Week 5 - Literature review: ODE Stability

Aim: Simulation of fluid sloshing effect in a gear-box. Objective: To understand and setup up a multiphase flow wherein fluid and structure interaction takes place. To understand the sloshing effect and set up the solver for the same. To understand the implementation of UDF utilised for defining the motion of the…

Aim: To perform analysis on the cyclone separator and calculate the separation efficiency and pressure drop. Objective: To develop an understanding of how discrete phase modelling works and implement the same for the given problem. To set up the domain and the solver for a cyclone separator and to evaluate the separating…

Aim: Performing a parametric study on the gate valve. Objective: To set up a parametric study of a valve based on the opening as an input parameter and flow rate as the output parameter. Evaluate the flow coefficient and flow factor corresponding to the lift of the valve and estimate the effect of the same. Introduction:…

Aim: Perform steady-state conjugate heat transfer analysis of a graphics card. Objective: To understand the setup and requirements of a conjugate heat transfer problem. To understand and evaluate the characteristics of such problems. To evaluate the temperature profiles and heat transfer coefficient at the region of interest…

Aim: Performing conjugate heat transfer analysis on an exhaust manifold. Objective: To familiarise with conjugate heat transfer (CHT) analysis. To set up solver for CHT analysis in a commercial CFD code (here, Ansys Fluent). To evaluate the heat transfer coefficient in the given heat transfer problem and validation of…

Aim: Study of Rayleigh Taylor instability Objectives: To understand and set up multiphase fluid flow problems without fluid interactions. To understand the instability associated with the mixing of fluids at different densities. To understand and evaluate the extent and behaviour of this mixing with the help of a dimensional…

Aim: Performing external fluid flow simulation over an Ahmed body. Objective: To understand the requirements of setting up an external fluid flow domain to obtain solution by CFD. To understand the importance of standard wind tunnel models (here, Ahmed body). To understand the requirements for implementation of given domain…

Aim: Simulation of flow over the cylinder and observing the Karman Vortex phenomenon Objective:  Prepare the computational domain for the given problem of an external fluid flow simulation Understand the formation of vortices around a bluff body, deduce the drag and lift coefficient and study the effect of Reynolds…

Aim: Performing CFD analysis of a mixing tee. Objective: Understand the concept of a mixing tee, its use and simulation. Understand and evaluate the problem statement and the required CFD approach to solve the problem. Judge the suitability of a turbulence model for the given problem (here, k-epsilon and k-omega SST) Introduction:…

Aim: Simulation of Hagen-Poisuille flow through a pipe in OpenFOAM. Objectives: Write a MATLAB program to generate blockMeshDict file for any grading scheme and wedge angle. Obtain a fully developed velocity profile and compare the results with analytical solutions. Theory: OpenFOAM (acronym for Open Source Field Operation…

Aim: Simulating a 2-D pipe flow on a backward facing step Objectives: Creating a geometry (backward facing step), defining its mesh using blockMesh object in OpenFOAM for the given specifications. Using the icoFoam solver (in OpenFOAM) for the geometry to obtain the solution. Determining the velocity profile and effect…

Aim: Deriving fourth order approximation of second order derivative using Taylor table Objective: Deriving fourth order approximation of second order derivative for central differencing, backward differencing and forward differencing schemes. Verify and evaluate these schemes for a given function Comparing the numerical…

Aim: Solving 2-D heat conduction equation (steady and unsteady) Objective: Solving the steady and unsteady state heat conduction equation by forming iterative solvers of Jacobi Gauss-Siedel Succesive over relaxation (SOR) The solvers are provided with a relaxation factor, and appropriate boundary condition; Thus evaluate…

Aim: To obtain solution of one dimension linear convection equation. Objective: Obtain numerical solution of linear convection equation by first order finite differencing schemes. Obtaining plots for the same; compare the initial velocity profile and the final velocity profile. Note the variations by keeping time step…

Aim: Write a program that compares first order, second order and fourth order derivatives. Objectives: To compute analytical derivative of given function. Compare this to numerical methods and evaluate the absolute error in various schemes Theory: In applied mathematics, discretization is the process of transferring continuous…

Aim: Write a program that compares first order, second order and fourth order derivatives. Objectives: To compute analytical derivative of given function. Compare this to numerical methods and evaluate the absolute error in various schemes Theory: In applied mathematics, discretization is the process of transferring continuous…

Aim: Write a MATLAB program to simulate motion of a pendulum with damping. Objective: Solving second order ODE which represents motion of pendulum Simulating the motion of pendulum Creating an animation of its motion using MATLAB Theory: Simple Pendulum: It is said that Galileo measured the periods of a swinging chandelier…

Aim: Sensitivity analysis of GRI-3.0 mechanism Objectives: Determine 10 most sensitive reactions from the GRI-3.0 mechanism Determine sensitivity with respect to temperature Output the reactions in decreasing order of sensitivity Theory: In any reaction mechanism, multiple intermediate reactions also occurs which affect…

Aim: Calculation of auto-ignition time of methane using Python and Cantera Objective: Plotting auto-ignition for constant temperature and varing pressure and for constant pressure and varying temperature. Observing and explaining the behaviour of change of molar concentration of given species. Theory: The auto-ignition…

Aim: Code a multivariate Newton-Raphson Iterator Objective: Solve the given set of differential equation by coding a multivariate newton-raphson iterator Solve using Implicit Euler method / Backward differencing for a given initial condition. Theory: In combustion mechanism, the rates of reactant comsumption and product…

Aim: Analysis of the stability of ODE solvers Objective: Understanding how and when an ODE becomes unstable Understanding the effect of ODE stability on engineering simulations Checking stability conditions for a variety of problems Theory: In mathematics, Ordinary differential equation (ODE) is a differential equation…

