AIM: To solve 2D Heat conduction Partial Differential equation for steady and transient state using iterative techniques (a) Jacobi (b) Gauss Seidel (c)Successive over Relaxation (SOR) methods through MATLAB code. Problem Definition Heat conduction equation is defined by the general PDE: α (∂2T/∂x2 + ∂2T/∂y2…

 Approach for Solving 1D Super-sonic nozzle flow simulation via MacCormack Method Solving the 1D nozzle flow problem in two approaches: Non-Conservative approach and Conservative approach using McCormack method. Conservative approach, the assumed control volume is fixed in position and in Non-conservative approach,…

Mesh Specifications:  Number of cells along the x-direction (longer dimension) = 200 Number of cells along the y-direction = 10 Grading factor near all walls - 0.2 A smaller grading factor produces a more uniform mesh.                     f = (size of end cell) / (size…

Objective of the Project:  To run simulation of internal flow through a pipe.  To calculate hydrodynamic entry length, total length of pipe.  To plot velocity profile across the pipe at different locations along the direction of flow.  To plot shear stress.   Introduction: We consider flow of fluids…

Aim Part 1: Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.  Part 2: a) Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10, 100, 1000, 10000 & 100000. (steady state solver)                                                                                                                                                       …

Introduction The wedge boundary condition for OpenFoam is suitable for the angle less than 5 degree and only supports for the 2D axi-symmetric cases, whereas the symmetric boundary condition are can be used for 2D and 3D geometry. In the challenge we have to compare the wedge boundary condition with symmetric boundary…

Aim To study the effect of equivalence ratio on Adiabatic Flame Temperature using the Newton Raphson method and Cantera. To calculate the Adiabatic Flame Temperature for the constant pressure with heat loss. To calculate the Adiabatic Flame Temperature for various fuel types such as alkanes, alkenes, and alkynes. …

1. Use the "moles" method/function of the A object and explain how it was calculated. In the dictionary command line, its given : O2=0.21 and N2=0.71 1 mole O2 = 0.79/0.21 moles of N2 = 3.76 moles of N2 Stiochiometric reaction of Methane and Air : CH4+2 (O2+3.76 N2)= CO2+2 H2O+2*3.76 N2 mixture (O2+N2) ~ 2 Moles ,i.e,…

1. Effect of preheating on aft, inlet temperature from 298 to 600 K The methane is mixed with air in a furnace with recuperator (preheating) CH4 + 2(O2 + 3.76N2) = CO2 + 2H2O + 7.52N2 Methane is considered as Fuel, Air is Oxygen and Nitrogen, products are  (CO2, H2O, and N2) Effect of preheating on AFT import cantera…

Aim To study and understand the concept of stability of ODE systems. When does an ODE become unstable? How does stability affect engineering simulations? Can stability condition be derived for all types of problems? Introduction We know that in CFD, we numerically simulate a physical system by solving its governing equations.…

Aim To solve ODE's using multivariant Newton Raphson method Introduction The Newton Raphson method is used to get the solutions of nonlinear coupled equations system. The Newton-Raphson method (also known as Newton's method) is a way to find an approximation for the root of a real-valued function f(x)=0">f(x)=0.…

Objective:  To write a code to calculate auto-ignition time for combustion of Methane under different operating conditions using cantera Part 1:Plot Auto Ignition time of Methane with a constant temperature of 1250 K and pressure varying from 1 to 5 atm Part 2: Plot Auto Ignition time of Methane with a constant…

Aim Write a code that takes all the reactions from the GRI mechanism and calculates 10 most sensitive reactions The sensitivity parameter should be with respect to the Temperature.     Theory Sensitivity analysis is a process to get relationship between the parameters and the output of a model. A generic ODE…

AIM  The aim is to derive reaction rate ODE of a simple reaction mechanism DERIVATION OF REACTION RATE  Consider the following reactions, lets number the following reactions. CO + O2 -> CO2 + O ---(1) O + H2O -> OH + OH--- (2) CO + OH -> CO2 + H ---(3) H + O2 -> OH + O ---(4) And now lets list all…