Week 3.5 - Deriving 4th order approximation of a 2nd order derivative using Taylor Table method

Aim - Plotting Pressure, Velocity and Temperture variations across the given Converging-Diverging Nozzle.  Theory :-     A de Laval nozzle or Convergent-Divergent nozzle is a tube which is pinched in the middle, making a carefully balanced, asymmetric hourglass shape.            …

Aim:  To simulate and practice the snappyHexMesh utility of OpenFOAM to generate mesh on a pipe and obstacle in box geometry. Objective: Mesh the given problems:- 1. Circular pipe (using blockMesh) 2. Circular pipe (using snappyHexMesh) 3. Obstacle in box, with box dimensions 20*8*8 (in meters using snappyHexMesh)…

Aim: To analyze the sensitivity of gri30 mechanism of all reactions. The sensitivity variable is Temperature. """ Sensitivity analysis code for Methane with respect to temperature """ import numpy as np import cantera as ct gas = ct.Solution('gri30.xml') temp = 1500 pres = ct.one_atm gas.TPX = temp,pres,{'CH4':1,'O2':2,'N2':7.56}…

Aim: Solving the Ignition Delay of Methane fuel using Cantera in Python. Plotting the variation of ignition delay with variation of temperature and pressure values. Obtaining the molar concentration of elements 'h2o, o2 and oh' and plotting the graph of both cases. Objective: Part1:-  simulate the Auto Ignition Time…

Aim: To solve a coupled non-linear system of ODE's using the Multivariate Newton-Raphson Method in Python. ODE's:     `(dy_1)/(dt) = -0.04y_1+10^4y_2y_3`     `(dy_2)/(dt) = -0.04y_1+10^4y_2y_3-3*10^7y_2^2`      `(dy_3)/(dt) = 3*10^7y_2^2` Theory:     Multivariate Newton-Raphson…

Introduction: A literature review of Ordinary Diffrential Equation ODE and it stability. 1. When does a ODE become unstable? Lets assume an ODE , `f(y) = dy/(dt) = -1000y-e^-t` this is the function of f(y,t).  To answer the question we will solve this equation numerically in Python and compare the results with…

Aim: To derive the reaction rates and production of each elementary species for the given simple elementary reations using the compact notations. Elementary Reactions:      `CO + O_2 overset(kf1)(iff)_(kr1) CO_2 + O ----------text(R1)`     `O + H_2O overset(kf2)(iff)_(kr2) OH + OH ----------text(R2)`…

Aim: To calculate the AFT and the combustion gains for the combustion of methane fuel in a furnace.  Objective:  1. Calculate the variation in AFT for different pre-heating temperatures. 2. Calculate the combustion gains and fuel saving due to pre-heating the fresh air. Assume the exit furnace temperature…

Aim: To work and get acquanited with the 'Quantity' class of Cantera library and handle mixtures with different aspects. Objectives:  1. Use the 'moles' method to calculate the nimber of moles of the object A in the given code and explain how to calculate analytically.  2. Use the mass_fraction_dict() method of the A object.…

Aim:- Compute the Adiabatic Flame Temperature for constant-pressure, constant volume processes. Plot the graph for the AFT with variation in Equivalence Ratio, Hydrocarbon Fuel with constant Carbon atoms and with variation in Carbon atoms. Objective:- 1. AFT variation with Equivalence Ratio in constant-volume process from…

LaTeX report PDF link: https://drive.google.com/file/d/1b0Sv3jsbgGUjK_IbxArlTORylZeyGvby/view?usp=sharing

The LaTeX code of the file is mentioned below with the link of the PDF. The PDF of the report also contains the link to the GitHub repository.https://drive.google.com/file/d/17sC718EAc1XHs526hOgBbb3LOFoW5U5e/view?usp=sharing \documentclass[a5paper]{report} \usepackage{graphicx} % Required for inserting images \usepackage{hyperref}…

Report is written in the LaTeX language here is the code and the link to the PDF file:Link: https://drive.google.com/file/d/1UrUmNiQjkvAGCXleuF8C1_V_OnYL0aRe/view?usp=drive_link \documentclass[a4paper]{report} \usepackage{graphicx} % Required for inserting images \title{\textbf{Creating a Custom IOObject in OpenFOAM}}…

Aim: To create a own customized solver, implement and execute it on Cavity tutorial in OpenFoam. This solver solves for a scalar field that is set in the domain.Solver Description: Use the icoFoam solver in the applications/solvers/incompressible/icoFoam directory to create your own solver - scalarFoamThe scalar transport…

Question1. Derive the expression for the `(delf)/(delx)` for a forward difference of second order. Solution: First let expand the term`f(x+2Deltax)` using Taylor Series`f(x + 2Δx) ≈ f(x) + 2Δx * f'(x) + (2Δx)^2 * f''(x) / 2 + ...` Now, let's expand `f(x + Δx)` in a similar fashion:…

AIM: 1. Create a .cpp file starting with: #include "fvCFD.H" int main( int argc, char *argv[] ) { Foam::argList::noBanner(); Foam::argList args(argc, argv); ... } Copy the cavity problem from $FOAM_TUTORIALS/incompressible/icoFoam. Find the value assigned to: transportModel & kinematic viscosity (nu) stored…

1. Copy the solver DPMFoam from the lagrangian library ( $FOAM_SOLVERS ) into your run folder ( $FOAM_RUN (use visual studio) Use wmake libso to compile the shared library associated with this, after making the appropriate changes Where is the resulting .so file found? (Attach image of the shared object…

