You are required to design a minimum length 2-dimensional rocket
engine nozzle for the specific conditions given below. The analytical procedure of Method
of Characteristics, as described in Section 11.7, p. 397 (new book p. 390), and Example
11.1, p. 401 (new book p. 394) of your hardcover textbook (Modern Compressible Flow
3rd Edition, by J.D. Anderson), may be used to solve this problem.
Matlab,
programming codes to calculate and develop the nozzle contour.
General Specifications:
(1) The rocket is to discharge into an atmosphere where the ambient pressure is
101.135 kPa.
(2) The propellant is a mixture of hydrogen and oxygen, with  = 1.22 and R = 519.6
J/(kg.K)
(3) The stagnation temperature T0 of the propellant is 3500 K, and the stagnation
pressure p0 of the propellant is 2528.38 kPa
(4) The total mass flow rate, , through the rocket nozzle is 200 kg/s
(5) The velocity of the fluid as it crosses the exit plane must be uniform and parallel to
the axis of the nozzle
(6) The overall expansion ratio Aexit/Athroat must be large enough so that the specific
kinetic energy of the exhaust gas, 0.5 Ve2 is as high as possible percentage of
specific stagnation enthalpy, h0, of the propellant. What is the best percentage of
this kinetic energy of exhaust with respect to the specific stagnation enthalpy, h0,
of the propellant?
(7) The geometry downstream of throat should not exhibit sharp corners of large
turning angles (this is required to avoid boundary layer separation due to sharp
corners)
(8) The length of the nozzle should be as short as possible subject to above constraints
.
Design Solution a description of design process, sample calculations, plots, table of
calculated results, and any program listing that he/she may have developed. A scaled
drawing of the nozzle must also be given.
As a reminder, the project will be graded on the following contents in the report.
(a) You must also show explicit calculations of the exit speed, Ve, and the exit
Mach number, Me.
(a) You must show a sample calculation of the characteristic lines that you use
to create the nozzle contour
(b) Use suitable number of characteristics (at least 50) to produce a smooth
contour.
(c) A table of the nozzle interior contour coordinates. The x, y coordinates
must be expressed in SI units, as measured from the axis of the nozzle as a
function of axial distance, x, from the throat section. Also, plot the contour
as A/Athroat vs. x/L, where A is the local nozzle area, Athroat is the throat area,
and L is the length of the nozzle.
(d) Provide a smoothed graphics of your final nozzle shape. No need to show
all the characteristic lines.
(e) Program listing must be presented.
(f) Provide plots and discussions of nozzle flow properties, such as Mach
number, pressure and temperature variations through the nozzle