Week 3 - Solving second order ODEs

Combustion:     Thermal NOx Thermal  is produced during the combustion process when nitrogen and oxygen are present at elevated temperatures. Prompt NOx Prompt NOx is formed from molecular nitrogen in the air combining with fuel in fuel-rich conditions which exist, to some extent, in all combustion…

Aim: To perform a parametric study on the gate valve simulation by setting the opening from 10 % to 80%. Obtain the mass flow rates at the outlet for each design point. Calculate the flow coefficient and flow factor for each opening and plot the graph. Discuss the results of the mass flow rate and flow coefficient. Geometry…

Cyclone separators Cyclone separators  are separation devices (dry scrubbers) that use the principle of inertia to remove particulate matter from flue gases. Cyclone separators is one of many air pollution control devices known as precleaners since they generally remove larger pieces of particulate matter. Cyclone…

Problem Statement: To Perform a steady-state conjugate heat transfer analysis on a model of a graphics card. Run the simulation by varying the velocity from 1m/sec to 5m/sec for at least 3 velocities and discuss the results. Find out the maximum temperature and heat transfer coefficient attained by the processor. Prove…

          Case 1: 0.5 mm Animation : https://youtu.be/USJaF1kKA Case 2: 0.3 mm Animation : https://youtu.be/lAVT82d9x6I Case 3:  Water and User-defined material(density = 400 kg/m3, viscosity = 0.001 kg/m-s) (0.3 mm)     Animation : https://youtu.be/F7jK4GFXDbE Conclusion: It is…

Problem statement:   Data visualizer  Write a  script should take column numbers as the input and plot the respective columns as separate images Each file should be saved by the name of the column The plot labels should be extracted from the file. If, I request for a plot between column 1 (crank angle) and…

Steps Followed: 1.Import Modules in sublime text Import numpy as npimport matplotlib.pyplot as pltfrom scipy.optimize import curve_fit 2. Call a function  def func(t,a,b): # calling a function return a*t+b 3. Call a function that returns temperature and cp value contained in the data file.  def read_file(): temperature=[]…

  Steps Followed: 1. Import below modules into the sublime text editor. import numpy as np from scipy.integrate import odeint import matplotlib.pyplot as plt import math 2. Define function that passes variables as argument  3. Define Variables as input  b=0.02 # Damping coefficient g=9.81 # Acceleration…

Objective:  Write  a  code that can solve an otto cycle and make plots for it. Otto Cycle :                 Process 0–1 a mass of air is drawn into piston/cylinder arrangement at constant pressure. Process 1–2 is an adiabatic (isentropic) compression…

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  BlockMeshDict File /*--------------------------------*- C++ -*----------------------------------* ========= | \ / F ield | OpenFOAM: The Open Source CFD Toolbox \ / O peration | Website: https://openfoam.org \ / A nd | Version: 7 \/ M anipulation | *---------------------------------------------------------------------------*/…

Objective is to write a code to solve the Quasi 1D Subsonic-supersonic nozzle flow equations using the Macormack Method.   Initials Conditions:. Where ,    Function for Non Conservative Form: function [mfr_nc,P,Mach_nc,v,rho,T,Temp_throat,p_throat,v_throat,rho_throat, Mach_throat,mfr_throat]=non_conservative_form(x,dx,n,gamma,nt,c)…

Code For Steady Solvers: close all clear all clc % Solve 2 Order 2D steady state heat conduction pde d^2T/dx^2+d^2T/dy^2=0 nx=11; ny=nx; L_x=1; L_y=1; x=linspace(0,L_x,nx); % Number of nodes along x direction y=linspace(0,L_y,ny);% Number of nodes along y direction y1=fliplr(y); dx=L_x/(nx-1); dy=L_y/(ny-1); [xx,yy]=meshgrid(x,y1);…

Write a code to solve the 1D linear equation.                Assume  the domain length is L = 1m The initial velocity profile is a step function. It is equal to 2m/s between x= 0.1 and 0.3 and 1m/s everywhere else. Constant Velocity, C = 1 Set time step = 0.01 Make the comparison…

  % call the function for skewed_left_side_scheme function skewed_left_error=skewed_left_side_approximation(x,dx) % analytical derivative = exp(x)*cos(x) exact_derivative=-2*exp(x)*sin(x); % Numerical derivative % skewed_left_side_approximation f(i-5),f(i-4),f(i-3),f(i-2),f(i-1),f(i) skewed_left_side_approximations=(3.750*(exp(x)*cos(x))-12.83333*(exp(x-dx)*cos(x-dx))+17.83333*(exp(x-(2*dx))*cos(x-(2*dx)))-13.000*(exp(x-(3*dx))*cos(x-(3*dx)))+5.08333*(exp(x-(4*dx))*cos(x-(4*dx)))-0.83333*(exp(x-(5*dx))*cos(x-(5*dx))))/(dx^2);…