The purpose of this project, is to setup and analyze a transient shock tube simulation using Converge Studio. The project will analyze how the interaction of the original shock waves and the reflected waves affect the fluid in the tube, and how the computational mesh has to be set in order to capture these high gradient…

This project objective is to simulate the Prandtl Meyer shock wave phenomena using Converge Studio. First, a quick literature review about shock waves and their boundary conditions is provided. Then , the problem is set up and solved, focusing in how the different paramenters in the simulation affect the shock wave location.…

This project main objective is the numerical solution of a 1D Supersonic Nozzle Flow using the Macormack Method. Although analytically identical, the numerical solution of conservation and nonconservation forms of the governing equations is usually different. That is the reason why both ways are solved and compared in…

This project purpose is to simulate the flow over an elbow body that contains a throttle using CONVERGE Studio. In this first part of the project, an steady state analysis will be set up. This means that the throttle will not move. This case helps set up the real analysis: check if the refinement of the mesh is the correct…

In this project, a simple program is created to solve the ODE for a simple pendulum motion, including dumping effects. Youtube Link https:/youtu.be/iVHRLvSZ6zo   clear all close all clc %System Parameters m=1; L=1; b=0.5; g=9.81; k=b/m; w=g/L; %Solving a second order differential equation t=[0 20]; theta0=[0 3]; [t,theta]=ode45(@(t,theta)pendulum(t,theta,k,w),t,theta0);…

SIMULATION OF FLOW THROUGH A PIPE. This project objective is to be able to accurately simulate the laminar incompressible flow through a pipe. The project will be broken into two different parts. This first part of the project will be focused on the simulation set-up. Based on a desired Reynols number and pipe diameter,…

This project main objective is to calculate the Adiabatic Flame Temperature using Python and Cantera. In the first part of the project, the effect of the equivalence ratio for the methane combustion in a constant volume chamber is analyzed, and the python and cantera results are compared and explain. Then, the second part…

In this project, the 2D Steady State and Transient Heat Conduction Equation is solved. For that, several iterative techniques (Jacobi, Gauss-Seidel, Successive Over-Relaxation) will be employed and compared. First, the numerical discretization is shown: 1) STEADY STATE 2D HEAT CONDUCTION Main Script %%%%%% Steady State…

The purpose of this project is to show the effect of initial temperature and pressure in the ignition delay in a combustion process. For this purpose, a Constant Volume Reactor and the corresponding network objects are created in Cantera, and the combustion process is simulated. 1) Effect of Initial Temperature in the…

Literature Review of ODE Stability The first thing I would like to mention is that there is an important different between the stability of an ODE, and the stability of the method use to solve that ODE. A solution of an ODE might be stable or unstable, regardless of the method used to solve it. However, for a stable ODE,…

The idea of this project is to get familiarized with the stability analysis for linear systems. To do that, we will solve a linear system with different implicit solvers, and we will compute the spectral radius. Then, we will change the spectral radius of the iteration matrix of each solver (diagonal magnification) and…

In this challenge, the efficiency of using a heat recuperator to pre-heat the air is analyzed. For that, we simulate a furnace burning methane and air mixture, and we analyze first how the pre-heating affects at the AFL, and then the total heat/work that could be extracted from the cycle. All this work is performed using…

This approximation is actually third order for the second derivative. However in the tutorial it was stating that the second order was being solved, when it really was the first order for the second derivative. For this, I assumed you were asking for an order that was 2 ahead from the one in the tutorial. I cant attach…

The fastest steady state simulation was the SOR method, while the fastest Transient simulation was the explicit method. Among the explicit methods however, SOR was also the fastest. Note that the explicit method could have been made To compare them, notice that the transient script will be run and only plotted the final…

The main purpose of this project is to get familiarized with OpenFoam and simulate the flow through a backward facing step. This problem is going to be solved for an incompressible laminar (low Re) flow, and therefore the icoFoam solver is used. The interest of this problem resides in the change of velocity when the flow…

The purpose in this project is to show the effect that the time step has in our previous calculations. This challenge supposes just a modification from the previous one. The new code is shown here; Function function FirstOrderWaveEquationTimeEffect(dt,color) %Inputs for the linear convection problem % dt=0.01; L=1; c=1;…

This projects aims to simulate a backward facing step flow using CONVERGE Studio. The flow is creating when a not reacting specie, air (23% O2 and 77% N2 in mass fraction), suffers a pressure gradient between the ends of the channel. The velocity, pressure and recirulation profiles will be analyzed. GEOMETRY AND CASE SETUP…

The objective of this part of the project, is to simulate the transient flow through an elbow pipe with a throttle valve in the middle. This valve will be rotating from zero to 25 degrees, and then stay steady.  Case Setup. In the steady state part of the project, the geometry was already imported from a CAD model…

The purpose of this project is to simulate the conjugate heat transfer in a pipe using Converge Studio. For this, an air flow is simulated through an aluminum pipe, which is receiveing a constant heat flux of 10,000 W/m2 at the outside wall. The objective is to understand the phenomena, run a grid dependence test and analyze…

This document represents the second part of the project related to the simulation of an incompressible laminar flow through a pipe. In the previous part of the project, a 4 edge degrees simulation was carried out using icoFoam and wedge boundary conditions. The purpose of this part is to employ the symmetry boundary conditions,…

As explained in the previous challenge, the stability of the transient methods depends on the factor k=alpha*dt/(dx^2). This factor is also known as CFL number.  The unstable solutions can look differently depending on the scheme (homogeneous vs alterning) but they will always show temperatures way too high or way…

 In this project, the 1D Linear wave equation is solved numerically, using FWD and BWD and a variable time step and grid size. This mathematical approximation was implemented in Matlab as follows.  function FirstOrderWaveEquation(n,dt) %Inputs for the linear convection problem % n=21; % dt=0.01; L=1; c=1; t=0.4;…

The purpose of this assignment is to create a Python program including a Multivariate Newton Rhapson Solver, to solve a non-linear coupled differential system. This method is really useful for stiff systems, where the explicit solver are unstable. The system of equations is: `dy_1/dt = -0.04*y_1 + 10^4*y_2*y_3` `dy_2/dt…

This project pretends to be a summary of my MSc Thesis on Water-enabled Propulsion Technologies for Interplantary Travel and Surface Exploration and Prospecting. This thesis is the result of my work at the Space and Terrestrial Robotic Exploration Laboratory at the University of Arizona. The first part of the project was…