Steady Vs Unsteady flow over a cylinder

Aim: An ODE is an equation with a function in one independent variable as unknown, containing not only the unknown function itself, but also its derivatives of various orders. Ordinary differential equations (ODEs) arise in many contexts of mathematics and natural sciences. From electrical circuits to structural mechanics…

Combustion of fuel involves burning/oxidation of fuel which results in release of heat. This heat is used to perform work.Below equation represents a combustion reaction for methane. CH4 + 2(O2 + 3.76N2) -> CO2 + 2H2O + 7.52 * N2 However, such reactions are not single step and goes through many sequence of elementary…

Introduction:Burning of fuel to extract work and heat has been used since time era. However, the process has evolved to improve theefficiency and amount of heat or work extracted. As many industries today rely on natural gas combustion it becomes necessary for industries to re-use the exhaust gasesto improve heating efficiency…

Sensitivity Analysis: For a set of chemical equations determining the effect of uncertainties in parameters and initial conditions on the solution of a set of ordinary differential equations is known as a sensitivity analysis. Because there are a number of reactions (both intermediate reactions and final reactions) occurring…

In the CFD domain, most of the heat transfer or fluid mechanics equations when discretised yield linear or non-linear system of equations depending upon the nature of partial differential equation they are derived from. When dealing with equations which are tightly coupled and linear in nature, finding a solution using…

Ahmed Body: Ahmed Body is a simplified car geometry which helps in carrying out experiments to understand the flow around an automobile vehicle. In industry, it is widely used as a benchmark to validate the simulation tools. Examining flow around an Ahmed Body helps in understanding how aerodynamic drag affects the fuel…

Conjugate Heat Transfer: The physical phenomenon where heat transfer takes place simultaneously in both solids and fluids is termed as conjugate heat transfer. However, the modes of heat transfer in solids and fluids vary. In solids, the heat transfer is predominantly by conduction mode and while in fluids it is governed…

Objective: Simulating fluid flow over a cylinder to understand the vortex formation.   When driving along a road it is a common safety measure to slow down at sharp corner turns in order to avoid being thrown off the road. This phenomenon can be observed as “separation of cars” of the road. A similar process…

Objective: To understand the variation of auto ignition temperature of a fuel during combustion at varied pressure and temperature. Auto Ignition Temperature and Auto Ignition Time: Auto ignition temperature: It refers to the temperature of fuel at which the fuel will auto ignite without external heat source. At elevated…

Objective: To understand the mixing effectiveness of two fluids in tee junction pipe   There are variety of industrial applications of fluid mixing, like fluid transportation, evaporative cooling, etc. It has been observed that mixing of two fluids in a tee junction is a simple and effective method to achieve good quality…

In this project, we will be observing the flow of a fluid in a pipe using OpenFOAM. Brief description of the physical scenario Boundary Layer - When a real fluid flows past a solid body or solid wall, the fluid particles stick to the boundary and the condition is known as the no-slip condition. This means that the velocity…

A=[1,2,3,4,5]% Above statement when executed will define a row matrix variable named as A, of five elements and will also print it on the command windowA =1 2 3 4 5   B=[1;2;3;4;5]% Above statement when executed will define a column matrix variable named as B, of five elements and will also print it on the command…

In this project we will simulate flow over backward facing step and velocity at a predetermined point will be observed.  Steps involved: 1. Geometry Setup and meshing 2. Setting up initial Conditions 3. Executing Solver - icoFoam 4. Post Processing of results    Geometry Setup and meshing The vertices…

Creating Taylor\'s table for  a) Central Difference Scheme    f(i) f\'(i) f\'\'(i) f\'\'\'(i) f\'\'\'\'(i) af(i-2) a -2 2 -4/3 2/3 bf(i-1) b -1 1/2 -1/6 1/24 cf(i) c 0 0 0 0/0 df(i+1) d 1 1/2 1/6 1/24 ef(i+2) e 2 2 4/3 2/3   b) Forward Difference Scheme   f(i) f\'(i) f\'\'(i) f\'\'\'(i) f\'\'\'\'(i)…

In this project we will be solving the 2D heat conduction equation using steady state analysis and transient state analysis. The 2D heat conduction equation is given by `frac {del ^2 T }{del ^2 t} = alpha(frac{del^2 T}{del^2x} + frac{del^2 T}{del^2y})`                   …

