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rotorpy/wind/dryden_utils.py

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+"""
+Utility scripts for the Dryden wind model
+The Dryden Gust model is implemented using this package: 
+https://github.com/goromal/wind-dynamics
+
+"""
+import numpy as np
+
+class GustModelBase():
+    """
+    """
+
+    def __init__(self, V, L, sigma, dt=0.05):
+        """
+        Inputs: 
+            V, average velocity through medium, m/s
+            L, characteristic length scale, m
+            sigma, turbulence intensity
+        """
+
+        self.dt = dt
+        b = 2*np.sqrt(3)*L/V
+        c = 2*L/V
+
+        self.alpha = sigma*np.sqrt(2*L/np.pi/V)
+        self.beta = self.alpha*b
+        self.delta = 2*c
+        self.gamma = c*c
+
+        self.u_km1 = 0
+        self.u_km2 = 0
+        self.y_km1 = 0
+        self.y_km2 = 0
+
+        self.initialized = True
+        return 
+    
+    def run(self, dt):
+        """
+        """
+
+        C1 = 1.0 + 2*self.delta/dt + 4*self.gamma/dt/dt
+        C2 = 2.0 - 8*self.gamma/dt/dt
+        C3 = 1.0 - 2*self.delta/dt + 4*self.gamma/dt/dt
+        C4 = self.alpha + 2*self.beta/dt
+        C5 = 2*self.alpha
+        C6 = self.alpha - 2*self.beta/dt
+
+        u_k = np.random.uniform(-1,1)
+        y_k = (C4*u_k + C5*self.u_km1 + C6*self.u_km2 - C2*self.y_km1 - C3*self.y_km2)/C1
+
+        self.u_km2 = self.u_km1
+        self.u_km1 = u_k
+        self.y_km2 = self.y_km1
+        self.y_km1 = y_k
+
+        return y_k
+    
+    def integrate(self, dt):
+        """
+        """
+
+        if (dt > self.dt):
+            t = 0
+            y = 0
+            while (t < dt):
+                t_inc = min(self.dt, dt - t)
+                y = self.run(t_inc)
+                t += t_inc
+            return y
+        else:
+            return self.run(dt)
+        
+class DrydenWind():
+    """
+    """
+
+    def __init__(self, wx_nominal, wy_nominal, wz_nominal, 
+                       wx_sigma, wy_sigma, wz_sigma, 
+                       altitude=2.0):
+        
+        self.wx_nominal, self.wy_nominal, self.wz_nominal = wx_nominal, wy_nominal, wz_nominal
+        self.altitude = altitude
+
+        Lz_ft = 3.281 * altitude
+        Lx_ft = Lz_ft / ((0.177 + 0.000823 * Lz_ft)**(1.2))
+        Ly_ft = Lx_ft
+
+        self.wx_gust = GustModelBase(1.0, Lx_ft/3.281, wx_sigma)
+        self.wy_gust = GustModelBase(1.0, Ly_ft/3.281, wy_sigma)
+        self.wz_gust = GustModelBase(1.0, Lz_ft/3.281, wz_sigma)
+
+        self.initialized = True
+
+        return
+    
+    def getWind(self, dt):
+        """
+        """
+
+        if self.initialized:
+            wind_vector = np.array([self.wx_nominal, self.wy_nominal, self.wz_nominal]) + np.array([self.wx_gust.integrate(dt), self.wy_gust.integrate(dt), self.wz_gust.integrate(dt)])
+        else:
+            wind_vector = np.array([0,0,0])
+
+        return wind_vector
+    
+
+if __name__=="__main__":
+
+    import matplotlib.pyplot as plt
+    import numpy as np
+
+    t = 100.0
+    dt = 0.05
+    x_mean = 0.0
+    y_mean = 1.0
+    z_mean = 0.0
+    x_sigma = 10.0
+    y_sigma = 0.0
+    z_sigma = 70.0
+
+    plt.rcParams.update({
+        "text.usetex": True,
+        "font.family": "serif",
+        "font.serif": ["Palatino"],
+    })
+
+    wind = DrydenWind(x_mean, y_mean, z_mean, x_sigma, y_sigma, z_sigma)
+
+    n = int(np.floor(t / dt)) + 1
+    x = np.linspace(0, t, n)
+    y = np.zeros((3,x.size))
+
+    for i in range(n):
+        y[:,i] = wind.getWind(dt)
+
+    fig, axs = plt.subplots(3)
+    fig.suptitle('Dryden Gust Velocities\n$\sigma_x=%f$, $\sigma_y=%f$, $\sigma_z=%f$' % (x_sigma, y_sigma, z_sigma))
+    axs[0].plot([0, t],[x_mean, x_mean])
+    axs[0].plot(x, y[0,:])
+    axs[0].set_ylabel('X Velocity')
+    axs[1].plot([0, t],[y_mean, y_mean])
+    axs[1].plot(x, y[1,:])
+    axs[1].set_ylabel('Y Velocity')
+    axs[2].plot([0, t],[z_mean, z_mean])
+    axs[2].plot(x, y[2,:])
+    axs[2].set_ylabel('Z Velocity')
+    axs[2].set_xlabel('Time (s)')
+
+    plt.show()