Flow with an incoming Mach number of 0.3 and an inlet total pressure of 300 psia enters a combustion chamber 18 in. long with a 5 in. diameter and a friction factor of 0.040. The total temperature increases from 1200°R to 2400°R. What is the total pressure ratio across the burner if the specific heat ratio is 1.30? Also determine the burner ratios for static temperature and pressure, and the exit Mach number. Plot the changes of these ratios and the Mach number as a function of axial position in the chamber (for incoming Mach number of 0.3 only).
Now investigate the effects of these ratios with different incoming Mach numbers. Vary the Mach number from 0 to 0.4 in increments of 0.05. On a single graph, plot each variable ratio (total pressure, static pressure, static temperature) and the exit Mach number against the incoming Mach number. (You will want to use a double-Y-axis plot, with the exit Mach number and pressure ratios on one axis, and the temperature ratio on the other axis.)
To solve this problem, you will need to numerically integrate the equations you develop from the table of influence coefficients. This is relatively easy if you replace all the differential terms (dM2, dT, etc.) with delta terms (DM2, DT, etc.) where a delta term represents a change in the variable in space. Divide the chamber into 100 increments, and use a backwards difference for each delta term (i.e. ΔM2 = M2i - M2i - 1). In this fashion, you can numerically integrate your way across the burner.
You may choose any computer language you prefer provided you are not using a commercial or other pre-written application to do the work for you (i.e., MATLAB, Mathematica, Excel, and other available software are not acceptable).
To complete this project, you must turn in the code listing, numerical results from your code (appropriately formatted and aligned for readability with exactly 3 decimal places), and your plots (with appropriate titles, axis labels, labeled legends, etc.).