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