initial commit

1d_sim.py

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+import numpy as np
+import matplotlib.pyplot as plt
+
+l_barrel = 2 #m
+d_barrel = 0.2 #m
+
+l_sabot = 0.03 #m
+mu_sabot = 0.04
+
+m_payload = 6 #kg
+
+vol_chamber = 0.015 #m^3
+p_chamber = 20e5 #Pa
+t_chamber = 300 #K
+gamma = 1.4
+
+dt = 0.00003
+
+a_b = d_barrel**2 * np.pi / 4
+
+def step(t, f, a, v, l, vol, p, temp):
+    global dt
+    ft = a_b * p - mu_sabot*d_barrel*np.pi*l_sabot*p
+    at = ft / m_payload
+    vt = v + at*dt
+    lt = l + vt*dt
+    volt = vol + vt*dt*a_b
+    pt = p * (vol/volt)**gamma
+    tt = t+dt
+    tempt = t_chamber * (vol_chamber/vol)**(gamma-1)
+    return tt, ft, at, vt, lt, volt, pt, tempt
+
+data = [(
+    0, 0, 0, 0, 0, vol_chamber, p_chamber, t_chamber,
+),]
+
+i = 0
+print(data[0])
+while data[-1][4] < l_barrel:
+    i+=1
+    print(i)
+    erg = step(*data[-1])
+    data.append(erg)
+
+print("done")
+
+tt, ft, at, vt, lt, volt, pt, tempt = np.transpose(data)
+
+plt.plot(lt, pt/1000)
+plt.xlabel("Weg ([m]")
+plt.ylabel("Pressure [bar]")
+plt.show()

calc.py

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+import numpy as np
+from scipy import constants
+import matplotlib.pyplot as plt
+
+# Konstanten und Physik
+
+gasses = { 
+    "air": {
+        "c_p": 1.005e3, # J/kgK
+        "c_v": 0.718e3, # J/kgK
+        "m_mol": 28.949e-3 , # kg/mol
+    },
+}
+
+gas = gasses['air']
+temp_r = 273.15+25
+r_s = constants.R / gas['m_mol']
+
+
+# Modellparameter
+
+sample_d = 0.2 #m 
+sample_l = 0.3 #m 
+sample_vel = 100 #m/s
+sample_m = 6 #kg
+
+chamber_p = 20e5 # Pa 
+
+sample_a = (sample_d/2)**2 * np.pi
+sample_v = sample_a * sample_l
+density = sample_m / sample_v #kg/m³
+e_kin = sample_m * sample_vel**2 / 2
+print(f"Probenenergie: {e_kin/1000:.0f} kJ")
+
+chamber_v = e_kin/ chamber_p
+# chamber_v = 0.05
+print(f"Chamber Volume = {chamber_v*1000:.1f} l")
+
+m_g = chamber_v*chamber_p / (r_s * temp_r)
+print(f"Gas-Masse = {m_g:.3f} kg = {m_g / (sample_m+m_g) *100:.2f} % der Systemmasse")
+
+# e_kin = (sample_m * sample_vel**2 / 2) + (m_g * sample_vel**2 /6)
+# print(f"kinetische System-energie = {e_kin:.0f} J")
+
+
+## isothermer Ansatz
+
+e_pot = chamber_p * chamber_v
+print(f"p V = {e_pot} J")
+l_f = chamber_v / sample_a
+print(f"l_f = V_c / A = {l_f:.3f} m")
+barrel_l = l_f * np.exp(e_kin /  e_pot)-l_f
+print(f"Lauflänge = {barrel_l:.3f} m")
+
+# Adiabatischer Ansatz
+
+gamma = gas['c_p']/gas['c_v']
+print(f"γ = {gamma}")
+
+l_f = chamber_v / sample_a
+const = chamber_v*chamber_p *(l_f**(gamma-1)) / (1-gamma)
+L = (e_kin/const + l_f**(1-gamma))**(1/(1-gamma)) - l_f
+
+print(f"Lauflänge L = {L:.3f}")
+
+# Grafiken
+
+def work(x):
+    return const *((l_f + x)**(1-gamma) - l_f**(1-gamma))
+
+def vel(x):
+    return np.sqrt(2*work(x) /sample_m)
+
+def vol(x):
+    return chamber_v + sample_a*x
+
+t_0 = 273.15+25
+
+def temp(x):
+    return t_0 * (chamber_v / vol(x))**(gamma-1)
+
+def pres(x):
+    return e_pot * (chamber_v / vol(x))**(gamma-1) / chamber_v
+    
+
+print(f"L = {L:.3f}")
+
+l_v = 3
+print(f"W(x={L:.3f}, p={chamber_p:.0e}) = {work(L):.3f}")
+print(f"p(x={L:.3f}, p={chamber_p:.0e}) = {pres(L):.2e}")
+print(f"V(x={L:.3f}, p={chamber_p:.0e}) = {vol(L):.2e}")
+print(f"ΔT(x={L:.3f}, p={chamber_p:.0e}) = { temp(L):.2f}")
+
+print(e_kin + vol(L)*pres(L))
+
+
+l_array = np.linspace(0,L,400)
+plt.plot(l_array, vel(l_array))
+plt.ylabel('Speed [m/s]')
+plt.xlabel('Sample Travel [m]')
+plt.show()