Aim : Simulate a Laminar Incompressible Newtonian flow through a pipe with different wedge angle of 10,24,45 degree and run the simulations for Symmetry Boundary Condition and Wedge Boundary Condition for all angles and validate the result with the Analytical H.P equation. Thoery : Wedge Boundary Condition : Wedge Boundary…

Aim :  To simulate an incompressible,laminar,Newtonian axi - symmetric fluid through a pipe.Apply the Wedge boundary condition to the geometry and automate a fully functional blockMeshDict file.Compare the numerical result with the analytical profile. Expected Results Validate Hydro-dynamic length with the numerical…

Aim : Finite Volume Method Literature and define Interpolation Schemes and Flux limiters in FVM. What is Finite Volume Method (FVM)  The Finite Volume Method(FVM) is a method of discretisation of set of governing partial differential equation into a system of linear algebric equation.The FVM uses Finite Volumes to…

Aim : Simulate flow in Backward Facing Step geometry in OpenFoam.Perform two case study for grading factor of 1 and other with grading factor with 0.2 . Desired output Measure the velocity profile at 0.085 m from the inlet of the geometry for both case studies and compare. You can use the plot over line tool for this.…

Aim : To simulate the Isentropic Flow through a Quasi 1D Subsonic-Supersonic Nozzle,for both Conservative and Non-Conservative form of Governing Equations and solve them using MacCormacks Technique.Expected Outcome : 1. Steady-state distribution of primitive variables inside the nozzle2. Time-wise variation of the primitive…

Aim : Solve the Steady ans Transient State for the 2-D Heat Conduction Equation with Implicit and Explicit schemes and implement the following Iterative Solvers for solving the Implicit Equation. Jacobi Method Gauss-Seidel Method Successive Over Relaxation Method Requirements : Boundary Conditions. Top Boundary = 600 K…

Aim : The objective is to derive a 4th order approximation of a 2nd order derivative using a Taylor Table method for approximation schemes of : Central Differencing Scheme Skewed right-sided scheme Skewed light-sided scheme  Theory : Taylor Series formula is a representation of any function as an infinite sum…

Aim : Simulating the combustion of Non-premixed natural gas and analyzing the species reaction using the line probe in CFD-Post. Objective : Part I Perform a combustion simulation on the combustor model and plot the variation of the mass fraction of the different species’ in the simulation using line probes…

Aim : To perform Parametric study on the Gate Valve by varying the lift of the gate disc from the 10 to 80% of the opening and simulate the results. Objective :  Obtain the mass flow rates at the outlet for each design point. Calculate the flow coefficient and flow factor for each opening and plot the graph. Discuss…

Aim : To perform analysis on cyclone separator and calculate the separation efficiency and pressure drop. Verify the effects of varying phase particle diameter and change in velocity of fluid and particles on the cyclone efficiency and pressure drop. Objective:- To write a few words about any four empirical models…

Aim : To simulate steady state Conjugate Heat Transfer (CHT) analysis on a 3-d model of graphics card and run simulations with different inlet velocities and discuss the result. Objective :  Run the simulation by varying the velocity from 1m/sec to 5m/sec for at least 3 velocities and discuss the results. Find out…

Aim : To simulate and analyze Rayleigh Taylor Instability of air and water material and state the effects of Atwood number and changes in grid on the instabilities. Introduction :                    MULTIPHASE : Multiphase flow is a simultaneous (parallel) flow of materials with different states or phase (liquid-gas).…

Aim : To simulate a Conjugate Heat Transfer analysis (CHT) on the exhaust port given. Theory :               Heat transfer is a discipline of thermal engineering that concerns the generation , use , conversion , and exchange of thermal energy between the physical systems. heat …

Aim : to simulate the external flow over Ahmed body and also calculate the aerodynamic forces over the body. Q1. Describe Ahmed's body and its importance?            1. Ahmed Body.            The Ahmed body is a generic car body (a simplified vehicle model). The…

Aim : To construct a 2-D structure and simulate the flow over a circular cylinder for steady and transient state and explain the phenomena of Von Karman Vortex Street. Requirement : 1. dimensions for creating the circular cylinder structure                        …

Aim: to perform a steady state simulation to compare the mixing effectiveness in a short and long version of MIXING-Tee when hot inlet temperature in 36°C and cold inlet temperature is 19°C for different            momentum ratio. Requirements and Formulas :     …

Aim : to create a wind tunnel around the tesla cybertruck and perform cfd mesh for the cybertruck. Requirement : 1.link to download the model.                      2. target mesh lenght for the parts :                         (a) body : 2mm                         (b) headlights : 3mm                         (c) tyres…

Aim : to merge an assemebly of an engine,gear box and transmission parts and perform Surface Wrap on the merge assembly of 3mm mesh lenght. Link Info : https://drive.google.com/file/d/1ZukzvPob-956pDQg-0pMz85Qz2QFYLSf/view?usp=share_link  the link for the complette model is pasted here as the file is not updating in choose…

Aim : for given model of BMW car perform mesh of the car with appropriate mesh lenght and quality criteria and also assign PID's to the surfaces and also create a Wind Tunnel around the car and perform            volumteric CFD mesh around the car and the wind tunnel volume. Link for the complete…

Aim : for the given model of turbo charger perform CFD Volumetric mesh for the required volumes for given mesh lenghts  for different parts. the access to the complete model is here as it was not uploading in the file section please access it from here: https://drive.google.com/file/d/1eUlJmpAJeToBrr78BP_cdOTLtwZ0fScP/view?usp=sharings…

Aim : To create a mesh of a pressure valve for three different mesh lenght of 1mm,3mm and 5mm and mesh element of  TRIA and conclude by observing all three cases and submit the file in zip format Procedure : 1. install the model from the given link.                    …