DERIVING 4th ORDER APPROXIMATION OF A 2nd ORDER DERIVATION USING TYLOR TABLE We may encounter a partial derivative equation with a 2nd order derivative when solving a CFD problem. Because of the equation's intricacy, we may have to use a numerical technique rather than an analytical one. When using a numerical technique,…

THE OBJECTIVE OF THE PROBLEM :  To solve the given 2D heat conduction problem for the steady and unsteady stade using different iterative solvers like Jacobi, Gauss-Seidel And Successive Over Relaxations iterative solvers and with the help of the given Boundary condition. Given Data and Assumptions to be considered…

The objective of the Problem : Simulate isentropic flow through a quasi 1D subsonic-supersonic nozzle using both the conservation and non-conservation forms of the governing equations, solve them using MacCormack's approach, and compare the results. Explanation :  We consider the study, isentropic flow through a convergent-divergent…

Introduction : Studying the flow behaviour through various structures is an important subject for a CFD engineer. When fluids flow through different geometries, they exhibit different velocity, pressure and flow properties. In this project, a Simulation of a flow-through backwards-facing step is done to study the flow…

Introduction :  The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. Similar to the finite difference method (FM) or finite element method (FEM), values are calculated at discrete places on a meshed geometry. One important…

Objectives of the Problem calculate adiabatic flame temperature, Adiabatic flame temperature variation with Equivalence ratio (In constant volume-chamber) Adiabatic flame temperature variation with Heat loss (In constant pressure-chamber) Adiabatic flame temperature variation with respect to Alkane, Alkene, Alkyne Adiabatic…

Aim  :  To work with Cantera's quantity class on a variety of projects and to demonstrate how mixture calculations are done Solution : 1. Use of moles method or function of A object and explain how it was calculated  The mole's function determines the number of moles if the object (consisting of the two…

Aim:1. What is the effect of preheating on the adiabatic flame temperature?2. Change pre-heating from 298 to 600K3. Explain your results4. Does preheat help with fuel-saving? If yes, how does combustion efficiency go up as a function of pre-heating temperature? Assume thatthe furnace exit temperature is 1700K Objectives…

Aim: The objective of this challenge is to derive the reaction rate of ODE's of a simple reaction mechanism and represent it in the form of compact notations. The compact notations for the reactions listed below will be derived. Reaction Mechanism `CO + O_2 hArr CO_2 + O` `O + H_2O hArr OH +OH` `CO + OH hArr CO_2 + H`…

INTRODUCTION Stability refers to the fact that errors at any point during the computation are not increased but rather attenuated as the computation advances. The sensitivity of a mathematical problem to changes in its input values is referred to as its condition. If the numerical approach changes the uncertainty of the…

Objective : The goal of this challenge is to build code that uses the multivariant Newton Rhapson approach to solve stiff ODE systems. We use an implicit technique to determine the answer because they are stiff systems. Backward differentiation iscalculated using the following formula. `f'(x_i) = frac(f(x_i) - f(x_(i-1)))(Deltax)`…

AIM:  The aim of this challenge is to simulate the autoignition temperature for methane OBJECTIVES :  With a constant temperature of 1250K and pressures ranging from 1 to 5 atm, the Auto Ignition time of methane varies.…

Aim: Using the Reactor Network in Cantera, determine the sensitivity factor for the GRI Mechanism. Objective: The purpose of this research is to learn more about the significance of sensitivity analysis. To write the code for the GRI mechanism's sensitivity analysis. To write a program that displays reaction strings in…

Objective: To investigate the variation of Mach number at different heights, as well as the variation of Mach number throughout the domain, to determine at what distance from the intake the flow becomes supersonic, and to compare the analytical results with the experimental results.   Introduction : A convergent-divergent…

Objecive: To use Ansys to simulate the pitot tube and to conduct literature research on pitot-static tubes. Establish a link between total (stagnation) and static pressure as well. Calculate the total and static pressures, as well as the velocity inaccuracy in percentages. Introduction  Pitot tubes are used to measure…

Objectives of the problem  : In this challenge, you are required to do a literature review of various turbulence models explained in the Turbulence modeling video (Week-5) and explain why DNS isn’t feasible according to Kolmogorov's scale. The below geometry performs a 3D simulation and explains the recirculation…

Problem :  In this project, the student will have to set up the domain for analysis of flow over an airfoil at the subsonic and supersonic regimes. The airfoil will be analyzed at 3 different angles of attack and the lift and drag coefficient will be compared in all cases Create a domain for flow analysis Setup simulation…

Objective : What are the approaches by which you would model moving zones? Which approach would you use to model unsteady phenomena? Simulate rotary motion for the geometry given Plot the velocity profile of the fluid motion Solution : In fluid flow, there are two forms of motion: rectilinear and rotating motion. Modeling…

Aim: To simulate the motion of blades in a turbomachinery component using an unsteady approach, Transient simulation: Transient simulations are performed when the parameters vary with time. Moving Mesh approach: In this approach, the Mesh is moving and the Mesh topology will change that is the mesh shape will vary with…

Objective: The goal is to simulate Broadband Noise across Ahmed's body and depict the drag and lift coefficients. Introduction : The sound or noise produced by the aerodynamic forces and motion of turbulent flow in the domain is referred to as aero-acoustics. Car mirrors, wheels, and airplane landing gear are all…

Aim: Creating your own OpenFOAM solver, and Running a cavity test case with the created solver  Procedure: Here in this challenge we are trying to solve the scalar transport equation in the solver, we are using icoFoam solver for this challenge The scalar transport equation is defined as: where s is the scalar…