follows
\begin{aligned}
C_{l,\text{dyn}}&=\frac{C_l^{st}(\alpha_{e,L})}{\alpha_{e,L}-\alpha_0} ,\quad \text{if dynamic stall active for $C_l$}\ \\
C_{l,\text{dyn}}&=C_l^{st}(\alpha_{34}) ,\quad\quad \text{otherwise} \\
C_{d,\text{dyn}}&=C_d^{st}(\alpha_{e,D})
\end{aligned}
Recalculation of intermediate variables are necessary to obtain \alpha_{e,L} and \alpha_{e,D}. The moment coefficient is calculated based on values at the aerodynamic center and mid-chord ("50"):
C_{m,\text{dyn}} = C_m^{st}(\alpha_{ac}) + \cos\alpha_{50} \left[C_l^{st}(\alpha_{34}) - C_l^{st}(\alpha_{50})\right]/4
where \alpha_{50} is computed the same way as \alpha_{34} (using the velocity at the aerodynamic center and the rotational rate of the airfoil) but using the distance from the aerodynamic center to the mid-chord (see :numref:`ua_notations`).
See :numref:`ad_ua_inputs` for a description of the inputs necessary in the AeroDyn primary file (e.g. UAMod)
See :numref:`airfoil_data_input_file` for a more comprehensive description of all the inputs present in the profile input file. Their default values are described in :numref:`UA_AFI_defaults`
See :numref:`ua_notations` for a list of notations and definitions specific to unsteady aerodynamic inputs.
An example of profile data (containing some of the unsteady aerodynamic parameters) is available here :download:`(here) <examples/ad_polar_example.dat>`.
The unsteady aerodynamic driver inputs are documented in :numref:`ua_driver`.
The default value for cd0 is the minimum value of the C_d curve between \pm20 degrees angle of attack.
\alpha_{c_{d0}} is defined to be the angle of attack where cd0 occurs.
After computing cd0, the C_n curve is computed by
C_{n}(\alpha) = C_l(\alpha) \cos\alpha + \left(C_d(\alpha) - c_{d0}\right) \sin\alpha
The slope of the C_n curve is computed as follows:
C_{n}^{Slope}\left(\frac{\alpha_{i+1} + \alpha_i}{2}\right) = \frac{C_n(\alpha_{i+1}) - C_n(\alpha_i)}{\alpha_{i+1} - \alpha_i}
C_{n,smooth}^{Slope} is a smoothed version of C_{n}^{Slope}, calculated using a triweight kernel with a window of 2 degrees.
C_{l}^{Slope}\left(\frac{\alpha_{i+1} + \alpha_i}{2}\right) = \frac{C_l(\alpha_{i+1}) - C_l(\alpha_i)}{\alpha_{i+1} - \alpha_i}
Using C_{n,smooth}^{Slope}, alphaUpper and alphaLower are computed:
alphaUpper is the smallest angle of attack value between \alpha_{c_{d0}} and 20 degrees where the C_{n,smooth}^{Slope} curve has started to decrease to 90% of its maximum slope.
C_{n,smooth}^{Slope}\left(\alpha^{Upper}\right) < 0.9 \max_{\alpha \in \left[\alpha_{c_{d0}}, \alpha^{Upper}\right]} C_{n,smooth}^{Slope}\left( \alpha \right)
alphaLower is the largest angle of attack value between -20 degrees and \alpha_{c_{d0}} where the C_{n,smooth}^{Slope} curve has started to decrease to 90% of its maximum slope.
C_{n,smooth}^{Slope}\left(\alpha^{Lower}\right) < 0.9 \max_{\alpha \in \left[\alpha^{Lower}, \alpha_{c_{d0}}\right]} C_{n,smooth}^{Slope}\left( \alpha \right)
Cn1 is the value of C_n(\alpha) at the smallest value of \alpha where \alpha >= \alpha^{Upper} and the separation function, f_{st}(\alpha) = 0.7.
Cn2 is the value of C_n(\alpha) at the largest value of \alpha where \alpha <= \alpha^{Lower} and the separation function, f_{st}(\alpha) = 0.7.
Cn_offset is the average value of the C_n curve at alphaUpper and alphaLower:
C_{n}^{offset} = \frac{C_n\left(\alpha^{Lower}\right) + C_n\left(\alpha^{Upper}\right)}{2}
C_nalpha is defined as the maximum slope of the smoothed C_n curve, C_{n,smooth}^{Slope} between \pm20 degrees angle of attack.
C_lalpha is defined as the maximum slope of the (un-smoothed) C_l curve, C_{l}^{Slope} between \pm20 degrees angle of attack.
The default alpha0 is computed as the zero-crossing of a line with a slope equal to C_lalpha that goes through the C_l curve at \alpha = \frac{\alpha^{Upper} + \alpha^{Lower}}{2}
\alpha_0 = \frac{\alpha^{Upper} + \alpha^{Lower}}{2} - \frac{C_l\left(\frac{\alpha^{Upper} + \alpha^{Lower}}{2}\right) }{C_{l,\alpha}}
Cm0 is the value of the C_m curve at alpha0: C_{m,0} = C_m\left(\alpha_0\right). If the C_m polar values have not been included, C_{m,0} =0.
alpha1 is the angle of attack above alphaUpper where the separation function, f_s^{st} is 0.7.
alpha2 is the angle of attack below alphaLower where the separation function, f_s^{st} is 0.7.
Cn1 is the value of the C_n curve at alpha1.
Cn2 is the value of the C_n curve at alpha2.
Outputting variables of the dynamic stall models is possible, but requires
to set preprocessor variable UA_OUTS and recompile the program (OpenFAST, AeroDyn Driver, or Unsteady Aero driver).