In this challenge, we will go through some basics for handling mixtures in Cantera.  import cantera as ct gas = ct.Solution(\"gri30.cti\") # Air/Oxidizer A = ct.Quantity(gas) A.TPX = 298.15, ct.one_atm, {\"O2\": 0.21, \"N2\": 0.79} A.moles = 9.52 print(\"Mass Fraction\", A.mass_fraction_dict()) # Fuel F = ct.Quantity(gas)…

pendulum_main.m clear all close all clc t = linspace(0,20,500); theta0 = [0 3]; g = 9.81; b = 0.05; m = 1; L = 1; ANON = @(theta0, t) ode_second_order_pendulum(theta0,t, g,b,m,L); [theta] = lsode(ANON, theta0, t); %Plotting variation of Angular displacement and velocity w.r.t. time figure(1) subplot(2,1,1) graphs = plot(t,…

LinearConvection_main.m clear all close all clc point_markers = [\'o\',\'+\',\'*\',\'x\' ]; dt=[1e-1,1e-2,1e-3,1e-4];%Looping over List of Grid Points for j=1:length(dt) start_time = time; %Inputs for linear convection problem L = 1; c = 1; n = 80; nt = 0:dt(j):0.4; %No of Time Steps x = linspace(0,L,n); dx = L /(n-1);…

discretization_main.m close all clear all clc % Discretization %f(x)= sin(x)/x^3; %f\'(x) =(x^3*(cos(x)) - 3 * x^2 * sin(x))/x^6 %analytical_derivative =(x^3*(cos(x)) - 3 * x^2 * sin(x))/x^6 x = pi /3; dx = linspace(pi/40,pi/4000, 10); for i=1:length(dx) first_order_error(i) = first_order_approximation(x, dx(i)); second_order_error(i)…

In this project, we will be observing the flow of a fluid in a pipe using OpenFOAM. Brief description of the physical scenario Boundary Layer - When a real fluid flows past a solid body or solid wall, the fluid particles stick to the boundary and the condition is known as the no-slip condition. This means that the velocity…

LinearConvection_main.m clear all close all clc for n=[20, 40, 80, 160] %Looping over List of Grid Points %Inputs for linear convection problem L = 1; c = 1; dt = 0.01; %Time Step nt = 0:dt:0.4; %No of Time Steps x = linspace(0,L,n); dx = L /(n-1); %start and end of square wave x_start = 0.1; x_stop = 0.3; n_start = nearest_value(x,x_start);…

In this project, we will be comparing the results obtained from the following methods: The Hagen-Poiseuille Equation(analytical) Simulation of flow through a pipe with wedge boundary condition and, Simulation of flow through a pipe with symmetry boundary condition.   Results from the previous project: For a laminar…

In this project we will observe quasi 1D flow through a convergent - divergent nozzle. We will be refering to the case set up for this problem from Chapter 7 of Computational Fluid Dynamics - John D Anderson.   Physical description of problem - The flow at the inlet comes from a reservior where the pressure and temperature…

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FDM vs FVM: In, finite difference method the computational domain is discretized into points and the equations are converted into discretized equations using various difference schemes (central difference scheme, forward difference scheme, backward difference scheme). In order to get the solution, the discretized equation…

discretization_main.m close all clear all clc % Discretization %f(x)= sin(x)/x^3; %f\'(x) =(x^3*(cos(x)) - 3 * x^2 * sin(x))/x^6 x = pi /3; dx = linspace(pi/40,pi/40000, 100); for i=1:length(dx) first_order_error(i) = first_order_approximation(x, dx(i)); second_order_error(i) = second_order_approximation(x, dx(i)); fourth_order_error(i)…

Combustion is a chemical phenomena of burning a fuel in presence of an oxidiser to get heat/work done. The amount of oxygen or oxidiser drives the chemical reaction. The stochiometery quantity of oxidiser is just the amount needed to completely burn the given quantity of fuel. If more than stochiometery quantity of oxidiser…

close all clear all clc % Set of equations for alkane i = 10; for no_of_moles_of_carbon=1:i q = no_of_moles_of_carbon; r = no_of_moles_of_carbon + 1 ; x1(no_of_moles_of_carbon) = 2*no_of_moles_of_carbon + r ; endfor % Set of equations for alkene for no_of_moles_of_carbon=1:i q = no_of_moles_of_carbon; r = no_of_moles_of_carbon…