MATLAB: Calculating Temperature & Density of Supersonic Nozzle Flow - Prof. Daniel R. Kirk, Assignments of Mechanical Engineering

Download MATLAB: Calculating Temperature & Density of Supersonic Nozzle Flow - Prof. Daniel R. Kirk and more Assignments Mechanical Engineering in PDF only on Docsity! MAE 1202: Aerospace Practicum Laboratory Homework #3 Due: February 20, 2009 YOU: Another laboratory homework assignment?!? But this is only a 2 credit class and there are already a bunch of lecture homework problems due next Wednesday. ME: This laboratory exercise is designed to help you with the lecture-based homework and even give you some of the answers to the lecture homework problems. It is also designed to give you more practice using MATLAB and to show you how when used by the forces of good it can be an extremely powerful engineering tool. 1. Consider homework problem 4.8: A supersonic nozzle is also a convergent-divergent duct, which is fed by a large reservoir at the inlet to the nozzle. In the reservoir of the nozzle, the pressure and temperature are 10 atm and 300 K, respectively. At the nozzle exit, the pressure is 1 atm. Calculate the temperature and density of the flow at the exit. Assume the flow is isentropic and, of course, compressible. The following MATLAB script will give you the answer to this problem. As you type in this script, make sure that you completely understand each line of the code. All the equations are taken from Equation 4.37 in the textbook. % Script to calculate isentropic relations % based on Equation 4.37 from Introduction to Flight close all; % closes any plot windows that may be open clear all; % clears all variables from memory from any previous scripts gamma=1.4; % Specific heat ratio for air R_universal=8314; % Universal gas constant M=28.97; % Molecular weight of air R=R_universal/M; % Gas constant for air % Enter relevant values p_inlet_atm=10; % inlet pressure in atmospheres p_inlet_pa=p_inlet_atm*101325; % inlet pressure in Pascals or N/m^2 p_exit_atm=1; % exit pressure in atmospheres p_exit_pa=p_exit_atm*101325; % exit pressure in Pascals or N/m^2 T_inlet=300; % inlet pressure in Kelvin % The inlet density may be found from the ideal gas equation rho_inlet=p_inlet_pa/(R*T_inlet); % Find the exit temperature PR=p_exit_atm/p_inlet_atm; % PR=pressure ratio T_exit=PR^((gamma-1)/gamma)*T_inlet % exit temperature in Kelvin TR=T_exit/T_inlet; % TR=temperature ratio % Find the exit density rho_exit=PR^(1/gamma)*rho_inlet % exit density in kg/m^3 DR=rho_exit/rho_inlet; % DR=density ratio The answer to problem 4.8 is: Texit=155.4 K and exit=2.27 kg/m3 1 Note: I am giving you the answer so you can check your work and ensure that you understand the problem completely – not just so you can turn it in for credit. Now that you have a fancy MATLAB script to answer problem 4.8, let’s see how useful it is. Notice that problem 4.8 is actually poorly written by the author – no where does it mention what type of gas is used! The MATLAB script assumed air since that is probably what is most common in a supersonic nozzle. However, other supersonic facilities or nozzles may have different gases flowing in them. Use the given MATLAB script to examine the same inlet and exit conditions but with the following gases: Helium (Molecular weight, M = 4.0, specific heat ratio,  = 1.667) Argon (Molecular weight, M = 39.94, specific heat ratio,  =1.667) Solid rocket combustion gas, which is a mixture of chemicals that you will learn a lot about during your senior year in MAE: 4262 (M=25, =1.2) What are the exit temperature and density for these three cases? Display your results in a suitable table (presented in a MS Word document) which shows the gases used and the exit temperature and density. Most solid rockets operate well into the upper atmosphere where the ambient pressure is less than 1 atmosphere. Furthermore, the combustion chamber gases are usually at pressures that are higher than 10 atmospheres. Re-run the solid rocket combustion gas case using the molecular weight and specific heat ratio (for helium and argon) given above, but with an inlet pressure (of the combustion chamber) of 25 atmospheres and an exit pressure (called the back pressure) equal to the ambient pressure at an altitude of 20 km. How different are your results from the pressures given in the initial problem? 2. Consider homework problem 4.20: A Pitot tube is mounted in the test section of a low- speed wind tunnel. The flow in the test section has a velocity, static pressure, and temperature of 150 MPH, 1 atm, and 70 ºF, respectively. Calculate the pressure measured by the Pitot tube. This problem can be solved by applying the ideal gas law to find the density in the test section and then calculating the total pressure using the Bernoulli equation. The answer to this problem is the total pressure = 2172 lb/ft2. Let’s now assume that we want to know the total pressure not only at 150 MPH but from speeds from 0 to 300 MPH, which is the incompressible flow limit discussed in the textbook. The following MATLAB script will generate a plot the total pressure vs. velocity. % Script to calculate total pressure inside a Pitot tube % for a low-speed subsonic wind tunnel based on Problem 4.20 close all; % closes any plot windows that may be open clear all; % clears all variables from memory from any previous scripts % Given data 2