Aim: Derive the reaction rate ODEs of simple mechanism using compact notations. Objective: Form reaction rate ODEs using compact notations. Theory: Reaction rate or rate of reaction is the speed at which a chemical reaction takes place. We define reaction rate as the speed at which reactants are converted into products.…

Aim: Write a Python code to calculate combustion efficiency of a heat recuperator on pre-heating. Objectives: Determine and visualize the effect of pre-heating on AFT Determine and visualize the effect of pre-heating on combustion efficiency and fuel savings (if any) Theory and Procedure: In general, the heat exchangers…

Aim: Write a Python code that processes air-fuel mixture using Cantera module Objectives: Handle mixtures of given hydrocarbon (here, methane) and air Compute its AFT by balancing of moles Understanding and implementing 'Quantity' class in Cantera Methodology: The balanced combustion equation for methane is as follows:…

Aim: Calculating adiabatic flame temperature (AFT) using Python and Cantera Objective: Obtain trend for AFT vs equivalence ratio AFT of combustion of methane in presence of heat loss (heat loss = 0.35) AFT comparison for general alkanes AFT comparison for 2 carbon atom species Theory: AFT represents total energy input…

Aim: Minimizing a given function subjected to a constraint. Objective: Minimize the equation: `f(x,y) = 5 - (x-2)^2 - 2(y-1)^2` Under constraint: `x + 4y = 3` Theory: Constrained minimization (constrained optimization) is the process of optimizing an objective function with respect to some variables in the presence of…

Aim: Write a Python script for file parsing of Converge CFD data file. Objective: Writing a script that extracts data from a compatible data file. Developing an interface wherein user can select set of data to visualize. Evaluation of basic engine performance for given conditions Theory: Parsing actually means to split…

  Aim: Write a Python code to fit a curve for given data set. Objective: Write a code to obtain a linear and cubic polynomial for given data set. (here, Cp vs Temperature values (specific heat at constant pressure)) Plotting the obtained curves. Studying fitness characteristics for the same. Theory: Curve fitting:…

Aim: Determining minimum pressure to break ice using an air cushion vehicle Objective: Finding minimum pressure for different thickness of ice sheets using Newton Raphson method. Finding a suitable relaxation factor at h = 0.6 ft. Tabulating and plotting the results. Theory: Newton Raphson Method: In numerical analysis,…

Aim: Write a MATLAB program to fit a curve for given data set. Objective: Write a code to obtain a linear and cubic polynomial for given data set. (here, Cp vs Temperature values (specific heat at constant pressure)) Plotting the obtained curves. Studying fitness characteristics for the same. Theory: Curve fitting: Several…

Aim: Write a Python code to simulate motion of a pendulum with damping. Objective: Solving second order ODE which represents motion of pendulum. Simulating the motion of pendulum. Creating an animation of its motion. Theory: Simple Pendulum: It is said that Galileo measured the periods of a swinging chandelier in church…

Aim: Write a Python code for plotting PV diagram of air standard cycle. Objectives: Plotting PV diagram (workflow diagram) for Otto cycle. Determining air standard efficiency (thermal efficiency). Theory: Air Standard Cycle: The cycle in which air is used as a working substance is called an air standard cycle. Air Standard…

Aim: Write a Python code to simulate forward kinematics of a 2R robotic arm. Objective: Simulate the movement of 2R robotic arm. Create animation of robotic arm's workspace. Theory: A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm. The arm may be the sum total of the…

Aim: Write a Python program to calculate drag force against a cyclist. Objectives: Calculate drag force Plot Velocity vs Drag Force Plot Coefficient of Drag Force vs Drag Force Theory: We know that we are submerged in a fluid called air. When a submerged body undergoes motion,it experiences a resistive force. This resistive…

Aim: To study stalagmite function and calculate global maxima using Genetic Algorithm in MATLAB. Objective: Study Genetic Algorithm and Stalagmite function Determination of global maxima by writing a MATLAB code Plotting graph on studies done on Genetic Algorithm Theory: Stalagmite Function: Stalagmite function is a mathematical…

Aim: Create a Rankine Cycle simulator using MATLAB/Octave Objective: Calculation of state points of any Rankine cycle Plotting of corresponding T-s and H-s curves of the cycle Theory: Vapour power cycle: The cycle in which vapour is used as a working substance is called a vapour power cycle. Rankine Cycle: Many impracticalities…

Aim: Write a program for parsing thermodynamic data. Objective: Write a function to read the data given in the file and extract the coefficients for each species to calculate enthalpy, entropy and specific heats for all the species in the data file. Calculate the molecular weight of each species and display it in the command…

Aim: Write a MATLAB program to simulate forward kinematics of a 2R robotic arm. Objective: Simulate the movement of 2R robotic arm Create animation of robotic arm's workspace Theory: A robotic arm is a type of mechanical arm, usually programmable, with similar functions to a human arm. The arm may be the sum total of the…

Aim: Write a MATLAB program for plotting PV diagram of air standard cycle Objective: Plotting PV diagram(workflow diagram) for Otto cycle Determining air standard efficiency (thermal efficiency) Theory: Air Standard Cycle: The cycle in which air is used as a working substance is called an air standard cycle. Air Standard…

Aim: Write a MATLAB program to calculate drag force against a cyclist Objectives: Calculate drag force Plot Velocity vs Drag Force Plot Coefficient of Drag Force vs Drag Force Theory: We know that we are submerged in a fluid called air. When a submerged body undergoes motion, it experiences a resistive force. This resisitive…