In this project, you will simulate one of the most important problems in aerospace applications- the convergent-divergent nozzle. You will solve the quasi 1D Euler's equations in Matlab to simulate and study the conditions for an isentropic flow inside a subsonic-supersonic nozzle. This project will provide insights into how a super-sonic aircraft is able to attain such speeds with the help of a simple convergent-divergent nozzle setup.
Step 1 - Setting up the mesh and initial/boundary conditions
Step 2 - Solve the governing equations in both conservative and non-conservative forms using MacCormack technique
Step 3 - Study the difference between conservative and non-conservative forms
In this project, you will solve the quasi 1D Euler's equations to simulate the conditions inside a subsonic supersonic nozzle. You will derive the governing equations for an isentropic inviscid flow through a nozzle in both conservative and non-conservative forms and non-dimensionalize them. You will then solve those equations using the MacCormack's technique. You will apply the appropriate boundary conditions and adopt a time marching procedure with adaptive time step control based on Courant number to arrive a steady-state distribution of flow properties. You will then validate the numerical solution of both forms with the analytical solution and provide a contrast between their solutions through various analyses. You will also perform a grid independence test on the solution.
The nozzle plays a vital role in the propulsion of an aircraft to speeds more than the speed of sound. It is known from the Newton's third law that, in order for a body to move forward, it needs to apply thrust in the opposite direction. In order to achieve supersonic speeds we need to eject out mass at supersonic speeds in the opposite direction. This is achieved with the help of a convergent-divergent nozzle setup. In this project you will learn how this nozzle works and accelerates the gases from subsonic to supersonic speeds. You will use the MacCormack's technique to solve the inviscid quasi 1D Navier-Stokes equations (Euler's equations) with second order accuracy in time and space. You will study the conservative and non-conservative forms of governing equations and how they are solved. You will also perform a grid-independent test and come up with an ideal mesh size.
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