1. Central Difference Scheme For finding the fourth order approximation of a second order derivative with central difference method, we will have to take the numerical stencil consisting of four terms i.e. two on each side of the f(i) as shown in the figure. thus we will define the the second order derivative as `frac{d^2f}{dx^2}=frac{af(i-2)+bf(i-1)+cf(i)+df(i+1)+ef(i+2)}{Deltax^2}+O(x^4)`…

Objective: In this project is to write code solve the 1D supersonic nozzle flow equations using the Macormack Method. You will be implementing both the conservative and non-conservative forms of the governing equations You will perform grid dependence test Conservative and non conservative method Mathematically there is…

1.) STEADY STATE PROGRAM For Solving 2D Heat conduction problem in steady state. First we will take a steady state heat conduction equation: `frac{delta^2T}{deltax^2}+frac{delta^2T}{deltay^2}=0`       .................(1) Approximating the first two terms with the central difference scheme: `frac{delta^2T}{deltax^2}=frac{Tunderset(i-1,j)(…

Objective: To simulate the flow through a backward facing step using the icoFoam solver in OpenFoam and to compare the velocity profile at a given point for different grading of mesh. We will here use the icoFoam solver for solving the flow simulation in the geometry shown below: This problem has to be solved with 5 blocks…

In CFD there are three known methods to solve the governing equation. In the last challenges we have already completed and worked with Finite difference methods. The Finite Volume Method is used for representing and evaluating the governing equations in the terms of surface integrals. Similar to FDM in FVM the values are…

Objective: Writing a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading schemes. Show that the velocity profile is fully developed Post process velocity and shear stress Considering a cylinderical pipe with the working fluid water entering the pipe with the laminar…

Objective: Writing a program in Matlab that can generate the computational mesh automatically for any wedge angle and grading schemes. Obtain results for the pipe flow with symmetry BC. Angles to test 10,25,45 Post process velocity and shear stress The results for the wedge boundary conditions can be seen here https://skill-lync.com/projects/week-11-simulation-of-flow-through-a-pipe-in-openfoam-4…

OBJECTIVE:  To analyze the mixing effectiveness of the mixing tee (Like pipe who has two Inlet and one Outlet) using different momentum ratios and different lengths. a) Find out Velocity and temperature contour plots along and across the pipe. b) Find out Velocity and temperature line plots along and across the length…

Objective: To simulate the fow over a cylinder and the process of kamran vortex street, or vortex shedding.  Perform both steady and unsteady simulations and calculate the Strouhal Number. Determining the coefficient of drag and lift over a cylinder and study the effect of Reynolds number on it. Study of vortex shedding…

Objective: Significance of a Ahmed Body. To simulate the Ahmed Body and calculate the lift and drag coefficients and perform the grid impedence test. Introduction: Importance of Ahmed Body: Ahmed Body is a benchmark model widely used in the automotive industry for validating the simulation tools. The ahmed body shape is…

Objective: Disscuss importance of Conjugate Heat Transfer Analysis. Simulate Exhaust port model in fluent while maintaining the proper Y+ value according to the turbulence model. Calculating the wall/surface heat transfer coefficient on the internal solid surface & show the velocity & temperature contours in appropriate…

OBJECTIVES To understand Rayleigh Taylor instability and some CFD models that have been based on the mathematica analysis of Rayleigh Taylor waves. To perform the Rayleigh Taylor Instability simulation for different mesh sizes and compare them. To find out the affect of Atwood number variation on Ryaleigh Taylor Instability.…

Aim: Conjugate heat transfer Analysis on Graphic Card. Objectives: 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 that the simulation has achieved convergence…

Objective: To perform analysis on cyclone seperator and calculate the seperation efficieny and pressure drop. To study different emperical formulas used to calculate the cyclone seperator efficiency. To perform an analysis on cyclone seperator model and understanding its working. To understand the effects of velocity and…

AIM Parametric Study for a Gate Valve Objectives To perform the parametric study on the gate valve by simulating the opening of gate valve ranging from 10mm to 80mm. To obtain the mass flow rate for each design point. Calculate the flow factor and flow coefficeint for each design point. Introduction The gate valve is the…

OBJECTIVES: 1) To Perform a combustion simulation on the combustor model and plot the variation of the mass fraction of the different species’ in the simulation and also plot for CO2, H2O, CH4, N2, O2, NOx emissions & Soot formation.  2) To Observe the effect of adding the water content in the fuel.…

AIM: Examining the Adiabatic Flame Temperature of Methane air mixture by different equivalence ratio in constant volume chamber. Further trhe results have to be validated with cantera. Examining the Adiabatic Flame Temperature of Methane Air Combustion in constant pressure including hewat loss. Examining the flame temperature…

AIM The aim of this challenge is to work on the quantity class of the cantera. OBJECTIVE The calculation of the adiabatic flame temperature of gas mixture using the quantity class Python Code for Calculation for Mass and Mole Fraction of Air import cantera as ct gas = ct.Solution('gri30.cti') air = ct.Quantity(gas) air.TPX…

Objective:- To know the effect of the range of inlet air preheating from 298k to 600k on the adiabatic flame temperature of Methane. To know the effect of pre-heating temperature on combustion efficiency. Given:- Device-Recuperator (constant pressure heat exchanger) Fuel-CH4 Programs used- Python and Cantera Theory:- Recuperator…

 AIM:  To derive the reaction rate ODEs & production of each species for the simple reaction mechanism as shown. Derivation: First we will start with the compact notation for the given species and the reaction as shown: Species Notations: j Species 1 CO 2 `underset(2)(O)` 3 `Cunderset(2)(O)` 4 O 5 `underset(2)(H)O`…

Aim: To study stability of an ODE and its effect on engineering simulation. AN ODE contains derivatives of one or more functions of an independent variable. To solve an ODE we need to determine the function or set of functions that satisfy the equation. Al though many differential equations cannot be solved or are very…

Aim: To solve the system of equations using multivariate newton raphson solver.   From the equations above they are coupled and can only be solved by the set of equations. These types of equations are generally stiff and are solved with implicit technique. Here for each time phase newton raphson is used. As for each…

AIM: To determine Auto-ignition delay for methane combustion for the cases as shown: For varying temperature from 950K to 1450K under constant pressure. For varying pressure 1bar – 5bar under constant temperature. Finding the molar concentration of H2O, O2, OH When temperature is 1000K and 5 bar. When temperature…

OBJECTIVE: To determine the 10 most sensitive reactions of GRI -3.0 mechanism. To determine the sensitivity with respect to temperature. Output the reactions in decreasing order of sensitivity THEORY: In a reaction mechanism, multiple intermediate reactions take place to get the final output. These intermediate reactions…