Studying the variation of Adiabatic Flame Temperature with various parameters under constant pressure and constant volume using Python and Cantera

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Objective To derive the fourth order approximation schemes for the second order derivative of a function using central differencing, skewed right side differencing and skewed left side differencing approach and to draw a comparison between the errors arising from these approaches along with forward and backward differencing…

Objective:  To derive the Reynold\'s Averaged Navier-Stokes (RANS) equations Solution: The Reynold\'s Averaged Navier-Stokes equations are NS equations that are time-averaged after applying Reynold\'s decomposition technique to the General NS equations. Solving the Navier-Stokes equations directly (Direct Numerical…

Objective: To set up a transient shock tube simulation in Converge CFD and to post-process the results in Paraview. Theory- Shock tube A shock tube is a device used to generate shocks. This device is used in experiments for determining the ignition delay of fuel when subjected to the auto-ignition temperature. The generated…

Objective: 1. To perform a Conjugate Heat Transfer simulation for a flow through a solid pipe and to perform a grid-dependence test on the simulation. 2. To understand the concept of super-cycling and to study the effect of the super-cycle stage interval on the simulation result. 1. Problem Definition Air is flowing through…

Objective: 1. To explain the physics behind the formation of a shock wave and to perform a literature search on the type of boundary conditions used for shock flow problems. 2. To simulate the Prandtl-Meyer shock problem and to study the effect of the Sub-Grid Scaling (SGS) temperature value on cell count and shock location.…

Objective: To perform a steady-state simulation of flow across an elbow with throttle inside using Converge CFD and to post-process the simulation results using Paraview. Problem Definition: The elbow geometry and the throttle positioning are shown below; The bottom view is as shown below; The throttle is a separate body…

Objective: To simulate flow over a backward-facing step using Converge CFD for three different mesh sizes as stated below and to compare the results. 1. Mesh1 - dx = dy = dz =2e-3m 2. Mesh2 - dx = dy = dz =1.5e-3m 3. Mesh3 - dx = dy = dz =1.0e-3m Problem Definition: The geometric specification for the backward-facing mesh…

Objective: To set up and run a channel flow simulation using Converge CFD and to post-process the results using Paraview for three different mesh sizes, and also to compare the results. The mesh sizes for simulation are as follows; 1. dx = 2e-4; dy = 2e-4; dz = 2e-4 2. dx = 1.5e-4; dy = 1.5e-4; dy = 1.5e-4 3. dx = 1.2e-4;…

Objective: To write a code to perform a 1D Flame Speed Analysis for Methane and Hydrogen.  Approach: The flame speed analysis can be performed in Python with the help of Cantera module. The 'Burner Stabilized Flame' approach where the reference coordinates are fixed at the flame front has been used to solve for the…

Objective: 1. To write a reaction mechanism reduction code for the GRI30 mechanism and determine the minimum mechanism size required to compute the maximum temperature and the ignition delay for given tolerance criteria based on the Temperature sensitivity computed for all combinations of the following state values. Temperature…

Objective 1. To perform steady state and transient state analysis of a 2D heat conduction equation with the help of iterative solvers like Jacobi, Gauss-Seidel, and SOR on a unit square domain with equal grid points along X and Y axes with the boundary conditions as 400K on the left, 800K on the right, 600K on the top…

Objective The objective is to write a program in Matlab to simulate the motion of a simple pendulum with damping. Governing Equation The equation of motion for a simple pendulum of mass \'m\', length \'L\' and damping coefficient \'b\' covering an angular displacement \'theta\' in time \'t\' under the acceleration due…

Objectives 1. To write code to solve the Quasi 1D subsonic- supersonic nozzle flow equations in conservation and non- conservation forms of the governing equations. 2. To perform the grid dependency test. 3. To determine the minimum number of iterations required for convergence and to find out which form of governing equations…

1. OBJECTIVES  1. To simulate the laminar flow of water through a circular pipe with the icoFoam solver and compare the results of simulation with the analytical solutions given by Hagen Poiseuille equations. 2. To write a Matlab program to automatically generate the computational mesh for any wedge angle and grading…

1. OBJECTIVE To simulate the laminar flow through a circular pipe using the symmetry boundary condition and to compare the results with that of the wedge boundary condition simulation and the analytical solution obtained using the Hagen Poiseuille law for wedge angles of 10, 25 and 45 degrees.   2. THE PREMISE OF…

Objective: To derive the reaction rate ODEs of the following reaction mechanism using compact notation. `CO + O_2 <=> CO_2 + O` `O + H_2O <=> OH + OH` `CO + OH <=> CO_2 + H` `H + O_2 <=> OH + O` Solution: There are 4 reactions and 7 species in the reaction mechanism. Let i be the reaction index…

Objective To simulate the flow through a backward facing step using the icoFoam solver in OpenFOAM and to study the effect of mesh grading factor on the velocity magnitude profile. Mesh specification Number of cells along x-direction (longer dimension) = 200 Number of cells along y-direction = 20 Creating the mesh The…

1. Objective: 1.1. To study the effect of pre-heating on the adiabatic flame temperature for the combustion of methane inside a furnace by varying the temperature of inlet air. 1.2. To study the effect of preheated air temperature on the efficiency of combustion of the fuel assuming that the furnace exit temperature is…

Objectives: To write Python scripts for the following; 1. To study the effect of equivalence ratio on the final adiabatic flame temperature in constant volume combustion of methane and compare the results with Cantera. 2. To compute the adiabatic flame temperature for constant pressure combustion of methane with heat_loss…

Objective: To write a Python code using the Cantera module to determine and plot the \'n\' number of most sensitive reactions to Temperature out of the \'N\' number of total reactions in the GRI30 mechanism for the auto-ignition of methane. Python Script: The following Python script demonstrates how to determine and plot…

Objective: To study and understand the concept of stability of ODE systems and answer the following questions with the backing of suitable computer programs. 1. When does an ODE become unstable? 2. How does stability affect engineering simulations? 3. Can stability condition be derived for all types of problems?  …

Objective: To arrive at the adiabatic flame temperature for the combustion of methane in air at stoichiometry under constant pressure by treating methane and air as two separate quantities using the \'Quantity Class\' in Cantera. Solution: 1. Calculation of moles of air: When using the \'moles\' function of class \'Quantity\',…

objective: To simulate a simple stiff non-linear coupled 3-ODE system using the multi-variate Newton- Raphson solver with implicit time integration for a time of 10 minutes. The ODEs are as follows; `dy_1/dt = -0.004 y_1 + 10^4 y_2 y_3` `dy_2/dt = 0.004 y_1 - 10^4 y_2y_3 - 3*10^7 y_2^2` `dy_3/dt = 3*10^7 y_2^2` Solution:…

Objective: 1. To calculate the ignition delay time for the auto-ignition of methane and to study the trend of variation of ignition time delay using Python and Cantera for the following conditions;   1.1 A constant temperature of 1250 K and pressure varying from 1 to 5 atm.   1.2 A constant pressure of 5 atm…