Changes between Version 48 and Version 49 of 1DPulsedJets

Timestamp:

03/30/12 13:05:46 (13 years ago)

Author:

ehansen

Comment:

—

1DPulsedJets

@@ -224 +224 @@
 The shock jump equations for a stationary shock are used to solve for the initial post-shock values.  The post-shock velocity v,,2,, can be written as:
 
-
-where v,,1,, is the ambient velocity, and M is the ambient mach number.  Remember that the mach number M = v,,1,,/c where c is the ambient sound speed, and [[latex($c = \sqrt{\frac{\gamma P_{1}}{\rho_{1}}}$)]] where P,,1,, is ambient pressure, and [[latex($\rho_{1}$)]] is ambient density.
-
-The post-shock density and pressure ([[latex($\rho_{2}$)]] and P,,2,, respectively) can be found by using mass flux and momentum flux conservation across the shock:
+[[latex($v_2 = v_1 \frac{(\gamma - 1)M^2 + 2}{(\gamma + 1)M^2} $)]]
+
+where v,,1,, is the ambient velocity, and M is the ambient mach number.  Remember that the mach number M = v,,1,,/c where c is the ambient sound speed, and [[latex($c = \sqrt{\frac{\gamma P_{1}}{\rho_{1}}}$)]] where P,,1,, is ambient pressure, and [[latex($\rho_{1}$)]] is ambient density.  The post-shock density and pressure ([[latex($\rho_{2}$)]] and P,,2,, respectively) can be found by using mass flux and momentum flux conservation across the shock:
+
+[[latex($\rho_1 v_1 = \rho_2 v_2$)]]
+
+[[latex($\rho_1 v_1 ^2 + P_1 = \rho_2 v_2 ^2 + P_2$)]]
 
 These post-shock values become the boundary conditions for the fluid equations in the cooling region:
+
+[[latex($\rho v = \rho_2 v_2$)]]
+
+[[latex($\rho v ^2 + P = \rho_2 v_2 ^2 + P_2$)]]
+
+[[latex($\frac{d}{dx}(\frac{1}{2}\rho v ^3 + P v) = -\Lambda$)]]
 
 where [[latex($\rho$)]], v, and P represent the density, velocity, and pressure in the cooling region as functions of x, and [[latex($\Lambda$)]] is the cooling rate.