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1-D Nozzle
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#This code solves the flow in a 1D convergent divergent nozzle using
#finite difference method
import numpy as np; import matplotlib.pyplot as plt
print('All Modules Imported \n\n\n')
grid=np.linspace(0,3,31) #grid set
A=1 + 2.2 * (grid-1.5)**2 #Area
Ro=1- 0.3146*grid #Density
T = 1 - 0.2314*grid #Temperature
V= (0.1 + 1.09*grid)*np.sqrt(T) #Velocity
M=V/np.sqrt(T)
Mdata=[M[15]]
Mdataex=[M[30]]
Mdatain=[M[0]]
print('V is ',V)
t=0
itr=1
while(1):
delt=(0.5*(0.1/(np.sqrt(T)+V))).min()
i=1
RoDdata=[0]
VDdata=[0]
TDdata=[0]
while i<30:
RoD=(((-Ro[i]*((V[i+1]-V[i])/0.1)))-((Ro[i]*V[i]*((np.log(A[i+1])-np.log(A[i]))/0.1)))-((V[i]*((Ro[i+1]-Ro[i])/0.1))))
RoDdata.append(RoD)
VD=(-V[i]*((V[i+1]-V[i])/0.1)) - (((T[i+1]-T[i])/0.14)+((T[i]*Ro[i+1]-T[i]*Ro[i])/(0.14*Ro[i])))
VDdata.append(VD)
TD=-V[i]*((T[i+1]-T[i])/0.1)-((1.4-1)*T[i])*( ((V[i+1]-V[i])/0.1) + V[i]*((np.log(A[i+1])-np.log(A[i]))/0.1))
TDdata.append(TD)
i=i+1
RoDdata.append(0)
VDdata.append(0)
TDdata.append(0)
Robar=Ro + np.asarray(RoDdata) * delt
Vbar=V + np.asarray(VDdata) * delt
Tbar=T + np.asarray(TDdata) * delt
i=1
RoDdata2=[0]
VDdata2=[0]
TDdata2=[0]
while i<30:
RoD=(((-Robar[i]*((Vbar[i]-Vbar[i-1])/0.1)))-((Robar[i]*Vbar[i]*((np.log(A[i])-np.log(A[i-1]))/0.1)))-((Vbar[i]*((Robar[i]-Robar[i-1])/0.1))))
RoDdata2.append(RoD)
VD=(-Vbar[i]*((Vbar[i]-Vbar[i-1])/0.1)) - (((Tbar[i]-Tbar[i-1])/0.14)+((Tbar[i]*Robar[i]-Tbar[i]*Robar[i-1])/(0.14*Robar[i])))
VDdata2.append(VD)
TD=-Vbar[i]*((Tbar[i]-Tbar[i-1])/0.1)-((1.4-1)*Tbar[i])*( ((Vbar[i]-Vbar[i-1])/0.1) + Vbar[i]*((np.log(A[i])-np.log(A[i-1]))/0.1))
TDdata2.append(TD)
i=i+1
RoDdata2.append(0)
VDdata2.append(0)
TDdata2.append(0)
RoDavg=0.5 * (np.asarray(RoDdata) + np.asarray(RoDdata2))
VDavg=0.5 * (np.asarray(VDdata) + np.asarray(VDdata2))
TDavg=0.5 * (np.asarray(TDdata) + np.asarray(TDdata2))
Ro=Ro + np.asarray(RoDavg) * delt
V=V + np.asarray(VDavg) * delt
T=T + np.asarray(TDavg) * delt
V[0]= 2*V[1] - V[2]
Ro[0]= 2*Ro[1] - Ro[2]
T[0]= 2*T[1] - T[2]
V[30]= 2*V[29] - V[28]
Ro[30]= 2*Ro[29] - Ro[28]
T[30]= 2*T[29] - T[28]
P = Ro * T
M=V/np.sqrt(T)
Mdata.append(M[15])
Mdataex.append(M[30])
Mdatain.append(M[0])
t= t + delt
itr=itr+1
print('Iteration number : ',itr)
if (np.absolute(Mdata[-1]-Mdata[-2])) < 0.0000001:
break
print('\n\n P is ',P)
print('\n\n mach no. is ',M)
print('\n\n V, Ro & T are ',V,'\n\n', Ro,'\n\n', T)
print('\n\n Iterations required = ',itr-1, '\n\n Time = ',t, ' seconds')
plt.plot(np.arange(itr),Mdata,'-',np.arange(itr),Mdataex,'-',np.arange(itr),Mdatain,'-')
plt.xlabel('X coordinate --> Iterations')
plt.ylabel('Y coordinate --> Mach Number')
plt.title('Variation in Mach number')
plt.legend(['Throat','Exit','Inlet'],bbox_to_anchor=(0,0),loc=4)
plt.show()