add unstarted case to ramjet example

examples/ramjet-working.py

@@ -21,16 +21,16 @@
 
 gam  = 1.4   # assumed constant
 npts = 50
-M0   = 3.
+M0   = 2.8
 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
+A3A2 = 1./A2A0*0.9
+A8A2 = .8*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)
+fig.suptitle('Flow features on RAMJET, $M_0=%.2f$, $M_2=%.2f$, $A_8/A_2=%.2f$, $\gamma = %.1f$'
+    %(M0, M2, A8A2, gam), fontsize=12, y=0.93)
 
 plt.subplot(311)
 plt.ylabel('$p_{i3}/p_{i0}$', fontsize=10)
@@ -41,7 +41,8 @@
 plt.grid(which='major', linestyle=':', alpha=0.5)
 
 plt.subplot(313)
-plt.ylabel('$M_{4}$', fontsize=10)
+plt.ylabel('$T_{i4}/T_{i3}$', fontsize=10)
+plt.ylabel('$M_{3}$', fontsize=10)
 plt.grid(which='major', linestyle=':', alpha=0.5)
 
 # --- (FS) fully supersonic flow (not expected on design)
@@ -55,15 +56,14 @@
 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)
+FSm3    = M3sup*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')
+plt.plot(FSalpha, FSm3, '-', color='#ff0000')
 
 # --- (CW) conventional working state
 
@@ -74,7 +74,7 @@
 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 "           unstart 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))
@@ -88,14 +88,59 @@
 plt.subplot(312)
 plt.plot(CWalpha, CWpi4, '-', color='#bb0000')
 plt.subplot(313)
-plt.plot(CWalpha, CWm4, '-', color='#bb0000')
-plt.show
+plt.plot(CWalpha, CWm3, '-', color='#bb0000')
+
+# --- (UC) unstarted channel (A8 is sonic)
+
+alphamax = 1.1*alphamax
+# M8 is sonic so M4 is known
+UCm4     = mf.Mach_Sigma(A3A2/A8A2, .1, gam)  # look for subsonic value
+UCm3low  = mf.Mach_Sigma(A3A2, .1, gam)       # look for subsonic value
+alphamin = ray.Ti_Ticri(UCm4, gam)/ray.Ti_Ticri(UCm3low, gam)
+print "           (restart) choked throat for Ti4/Ti0 = %6.3f"%(alphamin)
+A1A2 = mf.Sigma_Mach(sw.downstream_Mn(M0, gam), gam)
+print "  critical flow for unstart condition if A1/A2 = %6.3f"%(A1A2)
+print "                                         A1/A0 = %6.3f"%(A1A2*A2A0)
+
+UCalpha = np.log10(np.logspace(alphamin, alphamax, npts+1))
+UCpi0   = sw.Pi_ratio(M0)
+UCm3    = ray.SubMach_TiTicri(ray.Ti_Ticri(UCm4, gam)/UCalpha, gam)
+UCpi3   = UCpi0*np.ones(npts+1)
+UCpi4   = UCpi3*ray.Pi_Picri(UCm4, gam)/ray.Pi_Picri(UCm3, gam)
+UCm4    = np.ones(npts+1)*UCm4
+
+plt.subplot(311)
+plt.plot(UCalpha, UCpi3, '-', color='#990000')
+plt.subplot(312)
+plt.plot(UCalpha, UCpi4, '-', color='#990000')
+plt.subplot(313)
+plt.plot(UCalpha, UCm3, '-', color='#990000')
+
+# --- (RC) unstarted but choked channel (A2 and A8 are sonic)
 
-# --- unchoked channel
+alphamax = alphamin
+RCm4     = mf.Mach_Sigma(A3A2/A8A2, .1, gam)  # look for subsonic value
+RCm3low  = mf.Mach_Sigma(A3A2, 2., gam)       # look for supersonic value
+alphamin = ray.Ti_Ticri(RCm4, gam)/ray.Ti_Ticri(RCm3low, gam)
 
+RCalpha = np.log10(np.logspace(alphamin, alphamax, npts+1))
+RCpi0   = sw.Pi_ratio(M0)
+RCm3    = ray.SubMach_TiTicri(ray.Ti_Ticri(RCm4, gam)/RCalpha, gam)
+RCpi3   = RCpi0*mf.Sigma_Mach(RCm3, gam)/A3A2
+RCpi4   = RCpi3*ray.Pi_Picri(RCm4, gam)/ray.Pi_Picri(RCm3, gam)
+RCm4    = np.ones(npts+1)*RCm4
+
+plt.subplot(311)
+plt.plot(RCalpha, RCpi3, '--', color='#000000')
+plt.subplot(312)
+plt.plot(RCalpha, RCpi4, '--', color='#000000')
+plt.subplot(313)
+plt.plot(RCalpha, RCm3, '--', color='#000000')
+
+#
 
 #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()
+fig.savefig('Ramjet-Working.pdf', bbox_inches='tight')
+plt.show