The outputs are written in output files with extension *.UA.out.
To activate these outputs with cmake, compile using -DCMAKE_Fortran_FLAGS="-DUA_OUTS=ON"
When using the driver, there is no need to use this preprocessor variable.
Aeroelastic simulations of an isolated 2D section are possible using the driver in order to use the unsteady aerodynamic model in a simplified context. See :numref:`ua_driver`. The theory and description for the aeroelastic simulation can be found in :cite:`ad-UAElast:torquepaper`.
A driver is available to run simulations for a single airfoil.
Different kind of simulations are possible:
- using sinusoidal variation of the angle of attack,
- user defined time series of angle of attack, relative wind speed and pitch rate.
- aero elastic simulations with 3 degrees of freedom for the elastic motion of the section in it's 2D plane (flap, edge and torsion), with possibility to prescribe time series of the wind speed, or prescribe the motion of the section.
The theory and description for the aeroelastic simulation can be found in :cite:`ad-UAElast:torquepaper`.
Using cmake, the driver is compiled using make unsteadyaero_driver, resulting as an executable in the aerodyn folder.
An example of input file for the unsteady aerodynamic driver can be found in the r-test repository.
The differente inputs are described below.
Environmental conditions
FldDens: Density of working fluid (kg/m^3)
KinVisc: Kinematic viscosity of working fluid (m^2/s)
SpdSound: Speed of sound of working fluid (m/s)
Unsteady aerodynamics options
UAMod : Unsteady Aero Model Switch (switch) {2=B-L Gonzalez, 3=B-L Minnema/Pierce, 4=B-L HGM 4-states, 5=B-L 5 states, 6=Oye, 7=Boeing-Vertol} [used only when AFAeroMod=2]
FLookup : Flag to indicate whether a lookup for f' will be calculated (TRUE) or whether best-fit exponential equations will be used (FALSE); if FALSE S1-S4 must be provided in airfoil input files (flag) [used only when AFAeroMod=2]
Airfoil properties
AirFoil: Airfoil table (Column 1: Angle of Attack (AoA), column 2: Lift coeff, column 3: Drag coeff).
Chord : Chord length (m)
Vec_AQ : Vector from reference point "A" to aerodynamic center (~quarter chord) "Q" in airfoil coordinates and in chord length. If "A" is at mid chord values are likely (0, -0.25) (-)
Vec_AT : Vector from reference point "A" to three-quarter chord point "T" in airfoil coordinates and in chord length. If "A" is at mid chord values are likely (0, 0.25) (-)
UseCm : Use Cm (moment coefficient) data in airfoil table {true/false}
Simulation control
SimMod: Simulation model {1=reduced frequency model, 2=prescribed-aero time series, 3=elastic cross section}
Reduced-frequency simulation (SimMod=1)
InflowVel : Inflow velocity (m/s)
NCycles : Number of angle-of-attack oscillations over the length of the simulation (-)
StepsPerCycle : Number of timesteps per cycle (-)
Frequency : Frequency for the airfoil oscillations (Hz)
Amplitude : Amplitude of the angle of attack oscillations (deg)
Mean : Cycle mean (deg)
Phase : Initial phase (num steps).
Prescribed aerodynamic simulation inputs (SimMod=2)
TMax_PA : Total run time (s)
DT_PA : Recommended module time step (s)
AeroTSFile: Time series data in delimited input file (e.g. csv) with 1 header line, 4 columns: Time (s), angle-of-attack (deg), InflowVel (m/s), Pitch rate (rad/s)
Aeroelastic simulation (SimMod=3)
The theory for the aeroelastic simulation can be found in :numref:`ua_aeroelasttheory`.
TMax : Total run time (s)
DT : Time step (s).
ActiveDOF : List of Degrees of freedom that are active (true or false)
InitPos : List of initial positions for the elastic degrees of freedom (m, m and rad)
InitVel : List of initial velocities for the elastic degrees of freedom (m/s, m/s, and rad/s)
GFScalingL1 : Generalized force scaling factors to convert from section loads to generalized loads (3x3). Three values per line.
MassMatrixL1 : Mass matrix (3x3). Three values per line.
DampMatrixL1 : Damping matrix (3x3). Three values per line.
StifMatrixL1 : Stiffness matrix (3x3). Three values per line.
Twist : Fixed twist of the section when torsion degree of freedom is zero (deg)
InflowMod : Model for the inflow velocity. {1: constant velocity, 2: time series}
Inflow : Inflow velocity in x and y direction [used only when InflowMod=1]
InflowTSFile : Input file for inflow velocity. Delimited file (e.g. csv) with one header line, three columns: Time (s), Ux (m/s), Uy (m/s). [used only when InflowMod=2]
MotionMod : Model for the motion of the degrees of freedom {1: dynamic, 2: prescribed}
MotionTSFile : Input file for prescribed motion. Delimited file (e.g. csv) with one header line, 10 columns: Time (s), x (m), y (m), th (rad), velocities, and accelerations. [used only when InflowMod=2]
Output control
SumPrint : Write unsteady aerodynamics summary file (flag)
WrAFITables : Write back the aerodynamic coefficients used internally (flag)
Example CSV input files
The unsteady aerodyn driver now relies on CSV files for it's input time series. The time column does not need to be at a constant time step, but needs to be monotonously increasing.
Prescribed aero input (SimMod=2):
Inflow file input (SimMod=3, InflowMod=2):
Motion file input (SimMod=3, MotionMod=2) (note in this dummy exmaple velocities and accelerations are not provided, but preferably they should be):