Rayleigh

- Shock wave: syntax of comment fix
- add inverse Mach from Ti ratio
- example: Rayleigh heating
- example: Ramjet working line, full supersonic and conventional working line

aero/Rayleigh.py

@@ -53,3 +53,15 @@ def NormdS(Mach, gamma=1.4):
     m2 = np.square(Mach)
     return np.log(m2*((gamma+1)/(1+gamma*m2))**((gamma+1)/gamma))
 
+def SubMach_TiTicri(Tiratio, gamma=1.4):
+    """ computes Mach number from Ti/Ti_cri ratio (<1)
+    """
+    alpha = np.sqrt(1.-Tiratio)
+    return np.sqrt((1.-alpha)/(alpha*gamma+1))
+
+def SupMach_TiTicri(Tiratio, gamma=1.4):
+    """ computes Mach number from Ti/Ti_cri ratio (<1)
+    """
+    alpha = np.sqrt(1.-Tiratio)
+    return np.sqrt((1.+alpha)/(1.-alpha*gamma))
+

aero/ShockWave.py

@@ -72,14 +72,16 @@ def local_f(sig):
     return IterativeSolve.secant_solve(local_f, deflection, degree.asin(1./Mach)+deflection)
 
 def sigmaMax(Mach, gamma=1.4):
-    " computes the MAXIMUM shock angle (always subsonic downstream flow)
+    """ computes the MAXIMUM shock angle (always subsonic downstream flow)
+    """
     M2 = np.square(Mach)
     ka = (M2-1.)*(1.+.5*(gamma-1.)*M2)
     kb = .25*((gamma+1.)*M2-(3.-gamma))*M2 + 1.
     return degree.atan(np.sqrt((kb+np.sqrt(kb**2+ka))/ka))
 
 def sigmaSonic(Mach, gamma=1.4):
-    " computes the shock angle for a downstream SONIC Mach number
+    """ computes the shock angle for a downstream SONIC Mach number
+    """
     M2 = np.square(Mach)
     ka = gamma-3+M2*(gamma+1)
     kb = (gamma+1)*(np.square(M2-3)+gamma*np.square(M2+1))

doxygen.conf

@@ -1397,7 +1397,7 @@ FORMULA_TRANSPARENT    = YES
 # The default value is: NO.
 # This tag requires that the tag GENERATE_HTML is set to YES.
 
-USE_MATHJAX            = NO
+USE_MATHJAX            = YES
 
 # When MathJax is enabled you can set the default output format to be used for
 # the MathJax output. See the MathJax site (see:

examples/ramjet-working.py

@@ -0,0 +1,101 @@
+# -*- coding: utf-8 -*-
+"""
+Design of Ramjet
+@author: j.gressier
+all sections are normalized by A0, section of upstream flow
+- 1 is flow section in inlet (possibly decelerated by external compression)
+- 2 is the inlet throat
+- 21 or 22 are the upstream and downstream sections at the normal shock in the inlet
+- 3 is the beginning of the combustor
+- 4 is the end of the combustor (A3=A4)
+- 8 is the throat of the nozzle
+- 9 is the nozzle exit
+"""
+
+import numpy                 as np
+import matplotlib.pyplot     as plt
+import aero.Isentropic       as isent
+import aero.MassFlow         as mf
+import aero.ShockWave        as sw
+import aero.Rayleigh         as ray
+
+gam  = 1.4   # assumed constant
+npts = 50
+M0   = 3.
+M2   = 1.5
+A2A0 = mf.Sigma_Mach(M2, gam)/mf.Sigma_Mach(M0, gam)
+print "A0/A2 for isentropic compression from Mach %4.2f to %4.2f : %6.3f"%(M0, M2, 1./A2A0)
+A3A2 = 1./A2A0
+A8A2 = .6*A3A2
+
+fig=plt.figure(1, figsize=(10,12))
+fig.suptitle('Flow features on RAMJET, $M_2=%.2f$, $A_8/A_2=%.2f$, $\gamma = %.1f$'
+    %(M2, A8A2, gam), fontsize=12, y=0.93)
+
+plt.subplot(311)
+plt.ylabel('$p_{i3}/p_{i0}$', fontsize=10)
+plt.grid(which='major', linestyle=':', alpha=0.5)
+
+plt.subplot(312)
+plt.ylabel('$p_{i4}/p_{i0}$', fontsize=10)
+plt.grid(which='major', linestyle=':', alpha=0.5)
+
+plt.subplot(313)
+plt.ylabel('$M_{4}$', fontsize=10)
+plt.grid(which='major', linestyle=':', alpha=0.5)
+
+# --- (FS) fully supersonic flow (not expected on design)
+
+M3sup    = mf.Mach_Sigma(A3A2*mf.Sigma_Mach(M2, gam), gam)
+M4max    = mf.Mach_Sigma(A3A2/A8A2, 2., gam)  # look for supersonic value
+alphamax = ray.Ti_Ticri(M4max, gam)/ray.Ti_Ticri(M3sup, gam)
+print "unchoking of fully supersonic flow for Ti4/Ti0 = %6.3f"%(alphamax)
+
+FSalpha = np.log10(np.logspace(1., alphamax, npts+1))
+FSm4    = ray.SupMach_TiTicri(FSalpha/alphamax*ray.Ti_Ticri(M4max, gam), gam)
+FSpi4   = ray.Pi_Picri(FSm4, gam)/ray.Pi_Picri(M3sup, gam)
+FSpi3   = np.ones(npts+1)
+plt.subplot(311)
+plt.ylabel('$p_{i3}/p_{i0}$', fontsize=10)
+plt.plot(FSalpha, FSpi3, '-', color='#ff0000')
+plt.subplot(312)
+plt.ylabel('$p_{i4}/p_{i0}$', fontsize=10)
+plt.plot(FSalpha, FSpi4, '-', color='#ff0000')
+plt.subplot(313)
+plt.ylabel('$M_{4}$', fontsize=10)
+plt.plot(FSalpha, FSm4, '-', color='#ff0000')
+
+# --- (CW) conventional working state
+
+# M8 is sonic so M4 is known
+CWm4 = mf.Mach_Sigma(A3A2/A8A2, .1, gam)  # look for subsonic value
+
+CWm3low  = sw.downstream_Mn(M3sup, gam)
+alphamin = ray.Ti_Ticri(CWm4, gam)/ray.Ti_Ticri(CWm3low, gam)
+CWm3high = mf.Mach_Sigma(A3A2*mf.Sigma_Mach(sw.downstream_Mn(M2, gam), gam), .1, gam)
+alphamax = ray.Ti_Ticri(CWm4, gam)/ray.Ti_Ticri(CWm3high, gam)
+print "         unchoking of inlet throat for Ti4/Ti0 = %6.3f"%(alphamax)
+print "             fully supersonic flow for Ti4/Ti0 = %6.3f"%(alphamin)
+
+CWalpha = np.log10(np.logspace(alphamin, alphamax, npts+1))
+CWm3    = ray.SubMach_TiTicri(ray.Ti_Ticri(CWm4, gam)/CWalpha, gam)
+CWpi3   = mf.Sigma_Mach(CWm3, gam)/mf.Sigma_Mach(M2, gam)/A3A2
+CWpi4   = CWpi3*ray.Pi_Picri(CWm4, gam)/ray.Pi_Picri(CWm3, gam)
+CWm4    = np.ones(npts+1)*CWm4
+
+plt.subplot(311)
+plt.plot(CWalpha, CWpi3, '-', color='#bb0000')
+plt.subplot(312)
+plt.plot(CWalpha, CWpi4, '-', color='#bb0000')
+plt.subplot(313)
+plt.plot(CWalpha, CWm4, '-', color='#bb0000')
+plt.show
+
+# --- unchoked channel
+
+
+#plt.minorticks_on()
+plt.grid(which='major', linestyle=':', alpha=0.5)
+#plt.grid(which='minor', linestyle=':', alpha=0.5)
+fig.savefig('Rayleigh-TS.pdf', bbox_inches='tight')
+#show()

examples/rayleigh-heating.py

@@ -0,0 +1,33 @@
+# -*- coding: utf-8 -*-
+"""
+Plot of Rayleigh curves in several diagrams
+@author: j.gressier
+"""
+
+import numpy                 as np
+import matplotlib.pyplot     as plt
+import aero.Rayleigh         as ray
+
+npoints = 100
+gam     = 1.4
+
+fig=plt.figure(1, figsize=(10,8))
+fig.suptitle('Mach number evolution when heating, $\gamma = %.1f$'%gam, fontsize=12, y=0.93)
+
+for M0 in [.1, .2, .3, .4, .5, .6, .7, .8, .9, 1.2, 1.5, 2., 3., 4., 6., 10., 20.]:
+#for M0 in [.1, .5]:
+    Timax = ray.maxTiratio_Mach(M0, gam)
+    Ti    = np.log10(np.logspace(1., Timax, npoints+1))
+    Mach  = ray.SubMach_TiTicri(Ti/Timax, gam) if M0 < 1 else ray.SupMach_TiTicri(Ti/Timax, gam)
+    plt.plot(Ti, Mach, '-', color='#ff0000')
+
+plt.axis([1., 10, .1, 10.])
+plt.ylabel('Mach number', fontsize=10)
+plt.xlabel('$T_i/T_{i0}$', fontsize=10)
+plt.loglog()
+#plt.ticklabel_format(axis='both', style='plain')
+#plt.minorticks_on()
+plt.grid(which='major', linestyle=':', alpha=0.5)
+plt.grid(which='minor', linestyle=':', alpha=0.5)
+fig.savefig('Rayleigh-heating.pdf', bbox_inches='tight')
+#plt.show()